User Guides for Noise Modeling of Commercial Space Operations—RUMBLE and PCBoom (2018)

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P a r t I I PCBoom Sonic Boom Model for Space Operations Version 4.99 User Guide Kevin A. Bradley Clif Wilmer Vincent San Miguel Wyle Laboratories, Inc. Arlington, VA

C O N T E N T S 113 Chapter 13 Introduction to PCBoom 113 13.1 About PCBoom 113 13.2 Organization of User Guide 114 Chapter 14 Technical Reference 114 14.1 Sonic Boom Background 117 14.2 Sonic Boom Theory 119 14.3 Propagation Using Geometrical Acoustics 122 14.4 Signature Aging 125 Chapter 15 Program Installation and Execution 129 Chapter 16 PCBoom Input Files 129 16.1 Case Description 129 16.2 Ground Pressure and Latitude 131 16.3 Atmosphere Specification 134 16.4 Ray Tracing Altitude Extent Specification 136 16.5 Signature and Vehicle Input Mode 144 16.6 Ray Tracing Azimuthal Control 146 16.7 Flight Trajectory Specification 148 Chapter 17 Sonic Boom Metrics 149 Chapter 18 PCBoom Output Files 150 Chapter 19 Error and Warning Messages 153 Chapter 20 Sample Cases 153 20.1 Sample Case 1: Vertically Launched, Two-Stage-To-Orbit Vehicle 155 20.2 Sample Case 2: Horizontally Launched, Suborbital Vehicle 160 Chapter 21 PCBoom Data Display and Grid Output 160 21.1 WCON Control Features 162 21.2 PCBoom Noise Grid Output for NMPlot 168 21.3 PCBoom Noise Grid Output for AEDT 170 Chapter 22 Generating Sonic Boom Source Signatures 170 22.1 Carlson’s Simplified N-Wave Method 173 Chapter 23 Approval Process Guidance for Commercial Space Noise Studies 173 23.1 Procedure for Review of Non-Default Methods and Data 174 23.2 List of Common Methods/Data and AEE Review Requirements 175 23.3 Guidance Regarding a Request to Use Non-Default Methods/Data 177 References 178 Abbreviations

113 13.1. About PCBoom The sonic boom model is based on PCBoom4 (hereafter referred to as PCBoom), a com- puter program that predicts the sonic boom amplitudes from supersonic vehicles. PCBoom is a mature program developed by Wyle, Inc. in response to the need for a sonic boom model suitable for environmental analysis of commercial space vehicles and operations. It is designed to ana- lyze sonic booms from single flight operations. The user specifies the vehicle type (sonic boom source), atmosphere, and flight trajectory. Primary outputs are a graphical representation of the boom footprint including contour plots of sonic boom metrics, such as peak overpressure, and isopemps. PCBoom is designed to be compatible with and can be integrated with the FAA AEDT. 13.2. Organization of User Guide This user guide provides instruction on how to install, run, and interact with PCBoom. The guide is organized into the following sections: • Chapter 13 introduces PCBoom. • Chapter 14 presents the technical details of the methodologies employed by PCBoom. • Chapter 15 provides detailed instructions on how to install and run PCBoom. • Chapter 16 defines the input files necessary to operate PCBoom. • Chapter 17 describes the sonic boom metrics calculated by PCBoom. • Chapter 18 describes the output files generated by PCBoom. • Chapter 19 provides a list of potential warnings and errors that might be encountered during a run. • Chapter 20 presents example cases, which take users step-by-step through the process of creating and running PCBoom for a vertical launch case and a suborbital flight case. • Chapter 21 provides instruction on PCBoom data display features and generating noise grids. • Chapter 22 provides instruction on how to generate sonic boom source signatures. • Chapter 23 provides guidance on the approval process when using PCBoom to conduct envi- ronmental modeling for FAA actions subject to NEPA. C h a p T E r 1 3 Introduction to PCBoom

114 14.1 Sonic Boom Background A sonic boom occurs when a vehicle operates at supersonic conditions, generating a wave field that can propagate to the ground which is heard as a sonic boom. Figure 52 shows a classi- cal sketch of a sonic boom wave cone generated by an aircraft in steady non-accelerating level flight. The wave cone is attached to the aircraft and follows along behind it, much like the wake of a ship on water. While Figure 52 shows a nominally simple cone, the shape of the wave cone in more realistic environments and operating conditions can vary greatly, being influenced by the effects of both flight maneuvers and atmospheric gradients. The wave cone extends toward the ground, resulting in a hyperbolic interception known as the isolabe. As the vehicle travels forward, the isolabe travels as well, sketching out what is referred to as the “boom carpet,” which represents all of the ground positions at which a sonic boom will be heard. Wave cones do not extend indefinitely, either diminishing due to attenuation or refracting away from the ground due to temperature gradients in the atmosphere. By the time the sonic boom has reached the ground, the originally complex waveform will generally coalesce into two peaks corresponding with a bow shock and a tail shock, separated by linear expansion. This signature is known as an “N-wave,” as represented in the callout plot shown in Figure 52. The N-wave begins with a sharp rise due to compression at the nose of the vehicle, followed by linear expansion, and concluded with recompression at the rear of the vehicle. Sonic boom wave cones are not generated fully formed at a single point in time, instead result- ing from the accumulation of all previous pressure disturbance events that occurred during the vehicle’s time history. Although the wave cone’s position and physical properties can be calcu- lated in a straightforward manner from an aircraft-fixed reference frame, it becomes more con- venient to adopt a ray perspective when attempting to calculate sound metrics in a ground-fixed observer’s reference frame. Figure 53 shows the viewpoint of rays carrying acoustic energy and emanating outwards from the source that can be tracked until they reached the ground. Unlike wave cones, ray cones are fully determined at a single point in time and are independent of future maneuvers. They are orthogonal to wave cones and represent all paths that sonic boom energy will take from the point they are generated until a later point in time when they hit the ground. Ray cones consist of rays (bundles are referred to as ray tubes and are explained later) generated at particular time steps and azimuthal angles, which travel through the atmosphere and may eventually reach the ground. The ray perspective is particularly useful when consid- ering refraction due to atmospheric gradients, as shown in Figure 54, or the effects of aircraft maneuvers, where rays can coalesce into high amplitude focal zones, as shown in Figure 55. When the ray cone hits the ground, the resulting intersection is called an “isopemp.” The isopemp is forward-facing and falls a distance ahead of the vehicle called the “forward throw.” At each new point in the trajectory, a new ray cone is generated, resulting in a new isopemp that C h a p t e r 1 4 Technical Reference

technical reference 115 Figure 52. Sonic boom wave field. Figure 53. Wave versus ray viewpoints. Figure 54. Ray curvatures in a real atmosphere.

116 User Guides for Noise Modeling of Commercial Space Operations—rUMBLe and pCBoom strikes the ground. These isopemps are generated throughout the trajectory, sweeping out an area called the “boom footprint.” Note that the aircraft’s ground track need not pass through the foot- print; it is possible for an aircraft to generate a boom, turn, and never fly over its boom footprint. The patterns created by isopemps can reveal areas of boom focusing, which is particularly useful when considering maneuvering flight. Figure 55 shows rays generated from different time steps in the trajectory of an accelerating aircraft crossing and tracing out a caustic line, rep- resenting a region of focusing also sometimes referred to as a superboom. Figure 56 shows the associated isopemp pattern on the ground for the same accelerating maneuver, with the vehicle starting at the “+” symbol and traveling from left to right. The acceleration maneuver results in a concentrated wavefront. Note how the isopemps overlap in the focus region, and how there is no boom on the ground before the onset of the focal zone. Focal zones are generally associated with the edge of a boom footprint, and often required refined detail to properly represent. While focal zone dimensions tend to be very small, boom amplitudes within them can be three to five times stronger than that of nearby carpet booms. Figure 52 and Figure 53 may give the impression that the boom footprint is generally associ- ated with rays generated from the bottom of an aircraft. This is the case for aircraft at moderate climb and dive angles, or in level flight as shown in Figure 57. For an aircraft in a sufficiently steep dive, such as in Figure 58, the entire ray cone may intersect the ground, resulting in an elliptical or even circular isopemp. This is of particular importance for space flight reentry analysis, where descent at times may be nearly vertical. Conversely, if a vehicle is climbing at an angle steeper than the ray cone half angle, rays from that part of its trajectory will not reach the ground. This is important for vertical launches, where the ascent stage of a launch vehicle typically begins at a steep angle. In these cases, sonic booms are not expected to reach the ground unless refracted back downwards by gradients in the atmosphere. Figure 55. Ray crossing and convergence in an acceleration-induced focus. Figure 56. Isopemp convergence in an acceleration- induced focus.

technical reference 117 14.2 Sonic Boom Theory Sonic boom calculations can be divided into three major elements: • Prediction of the pressure disturbance in the vicinity of the vehicle. A near field pressure distribu- tion is required at a reference radius large enough such that the pressure disturbance can be considered a locally axisymmetric acoustic wave, and small compared to atmospheric gradi- ents. For supersonic slender bodies, this source function can be calculated directly from vehicle geometry via area rule methods. The source function can also be obtained empirically from wind tunnel or flight test measurements, or numerically from Computational Fluid Dynamics (CFD) calculations. Section 16.5 describes the currently available methods for using vehicles and signature data in PCBoom4. • Calculation of linear acoustic propagation to large distances, accounting for winds and atmo- spheric gradients. This is accomplished by the method of geometrical acoustics. The linear ray field computed depends only on the vehicle kinematics and atmospheric properties. The amplitude of the propagating acoustic disturbance is governed by the change in area of the ray tubes (bundles of differentially separated rays) and local acoustic impedance. Section 14.3 describes the application of linear acoustic principles to sonic boom. • Calculation of the nonlinear steepening of the boom signature as it propagates. One tech- nique employs a cumulative “advance” or “age” parameter which is computed as part of the geometrical acoustics solution. This age parameter defines the differences in arrival time, Figure 57. Ray cone in level flight. Figure 58. Ray cone in diving flight.

118 User Guides for Noise Modeling of Commercial Space Operations—rUMBLe and pCBoom at various distances along a ray, between an infinitesimal strength acoustic wave and a unit- strength wave. The nonlinear distortion of each part of the boom signature consists of an advance proportional to its original strength multiplied by the age parameter. Signature aging and steepening techniques are described in Section 14.4. These three elements are the standard components of sonic boom calculation programs. Fig- ure 59 shows the typical computational workflow for a sonic boom propagation model. Note that elements (1) and (2) are carried out independently, and their results merge only when it is time to calculate the aged nonlinear signature calculation (3). There are a number of additional elements to sonic boom computation that must be consid- ered under certain circumstances: Prediction and computation of focal zone signatures. Focal zones exist where the ray tube’s area vanishes and the linear acoustic solution becomes singular. Diffraction effect limits these Aircraft Trajectory Atmosphere Ray Tracing Aircraft Geometry Flight Parameters Area Rule F-Function Ray Tube Area Age Parameter Acoustic Amplitude Aging/Steepening Shock Formation Ground Reflection Sonic Boom At Ground Figure 59. Logical flow of sonic boom calculations. The source signature procedure (dashed box) can be carried out independently from the ray tracing procedure.

technical reference 119 focused superbooms to be finite, and validated local solutions are available. Focus solutions must be locally applied to focal zones, using the adjacent geometrical acoustics calculation as a boundary condition. To date, PCBoom is the only sonic boom model to implement proper focal zone theory. Section 14.4 contains a brief description of theory and PCBoom-specific computational techniques for modeling focal zones. Computing finite shock thickness. Real shock waves have a finite thickness, dependent on shock amplitude and atmospheric conditions. This thickness is small compared to overall signa- ture length, and is typically neglected, with sonic boom shocks treated as zero-thickness jumps. This can be misleading, as shock structure affects the upper frequency content of booms and is therefore important when conducting loudness calculations. Shock structure is controlled by a combination of nonlinear steepening and molecular relaxation processes. Sufficient data are available to empirically define nominal shock rise times, which can be applied in a simple man- ner to nominal thin shock boom waveforms. The simplified finite shock thickness technique is included in PCBoom. The main ray tracing and signature aging module, FOBOOM, calculates signatures with thin shocks. The signature and footprint post-processing module PCBFOOT applies a Taylor structure to each shock in the signature. Propagation of sonic booms through turbulence. While most sonic boom propagation phys- ics is deterministic, turbulence in the atmosphere can introduce stochastic processes that affect waveforms passing through turbulent regions, most notably the turbulent boundary layer of the Earth’s atmosphere consisting of the last few thousand feet of propagation. In the context of sonic boom modeling, turbulence effects are applied as a statistical variation about the deter- ministic solution. Turbulence modeling is not a feature of PCBoom4, although it is employed as a post-processing function in later versions of the program. To improve modeling capabilities, NASA is currently conducting a research program, led by KBRwyle, to study the effects of tur- bulence on sonic boom propagation. 14.3 Propagation Using Geometrical Acoustics Sonic boom prediction consists of the nonlinear propagation of a near field aircraft pressure signature along linear acoustic rays. The process is illustrated in Figure 60. Here, a near field signature is generated by the supersonic aircraft and propagates along a ray tube. The shape of the acoustic signature is given by the F-function which is based on the aircraft’s configuration Figure 60. Schematic of sonic boom propagation along a ray tube.

120 User Guides for Noise Modeling of Commercial Space Operations—rUMBLe and pCBoom and aerodynamic loads. Acoustic rays, orthogonal to wavefronts, are traced by the method of geometrical acoustics [1]. Ray tracing yields the position of the boom and also its amplitude. Figure 61 illustrates the coordinates of rays emanating from their origin at the aircraft. Rays emanate in a ray cone that is orthogonal to the Mach cone. For a given flight path and atmospheric profile, there are two independent variables: the time t at the aircraft, and the azimuthal angle φ that identifies the ray of interest on that ray cone. The sense of φ is shown in the figure, with 0° pointing down in a vertical plane containing the flight path and +φ pointing out of the left wing. The original Thomas code calculated boom for a single pair of (t, φ) points. 14.3.1 Ray Paths Ray paths are computed by direct numerical integration of the eiconal using a simple linear predictor/corrector technique. An initial ray unit vector is taken as normal to the Mach cone at the aircraft, which is moving relative to the local wind. A ray tube is constructed from four corner rays, as sketched in Figure 62. The rays are separated by small but finite angle spacing Δφ (azimuth φ about the flight path is relative to a vertical plane) and time spacing Δt along the trajectory. The initial ray angles at the different time steps account for differences in flight path angle, heading, Mach angle, and their respective derivatives, so that the ray tube implicitly accounts for aircraft maneuver effects. The integration time steps along all four rays are coordi- nated such that a given number of steps correspond to a constant phase on all four rays. Figure 61. Initial ray cone and coordinates. Figure 62. Ray tube outlined by four corner rays, Dt and De apart.

technical reference 121 14.3.2 Ellipsoidal Earth Traditionally, sonic boom propagation is computed for a horizontally stratified atmo- sphere over a flat Earth. This is generally an acceptable approximation for primary downward- propagating booms, where propagation distances are short relative to Earth’s curvature and typical horizontal atmospheric gradients. There has been recent interest in long range sonic boom propagation, both for analysis of boom carpet edges from high-altitude flight and for analysis of over-the-top booms. For the long distances involved, the Earth’s curvature is not necessarily negligible. Space launch vehicle ascent and reentry are examples of long range boom propagation. For this reason, an ellipsoidal Earth model has been added to PCBoom4 to accommodate a full three dimensional atmosphere and a non-flat Earth. This section and the one following describe the Earth-fixed geocentric (EFG) coordinate system and 3-D ray tracing scheme that have already been implemented in later versions of PCBoom [2] [3]. There is nothing implicit about a near field signature or Whitham’s rule that limits analy- sis to the traditional flat stratified geometry. The crux of the ellipsoidal Earth extension is in implementing an appropriate ray tracing scheme. As long as one can compute ray paths and the relevant amplitude parameters, then subsequent propagation and steepening applies as usual. A full 3-D ray tracing in an EFG coordinate system, illustrated in Figure 63, has been imple- mented in later versions of PCBoom. Latitude, λ, is the elevation angle of a line that is normal to the local surface of the ellipsoid, and longitude, θ, is the angle east of the x-axis. The piercing point of the x-axis is the prime meridian at the equator. Aircraft location and flight parameters, as sketched in Figure 62, are generally defined in terms of local flat Earth coordinates, i.e., λ, θ (or local tangent plane x, y, that can be related to λ, θ) and altitude h above the ellipsoid (or above the geoid, which has a known offset to the ellipsoid). Calculation of EFG coordinates from λ, θ, h is explicit and straightforward. Once an initial ray position and vector are obtained, the ray path may be computed in EFG coordinates. 14.3.3 Schulten’s 3D Ray Path Integration Because the atmosphere curves along with the Earth’s surface, a 3-D atmospheric ray tracing scheme is needed. There are a number of 3-D ray tracing formulations in the literature, based on integration of ray trajectories derived from the eiconal equation. The method selected for use here is that presented by Schulten [4]. Figure 63. Ellipsoidal Earth and EFG coordinate system.

122 User Guides for Noise Modeling of Commercial Space Operations—rUMBLe and pCBoom The 3-D atmospheric extension requires 3-D derivatives of wind and sound speed gradients, as opposed to just the z-gradients required in the stratified model. This was set up as a simple shell atmosphere, with single profile normal to the local surface. Given a grid of profiles (as is available from 4-D weather forecasting systems) it would be very easy to extend this to include profile lookup for λ, θ for a full 3-D atmosphere. The atmosphere lookup routines already con- tain λ, θ as arguments, and the full 3-D gradient components needed are computed internally. Provision was needed for reflection of rays at the ground. This required coordination between origins and timing of the four rays in a tube, to ensure that they remained in phase while having different step sizes at their reflection points. Lateral cutoff limits in the horizontally stratified model were simple to obtain, using admit- tance ellipses similar to the method used in TRAPS [5]. Because a 3-D atmosphere does not have the spatial homogeneity of a traditional 2-D layered atmosphere, this process was no longer pos- sible. Admittance ellipses are used for general guidance, but it was necessary to use brute force and trace sample rays at all azimuths to establish which rays would reach the ground as either primary or various types of over-the-top rays. 14.4 Signature Aging Signature aging is conducted by advancing each portion of the signature proportionally to its original pressure. This results in the different portion of the signature advancing at differ- ent rates, stretching waveform and resulting in regions where the signature folds over itself. These double-valued regions do not, of course, actually happen. Instead, when a portion of the wave approaches vertical, the gradient becomes strong enough such that loss mechanisms become significant and a shock forms, with a balance between steepening and losses. When a shock forms, its propagation speed is governed by the Rankine-Hugoniot equations, and for weak shocks is the average of the isentropic speeds corresponding to the change in pres- sure just before and just after the shock. This leads to a simple “area balance” construction for insertion of shocks. The aging process is implemented in two steps: an “age parameter” that defines how much the wave has steepened, and a general area balance procedure. The advance sketch in Figure 64 depends only on this parameter and the F-function of each element. Figure 64. Evolution and steepening of sonic boom signature.

technical reference 123 14.4.1 The Age Parameter The age parameter [6] is a quantity based on the local speed of sound, scale factors, and the Blokhintsev invariant that defines how much the signature has steepened. This quantity is a function of the length along the signature, such that different portions of the signature age at different rates depending on the original pressure. An isentropic evaluation of the wave speed results in non-physical multiple-valued regions, equivalent to characteristics crossing. In reality, these multiple-valued regions never occur, and instead a shock forms. As with crossing characteristics, where a shock is fit at the angle bisecting the characteristics before and after it, PCBoom predicts an infinite slope at which that point is replaced with a shock whose speed is the average of the isentropic speeds ahead of and behind it. This property (shock at the average of the isentropic speeds on either side) leads to the area balance rule for shock fitting. The construction sketched in Figure 64 is completed, including the overlaps in the bottom sketch. A shock is inserted into each overlap region, positioned such that the overlap area ahead of it equals the area behind. The overlap regions are then deleted. The process can be intricate for complex signatures, but a systematic algorithm, described in the next section, is available and has been implemented in PCBoom. 14.4.2 Area Balance and the Middleton-Carlson-Hayes Method A general signature folding and shock fitting method was developed by Middleton and Carlson [7] and used in the ARAP [6] and TRAPS [5] codes. The key to this method is definition of a function that is the integral of the original F-function, so that area balance of the F-function corresponds to crossings in the integral function. The process, and rules for handling multiple crossings, is very well described in Middleton and Carlson, who give a step-by-step procedure for its application. Hayes et al. [6] noted a more convenient method, introducing an equivalent function that when plotted yielded the same result as Middleton and Carlson’s procedure. PCBoom implements aging by applying both Hayes’s method and Middleton and Carlson’s shock fitting procedure. The amplitude is then scaled via the Blokhintsev invariant. The proce- dure permits rapid calculation of the signature at any position along the ray. The age and ampli- tude parameters may optionally be written to an output file, and used to compute boom for other configurations at the same flight and atmospheric conditions. This file is exploited by the GENGS [8] system that is used for low boom shape optimization. Optimizers can cycle through several thousand configurations, and the ability to reuse the ray tracing results saves considerable computation time. 14.4.3 Focal Zones Focal zones occur when a combination of vehicle maneuvers and atmospheric gradients give rise to concave wavefronts, and the subsequent propagation distance is sufficiently long for the focal point to be reached. Conceptually, it is similar to focusing by a lens. The lens analogy can, however, be misleading. It is a good description for a wavefront with constant curvature. Except for rather special cases, an aircraft in motion will not generate such perfectly focusing waves. Curvature will vary, so that different portions of wavefront (generated at different times at the aircraft) will have different curvature. The focus point will thus move in space, and in two dimen- sions will trace out a line. This line (or surface in three dimensions) represents a focal zone. Math- ematically this zone is an envelope of rays, or a caustic. The location and shape of a caustic is defined by geometrical rays. The geometrical acoustics portion of standard sonic boom computer programs is adequate for location of foci. This was well verified by the experiences of Wanner et al. [9] in planning a sonic boom focus flight test

124 User Guides for Noise Modeling of Commercial Space Operations—rUMBLe and pCBoom program, and by NASA [10] in planning boom measurements from Saturn launches. Onyeonwu [11] developed a sonic boom prediction program which has the specific capability of identifying the location of focal zones. Determination of signatures at focus requires more geometrical information than location, however. The concept that a real focus is usually distributed over a caustic surface, rather than a point, suggests that focus amplification would depend on the extent of the caustic surface as compared to the original wavefront. A more quantitative viewpoint is that the caustic forms a boundary to the wave system within which diffraction effects play a key role in the focused sig- nature. Caustic location and geometry are defined from both atmospheric conditions as well as vehicle motions. The curvature of the caustic surface, an important parameter in the signature itself, is described in the treatment of focus behavior. There are a number of conceivable ray configurations which can lead to focus. Within PCBoom, however, only those which can be produced by a maneuvering vehicle in a smoothly varying atmosphere are of interest. The PCBoom Technical Reference [3] reviews the ray con- figurations associated with vehicle maneuvers and normal atmospheric gradients, and identifies the kind of foci which can occur and which are implemented in PCBoom.

125 PCBoom is a full-ray tracing model capable of calculating sonic boom overpressure footprints and ground signatures from supersonic vehicles performing arbitrary maneuvers. It comprises a suite of modules consisting of the following programs, run sequentially: • FOBOOM: the primary sonic boom computational solver. The source strength is either pro- vided by the user or calculated from a number of vehicle metrics and operating conditions, and propagated to the ground using acoustic ray tracing while accounting for arbitrary strati- fied atmospheric conditions. Foboom499.exe is the version provided with this distribution. • PCBFOOT: a post-processor that organizes FOBOOM output into structured files for the boom footprint and signatures at receiver points. Application of Taylor shock structures, if applicable, and the calculation of loudness metrics are completed here. • WCON: a GUI for displaying the boom footprint and signatures after PCBFOOT has been run. Some additional post-processing is done to obtain boom signatures, including secondary post boom U-waves, at selected locations. This module also provides functionality to export contours to ASCII format. Installation consists of moving the official distribution to any directory on the user’s computer. No additional setup is required. The official distribution contains FOBOOM, PCBFOOT, and WCON as executables located in the “.\bin” directory. A complete list of files included in the official distribution is provided in Table 10. The PCBoom workflow is conducted by running FOBOOM, PCBFOOT, and WCON in a sequential manner, as shown in Figure 65. A PCBoom project is created by defining the *.dat, *.trj, and *.att files – referred together as the PCBoom project files – and by using the fixed- format ASCII file descriptions discussed in Chapter 16. Users only need to be concerned about manually editing the field parameters in the PCBoom project files; all other resulting output files, if run successfully, can be passed as input into the next module without any additional editing. Each module generates at least one primary output file, with auxiliary output files being generated by supplying the appropriate command argument, as shown in this chapter. These auxiliary output files contain additional detailed information about the sonic boom propagation procedure, including flight maneuver data and signature evolution output, which may be useful for further post-processing. The final primary result is a contour plot of the sonic boom overpressures, isopemps, and signatures at ground level as visualized by WCON. A full list of files used by PCBoom as well as their descriptions are included in Table 11. Again, note that only the DAT, TRJ, and ATT files need to be defined by the user. All other user-specified files will be automatically generated during a successful run. C h a p t e r 1 5 Program Installation and Execution

126 User Guides for Noise Modeling of Commercial Space Operations—rUMBLe and pCBoom Filename Description Foboom499.exe PCBoom primary sonic boom solver, version 4.9 pcbfoot.exe PCBoom footprint and signature post-processor wcon.exe PCBoom contouring and visualization ShapeFactorDatabase.exe Launch vehicle shape factor database generator ShapeDatabase.ks Launch vehicle shape factor database Geometries.csv Launch vehicle geometry interface pcboom_guide.doc This document – the PCBoom user manual and technical reference example.dat PCBoom example case example.trj PCBoom example trajectory example.att Example atmospheric file Table 10. PCBoom distribution files. Figure 65. PCBoom workflow and i/o files. File Description I/O File Extension PCBoom case file I *.dat PCBoom trajectory file I *.trj PCBoom atmosphere file I *.att (Optional) PCBoom optfile (contains optional modes) I “optfile.txt” FOBOOM primary output file / PCBFOOT input file I/O *.out (Optional) FOBOOM verbose output file O *.un6 (Optional) FOBOOM signature evolution output file O *.u28 (Optional) FOBOOM Mach cutoff threshold output file O *.mco PCBFOOT boom footprint and isopemp output file / WCON input file I/O *.qwk (Optional) PCBFOOT ground signature file O *.sig (Optional) PCBFOOT ground signature index file O *.ind (Optional) PCBFOOT output in human-readable ASCII format O *.asc (Optional) WCON trajectory, overpressure, and isopemp contours output O *.pdx (Optional) WCON graphical image output O *.wmf Table 11. PCBoom input and output file descriptions.

program Installation and execution 127 To run FOBOOM from the command prompt: foboom499 casename[.dat] [ioutputs] [-optfile.txt] where • casename.dat is the name of the FOBOOM case input file. A file extension of *.dat is assumed if not directly specified. A detailed description of file formatting is provided in Chapter 16. • ioutputs (optional) specifies any additional desired output files (a detailed description of each output file is provided in Section 6). This is a numerical value, the sum of: – 1 display progress on screen, – 2 output a *.u28 file, – 4 output a *.un6 file, – 8 output an *.mco file • -optfile.txt (optional) refers to a text file containing additional modes. These modes begin with a keyword trigger followed by a user-defined argument, if any, as formatted in Table 12. Note that this command argument begins with a dash. The file name can be set to any valid file name, as long as the dash is present. If FOBOOM is run without any arguments, the version number and summary of options will be displayed. If footprints are desired, it must be run with full cutoff extents using a reasonable (5° or 10°) azimuthal spacing, and for at least two trajectory time steps at Mach number above cutoff. A full description of the PCBoom input file is provided in Chapter 16. To run PCBFOOT from the command prompt: pcbfoot casename.out [5] Here, casename.out is the output file generated by FOBOOM. This will generate a QWK file which will be input to WCON. • Specifying the optional “5” argument (without square brackets or quotations) signals the creation of signature files, casename.sig and casename.ind, as well as a summary ASCII file, casename.asc. These files are used to view boom signatures at ground level in WCON. Keyword Argument Type Description phishy Float Reduce the edges of the azimuthal extent from the cutoff by the user-defined angle, in degrees. gamfix Float Overwrite every trajectory point’s flight path angle by the user-defined angle, in degrees. tbelow Float Define an atmospheric temperature offset with the user-defined value, in °F. outpth String Define a new output directory location with the user-defined directory. The default directory is the directory containing the input case file. kmode Integer Define the Earth mode with the user-defined integer (1, 2, or 3). “1” defines an ellipsoidal Earth model, “2” defines a spherical Earth model, and “3” defines a flat Earth model. agemch N/A Force shock aging using the Middleton-Carlson-Hayes methodology [6], [7]. Shock aging with this method is the default procedure for all input modes except for the Carlson F-function mode (IMODE = 3, Chapter 16.5), where the shock is instead aged as a 4-point N-wave. topo String Load an elevation file from the user-defined path. The default mode assumes a flat topography. Table 12. Optfile formatting.

128 User Guides for Noise Modeling of Commercial Space Operations—rUMBLe and pCBoom To run WCON from the command prompt: wcon casename.qwk This will start WCON, an interactive GUI for viewing boom footprints and signatures. Users can plot overpressure and sound level contours, identify regions of focusing, and export results to both image and user-readable text files. If the argument “5” was specified when running PCBFOOT, then WCON can be used to display boom signatures via the following commands: • Pressing “r” or “R” within the footprint will display the boom signature for the nearest ray end. • Pressing “p” or “P” will open a dialog box, allowing users to view the boom signature at the specified (x, y) point. The boom signature is interpolated from the nearest ray ends.

129 The primary FOBOOM propagation input file is referred to as the PCBoom case input file (*.dat). This file is a fixed-format ASCII file and may be easily created or edited using any ASCII text editor such as Notepad, vi, or emacs; word processing programs such as Microsoft Word are not recommended for editing input files because they may insert additional formatting into the file. The input file consists of seven fundamental sections. Several of the keyword sections have multiple input formats, pointers to external input files, and different data formats, depending on the computational requirements and desired physical characteristics to be modeled. For each keyword section, the sequence and number of required line types are described. These line types are not necessarily the line number in the input file, and line types may be used by multiple input styles. The recommended order for the keywords is provided in Table 13. Within each keyword definition, the description will indicate whether specific columns in the DAT file are required by PCBoom, identified by “column,” or if only the position or sequence of the inputs is required, identified by “position.” Occasionally, the variable name is included in the line type descriptions. These are often referred to in other sections when inputs are linked in some manner. All keywords are to be immediately followed with the required input format as stated, with “Line 1” in the input format being the line immediately following the keyword itself. Numeric inputs are generally list directed; spacing does not matter, but all parameters must be present and in the correct order. Input lines containing strings are formatted, and spacing must be observed. An example of the DAT input file sections described in Table 14 is shown in Figure 66 for one of the sample case files, SampleCase1.dat, provided with the PCBoom software distribution. Each input file section is described following. 16.1 Case Description The first fundamental input section in a FOBOOM input file is the Case Description section. The user-defined case title is echoed in the output data files and serves as the name for each sce- nario run through PCBoom. Only one line of case description is permitted. The description is limited to a total length of 80 characters: any characters exceeding this length will be truncated. The case description format is provided in Table 14. 16.2 Ground Pressure and Latitude Atmospheric pressure, in units of pounds per square foot, is defined at the atmospheric ground altitude as shown in Table 15. C h a p t e r 1 6 PCBoom Input Files

130 User Guides for Noise Modeling of Commercial Space Operations—rUMBLe and pCBoom Section Input File Section 16.1 Case Description 16.2 Ground Pressure and Latitude 16.3 Atmosphere Specification 16.4 Ray Tracing Altitude Extent Specification 16.5 Signature and Vehicle Input Mode 16.6 Ray Tracing Azimuthal Control 16.7 Flight Trajectory Specification Table 13. Fundamental FOBoom input file sections. Table 14. Case description keyword format. Line Type Column Variable Type Description 1 1-80 String Case title description Figure 66. DAT input file sections. Line Type Position Variable Type Description 2 1 Float Atmospheric pressure at the ground (psf.) 2 Float Latitude, decimal degrees Table 15. Ground pressure and latitude keyword format description.

pCBoom Input Files 131 The ground altitude corresponds to the altitude of the first point in the atmosphere defini- tion. Note that the physical ground for signature output (defined in Section 16.4) does not have to correspond to the atmospheric ground. PCBoom is commonly run for a location with physical ground altitude different from the altitude where the atmosphere is defined. Latitude is used to compute the local effective value of gravity, accounting for the centrifugal force of Earth’s rotation and used in the hydrostatic atmosphere model. Setting the ground pressure value to zero specifies that an external atmosphere file (.att) will be read in, as described in Section 16.3. Specifying the latitude to 90 degrees sets gravity to zero, enabling the uniform atmosphere mode. 16.3 Atmosphere Specification PCBoom supports four different atmospheric modes as shown in Table 16. Each atmospheric mode is described in detail in the following sections. The file name is provided in the input *.cas file via Line Type 11, as shown in Table 17. An optional parameter, used only in conjunction with multiday external upper air profile, is also specified here. 16.3.1 ATT Atmosphere File The external .att file permits detailed description of the atmosphere in a separate ASCII input file with the file extension .att. To specify that an external file will be used, the ground pressure value in Line Type 2 must be set to zero, and a path pointing to the external file must be specified in Line Type 3. The data format for the external .att file is provided in Table 18. Note that the value of the first altitude in Line Type A4 must correspond to the ground pressure value set in Line Type 2. The 1D atmospheric profiles set for temperature, x-velocity, Atmosphere Input Mode Description .att file Altitude, temperature, winds, and humidity are read from a separate user-specified input file with extension .att. Uniform Atmosphere To enable this mode, a latitude of 90 degrees must be specified in line type 2 (Atmospheric Pressure and Latitude). Rawindsonde Balloon File Atmosphere defined in an external rawindsonde upper air file, with the specified formatting. Multiday Upper Air Profile File Atmosphere defined in an external multiday upper air profile file as available from the University of Wyoming Sounding File Database [12]. Table 16. PCBoom atmosphere input modes. Line Type Position Variable Type Description 3 1 String Name of external file, maximum of 255 characters. (2) String (Optional) Five character string in the format of “ttZdd”, where “tt” is the time of the profile (usually 00 or 12), “Z” is the uppercase letter, and “dd” is the day of the month. “tt” and “dd” must correspond to a sounding in the file. This is only used for multiday external upper air profile files. Omit if not needed. Table 17. External atmosphere file keyword format description.

132 User Guides for Noise Modeling of Commercial Space Operations—rUMBLe and pCBoom y-velocity, and pressure do not need to match each other, i.e., there can be any number of alti- tude pairs for each atmospheric variable. Altitudes are defined as kilofeet above mean sea level (MSL), so only values greater than or equal to zero are expected. Wind velocities are defined in the vector sense, and can include nega- tive values. User-defined pressure values are expected to be greater than zero. If pressure values are not defined, a pressure table will be internally generated based on the ground pressure pro- vided in Line type A2. An example external atmosphere file is provided in Figure 67. This .att file is created by sequencing fundamental input sections “Case Description” (Table 14), “Ground Pressure and Latitude” (Table 15), and “Atmosphere” (Table 18). The following example sets wind velocity to zero and omits a specification for pressure. This example atmosphere file is shown with alti- tudes up to 80 Kft, useful for modeling aircraft. The atmosphere file provided with the PCBoom 4.99 distribution, std1976.att, comes with a high-altitude extension to 600 Kft, appropriate for spacecraft sonic boom analysis. 16.3.2 Uniform Atmosphere Specifying latitude to 90 degrees sets gravity to zero, enabling uniform atmosphere mode. Gravity is by default used for the hydrostatic atmosphere model, which also includes models to Line Type Position Variable Type Description A1 1 String Title description A2 1 Float Atmospheric pressure at the ground (psf). A3 1 Integer Number of pairs of altitude and temperature to follow. A4 1 Float Altitude of temperature point (kft, MSL) 2 Float Corresponding temperature (°F) Note: Repeat for the number of points defined in Line Type A3. The value of the first altitude point must correspond to the ground pressure value set in Line Type 2. Sequence is ordered from lowest to highest altitude. A5 1 Integer Number of pairs of altitude and wind velocity (x-component) to follow. A6 1 Float Altitude of wind velocity (x-direction) point (kft, MSL) 2 Float Corresponding wind velocity in the x-direction (ft/s). Wind is defined in the vector sense, i.e. in the direction the wind is blowing toward, rather than in the meteorological “from” sense. Note: Repeat for the number of points defined in Line Type A5. Sequence is ordered from lowest to highest altitude. A7 1 Integer Number of pairs of altitudes and wind velocity (y-component) to follow. A8 1 Float Altitude of wind velocity (y-direction) point (kft, MSL) 2 Float Corresponding wind velocity in y-direction (ft/s). Wind is defined in the vector sense, i.e., in the direction the wind is blowing toward, rather than in the meteorological “from” sense. Note: Repeat for the number of points defined in Line Type A7. Sequence is ordered from lowest to highest altitude. A9 1 Integer Number of pairs of altitudes and atmospheric pressure to follow. A10 1 Float Altitude of atmospheric pressure point (kft, MSL) 2 Float Corresponding atmospheric pressure (psf) Note: Repeat for the number of points defined in Line Type A9. Sequence is ordered from lowest to highest altitude. Table 18. Atmosphere keyword format description.

pCBoom Input Files 133 account for the centrifugal force of Earth’s rotation. The uniform atmosphere mode must be specified with a constant temperature. 16.3.3 Rawindsonde Balloon File The atmosphere may also be defined using a common rawindsonde data format. This feature is specified by setting the ground pressure in Line Type 2 to the value “−1.” A truncated example is provided in Figure 68. This is the format supplied by NASA for the Shaped Sonic Boom Experiment. 16.3.4 Multiday Upper Air Profile A multiday upper air profile contained in an external file may be used to define the atmo- sphere. Formats for these upper air profiles may be found at http://weather.uwyo.edu/upperair/ sounding.html. U.S. Standard Atmosphere, No Winds 2116. 41 0. 59.0 1. 55.5 2. 51.9 3. 48.3 4. 44.7 5. 41.1 6. 37.6 7. 34.0 8. 30.5 9. 26.9 10. 23.4 11. 19.8 12. 16.2 13. 12.7 14. 9.1 15. 5.5 16. 2.0 17. -1.6 18. -5.1 19. -8.7 20. -12.3 21. -15.8 22. -19.4 23. -22.9 24. -26.5 25. -30.0 26. -33.6 27. -37.2 28. -40.7 29. -44.3 30. -47.8 31. -51.4 32. -54.9 33. -58.5 34. -62.1 35. -65.6 36. -69.2 37. -69.7 38. -69.7 39. -69.7 80. -69.7 0 0 Figure 67. Example external atmosphere (.att) file.

134 User Guides for Noise Modeling of Commercial Space Operations—rUMBLe and pCBoom A range of dates must be specified, and the generated web page saved as an ASCII text file. The file name is specified in Line Type 11, Table 17. A truncated example file is provided in Figure 69. 16.4 Ray Tracing Altitude Extent Specification The altitude extent is used to define the altitudes at which a sonic boom signature will be output. Defining the number of altitudes as zero will cause FOBOOM to only output sonic boom signatures at the ground and trigger the use of Simple (SMP) Mode. Defining a number GP022401204 TEST NBR 00171 W9000 GPS EDWARDS AFB, CA 1100Z 28 AUG 05 ALT DIR SPD SHR TEMP DPT PRESS RH ABHUM DENSITY I/R V/S VPS PW GEOMFT DEG KTS /SEC DEG C DEG C MBS PCT G/M3 G/M3 N KTS MBS MM 2372 220 5.1 .000 24.6 7.3 928.00 33 7.43 1081.27 285 674 10.21 0 2500 237 9.9 .070 25.9 3.8 923.92 24 5.80 1072.96 273 675 8.00 0 3000 273 21.2 .049 28.3 3.9 908.10 21 5.81 1045.93 267 678 8.08 1 3500 291 16.2 .026 27.6 1.7 892.62 19 4.97 1030.83 259 677 6.90 2 4000 257 7.8 .036 27.7 -1.2 877.33 15 4.02 1013.43 249 677 5.58 3 4500 267 1.6 .021 29.6 -14.0 862.38 5 1.48 991.45 229 679 2.07 3 5000 326 6.5 .020 28.5 -20.8 847.69 3 0.84 978.50 223 677 1.17 3 … snip … 63000 123 20.4 .007 -69.4 -96.1 66.19 1 0.00 113.17 25 556 0.00 5 TERMINATION 63716 GEOPFT 19421 GEOPM 63.0 MBS TROPOPAUSE 52017 FEET 114.80 MB -72.4 C -98.2 C MANDATORY LEVELS GEOPFT DIR KTS TEMP DPT PRESS RH 2464 227 5 25.3 3.3 925.0 24 4915 300 7 28.8 -20.6 850.0 3 10423 326 5 14.9 -26.8 700.0 4 19412 105 1 -6.3 -53.9 500.0 1 25013 293 17 -17.6 -61.1 400.0 1 31837 303 29 -35.2 -49.6 300.0 21 35948 298 32 -40.8 -76.3 250.0 1 40823 297 32 -51.1 -83.3 200.0 1 46761 294 23 -64.8 -92.8 150.0 1 54675 296 11 -73.8 -93.9 100.0 3 61646 120 16 -67.9 -95.0 70.0 1 SIGNIFICANT LEVELS GEOMFT DIR KTS TEMP DPT PRESS IR RH 2372 220 5 24.6 7.3 928.0 285 33 2611 250 16 27.2 4.8 920.4 274 24 3006 273 21 28.3 4.0 907.9 267 21 4159 236 7 27.3 -2.6 872.5 246 14 4507 269 2 29.6 -14.2 862.2 229 5 12469 67 12 10.1 -33.3 650.2 179 2 16069 154 4 3.5 -47.8 568.9 160 1 19999 59 2 -7.9 -54.9 489.3 143 1 20442 336 4 -7.5 -54.7 480.9 141 1 24963 296 17 -17.4 -61.0 401.7 122 1 25024 295 18 -17.5 -61.0 400.7 122 1 27426 297 23 -22.7 -64.4 363.0 113 1 32779 311 30 -37.6 -51.9 288.9 95 20 37461 295 27 -43.2 -78.0 234.6 79 1 46429 291 25 -64.1 -92.3 153.6 57 1 52194 268 6 -72.4 -98.2 114.8 44 1 54495 261 14 -73.2 -90.8 102.0 40 3 57678 16 5 -71.1 -89.2 86.6 33 3 58925 73 16 -67.5 -87.1 81.3 31 3 62386 100 21 -68.8 -88.9 68.3 26 2 63969 126 2 -67.8 -94.9 63.0 24 1 TERMINATION 999 999 NNNN Figure 68. Example rawindsonde balloon file.

pCBoom Input Files 135 72403 IAD Sterling Observations at 00Z 01 Jan 2007 ----------------------------------------------------------------------------- PRES HGHT TEMP DWPT RELH MIXR DRCT SKNT THTA THTE THTV hPa m C C % g/kg deg knot K K K ----------------------------------------------------------------------------- 1015.0 88 7.8 -0.2 57 3.73 150 10 279.8 290.3 280.4 1000.0 212 6.8 -0.2 61 3.79 145 13 279.9 290.7 280.6 988.7 305 6.0 -0.3 64 3.79 150 12 280.1 290.8 280.7 983.0 353 5.6 -0.4 65 3.80 152 13 280.1 290.9 280.8 952.4 610 3.5 1.1 84 4.37 160 17 280.5 292.8 281.2 946.0 665 3.0 1.4 89 4.50 166 19 280.6 293.2 281.3 … snip … 13.2 28956 -54.3 -87.1 1 0.02 55 13 752.8 753.0 752.8 12.7 29227 -53.9 -86.9 1 0.02 37 17 763.3 763.5 763.3 12.6 29261 -53.9 -86.9 1 0.02 35 17 764.4 764.6 764.4 10.4 30480 -55.0 -87.1 1 0.02 100 13 803.3 803.5 803.3 10.2 30630 -55.1 -87.1 1 0.02 808.2 808.5 808.2 Station information and sounding indices Station identifier: IAD Station number: 72403 Observation time: 070101/0000 Station latitude: 38.97 Station longitude: -77.47 Station elevation: 88.0 Showalter index: 6.31 Lifted index: 22.88 LIFT computed using virtual temperature: 23.21 SWEAT index: 257.17 K index: 22.20 Cross totals index: 19.40 Vertical totals index: 20.30 Totals totals index: 39.70 Convective Available Potential Energy: 0.00 CAPE using virtual temperature: 0.00 Convective Inhibition: 0.00 CINS using virtual temperature: 0.00 Bulk Richardson Number: 0.00 Bulk Richardson Number using CAPV: 0.00 Temp [K] of the Lifted Condensation Level: 271.93 Pres [hPa] of the Lifted Condensation Level: 901.58 Mean mixed layer potential temperature: 280.11 Mean mixed layer mixing ratio: 3.91 1000 hPa to 500 hPa thickness: 5548.00 Precipitable water [mm] for entire sounding: 27.26 72403 IAD Sterling Observations at 12Z 01 Jan 2007 ----------------------------------------------------------------------------- PRES HGHT TEMP DWPT RELH MIXR DRCT SKNT THTA THTE THTV hPa m C C % g/kg deg knot K K K ----------------------------------------------------------------------------- 1003.0 88 8.2 7.6 96 6.57 0 0 281.1 299.3 282.2 1000.0 110 8.2 7.7 97 6.63 185 5 281.4 299.7 282.5 976.9 305 11.2 11.0 98 8.50 215 14 286.3 310.1 287.8 974.0 329 11.6 11.4 99 8.76 215 15 286.9 311.5 288.4 … snip … Figure 69. Example multiday upper air profile. of altitudes greater than zero will cause sonic boom signatures to be output at the user-defined altitudes. A maximum of 49 altitudes can be defined. Most cases where only sonic boom foot- prints at ground level are required can be run in SMP mode. Ray tracing parameters dictate the altitude at which ray tracing should stop. An altitude below ground level is needed to properly trace caustics near the ground, and is by default set to 2,000 ft below ground level. Users can also specify bracketing altitudes within which foci should be considered. If a focus occurs above the upper user-defined limit, then the post-focus boom at the ground will be ignored. The lower bound is typically set to 1,500 ft below ground level. The upper bound should nominally be set above the maximum flight altitude, unless focal zone detail (i.e., the post-focus U-wave) is not of interest, in which case

136 User Guides for Noise Modeling of Commercial Space Operations—rUMBLe and pCBoom a value of 5,000 ft AGL will suffice. Table 19 shows the altitude extent and ray tracing control parameters. Note that in SMP mode, Line Types 6 and 8 are not read in. Instead, default values as defined previously are used. Note also that the ground altitude defined here does not have to correspond to the atmospheric ground defined in Table 18. Users already familiar with PCBoom will note that the BURGERS keyword has been omitted, as this distribution has not been provided with the Burger’s solver. 16.5 Signature and Vehicle Input Mode The Signature and Vehicle Input section allows users to describe how the noise source is defined. Four different input modes are supported, as shown in Table 20. See Chapter 22 for instructions on generating a user-created source signature. PCBoom is capable of supporting an additional three modes (4, 5, and 6), but they are pro- prietary CFD and geometry related methods that require additional modules and routines not Line Type Position Variable Type Description 4 1 Integer Number of altitudes at which to output sonic boom and signature, including the physical ground altitude. Specifying a value of “0” will cause results to only be output at the ground and trigger SMP mode. 5 1 Floats Output altitudes, in descending order, beginning with the highest altitude and ending at the ground. Note: If SMP mode is specified, only one altitude at ground level is expected. 6 1 Float Distance below ground altitude [Default: 2,000 ft] 2 Float Upper bracketing altitude for foci [Default: above flight altitude] 3 Float Lower bracketing altitude for foci [Default: 1,500 ft below ground] Note: If SMP mode is specified, default values are used. 7 1 Float Ground reflection factor. A factor of “1.9” is standard. Use “1.0” if the free-field boom is desired. 8 1 Float The ratio, R0 /L, of the radius from the vehicle, R0, over the vehicle length, L. Signifies the distance away from the vehicle at which ray tracing will begin. All altitudes defined in Line Type 5 must be below the flight altitude minus the radius R0. [Default: 1.0] Note: If SMP mode is specified, the default value is used. Table 19. Altitude extent and ray tracing control format description. Signature Input Mode 1 – Thomas Pairs of p/p∞ and x are specified, applicable to only one azimuth and one flight condition, full-scale and model length inputs. 2 – Simple F- function Pairs of F-function and x are specified. The user-defined F-function is internally scaled to other loads, flight parameters, and azimuths by Carlson’s formulae. Carlson’s shape factor curves are used [13]. 3 – Carlson’s F-function Carlson’s simplified equivalent N-wave shape, calculated via Lifting Body Entry vehicle inputs or Launch Vehicle Mode inputs (includes N-wave generation from underexpanded plumes) 7 – Tiegerman Blunt Body Tiegerman drag-dominated hypersonic blunt body mode. This is a special mode, needing some expertise to apply properly. Table 20. PCBoom signature and vehicle input modes.

pCBoom Input Files 137 Line Type Position Variable Type IMODE Description 9 1 Integer - Signature input mode (IMODE): [1, 2, 3, or 7] as described in Table 20. Table 21. Signature and vehicle input mode format description. Line Type Position Variable Type Description 10A 1 Integer Number of points in the signature to follow. If set to zero, the signature will be read from a file described using Line Type 11A, and Line Type 12A will not be used. 11A 1 String Path to external file (only defined if Line Type 10A is set to zero). The external file is described in Table 23. Note: If no external file is used, omit this line. 12A 1 Float Axial distance along the vehicle (ft.). There must be at least two points defined 2 Float Pressure distribution, p/p∞ Note: Repeat for the number of points defined in Line Type 10A. Omit if Line Type 11A is defined. 13A 1 Float Full-scale vehicle length (ft.) 2 Float Model length (ft.) Table 22. Mode 1 original Thomas mode format description. included in PCBoom v4.90g. The IMODE format description is provided in Table 21, and con- tinued for each individual IMODE in Table 22 through Table 36. 16.5.1 IMODE 1 – Original Thomas Form Mode 1 is the original input format used in the Waveform Parameter Method, the Thomas program that PCBoom was originally based on [14]. This input format allows users to define the vehicle’s pressure signature at a single azimuth as a list of Δp/p∞ and axial x pairs, where Δp = p – p∞ represents the local overpressure and p∞ is the ambient atmospheric pres- sure. The original Thomas model was intended for direct input of wind tunnel model data, so the axial coordinate, x, can be defined for either a full-scale length with a corresponding user-defined aircraft length, or for a subscale length with a corresponding model length, as described in Line Type 13A. Signatures can be defined in the input case file, or in an external file as described by Line Type 11A and Table 23. This mode is appropriate for only one azimuth. Line Type Position Variable Type Description B1 1 String Title description B2 1 Integer Number of source signature points to follow B3 1 Float Axial distance along the vehicle (ft.). There must be at least two points defined 2 Float (IMODE 1) Pressure distribution, p/p∞, or (IMODE 2) F-function Note: Repeat for the number of points defined in Line Type B2. Table 23. Mode 1 or Mode 2 external file format description.

138 User Guides for Noise Modeling of Commercial Space Operations—rUMBLe and pCBoom 16.5.2 IMODE 2 – Simple F-function Mode Mode 2 is the simple F-function input mode and is useful if Δp/p∞ is known only at the 0° (downward, undertrack) azimuthal angle and booms are expected to be N-waves. Line Type 12B specifies the input F-function for a steady level flight at the Mach number and local atmospheric pressure values defined in Line Type 13B (Table 24). The shape factor is defined using a precomputed curve as defined in Line Type 14B. This input F-function is internally scaled to other loads, operating conditions, and azimuths via Carlson’s for- mulae, allowing for a full boom footprint to be generated over the course of a full flight trajectory. The contributions of the vehicle’s shape and lift distribution on boom generation are con- tained within the shape factor parameter, for which Carlson has developed a number of curves [13]. Carlson’s simplified method, which is based on linearized supersonics, is not sensitive to small changes in the vehicle’s profile, allowing many different but similarly shaped types of air- craft to be grouped together, as seen in Table 25. Line Type Position Variable Type Description 10B 1 Integer Number of points in the signature to follow. If set to zero, the signature will be read from a file described using Line Type 11B and Line Type 12B will not be used. 11B 1 String Path to external file (only defined if Line Type 10B is set to zero). The external file is described in Table 23. Note: If no external file is used, omit this line. 12B 1 Float Axial distance along the vehicle (ft.). There must be at least two points defined 2 Float F-function distribution Note: Repeat for the number of points defined in Line Type 10B. Omit if Line Type 11B is defined. 13B 1 Float Vehicle length (ft) 2 Float Vehicle weight (klbs) 3 Float Nominal Mach number at which the F-function is defined 4 Float Ambient local pressure at the vehicle at which the F-function is defined (psf.) 14B 1 Integer Carlson shape factor curve, as defined in Table 25, between “1” – “8” Table 24. Mode 2 simple F-function mode format description. Curve Number Description 1 Large fighter: F101 2 Small fighter: F104 3 Medium bomber: B-58, SR-71 4 Large bomber: B-70 5 Fixed wing fighters: F-15, F-16 6 Variable sweep airplanes: B-1, F-111, F-14 7 Large delta wing: Concorde 8 Shuttle Orbiter 9 - 16 Triggers Launch Vehicle Mode (Mode 3B), analogous to curves 1 – 8, plus 8 17 Triggers Axisymmetric Mode (Mode 3C) 18 Triggers Shape Factor Table Lookup Mode (Mode 3D) 19 Triggers Launch Vehicle Database Mode (Mode 3E) Table 25. Carlson shape factor curve numbers.

pCBoom Input Files 139 16.5.3 IMODE 3 – Carlson’s F-function Mode Mode 3 is used to generate an N-wave F-function based on Carlson’s simplified model [13]. There are five input formats that can be used with Mode 3: 1. (Mode 3A) Basic Carlson F-Function Mode – not to be confused with Mode 2, this gener- ates equivalent N-wave shapes via pre-programmed vehicle names or curve numbers (see Table 25), vehicle length, and vehicle weight. 2. (Mode 3B) Launch Vehicle Mode – similar to the Basic Carlson F-Function Mode, with the additional inputs of vehicle thrust and vehicle plume drag. This mode is used to account for the shocks generated from the presence of an underexpanded plume generated by the launch vehicle. 3. (Mode 3C) Axisymmetric Shape Factor Mode – a shape factor is provided as part of the tra- jectory. The shape factor is used to generate an axisymmetric F-function. 4. (Mode 3D) Shape Factor Table Lookup Mode – a shape factor table developed from wind tunnel or CFD data is used to inform the F-function. Typically used for lifting body reentry vehicles. 5. (Mode 3E) Launch Vehicle Database Mode – allows users to access predetermined source signatures created for current commercial space vehicles. 16.5.3.1 Mode 3A – Basic Carlson F-function Input Mode Mode 3A can be implemented in either Simple (SMP) Mode or in basic Carlson F-function input mode. The simple mode input is defined by invoking an aircraft name descriptor, as defined in Table 26. Note that the vehicle name must match exactly, with proper casing and dashes included. This will load the associated vehicle parameters and generate an equivalent N-wave F-function scaled to the user-defined length and weight parameters. Note that this mode can only be used if the number of altitude outputs defined in Line Type 4 is set to zero. The file format description for SMP mode is provided in Table 27. The basic Carlson F-function (non-SMP) mode provides additional inputs for scaling the F-function to the vehicle’s length, weight, Mach number, local atmospheric pressure, and shape factor, as described in Table 28. Vehicle Name Curve Number Length (ft) Weight (klbs) THRUST (klbf) DRAG (klbf) B-1 6 147.0 450.0 0 0 B-58 3 98 79.4 0 0 B-70 4 200 495.0 0 0 F-4 1 60 45.0 0 0 F-5 2 47 20.0 0 0 F-14 6 62 55.0 0 0 F-15 5 64 47.0 0 0 F-16 5 48 25.2 0 0 F-18 5 56 39.4 0 0 F-20 2 47 18.0 0 0 F-22 5 67 48.0 0 0 F-101 1 67 37.3 0 0 F-104 2 55 26.5 0 0 F-111 6 74 76.5 0 0 SR-71 3 107 90.0 0 0 T-38 2 47 20.0 0 0 Tornado 6 57 35.0 0 0 Concorde 7 190 387.0 0 0 Shuttle 8 121 187.0 0 0 Titan 13 183.4 2,000 2,500 500 Table 26. Pre-programmed vehicle names and parameters.

140 User Guides for Noise Modeling of Commercial Space Operations—rUMBLe and pCBoom 16.5.3.2 Mode 3B – Launch Vehicle Mode Launch vehicle mode is used when a vehicle is expected to emit an underexpanded plume, which will generate its own pressure waves and must be accounted for in the sonic boom propa- gation analysis. The signature is again calculated from Carlson’s simplified N-wave method, and is based on a shape factor corresponding to Tiegerman’s hypersonic boom theory [15], a drag corresponding to the engine’s plume drag, and a reference length calculated from the Jarvinen- Hill universal plume model [16]. If plume drag is not known, it can be estimated as roughly 20% of the rocket thrust for most current large launch vehicles. This mode is triggered by specify- ing a shape factor curve number (described in Table 25) greater than 8 in Line Type 11D and specifying a thrust value greater than zero. Note that curve numbers 9 through 16 correspond to vehicles from curves 1 through 8, with plume calculations in effect. Axisymmetric shape factor mode (curve number 17) and shape factor table lookup mode (curve number 18) can be run without plume calculations by specifying Line Type 10D with zero thrust. The format descrip- tion for Mode 3B is provided in Table 29. Line Type Position Variable Type Description 10C 1 String Vehicle name (maximum 8 characters), as defined in Table 26 (note that dashes are included in the name) Table 27. Mode 3A Carlson SMP mode format description. Line Type Position Variable Type Description 11C 1 Float Vehicle length (ft) 2 Float Vehicle weight (klbs) 12C 1 Integer Carlson shape factor curve, as defined in Table 25, between “1”-“8” 2 String Path to the shape factor table file, only used in Mode 3D. For Mode 3A, enter “nul” (without the quotes). Table 28. Mode 3A basic Carlson F-function mode format description. Line Type Position Variable Type Line Type 10D 1 Float Vehicle length (ft) 2 Float Vehicle weight (klbs) 3 Float Total thrust (klbf) 4 Float Total plume drag (klbf) 5 Float Vehicle angle of attack (deg) (6) Float User-specified shape factor override. If no override is desired, set to zero. Note: These values can be overwritten in the trajectory file to account for booster separation, staging, and other mission events. 11D 1 Integer Carlson shape factor curve, as defined in Table 25, greater than “8” 2 String Path to the shape factor table file, only used in Mode 3D. For Mode 3B, enter “nul” (without the quotes). 12D 1 String Path for plume data output file, needed to interface with H.K. Cheng et al.’s (University of Southern California) underwater penetration model [17]. Note: If this output is not needed, place a blank line here. Table 29. Mode 3B launch vehicle mode format description.

pCBoom Input Files 141 16.5.3.3 Mode 3C – Axisymmetric Shape Factor Mode The axisymmetric shape factor mode is used when the vehicle’s geometry can be sufficiently described using an axisymmetric shape factor. To trigger this mode, set the shape factor curve ID in Line Type 11E to “17” (Table 30). The shape factor is directly supplied by the user as part of the trajectory, using the “NEWLOAD” keyword as defined in Section 16.7. Note that this mode can also be run in Launch Vehicle Mode by supplying the optional launch vehicle parameters in Line Type 10E. 16.5.3.4 Mode 3D – Shape Factor Table Lookup Mode The third option for Mode 3 is the Shape Factor Table Lookup Mode, typically used for lift- ing body entry vehicles where the shape factor table has been computed by the user from wind tunnel or CFD data. This mode is activated by setting the shape factor curve number to “18” in Line Type 11F in Table 31. The user-provided table provides a lookup to obtain shape factors as a function of angle of attack and azimuthal angle, as described in Table 32. 16.5.3.5 Mode 3E – Launch Vehicle Database Mode The fifth and final mode allows users to access predetermined source signatures from a data- base of launch vehicles. A database of sonic boom source signatures has been created for current commercial space vehicles. This database contains 14 launch vehicles in commercial use as of 2016, and includes hybrid lift vehicles as well as conventional rocket bodies. N-wave F-functions were generated from geometries using the Carlson method described in Chapter 22.1. Shape fac- tors were generated for each vehicle, accounting for changes in geometry due to different payload fairings, booster ejections, and staging events resulting in a total of 33 unique shapes and sonic boom source signatures. The format of the launch vehicle database is shown in Table 33 and the vehicles in the database are shown in Table 34. Mission events with numerical IDs, shown in Table 35, prompt changes in vehicle geometry and thrust, resulting in a change in the vehicle’s shape factor and thus the source signature. Line Type Position Variable Type Line Type 10E 1 Float Vehicle length (ft) 2 Float Vehicle weight (klbs) (3) Float (Launch Vehicle Mode) Total thrust (klbf) (4) Float (Launch Vehicle Mode) Total plume drag (klbf) (5) Float (Launch Vehicle Mode) Vehicle angle of attack (deg) (6) Float (Launch Vehicle Mode) Vehicle shape factor Note: Omit positions (3) – (6) if not in Launch Vehicle Mode. Note: These values can be overwritten in the trajectory file to account for booster separation, staging, and other mission profile events. 11E 1 Integer Carlson shape factor curve ID, as described in Table 25, set to “17” 2 String Path to the shape factor table file, only used in Mode 3D. For Mode 3C, enter “nul” (without the quotation marks). 12E (1) String (Launch Vehicle Mode) Path for plume data output file, needed to interface with H.K. Cheng et al.’s (University of Southern California) underwater penetration model [17]. Note: If Launch Vehicle Mode is specified but this output is not needed, place a blank line here. If any other mode is specified, omit this line. Table 30. Mode 3C axisymmetric shape factor mode format description.

142 User Guides for Noise Modeling of Commercial Space Operations—rUMBLe and pCBoom Line Type Position Variable Type Line Type 10F 1 Float Vehicle length (ft) 2 Float Vehicle weight (klbs) (3) Float (Launch Vehicle Mode) Total thrust (klbf) (4) Float (Launch Vehicle Mode) Total plume drag (klbf) (5) Float (Launch Vehicle Mode) Vehicle angle of attack (deg) (6) Float (Launch Vehicle Mode) Vehicle shape factor Note: Omit positions (3) – (6) if not in Launch Vehicle Mode. Note: These values can be overwritten in the trajectory file to account for booster separation, staging, and other mission profile events. 11F 1 Integer Carlson shape factor curve ID, as described in Table 25, set to “18” 2 String Path to the shape factor table file, contained in the working directory. 12F (1) String (Launch Vehicle Mode) Path for plume data output file, needed to interface with H.K. Cheng et al.’s (University of Southern California) underwater penetration model [17]. Note: If Launch Vehicle Mode is specified but this output is not needed, place a blank line here. If any other mode is specified, omit this line. Table 31. Mode 3D shape factor table mode format description. Line Type Position Variable Type Line Type C1 1 String Title description C2 1 Integer Number of angles of attack C3 1 Float List of angles of attack, on the same line, space delimited C4 1 Float Table corresponding to shape factors at each angle of attack for each azimuth starting at 0° and ending at 180° with 10° spacing. Each line contains a list of shape factor for each angle of attack, space delimited, for a single azimuthal angle. The next line contains a list for the next azimuth, and so on. There will be 19 lines corresponding to 19 azimuthal angles. Table 32. Mode 3D shape factor table lookup file format. These events can only be done once per mission. Events “A” and “B” (corresponding to engine ignition and cutoff) determine whether an over expanded plume is being generated. Plumes have a significant effect on sonic booms and often dominate the source signature. These events can hypothetically be done as many times as possible, but generally occur once per stage separation (i.e., engine cutoff, followed by stage separation, followed by next stage engine ignition). Specifying Event “A” for launch ignition is not required, as that event is assumed. To generate this database, launch vehicle geometries [18] were created and used as input to a numerical implementation of Carlson’s simplified method. Vehicles characterized by con- ventional rocket bodies were treated as axisymmetric. Hybrid launch vehicles like Pegasus XL and SpaceShipTwo were treated as lifting bodies, with the effects of lift on the source signature being included in the model. The geometric shapes used for the 14 launch vehicles in their default (i.e., launch) configuration can be found in Figure 70. The launch vehicle database file (ShapeDatabase.ks) is shown in part in Figure 71.

pCBoom Input Files 143 Line Type Position Variable Type Line Type 10G 1 Float Vehicle length (ft). For Mode 3E, set to zero. 2 Float Vehicle weight (klbs). For Mode 3E, set to zero. 3 Float Total thrust (klbf). For Mode 3E, set to zero. 4 Float Total plume drag (klbf). For Mode 3E, set to zero. 5 Float Vehicle angle of attack (deg). For Mode 3E, set to zero. (6) Float User-specified shape factor override. For Mode 3E, set to zero. Note: These values can be overwritten in the trajectory file to account for booster separation, staging, and other mission events. 11G 1 Integer Carlson shape factor curve, as defined in Table 25, set to “19.” 2 String Path to the shape factor table file, only used in Mode 3D. For Mode 3E, enter “nul” (without the quotes). 12G 1 String Launch vehicle database ID, as described in Table 34. 2 Integer The number of mission profile events to follow 3 Character A character specifying the mission event, from 1-4 or A-B, as described in Table 35. 4 Float The time step, in seconds, at which this event occurs. Note: Positions 3 and 4 are repeated for the number of events defined in Position 2. 13G 1 String Path for plume data output file, needed to interface with H.K. Cheng et al.’s (University of Southern California) underwater penetration model [17]. Note: If this output is not needed, place a blank line here. Table 33. Mode 3E launch vehicle database format. ID Vehicle Manufacturer / Operator Possible Events A200 Antares 200 Series (220, 221, 222, 230, 231, 232) Orbital ATK 2, 3, A, B AV401 Atlas V 401, 402 United Launch Alliance (ULA) 2, A, B AV411 Atlas V 411 United Launch Alliance (ULA) 1, 2, A, B AV421 Atlas V 421 United Launch Alliance (ULA) 1, 2, A, B AV431 Atlas V 431 United Launch Alliance (ULA) 1, 2, A, B AV521 Atlas V 521, 522 United Launch Alliance (ULA) 1, 2, A, B D4M Delta IV Medium United Launch Alliance (ULA) 2, A, B D4MP42 Delta IV Medium+(4,2) United Launch Alliance (ULA) 1, 2, A, B D4MP52 Delta IV Medium+(5,2) United Launch Alliance (ULA) 1, 2, A, B D4MP54 Delta IV Medium+(5,4) United Launch Alliance (ULA) 1, 2, A, B F912 Falcon 9 FT (v1.2) SpaceX 2, A, B MT1 Minotaur I Orbital ATK 2, 3, 4, A, B PXL Pegasus XL Orbital ATK 2, 3, 4, A, B SS2 SpaceShipTwo Virgin Galactic A, B Table 34. List of default launch vehicles in source signature database. Event ID Mission Event 1 Booster separation 2 Stage 1/2 separation 3 Stage 2/3 separation 4 Stage 3/4 separation A Engine ignition B Engine cutoff (MECO / SECO) Table 35. Mission event IDs.

144 User Guides for Noise Modeling of Commercial Space Operations—rUMBLe and pCBoom Figure 70. Radial distributions of selected launch vehicles (default configurations, all in meters). 16.5.4 Mode 7 – Tiegerman’s Blunt Body Mode The Tiegerman Blunt Body model is used for drag-dominated hypersonic blunt bodies, and has been successfully used to very predict the boom from a re-entering comet sample probe [19]. The input format for the Tiegerman mode is provided in Table 36. 16.6 Ray Tracing Azimuthal Control These parameters set key propagation features that control the azimuthal extent over which to compute the sonic boom signatures as well as the numerical integration parameters for the computed ray tubes. The input format is described in Table 37.

pCBoom Input Files 145 Figure 71. Launch vehicle database file (ShapeDatabase.ks). Line Type Position Variable Type Line Type 10H 1 Float Vehicle length (ft) 2 Float Vehicle weight (klbs) Table 36. Mode 7 Tiegerman blunt body mode format description. Line Type Position Variable Type Line Type 15 1 Float Ray tube angular width (deg). Default of [0.5°] 2 Float Trajectory increment for caustics (ft). Default of [500 ft] 3 Float Time step integration along a ray (s). Default of [0.5 s] 16 1 Integer Number of azimuthal angles, defined in Line Type 17, at which to compute the boom. Default of [0] 17 1 Float List of azimuthal angles (deg). Only used if Line Type 16 is greater than zero. 18 1 Integer Azimuthal angle increment (deg), must be a whole number greater than zero. Only used if Line Type 16 is equal to zero. Default of [5]. Table 37. Ray tracing azimuthal control format description.

146 User Guides for Noise Modeling of Commercial Space Operations—rUMBLe and pCBoom Line Type Column Variable Name Line Type 20 2 – 8 KEYWORD Keywords, defined in Table 40. Note that the first column is left blank. 11 – 22 TSTART Time, or time increment, depending on keyword (s) 23 – 34 XPLANE X-position of vehicle (ft) 35 – 46 YPLANE Y-position of vehicle (ft) 47 – 58 FLTALT Current altitude (ft) 59 – 70 MACH Mach number 71 – 82 DMDT First derivative of Mach number (1/s) 83 – 94 D2MDT Second derivative of Mach number (1/s2) 95 – 106 HEAD Heading, clockwise from North (deg) 107 – 118 PSIDOT First derivative of heading (deg/s) 119 – 130 D2PSI Second derivative of heading (deg/s2) 131 – 142 FPA Flight path (climb) angle (deg) 143 – 154 GAMDOT First derivative of flight path angle (deg/s) 155 – 166 D2GAM Second derivative of flight path angle (deg/s2) 167 – 178 WEIGHT (NEWLOAD only) Total vehicle weight (klbs) 179 – 190 AL (NEWLOAD only) Aircraft length (ft) 191 – 202 THRUST (NEWLOAD only) Total vehicle thrust (klbs) 203 – 214 DRAG (NEWLOAD only) Plume drag (klbs) 215 – 226 ALPHA (NEWLOAD only) Angle of attack (deg) 227 – 238 FKS (NEWLOAD only) Vehicle shape factor Line Type 20 is repeated for as many trajectory points as needed. Table 38. Trajectory data column format. Line Type Column Variable Name Line Type 21 1 – 4 FILE Keyword “FILE,” left justified 6 – 66 TRJ file Path to trajectory file Table 39. External trajectory file description. 16.7 Flight Trajectory Specification The final input section in a PCBoom input case file is the vehicle’s flight trajectory. Trajectory data is defined in a fixed-format manner and may be provided either as an inline table within the .dat input file or as a separate .trj file. The trajectory data format is provided in Table 38. If the trajectory is provided in the .dat input file, then only Line Type 20 (repeated for as many trajectory points as needed) is used. Alternatively, the trajectory can be defined in the same format using an external .trj file. In this case, the path to the external file is provided within the .dat input file as shown in Table 39. The formatting of the external .trj file follows the same format described in Table 38. One of the external trajectory files that comes with PCBoom 4.99 is shown, in part, in Figure 72. Each trajectory point starts with a keyword describing the kind of data included in the trajec- tory point, as shown in Table 40. The most general (and accurate) method is to provide a full data description at each point using either NEWTIME (or blank) or NEWLOAD. Keywords TADVNCE and NEWDIRS are approximations typically used for creating fictitious trajectories or for modeling simple maneuvers. Note that all keywords are case sensitive.

pCBoom Input Files 147 Figure 72. Trajectory file example. Keyword Description Keyword Ignore line. This is used to set up column headings for the benefit of someone reading the file. REMARK Comment line. longlat Defines a geographic origin corresponding to the X, Y coordinate system. XPLANE and YPLANE fields must contain East longitude and North latitude, decimal degrees. These values are written to an origin file with extension .org, which is used as a reference when the footprint plotting module writes a GIS file. Only XPLANE and YPLANE variables are used; the others are to be left blank. geomode Coordinates XPLANE, YPLANE are provided in geographic units, decimal degrees. This must appear before any coordinate data lines. The first XPLANE, YPLANE pair is taken to be (0, 0) in a local Cartesian system. This provides partial compatibility with CISBoomDA trajectory files, though they must be reformatted to the proper FOBOOM style. Only XPLANE and YPLANE variables are used; the others are to be left blank. NEWTIME Complete vehicle trajectory point. All parameters through D2GAM are read. A blank (no keyword defined) is equivalent to NEWTIME. NEWLOAD Same as NEWTIME, but with WEIGHT, AL, THRUST, DRAG, ALPHA, and FKS also read in. If any of these are blank, the last previous trajectory point’s value is used. Note that the parameters specified earlier in the vehicle definition (see Section 16.5) define these values at the first trajectory point. NEWLOAD can be used to overwrite these values to accommodate, for example, the staging of launch vehicles. TADVNCE Projects the current trajectory forward using the current position and derivatives. In this mode, only the first trajectory point at TSTART needs to be defined. TADVNCE is then used to extrapolate the trajectory for as many points as needed. NEWDIRS Same as TADVNCE, but allows users to define new values of the second derivatives. TSTART must be present (as in TADVNCE) and values must be present for the second derivatives that are to be updated. If left blank, the previous values will be used. END End of trajectory. Specified after the last point in the trajectory. All trajectories must end with this keyword. Table 40. Trajectory KEYWORD descriptions.

148 PCBoom computes full sonic boom waveforms. The footprint post-processor PCBFOOT and the signature post-processor WCON compute the sound metrics Pmax, Lpk, Lflt, CSEL, ASEL, and PL, as described below. Pmax – the peak overpressure in the signature, in units pounds per square foot (psf ). This is the traditional physical metric for N-wave sonic booms. Both Pmax and Pmin are presented. Lpk – the peak overpressure level, Lpk = 20 log10Pmax/Pref , where Pref = 20 µPa. This is the peak overpressure in decibel format. Lflt – the unweighted energy-integrated level, in dB. It is defined as 10 log 10 1 sec ,10 ^ 2 L P t P dtflt t ref ∫ ( )=        i where Pref = 20 µPa as above. The integration period is inclusive of the entire boom. This is essen- tially an unweighted sound exposure level, and is sometimes denoted ESEL. Note that the time integration is normalized by one second. CSEL – the C-weighted sound exposure level, as described in the ANSI 1996 standard [20]. ASEL – the A-weighted sound exposure level, as described in the ANSI 1996 standard [20]. PL – the loudness, in units PLdB. This metric as applied to sonic booms [21] is based on Stevens Mark VII loudness metric [22]. For sonic boom applications, each OTO band is first integrated over a time inclusive of the entire boom, similar to the equation used to compute Lflt, but with time normalization equal to the human auditory response time of 70 milliseconds, rather than a nominal 1 second. Pmax is the traditional measure of the amplitude of N-wave booms. CSEL is specified by stan- dards as discussed for quantification of high energy impulsive sounds, and correlates very well with peak overpressure via CSEL = Lpk – 25 db to within one or two decibles for most N-wave booms. It, however, correlates poorly with subjective loudness of booms. PL correlates very well with subjective loudness of booms across a wide variety of shapes, while ASEL works almost as well for simpler symmetric boom shapes [23]. C h a p t e r 1 7 Sonic Boom Metrics

149 PCBoom generates a number of intermediate and output files used throughout the PCBoom workflow. Optional detailed output files can also be generated for further user post-processing. Output files take the same file name as the PCBoom input case file by default. A list of output files is provided below: casename.out – the main output file from FOBOOM, in a format readable by PCBFOOT. Focus signatures are based on a single-shock solution and are reliable for N-waves and other simple signatures. For legacy mode analysis, PCBFOOT must be run for final post-processing. The .out file is always generated. casename.un6 – an “everything but the kitchen sink” output file containing detailed inter- mediate and final results, in a somewhat unstructured format. This output evolved from the original Thomas line printer output, from Thomas’ waveform parameter code [14], on which PCBoom was originally based on but is no longer used. casename.u28 – an output file that shows the evolution of the boom, and contains the sig- natures at all output altitudes. All data items (flight conditions, ray and signature coordinates, azimuth, and signatures) are labeled. The transition point from thin shock propagation is indi- cated. When FOBOOM is run in legacy mode, this file is written for only one ray – that at zero time, zero azimuth. casename.mco – an output file with Mach cutoff information. This is a special output file format that was incorporated for NASA flight test purposes. casename.qwk – a PCBFOOT output file that contains information regarding the boom foot- print and isopemps. This file is not meant to be in a human-readable format, and is intended to be read directly by WCON for post-processing. casename.sig – an optional PCBFOOT output file that contains boom signatures, created by passing in the argument “5” when running PCBFOOT. This file is required to view boom sig- natures in WCON. casename.pdx – an optional output file generated by WCON in a human-readable format. It contains location and magnitude values of contour lines as seen in the WCON visualizer. casename.wmf – an optional image output file in the Windows Metafile (.wmf) format gener- ated by WCON. C h a p t e r 1 8 PCBoom Output Files

150 C h a p t e r 1 9 The error and warning messages which FOBOOM may generate are itemized here along with an explanation of what is causing the message. If appropriate, recommended changes to the input file are provided. Occasionally, focusing conditions that cause the program to halt execution may occur. These focus abort codes are itemized here as well. Error and Warning Messages “AgeMCH: Exceeded max points, npts” The signature length, npts, has exceeded a limitation while in the AgeMCH routine during the interpolation of fill points. This can occur when the ray path being traced becomes unusually long. This can sometimes occur in isotropic atmospheres, where rays ≥90° never refract back down to the ground. Ensure that rays are not propagated from the ≥90° azimuth, as OTT is not supported in this release of PCBoom. “Fatal Error: NEWLOAD valid only for mode 3.” The NEWLOAD keyword was specified within the trajectory, but “CARLSON” mode was not the signature input mode specified in the input deck. “Fatal Error: invalid keyword keyword.” The last keyword “keyword” found in the flight trajectory is invalid. Please check the flight trajectory input format and fix the trajectory in the input deck, or the external trajectory file. “Fatal Problem: Negative ambient pressure at ray end.” Pressure at the ray end was found to be less than 0.0. Ensure that the atmosphere is properly defined. “Incompatible option: Cannot have both AGEout and OTTout...quitting.” Output of *.age and *.ssg files was specified through using the BURGERS keyword, the AGE keyword within the OPTIONS keyword section, or via the command line. OTT file output was also selected using either the OTT keyword within the run file or via the command line. These two outputs are incompatible and only one should be used at a time. The Burger’s solver is not provided in this distribution. “Incompatible option: “OTTout available only for 3-D ray tracing...quitting.” OTT output is only available for 3-D ray tracing modes, and is incompatible with legacy ray tracing modes. Please select a 3-D ray tracing mode if you wish to enable OTT output. “Input Error: LONGLAT keyword is not consistent with GEOMODE.” The LONGLAT keyword and GEOMODE keyword were both encountered in the same flight trajectory and are incompatible with one another. Please pick either GEOMODE or LONGLAT but not both.

error and Warning Messages 151 On occasion, when PCBoom is tracing rays and determining the geometry of a focus, certain unexpected exceptions to the geometric handling procedure occur. These are flagged with a negative integer focus abort code, written to the .out file, and an output message is generated to the .un6 file. Table 41 contains a listing of the focus abort codes and a brief description of the cause of error. The following lists the error messages from the .un6 file in alphabetical order and gives addi- tional information about the exceptions encountered in program execution. “Input Error: GEOMODE keyword is not consistent with Cartesian trajectory and LONGLAT.” The LONGLAT keyword and GEOMODE keyword were both encountered in the same flight trajectory and are incompatible with one another. Please pick either GEOMODE or LONGLAT but not both. “Overran dimension at Z = zvalue, primary boom case. Try again with bigger time step, or contact support.” An array dimension has been overrun within the TUBE routine while tracing a carpet boom or primary ray tube. “No valid vehicle source MODE selected. Revise the input file and try again.” The “MODE” keyword was specified without being followed by a valid vehicle mode keyword. Please pick the proper vehicle mode keyword and append the required data to the input deck immediately following the “MODE” keyword. “3-D focus trace lost: radcurv” Abort code: –12 A negative curvature of value “radcurv” was encountered causing the focus to be lost. “Caustic surface has intersected the lowest ALT: aborting” Abort code: –1 There was no focus found on the tube. Rather, a caustic was being traced which intersected the lowest altitude. “Focal points are straddling a cusp. 1” Abort Code: –2 Abort due to being on the cusp of a caustic. “Focus above ZMAX; will not affect ground.” Abort code: –4 The focus was found to be above ZMAX and will therefore not impact the ground. “Focus point is too close to vehicle 1” Abort code: –8 The focus was found to be too close to the vehicle, so we abort. “No curvature; aborting.” Abort code: –10 A zero or negative curvature was encountered. “Ray IRAY has turned upward at Z = altitude ft. with no focus but it’s below the ground. However, a caustic was being traced. Abort” Abort code: –3 A ray (IRAY) went below the ground (altitude) and turned upward, however a caustic was being traced at the time so this becomes an abort case.

152 User Guides for Noise Modeling of Commercial Space Operations—rUMBLe and pCBoom Code Description –1 Caustic intersected the lowest altitude –2 Focal points were straddling a cusp –3 An auxiliary ray cut off before focusing –4 Focus above ZMAX –5 The ray, in a carpet boom case, cut off –6 An auxiliary trajectory point is subsonic –7 N/A – Legacy versions only –8 Focus occurred less than 4 ray steps from the vehicle –9 Overran dimensions in tube (condition detected and NP1 set to –1 as a flag in tube). Note a focus issue –10 Both ray and caustic have zero curvature. Makes no physical sense, but can occur if the focus trace went bad in other ways. –12 3D radius of curvature is negative. Usually not actually negative but set to –1 by the curvature calculator when a focus point is missing. Essentially 3D version of –1, –3, –6 –13 Subroutine focfind failed to find the edge of the focal. Usually due to caustic radius being bigger than expected. –21, –23, –24 Aborts –1, –3, and –4, respectively, in dual mode. Table 41. Focus abort codes and descriptions.

153 This section provides instructions on how to promptly start using PCBoom Version 4.99 to compute sonic boom from spacecraft operations. To illustrate the process of running PCBoom, two sample cases are provided that model vertically and horizontally launched spacecraft. Installation consists of moving the official distribution to any directory on the user’s com- puter. No additional setup is required. Copy the PCB499 file folder that is included in zip file PCB499.zip to a location where PCBoom will be run (e.g., directly off of the C drive at C:\PCB499.) The PCB499 file folder contains all of the PCBoom executables and input data files required to run Sample Case 1 (vertically launched, two-stage-to-orbit vehicle) and Sample Case 2 (hori- zontally launched, suborbital vehicle.) 20.1 Sample Case 1: Vertically Launched, Two-Stage-To-Orbit Vehicle Sample Case 1 provides an example of how to model a vertically launched, two-stage-to- orbit (TSTO) vehicle that is based on a Delta IV Medium vehicle (D4M) launched from Cape Canaveral to a 185 km orbit. The data used in Sample Case 1 is for example only and does not represent real operations. The main PCBoom files for Sample Case 1 are: SampleCase1.dat (input/process control file), SampleCase1.trj (trajectory file), and std1976.att (atmosphere file). Instructions to run Sample Case 1: 1. From within Windows Explorer, open a Command Prompt Window for the PCB499 direc- tory (see Figure 73). In Windows 7 and 8, hold down the SHIFT key and then right click on the C:\PCB499 folder, then select “Open command window here.” Figure 74 shows the result- ing command prompt that can be used to run PCBoom from this directory. 2. Run the FOBoom program by typing ‘FOBoom499 SampleCase1.dat 5’ at the command prompt and pressing the ‘Enter’ key as shown in Figure 74. The optional “5” argument on the command line generates signature files that are used to view boom signatures at ground level in WCON. This case will take about 10 minutes to run, depending on computer system performance. 3. After Foboom499.exe has finished running, run the PCBfoot program by typing ‘PCBfoot SampleCase1.out 5’ at the command prompt and press ‘Enter’ as shown in Figure 75. 4. After PCBfoot has finished running, run the WCON program by typing ‘WCON SampleCase1.qwk’ at the command prompt and press ‘Enter’ as shown in Figure 76. 5. WCON results include sonic boom contours and isopemps as shown in Figure 77. Maxi- mum overpressure levels associated with the sonic boom contours are indicated in the legend located at the top right of the plot. After removing the isopemps (press F11) and using a C h a p t e r 2 0 Sample Cases

154 User Guides for Noise Modeling of Commercial Space Operations—rUMBLe and pCBoom Figure 73. Open a command prompt to run PCBoom. Figure 74. Running FOBoom from the command line. Figure 75. Running PCBfoot from the command line. Figure 76. Running WCON from the command line.

Sample Cases 155 mouse to create a zoom box around the boom contours, the contours will appear as they do in Figure 78. 6. WCON initially shows maximum overpressure contours, although the F12 key can be used to toggle between six metrics: maximum overpressure (psf), C-weighted SEL (dBC), peak level (dB), loudness (PLdB), A-weighted SEL (dBA), and Flat SEL (dBE). Figures 79 and 80 show the A-weighted SEL and peak level contours, respectively, for Sample Case 1. 20.2 Sample Case 2: Horizontally Launched, Suborbital Vehicle Sample Case 2 provides an example of how to model a suborbital vehicle that is dropped from an aircraft at 50,000 feet MSL and then uses rocket power to reach an apogee of about 350,000 feet before descending to a horizontal runway landing. The suborbital vehicle’s flight path is approximately 66 miles east of Cape Canaveral, headed north. The data used in Sample Case 2 is for example only and does not represent real operations. The main PCBoom files for Sample Case 2 are: SampleCase2.dat, SampleCase2.trj, and std1976.att. To run Sample Case 2, open a DOS command prompt for the directory containing the sample case files (e.g., C:\PCB499) and run FOBoom, PCBfoot, and WCON in succession (simi- lar to the instructions for running Sample Case 1 in Section 20.1) (see Figures 74 through 76). Run FOBoom from the DOS command prompt: C:\PCBoom>FOBoom499 SampleCase2.dat 5 Run PCBfoot from the DOS command prompt: C:\PCBoom>PCBfoot SampleCase2.out 5 Run WCON from the DOS command prompt: C:\PCBoom>WCON SampleCase2.qwk Figure 77. WCON display of maximum overpressure contours and isopemps for Sample Case 1.

Figure 78. WCON display of maximum overpressure contours and trajectory for Sample Case 1. Figure 79. WCON display of A-weighted SEL contours for Sample Case 1.

Sample Cases 157 After WCON starts up, the sonic boom contours (and isopemps) are displayed for Sample Case 2 as shown in Figure 81. After removing the isopemps (press F11) the boom contours will appear as they do in Figure 82. As mentioned previously, including “5” on the command line, when running FOBoom and PCBfoot, directs these programs to generate signature files that are used to view boom signatures at ground level in WCON. Different sonic boom contour shapes are observed for the two sample cases. The maximum overpressure contours for Sample Case 1 (Figure 78, vertically launched TSTO vehicle) have a crescent shape on the ground that is influenced by the modeled vehicle source and trajectory. During a real vertical launch, no boom would be expected to occur at the ground during the vertical ascent phase of the flight because the acoustic energy (modeled as energy propagating along ray tubes) is directed upward, unless the atmosphere causes this energy to refract back to the ground. As the spacecraft pitches over to access the specified target orbit, the sonic boom energy (rays) would intersect the ground. The modeled maximum overpressure contour for Sample Case 1 is shown in Figure 78. In comparison, the contours for Sample Case 2 form a semicircle (or semioval) due to the modeled vehicle source and suborbital flight trajectory. During a real suborbital flight opera- tion of the type expected for space tourism, as the spacecraft ascends to apogee using rocket power, no boom is expected to be observed on the ground unless caused by the atmosphere. During descent, the spacecraft has a steep (high negative angle) flight path angle that results in sonic boom energy intersecting the ground and forming more of a semicircle or circular/oval shape, than if the vehicle descended at a more shallow flight path angle. The modeled maximum overpressure contour for Sample Case 2 is shown in Figure 82. Figures 83 and 84 show the A-weighted SEL and peak level contours, respectively, for Sample Case 2.

Figure 81. WCON display of maximum overpressure contours and isopemps for Sample Case 2.

Figure 83. WCON display of A-weighted SEL contours for Sample Case 2.

160 21.1 WCON Control Features PCBoom displays sonic boom footprints and signature output using the program wcon. When wcon is started, the footprint display shows the following on an X-Y plot: • Contours of equal overpressure, psf • The trajectory • The isopemps • A legend of contour levels • A size scale • A user-editable legend The contour values and the scale of the plot can be adjusted. Any of the components can be moved to any position. The sonic boom signature can be displayed at any point within the footprint. The signature displayed can be associated with a particular ray or at a specific point on the ground. There is an information box on the right side of the screen that displays information about the footprint, and also contains a summary of available functions. 21.1.1 Summary Data Display The lower half of the information box shows information about the boom on the ground and its origin at the aircraft. The coordinates of the current position of the mouse pointer are shown, in feet, as xg, yg. Below this are the properties of the boom on the ray whose ground intercept is xg, yg. These are: • psf, the boom overpressure • tac and phi, the time and azimuth at which this ray originated • xac, yac, zac, the coordinates of the aircraft at the ray origination time • M, the Mach number at that time This information display is active even if the pointer is outside the footprint: data for the clos- est ray are always shown. 21.1.2 Footprint Display Options Most available options are summarized in a list on the right of the screen. These options are: • PgUp: zoom out x2 Zoom out by a factor of two, keeping the same center • PgDn: zoom in x2 Zoom in by a factor of two, keeping the same center C h a p t e r 2 1 PCBoom Data Display and Grid Output

pCBoom Data Display and Grid Output 161 • Home: zoom original Zoom to the original (default) size and position • Click L: zm window Select a zoom box. Click left (and release) to set one corner. Move the mouse to the other corner and click to complete the box. ESC to abandon. • Click R: pan data Pan (move) the selected entity (See F2 for selection of entity.). Right click (and release) in the middle of the entity. Move the mouse to the target position, and right click again. • F2: chg pan select Choose the entity that will be panned. Pressing F2 successively cycles through data (the footprint: contours, isopemps and trajec- tory), the size scale, the contour value legend, and the title block. • F8: traj on/off Toggle the trajectory display on and off • F9: conts on/off Toggle the contour display on and off • F11: pemps on/off Toggle the isopemp display on and off • F12: change metrics Toggle between six metrics: maximum overpressure (psf), C-weighted SEL (dBC), peak level (dB), loudness (PLdB), A-weighted SEL (dBA), and Flat SEL (dBE). • F4: change levels Change the levels of the contours. Pressing this will bring up a dia- log box, where you can specify six levels. The level dialog indicates the minimum and maximum boom values. Levels must be entered in ascending order, i.e., lowest value first (top of list). If you want to display fewer than six contour levels, enter the ones you want first, then enter zero(s) for the last value(s) (bottom of list). • F5: change title Press this to edit the title. The default is the case name. The title editor uses standard editing keys. • F6: Graphic Output This brings up a dialog for graphical output: either print the cur- rent graphical display, or write a CGM file of the current display. Selecting “Print” brings up a standard Windows print dialog. Selecting “CGM Output” brings up a standard Windows file dialog. In either case, the current scale is displayed, and you can change that if desired. You can also “Rescale Only.” • F7: ASCII Output Output three types of files which include the name of the current case: (1) an ASCII format (*.pdx) file containing the vector coordi- nates of the contours, isopemps and trajectory; the .pdx file contains Cartesian form contours that can be converted to geographic con- tours for use in a GIS; (2) an ASCII NMGF (*.grd) file, containing the isopemp coordinates, noise levels, and trajectory coordinates, which is for use with NMPlot; and (3) an ASCII NMGF file named (*_CART.grd), which has the same information as (2), but which also includes the NMGF CART specification for use with AEDT. • Q or q Back to menu Quit this display and return to PCBoom4’s main menu. • F1 for help Display this file. 21.1.3 Signature Display The boom signature at the ground can be displayed by moving the mouse pointer to the desired position pressing either r (or R), p (or P), or l (or L). • Pressing r/R will display the signature at the nearest ray. The signature will then be shown. This will be a single wave associated with that ray. • Pressing p/P will show the signature at a specific point. A dialog will first appear showing the mouse pointer coordinates. These can be edited to any desired value. After closing

162 User Guides for Noise Modeling of Commercial Space Operations—rUMBLe and pCBoom the coordinate dialog, the ground signature will be shown. In complex regions (gener- ally the case near a focus) this can be a compound signature, comprised of booms from several rays. • Pressing l/L will show the signature at a specific point if the case was run in geographic mode. Geographic mode is active if the trajectory was specified in latitude and longitude. Operation of l/L is the same as p/P, except that geographic coordinates are shown in the dialog. A time plot of the signature is displayed. All relevant supporting data is shown above the plot. The following command keys are active while the signature is displayed: • t Show the time plot of the signature • s Show the spectrum (energy spectral density) of the boom • r Show the residual shock spectrum of the boom • F6 Graphical output, similar to that for the main screen. This will output the current display. A dialog is displayed offering the choice of printer or CGM output. • F7 Tabular (ASCII file) output. In “t” mode, the time data will be output. In “s” or “r” mode, both the spectrum and the residual shock spectrum will be output. A dialog is displayed allowing a choice of file name. • F1 Display this file • ESC Return to the footprint display • 0-9 Change scale of current time plot • a Autoscale current time plot Left click will show the maximum value to the left of the mouse pointer Right click, move, right click will show the maximum value between the two clicks Summary instructions for F1 and ESC are shown in the upper right corner of the plot. These, and data displayed from mouse clicks, are not included in any output. 21.2 PCBoom Noise Grid Output for NMPlot WCON generates PCBoom output as described in the previous section. After the sonic boom metric and levels have been selected in WCON, pressing the F7 key generates a grid (*.grd) file, in ASCII NMGF format, that can be imported into NMPlot; a second grid file is also generated that has a minor variation in format for use with AEDT (see Section 21.3). NMPlot is a Microsoft Windows application for viewing and editing sets of geo-referenced data points and is particu- larly useful for producing contour plots and combining and performing mathematical opera- tions on grids. Figure 85 shows a summary of the A-weighted SEL grid file for Sample Case 1; when a grid file is imported into NMPlot (e.g., SampleCase1_dBA.grd), the grid summary screen appears first. To view an initial plot of the SELA contours, select the GRID option from the NMPlot main menu, then select Create Plot of this Grid. The initial plot of ASEL contours is shown in Fig- ure 86. These contours are not automatically generated with optimal default contour values, therefore it is recommended that the user set the contour values manually. To manually set the contour values, select PLOT from the main menu followed by OPTIONS and then in the plot options screen select the radio button to manually specify the contour values as shown in Figure 87. In this case the ASEL contour values specified are 40, 50, 60, 70, 80, and 85 dB. After entering the contour values, select the Apply button followed by the Ok button at the bottom of the screen. The resulting 40 through 85 dB ASEL contours for Sample Case 1 are shown in Figure 88; Figure 89 shows these same contours along with the grid control points (isopemp or ray endpoint coordinates).

pCBoom Data Display and Grid Output 163 Figure 85. NMPlot grid summary screen. Figure 86. NMPlot initial contour plot screen.

164 User Guides for Noise Modeling of Commercial Space Operations—rUMBLe and pCBoom Figure 87. NMPlot screen to manually specify contour levels. Figure 88. NMPlot contour plot screen showing A-weighted SEL contours.

pCBoom Data Display and Grid Output 165 Figure 89. NMPlot contour plot screen showing PCBoom grid control points. Within NMPlot the user can mouse around the contour field to see the noise levels at any point. Contours can be exported in shapefile format (.shp, .shx, and .dbf) and then imported to a GIS to create custom maps, such as the examples shown in Figures 90 and 91. A few important points should be mentioned about the fidelity of the noise grids that PCBoom/WCON output. WCON noise grids contain grid control points and associated levels. The grid control points are the isopemp coordinates or ray endpoint coordinates determined by PCBoom. This is PCBoom’s native grid which provides the highest fidelity data possible for the input parameters specified. The user does have some control over the size and fidelity of the output grid. Depending on performance, the user may need to adjust the number of grid control points that WCON writes to the grid files (*.grd and *_CART.grd). The number of grid control points can be controlled by changing the parameters for ray tracing and azimuthal control that are set in the case file (*.dat), as described in Section 16.6. For example, Sample Case 2 comes with an azimuthal angle increment of 2 degrees which, when processed by PCBoom’s programs (FOBoom499, PCBfoot, and WCON), generates a grid containing about 35,000 points. To lower the number of grid control points, the user may choose to increase the azimuthal angle incre- ment to a different value, such as 5 degrees (default value), which would lower the number of grid points generated in this case to about 14,000. However, by progressively increasing the azimuthal angle increment, a loss of fidelity in the grid may result in important focal points or regions being excluded from the output grids. Users will need to determine what ray tracing and azimuth control settings provide the right balance for each case, though it is suggested to not set a value much larger than the default value of 5 degrees unless the resulting contours can be verified to include all significant levels.

166 User Guides for Noise Modeling of Commercial Space Operations—rUMBLe and pCBoom Figure 90. GIS map of sonic boom contours for Sample Case 1: vertically launched TSTO vehicle.

pCBoom Data Display and Grid Output 167 Figure 91. GIS map of sonic boom contours for Sample Case 2: horizontally launched suborbital vehicle.

168 User Guides for Noise Modeling of Commercial Space Operations—rUMBLe and pCBoom Complex data sets, such as the A-weighted SEL grid generated for Sample Case 2, may place a heavy burden on NMPlot depending on the user’s system performance; grid files may take more than 5 minutes to load and operations within NMPlot may initially be slow. Performance degra- dation in NMPlot when loading some complex data sets generated by WCON appears to be due to two factors. The first factor is null regions where no data is present. The second factor is either the contouring algorithm used by NMPlot, or the rendering of those contours by NMPlot. Due to the null regions where no data exists created by PCBoom/WCON, the distance between regions with significant data, and the variation present within the data from isopemp point to isopemp point cause NMPlot to generate very complex contours from the resulting output. By default, NMPlot generates nine contour sets including five primary level contours and one secondary level in between each primary level. Because the isopemp points are distant from one another and there is significant variation within the resulting data set, there is the potential for each point to get its own contours out toward the edges of the carpet as well as the potential for very intricate contour- ing in locations where multiple isopemp sets are in close proximity. A large and complex data set (like Sample Case 2) where isopemp points are nearly overlapping in a ring around a center which is a null/data free region, can result in a very complex set of contours along the outer ring where there is data with very high variation, forcing contouring to wind around closely located points, while also imposing a requirement to enclose those contours due to the lack of data within the center ring. Unfortunately, the removal of data purely based on level within this highly complex central region would result in an inaccurate picture of the acoustic impact. Though the images may be small on the screen it should not be overlooked that each isopemp point may be depicting the acoustic impact over a very large area in the real world due to the scales involved. Noise grids loaded into NMPlot correctly include the maximum level indicated by WCON. NMPlot also shows the correct general shape and extent of the contours as they are represented in WCON. In some cases, such as Sample Case 1, the resulting contours generated from both programs compare well. Contours generated from more complex data sets may not compare as well, in terms of fine details, since the contouring algorithm used in NMPLot is not the same as the contouring algorithm used in WCON. NMPlot is a leading tool for noise grid manipulation which can be downloaded for free from Wasmer Consulting’s website at http://wasmerconsulting.com/nmplot.htm. 21.3 PCBoom Noise Grid Output for AEDT AEDT users may import PCBoom grid files containing isopemp coordinates (ray endpoint coordinates) and levels that are in ASCII NMGF format. The grid file for use with AEDT is simi- lar to the grid file that is used by NMPlot except that AEDT currently requires that the NMGF “CART” specification be included in the grid file; thus, two different format grid files are gener- ated by WCON. After the sonic boom metric and levels have been selected in WCON, pressing the F7 key generates two grid files: one grid file that can be imported by NMPlot (e.g., Sample- Case1_dBA.grd) and one grid file, with the CART specification included, that can be imported by AEDT (e.g., SampleCase1_dBA_CART.grd). An example of how AEDT currently handles PCBoom grid files is provided in Figure 92 which shows a display of the A-weighted SEL grid for Sample Case 1 in the metric results screen. In this example, file SampleCase1_dBA_CART.grd was imported into AEDT as receptor points and the metric value at each grid point displayed using a color map. Currently, AEDT does not support contouring of irregular grids, such as the type generated by PCBoom, or combining two differ- ent grid sets for the purpose of contouring, because these imported receptors are brought in as points, and contouring in AEDT can only be done on receptor grids. However, these function- alities are being investigated and are planned for future implementation.

pCBoom Data Display and Grid Output 169 Figure 92. AEDT metric results screen showing PCBoom grid control points and A-weighted SEL values.

170 C h a p t e r 2 2 Generating Sonic Boom Source Signatures 22.1 Carlson’s Simplified N-Wave Method A method for generating F-functions based on linearized supersonic theory is described in Carlson’s simplified method [13]. Only the vehicle operating conditions that govern the gen- eration of the sonic boom, as well as a general description of the vehicle geometry, are required. The method calculates the shape factor, KS, as well as the F-function associated with the vehicle at the specified operating conditions. The method begins with the definition of the vehicle’s cross-sectional area, A(x), defined along the vehicle’s axial length. Note that for Carlson’s method, the areas need not be defined along Mach planes, and that little loss of accuracy results from this simplification. A detailed descrip- tion of the geometry is not required for this step, although care should be taken to ensure that the maximum cross-sectional area and its location are correct. If applicable, the area of stream tubes unaffected by the vehicle’s geometry, such as those entering air-breathing engine inlets, should be subtracted from the total cross-sectional area. The next step involves the calculation of the equivalent area due to lift, B(x), defined by the equation , 2 0 B x F p M S b d L v x ∫ ( )( ) = β γ ξ ξ i i i i where x = the distance from the vehicle nose to a point measured backwards along the flight path, 12Mβ = − = the Prandt-Glauert factor, γ = 1.4 = the specific heat ratio, and pv = the local atmospheric pressure at the vehicle’s altitude in pascals. The lift force, FL, for a vehicle in steady level flight is given by the weight component normal to the flight path and directed along the initial ray azimuthal angle, cos cos ,F mgL v= γ θ where m = the vehicle mass in kilograms, g = the standard gravitational acceleration, γv = the flight path angle of the vehicle in degrees, and q = the ray path azimuthal angle in degrees.

Generating Sonic Boom Source Signatures 171 Note that this does not take into account flight path curvature or vehicle acceleration, and therefore does not apply to maneuvering flights. The term 1 0S b d x ∫ ( )ξ ξ represents the ratio of the planform area spanned from the nose to the distance x, where b = the local span of the vehicle planform, x = a dummy variable representing length along the longitudinal axis, and S = the total vehicle planform area in square meters. Once A(x) and B(x) are determined, the total effective area distribution of the vehicle can be calculated through a simple summation of the two area components, .A x A x B xe ( ) ( ) ( )= + In sum, the total effective area distribution represents the volume of air displaced by both the solid body and the effects of lift. From this resulting distribution, the maximum effective area Ae,max can be determined, as well as the effective length, le. The effective area, Ae,1, at the point half way to this effective length can then also be obtained, as shown in Figure 93. Once these effective areas are identified, the ratio Ae,1/Ae,max can be calculated and used with the shape factor parameter curve determined by Carlson and shown in Figure 94. The shape factor, KS, can then be solved for using the maximum effective area, the corre- sponding effective length, le, and the vehicle reference length, l. For typical supersonic vehicles, the fuselage length can be used as the reference length. Once the shape factor is determined, Carlson provides a simple relationship to obtain an N-wave F-function, where the wave has equal peak positive and negative strengths, ±3.46 K s2 l , separated by linear expansion as shown in Figure 95. Carlson’s original sketch provides leeway for interpreting a finite rise time in the signature but withholds from providing any recommendation for calculating it. As calculating rise times can be a complicated nonlinear process, a rise time of zero is sometimes assumed when generating F-functions using this simplified method. This method has been validated for supersonic aircraft ranging from bombers and fighters to supersonic transport vehicles, as well as for launch vehicles, including the Saturn V rocket and the Space Shuttle orbiter [13]. This method was used to generate the source signatures found in the sonic boom source signature database, as described in Section 16.5. Figure 93. Total effective area curve for an example vehicle.

172 User Guides for Noise Modeling of Commercial Space Operations—rUMBLe and pCBoom 0 0.1 0.2 0.3 0.4 0.5 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.6 0.7 0.8 0.9 1 Figure 94. Carlson’s shape factor parameter curve. Figure 95. N-wave F-function with zero rise time.

173 The FAA Office of Environment and Energy (AEE) has approved models for detailed noise analysis. Prior written approval from AEE is required to use another equivalent methodol- ogy or computer model. Modification to standard or default data also requires prior written approval from AEE. PCBoom has been designated an approved modeling method by AEE for sonic boom analysis of commercial space operations [FAA, 2015]. The most current version of FAA’s 1050 desk reference should be consulted to confirm the list of FAA-approved models for detailed noise analysis. Additionally, review and approval of the use of non-default model- ing data may be required, such as user-defined vehicles, trajectories, and atmospheric profiles. The approval of particular non-default methods or data in past studies does not guarantee approval in a future study. Each modeling situation is unique and must be evaluated on a case-by-case basis. This section provides guidance to develop an official approval process to conduct reviews of modeling methodology and input data used in PCBoom. The guidance also addresses the essential components of the review package that PCs must submit to AST for review. The review process is a quality control check on the modeling inputs and methodologies used for environ- mental assessment of space operations. The guidance presented here is similar to the review and approval process that FAA uses for commercial airport noise studies [24], but it is tailored spe- cifically for PCBoom. Note that the information presented here is not the official AEE internal review and approval process. Section 23.1 describes procedures for review of non-default methods and data, Section 23.2 provides a list of common data and whether review and approval should be required, and Section 23.3 provides guidance regarding information to submit for review of non-default methods and data. 23.1 Procedures for Review of Non-Default Methods and Data Below is a description of the required steps for AEE review and approval to use non-default methods and data. 1. Initial communication between the PC, in coordination with the PS, and FAA PM in the region, district office, or service center to determine if the proposed non-default methods/ data require formal review by AEE. As part of this discussion, the PC should be prepared to explain the reason for the use of non-default methods/data to the PM and AEE. 2. The PC must then submit a review package to AST, in coordination with the PS and PM. Infor- mation in the review package must be complete and presented in a clear manner. The informa- tion and the review process must be well-documented and may be included as an appendix C h a p t e r 2 3 Approval Process Guidance for Commercial Space Noise Studies

174 User Guides for Noise Modeling of Commercial Space Operations—rUMBLe and pCBoom to an EA, EIS, or study report as part of the NEPA documentation. The format of the review package is described in Section 23.3. 3. After receiving the review package and checking it for completeness, AST-100 will forward the review package to AEE. 4. Provided the review package is complete and contains all essential information, AEE will begin their review of the package. During the review period, AEE may discuss the review package, gather more facts, and clarify the technical issues directly with the PC. Unless policy implica- tions or substantive issues arise, AEE does not need to coordinate with other FAA headquarters offices or the PM during this period, other than providing emails on the status of its review, as appropriate. 5. AEE will prepare a letter addressed to the PM providing the decision on the review package. 6. AEE will forward the decision letter to the PM (with a cc: AST-100) by email. The PM should convey the decision to the PS and PC. 7. If AEE approves the use of non-default methods or data, the following must be included in the FAA’s project file: (a) a copy of AEE’s approval letter; and (b) a description of the approved non-default method(s) and/or data. Questions about the above procedures should be addressed to AST-100, whether the ques- tions pertain to the process or as applied to a specific project. Early and clear communications by the PC will reduce the chance of delay caused by an incomplete review package. 23.2 List of Common Methods/Data and AEE Review Requirements Sections 23.2.1 and 23.2.2 describe common data used to model commercial space opera- tions. For information on how to request changes to methods or data not listed in either section, please contact AEE. 23.2.1 Analysis Methods/Data that Do Not Require AEE Review and Approval The following analysis methods or data are recommended to not require AEE review and approval: • Default methods and data that are provided in PCBoom. • Trajectory information that is provided by a spacecraft manufacturer. Data may require custom editing by the user to smooth out spurious or irregular data. Therefore, it is recom- mended that users compare any modified trajectory data with the original data to make sure that the modified version retains the important features of the original trajectory. • Use of the U.S. Standard Atmosphere model [NASA and U.S. Air Force, 1976], with alti- tude extensions, or any atmosphere model native to PCBoom would not require review and approval. • Use of supplemental (i.e., other than DNL) noise metrics that are native to PCBoom, pro- vided that the study only reports the resulting noise levels and does not draw any specific conclusions about impacts or suggest that the impacts are significant. Conversely, the discus- sion must include effective language about existing scientific uncertainties and the lack of FAA assessment methodology, impact criteria, and policy guidance in the area examined by supplemental metrics. Although the above methods/data do not require approval, they should be well documented in the NEPA documentation.

approval process Guidance for Commercial Space Noise Studies 175 23.2.2 Analysis Methods/Data that Do Require AEE Review and Approval The following analysis methods or data are recommended to require AEE review and approval. • Sensitivity – Any supplemental noise analysis that involves impacts that are likely to be highly contro- versial on environmental grounds. – Any supplemental noise analysis that involves Section 4(f) properties (including, but not limited to, noise-sensitive areas within national parks; national wildlife and waterfowl refuges; and historic sites including traditional cultural properties) where a quiet setting is a generally recognized purpose and attribute. • Supplemental Noise Metrics – Noise metrics that are not native to PCBoom. – Interpretation of impacts or significance for supplemental noise metrics that are listed in the 1050.1F Desk Reference. – Supplemental noise analysis that is focused on one or more secondary or indirect effects (e.g., sleep disturbance, health effects, classroom learning, low frequency impacts), regard- less of the supplemental metric(s) used. • Spacecraft and Trajectories – Spacecraft that are not native to PCBoom. – User-defined trajectories not provided by a spacecraft manufacturer. • Non-default weather data used for the analysis of sonic boom. • Alternative models and methodologies that are not native to PCBoom. 23.3 Guidance Regarding a Request to Use Non-Default Methods/Data The following information is always required for any request to use non-default methods or data: 1. Background. Briefly describe the project, including location, for which non-default methods or data are needed. State the type of analysis (e.g., EA, EIS, or other type of NEPA analysis). Include any additional relevant information. 2. Statement of Benefit. Briefly describe why the non-default methods or data are needed for this project, how the non-default methods or data are more appropriate, and why the default method or data are not sufficient. The sections below discuss the additional PCBoom-specific information required to be sub- mitted for specific types of non-default methods or data. 23.3.1 Non-Standard PCBoom Input Data Review PCBoom allows for the creation of user-defined spacecraft vehicles, trajectories and atmo- spheric data that differ from default data provided in PCBoom. If analysts use non-default user- defined spacecraft, trajectories, and/or atmospheric profiles that are not native to PCBoom for noise analyses, AEE approval is required (see Section 23.2.2). Additional information to include in a submittal package requesting AEE approval for use of user-defined launch site (location) data, sonic boom signature/spacecraft input data, trajecto- ries, or atmospheric profiles is outlined below. 1. Spacecraft Information (Signature and Vehicle Input Mode) – Thomas input format – Simple F-function

176 User Guides for Noise Modeling of Commercial Space Operations—rUMBLe and pCBoom – Carlson’s F-function (Mode 3B and Mode 3E are most likely to be used by practitioners) � (Mode 3B) Launch Vehicle Mode – similar to the Basic Carlson F-function Mode, with the additional inputs of vehicle thrust and vehicle plume drag. This mode is used to account for the shocks generated from the presence of an underexpanded plume generated by the launch vehicle. � (Mode 3E) Launch Vehicle Database Mode – provides access to predetermined source signatures from a database of launch vehicles. The user may develop new sonic boom source signatures and add these to the database. � Data requirements for Mode 3B and Mode 3E are: • Vehicle Length (feet) • Vehicle Weight (klbs) • Total Thrust (klbf) • Total Plume Drag (klbf) • Vehicle Angle of Attack (degrees) • User-Specified Shape Factor – Tiegerman Blunt Body Reentry Mode (likely to be used by practitioners) � Data requirements are: • Vehicle Length (feet) • Vehicle Weight (klbs) 2. Trajectory Information – Time – Latitude and Longitude (degrees) – Altitude (feet MSL) – Mach Number – Flight Path Heading (degrees) – Flight Path Angle (degrees) � Use of NEWLOAD command additionally requires total vehicle weight, spacecraft length, total vehicle thrust, plume drag, angle of attack, and vehicle shape factor 3. Atmospheric Profile Information – Altitude (feet MSL) – Temperature (degrees Fahrenheit) – Pressure (psf) – Wind Velocity (x-component, feet/second) – Wind Velocity (y-component, feet/second) – Humidity (%) – Atmospheric Pressure at the Ground (psf) Chapter 16 provides additional details about the input data required.

177 1. D. I. Blokhintsev, “The Propagation of Sound in an Inhomogeneous and Moving Medium I,” J. Acoust. Soc. Am., no. 18, pp. 322-328, 1946. 2. K. J. Plotkin, J. A. Page and E. A. Haering, Jr., “Extension of PCBoom to Over-the-Top Booms, Ellipsoidal Earth, and Full 3-D Ray Tracing,” AIAA 2007-3677, May 2007. 3. K. J. Plotkin, J. A. Page and C. Wilmer, “PCBoom Version 6.6 Technical Reference and User Manual,” Wyle Report WR 10-10, Arlington, VA, Dec 2010. 4. J. B. Schulten, “Computation of aircraft noise propagation through the atmospheric boundary layer,” NLR TP 97-374, 1997. 5. A. D. Taylor, “The TRAPS Sonic Boom Program,” NOAA Technical Memorandum ERL-87, 1980. 6. W. D. Hayes, R. C. Haefeli and H. E. Kulsrud, “Sonic Boom Propagation in a Stratified Atmosphere, with Computer Program,” NASA CR-1299, Washington D.C., 1969. 7. W. D. Middleton and H. W. Carlson, “A Numerical Method for Calculating Near-Field Sonic-Boom Pres- sure Signatures,” NASA TN D-3082, Hampton, VA, 1965. 8. K. J. Plotkin, “Low Boom Supersonic Vehicle Shaping Tools, Including Three-Dimensional Effects,” Wyle Report WR 09-15, June 2009. 9. J.-C. L. Wanner, J. Vallee, C. Vivier and C. Thery, “Theoretical and Experimental Studies of the Focus of Sonic Booms,” J. Acoustic. Soc. Am, no. 53, 1, pp. 13-32, 1971. 10. P. F. Holloway, G. A. Wilhold, J. H. Jones, F. Garcia and R. M. Hicks, “Shuttle Sonic Boom—Technology and Predictions,” AIAA paper 73-1039, Oct. 1973. 11. R. O. Onyeonwu, “A Numerical Study of the Effects of Aircraft Maneuvers on the Focusing of Sonic Booms,” UTIAS Report No. 192, Nov. 1973. 12. Department of Atmospheric Science, University of Wyoming, “Weather—Upper Air—Sounding Data,” [Online]. Available: http://weather.uwyo.edu/upperair/sounding.html. [Accessed 20 September 2016]. 13. H. W. Carlson, “Simplified Sonic-Boom Prediction,” NASA TP-1122, Hampton, VA, 1978. 14. C. L. Thomas, “Extrapolation of Sonic Boom Pressure Signatures by the Waveform Parameters Method,” NASA TN-D-6832, Moffett Field, CA, 1972. 15. B. Tiegerman, “Sonic Booms of Drag-Dominated Hypersonic Vehicles,” Ph.D. Thesis, Cornell University, Ithaca, NY, 1975. 16. P. O. Jarvinen and J. A. F. Hill, “Universal Model for Underexpanded Rocket Plumes in Hypersonic Flow,” in 12th JANNAF Liquid Meeting, Las Vegas, NV, 1970. 17. H. K. Cheng, C. J. Lee, M. M. Hafez and W. H. Guo, “Sonic Boom Propagation and Submarine Impact: A Study of Computational and Theoretical Issues,” AIAA-96-0755, Reno, NV, 1996. 18. Federal Aviation Administration, “The Annual Compendium of Commercial Space Transportation: 2016,” 2016. 19. K. J. Plotkin, R. J. Franz and E. A. Haering Jr., “Prediction and Measurement of a Weak Sonic Boom from an Entry Vehicle,” J. Acoust. Soc. Am., vol. 120, no. Paper 2a PA3, p. 3077, 2006. 20. American National Standards Institute, “Quantities and Procedures for Description and Measurement of Environmental Sound: Part 4,” ANSI S12.9, Part 4, 1996. 21. K. P. Shepherd and B. M. Sullivan, “A Loudness Calculation Procedure Applied to Shaped Sonic Booms,” NASA TP-3134, Hampton, VA, 1991. 22. S. S. Stevens, “Perceived Loudness of Noise by Mark VII and Decibels (E),” J. Acoust. Soc. Am., vol. 51 (2), pp. 575-601, 1972. 23. J. D. Leatherwood, B. M. Sullivan et al., “Summary of Recent NASA Studies of Human Response to Sonic Booms,” J. Acoust. Soc. Am., vol. 111(1) (Part 2), pp. 586-598, 2002. 24. Federal Aviation Administration, “Guidance on Using the Aviation Environmental Design Tool (AEDT) to Conduct Environmental Modeling for FAA Actions Subject to NEPA,” September 12, 2016. References

178 AEDT Aviation Environmental Design Tool AEE Office of Environment and Energy AGL Above Ground Level ANSI American National Standards Institute ARAP ARAP Sonic Boom Program ASCII American Standard Code for Information Exchange ASEL A-weighted Sound Exposure Level AST Office of Commercial Space Transportation CFD Computational Fluid Dynamics CSEL C-weighted Sound Exposure Level D4M Delta IV Medium dB Decibel deg Degree DNL Day-Night Average Sound Level EA Environmental Assessment EFG Earth-fixed Geocentric (coordinate system) EIS Environmental Impact Statement ESEL Unweighted Sound Exposure Level FAA United States Federal Aviation Administration ft Feet (length) GENGS Low Boom Supersonic Vehicle Shape Optimization Tools GIS Geographic Information System GUI Graphical User Interface i/o Input/Output lbs Pound (mass) lbf Pounds (force) Lpk Peak Overpressure Level (dB, referenced to 20 µPa) Lflt Unweighted Energy-integrated Level (dB, referenced to 20 µPa) MECO Main Engine Cut Off MSL Mean Sea Level NASA National Aeronautics and Space Administration NEPA National Environmental Policy Act NMGF Noise Model Grid Format Pa Pascal (unit of pressure, one Newton per square meter) PC Project Consultant PM Project Manager PS Project Sponsor PL Loudness, dB Abbreviations

Abbreviations 179 Pmax Peak overpressure (unit of pressure, pounds per square foot) psf Pound-force per Square Foot s, sec Second (time duration) SECO Second Stage Engine Cut Off SMP Simple (PCBoom operation mode) TRAPS TRAPS Sonic Boom Program TSTO Two-stage-to-orbit ULA United Launch Alliance U.S. United States