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Commercial Space Vehicle Emissions Modeling 7 2 Literature Review A literature review was conducted to identify sources relevant to commercial space vehicle emissions modeling. Sources were evaluated based on their usefulness in providing: ï Emissions data to establish the pollutants emitted by different types of rocket propellants, ï Engine performance data to establish the amount of propellant burned, and ï Trajectory data to establish the amount of time spent in each altitude band. Relatively few relevant sources for commercial space vehicle emissions modeling were found in the open literature. Multiple factors are responsible for the sparsity of published data. For example, emissions data for solid rocket motors are often classified or export-controlled due to the military applications of solid propellants. Similarly, performance specifications and trajectory data for many current and in-development commercial space vehicles are considered proprietary by manufacturers. The most detailed rocket emissions and operational data sources in the open literature are for National Aeronautics and Space Administration (NASA) vehicles and launch sites. The following sections summarize the relevant literature sources for commercial space vehicle emissions modeling: ï Section 2.1 describes emissions data for the major chemical species emitted by different rocket propellants, ï Section 2.2 presents engine performance data to estimate the amount of propellant burned by current commercial space vehicles, and ï Section 2.3 discusses trajectory data for historical and nominal rocket launches. 2.1 Emissions Data Since the inception of space flight, the need to optimize rocket performance has motivated research into the chemical kinetics involved in producing thrust in rocket engines. Thrust production involves a series of complex chemical reactions, as shown in Figure 6. First, combustion occurs between the fuel and oxidizer inside the rocket engine. In liquid-propellant rocket engines, the liquid fuel and liquid oxidizer react at high temperatures and pressures inside the main combustion chamber. In solid- propellant rocket motors, the exposed surfaces of the solid propellant grain combust at high temperatures and pressures after ignition. Next, the products of combustion expand and accelerate through the nozzle, where additional chemical reactions may occur. The process of expelling mass at high velocities through the nozzle produces thrust. However, the combustion products expelled through the nozzle are emitted into the atmosphere as pollutants. The chemical species present at the nozzle exit plane are called the primary emissions of the rocket engine. Since the temperature of the rocket exhaust at the nozzle exit plane is extremely high, the chemical species in the exhaust plume may continue to react with each other and with the surrounding air in a process called afterburning. The products formed by afterburning and other reactions in the plume are called secondary emissions. Thus, the chemical species emitted into the atmosphere after the rocket has passed by and the exhaust plume has cooled to the ambient
Commercial Space Vehicle Emissions Modeling 8 temperature include contributions from both the primary and secondary emissions. The commercial space vehicle emissions model is designed to estimate these final emissions, as they are the chemical species that the vehicle ultimately emits into the atmosphere. Figure 6. Diagram of the chemical processes in a rocket engine that produce the primary, secondary, and final emissions. 2.1.1 Qualitative Emissions Data The emissions produced by a rocket engine depend on the chemical composition of the rocket propellant. Rocket propellants consist of a fuel and an oxidizer, and they are categorized based on their state of matter and the manner in which they react. Most launch vehicles employ liquid, solid, hypergolic, or hybrid propellants. Historically, most liquid-propellant rocket engines have used a combination of liquid oxygen (LOX) as the oxidizer and liquid hydrogen (H2) or a highly refined form of kerosene called RP-1 as the fuel. New engines that use liquid methane (CH4) or ethanol as the fuel are currently under development. Modern solid-propellant rocket motors use a propellant mixture consisting of powdered aluminum (Al) as the fuel, powdered ammonium perchlorate (NH4ClO4) as the oxidizer, and a rubbery binder such as hydroxyl-terminated polybutadiene (HTPB) or polybutadiene acrylonitrile (PBAN) that is also consumed as fuel . This solid propellant mixture is called ammonium perchlorate composite propellant (APCP), but it is often identified as HTPB or PBAN based on its binder. Hypergolic propellants, which ignite spontaneously on contact between the fuel and oxidizer, are uncommon in US launch vehicles, but they have been used extensively in European and Chinese rockets. Hybrid-propellant rocket engines, which employ a liquid oxidizer and solid fuel, are currently under development.
Commercial Space Vehicle Emissions Modeling 9 Primary Emissions Table 1 summarizes the major primary emissions species produced by each common type of rocket propellant. The primary emissions are the chemical species present at the nozzle exit plane. The major products of combustion and the evolution of the reacting flow within the nozzle are well understood because this knowledge is essential for predicting thrust . However, significant knowledge gaps still remain concerning these major primary emissions. For example, alumina (Al2O3) is emitted from solid-propellant rocket motors as particulate matter (PM), but little is known about the size distribution of the particles and how many are PM10 (<10 Âµm in diameter), PM2.5 (<2.5 Âµm in diameter), PM1 (<1.0 Âµm in diameter), or smaller. Table 1. Major primary emissions species for common types of rocket propellants. Type Oxidizer Fuel Major Primary Emissions Liquid LOX (O2) Hydrogen (H2) H2O, H2 LOX (O2) RP-1 (kerosene) H2O, CO2, CO, H2 LOX (O2) Methane (CH4) H2O, CO2, CO, H2 Solid Ammonium perchlorate (NH4ClO4) Aluminum (Al) & HTPB or PBAN Al2O3, CO, HCl, H2O, N2, CO2, H2, Cl, NOx Hypergolic Nitrogen tetroxide (N2O4) Hydrazine (N2H4), MMH, or UDMH N2, CO2, H2O, CO, NOx Hybrid Liquid (e.g., N2O) Solid (e.g., HTPB) Varies (e.g., H2O, CO2, CO, H2, N2, NOx) As noted in Table 1, the major primary emissions species produced by hybrid rocket propellants vary depending on the solid fuel and liquid oxidizer. Hybrid propellants typically use hydrocarbons as the solid fuel, but the liquid oxidizer may be O2, N2O, or some other oxygen-containing chemical species. If the oxidizer contains nitrogen, the major primary emissions species will include N2 and NOx. In addition to the primary emissions listed in Table 1, other minor chemical species may be formed due to incomplete combustion and nonequilibrium processes inside the rocket engine: ï Black carbon (BC), commonly known as soot, is formed due to incomplete combustion of carbon-containing propellants; ï Combustion inefficiencies in hydrocarbon-containing propellants could result in trace amounts of a complex mix of hydrocarbon emissions; and ï Impurities in the fuel could result in trace amounts of other emissions species that depend on the chemical composition of the impurities. These minor products of combustion may have significant environmental impacts, even in small quantities. However, the incomplete combustion and nonequilibrium processes that produce these
Commercial Space Vehicle Emissions Modeling 10 minor products of combustion are difficult to accurately measure or model. Thus, these minor species are poorly understood compared to the major primary emissions listed in Table 1. Secondary Emissions In addition to the primary emissions formed inside the rocket engine, secondary emissions are formed outside the rocket engine due to chemical reactions in the high-temperature exhaust plume. For example: ï Nitrogen oxides (NOx) are formed by reactions between the high-temperature exhaust products and the nitrogen (N2) in the surrounding atmosphere. ï Hydrogen molecules (H and H2) at the nozzle exit plane react with oxygen molecules (O2) from the surrounding air to form water vapor in the exhaust plume. ï Carbon monoxide (CO) at the nozzle exit plane is oxidized to carbon dioxide (CO2) in the exhaust plume. ï Hydrogen chloride (HCl) may dissociate into chlorine molecules (Cl and Cl2) in the exhaust plume at a rate that depends on solar radiation. Although the chemical composition of the exhaust plume has been studied for military applications such as detection and targeting, detailed results are not available in the public domain. Additionally, the evolution of individual pollutant species in the rocket exhaust plume has received only limited attention from the rocket propulsion community . The dearth of studies investigating rocket emissions in relation to environmental impacts may be due to the absence of environmental regulations targeted at limiting rocket emissions. 2.1.2 Quantitative Emissions Data The previous section provides a qualitative understanding of the chemical species emitted by each type of rocket propellant. However, quantitative estimates of the emissions are required for the commercial space vehicle emissions model. The following sources provide background information and their own literature summaries of quantitative emissions data: ï Rocket Exhaust Plume Phenomenology by Simmons  provides an overview of the gas dynamics of rocket exhaust plumes and the physical properties of exhaust constituents. ï The Liquid Propellant Engine Manual  published by the Chemical Propulsion Information Agency provides rocket performance data for a variety of government-sponsored activities. However, this information is export-controlled and is not published for the general public. ï A 2017 FAA report by Dr. Miake-Lye, âFinal Report on Assessing Future Space Launch Emissions and Their Environmental Impactâ , cites numerous references for emissions measurements and estimates used in prior rocket environmental impact assessments. This current literature review leverages and expands upon Dr. Miake-Lyeâs 2017 FAA report. The following sections summarize additional literature sources that provide quantitative emissions predictions and measurements for historical and current launch vehicles.
Commercial Space Vehicle Emissions Modeling 11 Emissions Predictions for Historical Launch Vehicles The most detailed emissions results that are publicly available in the literature are analyses of the Space Shuttle (Figure 7) and other NASA launch vehicles. Although these launch vehicles are not commercial space vehicles, the results are useful for estimating the quantities of pollutants emitted by different types of rocket propellants. The following sources include predictions of the emissions from the Space Shuttle and other retired or never-flown rocket engines: ï Pergament, et al. [11-13] computed the primary and secondary NOx emissions produced by the Space Shuttle solid rocket motors and compared the predictions to in situ measurements of the exhaust plume of a Titan III rocket. ï The Environmental Impact Statement (EIS) for the Space Shuttle Program  includes predictions  of the exhaust products produced at the nozzle exit plane and at a plane 1 km downstream of the nozzle for both the Space Shuttle solid rocket motors and the Space Shuttle Main Engines (SSMEs). ï The EIS for the Space Shuttle Advanced Solid Rocket Motor Program  and for testing at NASA Stennis Space Center  include predictions of several exhaust products (CO, NOx, Cl2, HCl, and Al2O3) produced during static testing of the solid rocket motors. ï Leone and Turns  computed the chlorine and NOx emissions as functions of altitude due to afterburning in the exhaust plumes of the Space Shuttle solid rocket motors and SSMEs. ï Denison, et al.  computed the mass flow rates of multiple exhaust species as functions of the distance behind the nozzle exit plane of a proposed solid rocket motor at altitudes of 18 km and 30 km. ï Zittel  computed the mass fractions of chlorine species in the exhaust plume of a Titan IV rocket (Figure 7) as functions of altitude and the distance behind the nozzle exit plane. Figure 7. Space Shuttle and Titan IV launches.
Commercial Space Vehicle Emissions Modeling 12 Emissions Predictions for Current Launch Vehicles The sources listed above are useful for estimating the quantities of pollutants emitted by different types of rocket propellants, but they are not specific to current commercial space vehicles. The following sources include predictions of the emissions for commercial space vehicles and engines: ï The 1996 Environmental Assessment (EA) of the Kodiak Launch Complex  lists the mass flow rates of HCl and Al2O3 emitted by several commercial solid rocket motors; the values are attributed to a telephone conversation with a representative of Thiokol Corporation. ï The 1997 EIS for Engine Technology Support for NASA's Advanced Space Transportation Program  focused on petroleum-based rocket engines. ï The 1998 EIS for the Evolved Expendable Launch Vehicle Program  and the subsequent supplemental EIS  in 2000 include predictions of the total masses of regulated exhaust species (including NOx, CO, PM, and HCl) emitted into different levels of the atmosphere by the Atlas V and Delta IV rockets. ï The 2007 EA for the Falcon 1 and Falcon 9 (Figure 8) at Cape Canaveral Air Force Station  includes predictions of the mole fractions of the combustion products at the nozzle exit plane. The EA also includes estimates of the concentrations of the species further downstream in the exhaust plume, but these estimates are subject to large uncertainty. ï The 2012 EA for the launch and re-entry of SpaceShipTwo at the Mojave Air and Space Port  includes estimates of SpaceShipTwo emissions. ï The 2020 EA for SpaceX Falcon launches at Kennedy Space Center and Cape Canaveral Air Force Station  includes predictions of the mass fractions of exhaust species in the main combustion chamber, gas generator, nozzle exit, and downstream of the Merlin 1D engine. ï Several other environmental documents, including the EAs for the E4 Test Stand  and A-3 Test Stand  at NASA Stennis Space Center and the EA for the Space Florida Launch Site Operator License at Launch Complex 46  at Cape Canaveral Air Force Station, provide information regarding the types of pollutants emitted by various rocket engines. Figure 8. Falcon 9 launch.
Commercial Space Vehicle Emissions Modeling 13 Black Carbon Emissions Estimates The quantitative emissions data in the sources listed above were predicted based on emissions models, and few of the results were confirmed by measurements. Additionally, most of these sources contained no data for black carbon emissions (Figure 9), which are not reliably predicted with existing models . The following references leverage comparisons between models and measurements to indirectly estimate the concentration of black carbon, or soot particles, in the exhaust plume: ï Plastinin, et al.  compared remote measurements of radiation intensity to modeled data to estimate the concentration of soot particles in the exhaust plumes of Atlas II and Atlas III rockets at an altitude of 21 km. ï Alexeenko, et al.  compared remote measurements of radiation intensity to modeled data to estimate the concentration of soot particles in the exhaust plume of an Atlas II rocket at altitudes of 15 and 40 km. ï Burt and Boyd  estimated the concentration of soot particles in a solid-propellant rocket exhaust plume at altitudes above 100 km based on a comparison between experimental and modeled results. Figure 9. The SpaceShipTwo exhaust plume contains black carbon. Emissions Measurements Few in situ measurements of rocket emissions have been performed, and most were designed to study stratospheric ozone depletion due to chlorine and NOx emissions from solid rocket boosters. These measurements have limited applicability to the commercial space vehicle emissions model. However, the following references describe measurement campaigns that may provide useful results for future model validation studies: ï Voigt, et al.  summarized several in situ measurements conducted by flying an airplane through the exhaust plumes of different rockets to quantify multiple exhaust species, including chlorine, NOx, water vapor, CO2, and PM. A number of these measurements were conducted in the exhaust plume of an Athena II solid rocket [35-40]. ï Measurements of emissions at altitude were performed by flying an aircraft through the exhaust plumes of Titan rockets during the Rocket Impacts on Stratospheric Ozone (RISO) study [41, 42] in the late 1990s and early 2000s.
Commercial Space Vehicle Emissions Modeling 14 2.2 Engine Performance Data The references provided in the previous section are useful for estimating the concentration of each chemical species emitted by a rocket engine, but the total amount of each species depends on the total amount of propellant burned by the rocket. Thus, the total amount of pollutants emitted into the atmosphere depends on the propellant mass flow rate and burn time. Estimates of the Mass Flow Rate The mass flow rate as a function of time is not publicly available for most commercial space vehicles. Instead, manufacturers typically provide rocket engine performance specifications such as the thrust and specific impulse . The thrust, ðð, is the force generated as a reaction to expelling mass at high velocities through the nozzle  and can be expressed as  ðð = ?Ì?ððððððð (1) where ?Ì?ð is the mass flow rate, and ðððððð is the equivalent exhaust velocity. The specific impulse, ð¸ð¸ð ð ðð, is a measure of the efficiency of the rocket engine  and can be expressed as ð¸ð¸ð ð ðð = ðððððð ðð0 (2) where ðð0 = 9.80665 m/s2 is the standard acceleration due to gravity at Earthâs surface. Equations (1) and (2) can be combined to give the instantaneous mass flow rate as ?Ì?ððð = ðð ðð0ð¸ð¸ð ð ðð (3) Equation (3) demonstrates that the instantaneous mass flow rate can be calculated directly from the thrust and specific impulse. However, the thrust and specific impulse both depend on the ambient pressure, which decreases with increasing altitude. Manufacturers often specify the thrust and specific impulse at sea level and in the vacuum of space , which provide the bounding cases at the lowest and highest altitudes, respectively. The sea level thrust and specific impulse can be substituted in to Eq. (3) to estimate the initial mass flow rate at liftoff. Alternatively, the average mass flow rate can be estimated from the total propellant mass consumed, ðððð, and the burn time, ð¡ð¡ðððððððð, as ?Ì?ððððððð = ðððð ð¡ð¡ðððððððð (4) Manufacturers often publish the maximum total propellant mass and the nominal burn time. A potential source of uncertainty arises from the use of the total propellant mass to estimate the average mass flow rate. The total propellant mass typically includes excess propellant margin that is not consumed during ascent, particularly for reusable booster stages that must reserve propellant for landing. Thus, the use of the total propellant mass will result in a slight overestimate of the average mass flow rate.
Commercial Space Vehicle Emissions Modeling 15 Engine Performance Data for Commercial Space Vehicles Table 2 lists the sea level thrust, sea level specific impulse, propellant mass per engine, nominal burn time, and estimated initial and average mass flow rates for the first-stage rocket engines of current commercial  and historical launch vehicles. The mass flow rates range from less than 10 kg/s for the Rocket Lab Rutherford engine to more than 4,000 kg/s for the Space Shuttle Reusable Solid Rocket Motor (RSRM). However, Table 2 demonstrates that the estimated initial and average mass flow rates are similar to each other for most rocket engines regardless of scale. This agreement provides confidence in the mass flow rate estimates. Table 2. Performance specifications for the first-stage rocket engines of current commercial and selected historical launch vehicles. Vehicle Engine Propellant T kN Isp s Mp 103 kg tburn s ?Ì?ððð kg/s ?Ì?ððððððð kg/s Ref. NASA Saturn V F-1 LOX/RP-1 6770 263 430 161 2625 2671 [47, 48] Space Shuttle SSME LOX/Hydrogen 1750 366 240 516 488 466 [43, 49] Space Shuttle RSRM APCP (PBAN) 11520 267 502 123 4395 4081  Northrop Grumman Antares 230 RD-181 LOX/RP-1 1824 313 120 209 594 572 [1, 50] Minotaur I M55A1 APCP (PBAN) 892 237 20.8 60.0 384 346 [43, 51] Minotaur IV SR-118 APCP (HTPB) 2224 282 45.4 56.6 804 802 [52, 53] Minotaur-C Castor 120 APCP (HTPB) 1686 280 48.9 79.4 614 616 [43, 54] Pegasus XL Orion 50SXL APCP (HTPB) 622 293 15.0 69.7 216 216 [43, 54] Rocket Lab Electron Rutherford LOX/RP-1 25 311 1.0 150 8.2 6.9 [55, 56] SpaceX Falcon 9 Merlin 1D LOX/RP-1 854 282 46.5 146 309 319 [57-59] United Launch Alliance (ULA) Atlas V RD-180 LOX/RP-1 3827 311 284 236 1254 1204  Atlas V AJ-60A APCP (HTPB) 1550 279 42.5 88.3 566 481 [43, 60] Delta IV RS-68A LOX/Hydrogen 3123 362 200 249 880 802 [43, 61] Delta IV GEM-60 APCP (HTPB) 887 274 29.7 90.8 330 327  Virgin Galactic SpaceShipTwo RocketMotorTwo N2O/HTPB 311 250 7.0 60.0 127 117 [26, 62] Several factors may account for the small differences between the estimated initial and average mass flow rates in Table 2. As discussed previously, the total propellant mass results in a slight overestimate of the average mass flow rate, particularly for reusable booster stages that reserve propellant for landing. For example, the average mass flow rate for the SpaceX Merlin 1D engine, which is used on the reusable first stage of the Falcon 9 rocket, is estimated to be greater than the initial mass flow rate. However, for many of the engines listed in Table 2, the opposite trend is observed: the initial mass flow rate is estimated to be greater than the average mass flow rate. This observation suggests that the instantaneous mass flow rate varies with time during ascent.
Commercial Space Vehicle Emissions Modeling 16 Constant Versus Time-Varying Mass Flow Rate As discussed previously, the thrust and specific impulse vary with time during ascent because they depend on the ambient pressure, which decreases with increasing altitude. However, the mass flow rate is not affected by the ambient conditions outside the nozzle because the exhaust velocity at the nozzle exit plane is supersonic. The conditions inside a supersonic nozzle do not depend on the conditions outside the nozzle because pressure waves, which propagate at the speed of sound, cannot travel upstream against a flow moving faster than the speed of sound . Thus, the mass flow rate is governed only by the conditions inside the rocket engine. For solid-propellant rocket motors, the mass flow rate varies directly with the exposed area of the grain, which is the shaped mass of solid propellant inside the rocket motor . The shape of the grain determines whether the exposed area remains relatively constant or changes significantly over time as it burns. Thus, variation in the mass flow rate for solid propellants is pre-determined based on the design of the grain and cannot be controlled after ignition. Conversely, liquid-propellant rocket engines have the ability to throttle up or down by controlling the mass flow rates from the main fuel and oxidizer valves . Figure 10 shows an example of the time- varying nominal thrust profile for the liquid-propellant SSME during the Space Shuttle ascent phase [63, 64]. The SSME is initially throttled to 104.5% of its rated power to clear the launchpad and begin its ascent. A short time later, the SSME is throttled back by approximately one-third during the period of maximum dynamic pressure, also known as Max Q, to ensure that the aerodynamic loads on the Space Shuttle remain below structural limits . Following Max Q, the SSME is again throttled up to 104.5% of its rated power. Late in the ascent phase, the SSME is slowly throttled back to ensure that the acceleration experienced by the crew and orbiter does not exceed 3 G . Based on Eq. (3), the mass flow rate through the SSME is proportional to the thrust profile shown in Figure 10. Figure 10. Nominal thrust profile for the SSME during the ascent phase . Time-resolved thrust profiles, such as the one shown in Figure 10, are not publicly available for most commercial launch vehicles. Instead, if no time-varying information is available, the average mass flow rate is assumed to remain constant throughout the ascent phase. This assumption is reasonable
Commercial Space Vehicle Emissions Modeling 17 for most launch vehicles. For example, Figure 11 shows the normalized mass flow rates for the first stages of the Saturn V rocket during the Skylab 1 mission  and the Saturn IB rocket during the Skylab 2 mission . The mass flow rates of both rockets are roughly constant from liftoff until center engine cutoff at approximately 140 s. Figure 11. Normalized mass flow rates for the first stages of the Saturn V and Saturn IB rockets during the ascent phases of the Skylab 1 and Skylab 2 missions [66, 67]. Some commercial space vehicles throttle back during Max Q in a manner similar to the Space Shuttle thrust profile shown in Figure 10. During this period of reduced throttle, the instantaneous mass flow rate is lower than either the initial or average mass flow rate. Thus, the assumption of a constant mass flow rate is conservative for modeling the emissions of launch vehicles that throttle back during Max Q. Since the duration of reduced throttle for Max Q is typically short compared to the burn time, the error associated with the constant mass flow rate assumption is reasonably small. 2.3 Trajectory Data The literature sources presented in the previous sections are useful for estimating the emissions and propellant mass flow rate for commercial space vehicles. The final component required for the emissions model is the vehicleâs trajectory. The trajectory determines the amount of time spent, and hence the total amount of pollutants emitted, into each altitude band. Typically, a launch vehicleâs trajectory is designed to maximize the total mass that can be delivered into a desired orbit . The trajectory depends on numerous variables such as: ï Payload mass, ï Empty mass of the launch vehicle, ï Performance of the launch vehicle, ï Aerodynamics of the launch vehicle, ï Atmospheric conditions and high-altitude winds, ï Latitude of the launch site, and ï Altitude and inclination of the target orbit.
Commercial Space Vehicle Emissions Modeling 18 The mass, thrust, and structural limits of the launch vehicle determine the maximum acceleration the vehicle can achieve. Within the atmosphere, trajectories are typically designed to use a gravity-turn maneuver, which maintains a zero-degree angle of attack between the vehicle and the flight path. This maneuver is intended to minimize the aerodynamic loading on the vehicle . Furthermore, trajectories are commonly redesigned on the day of launch based on the high-altitude wind speed and direction . Finally, the entire trajectory depends on the starting and ending states, namely, the location of the launch site and the velocity and altitude required to achieve the intended orbit. Different velocities and altitudes are required to attain low Earth orbit (LEO), geosynchronous transfer orbit, geosynchronous equatorial orbit, Sun-synchronous orbit, and interplanetary transfer orbit. Historical Trajectories An analysis of actual launch trajectories demonstrates the effects of the launch vehicle and target orbit on the trajectory. Numerous historical trajectories from NASA missions are publicly available. Table 4 lists the vehicle name and weight class, propellant type, mission name, available trajectory parameters, and literature reference for each of these publicly available trajectories. The weight classes, as defined in Table 3, are based on the maximum payload mass the launch vehicle can deliver to LEO . The trajectory parameters listed in Table 4 are the altitude (â), velocity (ð£ð£), acceleration (ðð), thrust (ðð), specific impulse (ð¸ð¸ð ð ðð), and mass flow rate (?Ì?ð). Solid black symbols indicate that these parameters are available as functions of time in the corresponding reference(s), whereas lighter gray symbols indicate that only time-averaged parameters are available. Most of the references listed in Table 4 are post-flight mission reports in which the trajectories were reconstructed using ground- based tracking and launch vehicle telemetry. One notable reference is âApollo by the Numbersâ , which summarizes many relevant time-averaged parameters for each of the manned Apollo missions. Table 3. Launch vehicle weight classes . Weight Class Payload Mass to LEO (103 kg) Small-lift launch vehicle 0 â 2 Medium-lift launch vehicle 2 â 20 Heavy-lift launch vehicle 20 â 50 Super-heavy-lift launch vehicle 50+
Commercial Space Vehicle Emissions Modeling 19 Table 4. Summary of publicly available historical launch vehicle trajectory data. Vehicle Class Propellant Mission â ð£ð£ ðð ðð ð¸ð¸ð ð ðð ?Ì?ð Ref. Saturn I Medium LOX/RP-1 Pegasus I ï¬ ï¬  Atlas-Centaur Medium LOX/RP-1 AC-6 ï¬ ï¬ ï¬ ï¬ ï¬ ï¬  Surveyor 3 ï¬ ï¬ ï¬ ï¬ ï¬  Titan II Medium Hypergolic Gemini 4 ï¬ ï¬ ï¬ ï¬ ï¬ ï¬  Gemini 5 ï¬ ï¬ ï¬ ï¬ ï¬ ï¬  Gemini 8 ï¬ ï¬ ï¬ ï¬ ï¬ ï¬  Gemini 10 ï¬ ï¬ ï¬ ï¬ ï¬ ï¬  Gemini 12 ï¬ ï¬ ï¬ ï¬ ï¬ ï¬  Saturn V Super- Heavy LOX/RP-1 Apollo 8 ï¬ ï¬ ï¬ ï¬ ï¬ ï¬  Apollo 9 ï¬ ï¬ ï¬ ï¬ ï¬ ï¬  Apollo 10 ï¬ ï¬ ï¬ ï¬ ï¬ [47, 81] Apollo 11 ï¬ ï¬ ï¬ ï¬ ï¬ [47, 82] Apollo 13 ï¬ ï¬ ï¬ ï¬ ï¬ ï¬ [83, 84] Apollo 14 ï¬ ï¬ ï¬ ï¬ ï¬ ï¬  Apollo 15 ï¬ ï¬ ï¬ ï¬ ï¬ ï¬  Apollo 16 ï¬ ï¬ ï¬ ï¬ ï¬ ï¬  Apollo 17 ï¬ ï¬ ï¬ ï¬ ï¬ ï¬ [88, 89] Skylab 1 ï¬ ï¬ ï¬ ï¬ ï¬ ï¬ [66, 90] Saturn IB Heavy LOX/RP-1 Skylab 2 ï¬ ï¬ ï¬ ï¬ ï¬ ï¬  Skylab 3 ï¬ ï¬ ï¬ ï¬ ï¬ ï¬  Skylab 4 ï¬ ï¬ ï¬ ï¬ ï¬ ï¬  Space Shuttle Super- Heavy LOX/Hydrogen & APCP (PBAN) STS-124 ï¬ ï¬ ï¬ ï¬  STS-133 ï¬ ï¬ ï¬ ï¬  STS-134 ï¬ ï¬ ï¬ ï¬  STS-135 ï¬ ï¬ ï¬ ï¬  ï¬ Time-resolved ï¬ Time-averaged
Commercial Space Vehicle Emissions Modeling 20 Comparison Between Trajectories The trajectory parameters listed in Table 4 were digitized from the graphs and tables contained in the original references. The altitude profiles for the individual Apollo missions were nearly identical to one another, so they were averaged together to create an average Apollo trajectory. Similarly, the individual Gemini and Skylab 2â4 altitude profiles were each averaged together for the same reason. Figure 12 compares the time-resolved altitude profiles of the Apollo, Gemini, Surveyor 3, and Skylab 2â4 missions. Although these missions flew on different types of launch vehicles, they all had similar low Earth orbits (the Surveyor 3 mission and most of the manned Apollo missions continued to the Moon, but they were injected into a parking orbit around the Earth prior to trans-lunar injection). The similarity between the altitude profiles shown in Figure 12 suggests that the target orbit has a significantly larger effect on the launch trajectory than the type of launch vehicle. Figure 12. Altitude profiles of different historical launch vehicles with similar target (parking) orbits. Figure 13 compares the time-resolved altitude profiles of the Apollo, Skylab 1, and Pegasus A missions. These missions all flew on launch vehicles from the Saturn family of rockets. However, the Skylab 1 and Pegasus A missions had higher-altitude target orbits than the parking orbit used by the Apollo missions. The significant differences between the altitude profiles shown in Figure 13 further suggest that the launch trajectory is determined more by the target orbit than by the type of launch vehicle.
Commercial Space Vehicle Emissions Modeling 21 Figure 13. Altitude profiles of similar historical launch vehicles with different target orbits. Figure 14 compares the time-resolved altitude profiles of the Space Shuttle STS-124 mission and the Blue Origin New Shepard and New Glenn rockets to the Apollo missions. The altitude profiles for the New Shepard and New Glenn were digitized from the nominal trajectories provided in the respective payload userâs guides for those vehicles [96, 97]. The Saturn V, Space Shuttle, New Shepard, and New Glenn are very different types of launch vehicles from different eras. Moreover, the New Shepard is a suborbital launch vehicle, and the target orbits for the other launch vehicles are all at different altitudes. Thus, the altitude profiles shown in Figure 14 diverge. Figure 14. Altitude profiles of different historical and in-development launch vehicles with different target orbits.
Commercial Space Vehicle Emissions Modeling 22 Trajectories below the KÃ¡rmÃ¡n Line Although the altitude profiles shown in Figure 13 and Figure 14 diverge due to the different target orbits, the most significant differences do not occur until high altitudes. The commercial space vehicle emissions model is only intended to estimate emissions within the atmosphere. The internationally recognized boundary between Earthâs atmosphere and outer space is known as the KÃ¡rmÃ¡n line and is defined at an altitude of 100 km. The altitude profiles shown in Figure 12, Figure 13, and Figure 14 are plotted at altitudes below the KÃ¡rmÃ¡n line in Figure 15. The differences between the launch vehicle trajectories are significantly smaller within the atmosphere than outside the atmosphere. Figure 15. Altitude profiles of historical and in-development launch vehicles below the KÃ¡rmÃ¡n line (100 km). Altitude profiles are required for the commercial space vehicle emissions model in order to calculate the amount of time a vehicle spends in each altitude band. The time duration in each altitude band is then used to estimate the total amount of pollutants emitted into the altitude band. As an example, the altitude profiles in Figure 15 were used to calculate the amount of time that each rocket spends in various altitude bands during ascent, and the results are presented in Figure 16. These results demonstrate that a relatively small number of example altitude profiles can adequately capture the variation in time duration per altitude band for most of these historical launch trajectories.
Commercial Space Vehicle Emissions Modeling 23 Figure 16. Time duration in each altitude band for historical and publicly available trajectories. Trajectory Design and Optimization Software In addition to the publicly available trajectory data discussed above, multiple software packages for designing and optimizing launch vehicle trajectories were identified during this literature review. These software packages, developers, and availability are listed in Table 5. Many of the software packages described in the literature were originally developed by NASA. In particular, POST2 and OTIS4 have been widely used in trajectory design and optimization studies for conceptual and operational launch vehicles . Both POST2 and OTIS4 have been shown to produce similar high-quality results . However, the NASA-developed software packages are either export- controlled or unavailable for distribution outside NASA. Similarly, TAOS, a trajectory software package developed by Sandia National Laboratories, is only available to U.S. government agencies and approved contractors. Several commercial software packages, such as SpaceWorks QuickShot and ASTOS, are available for purchase. QuickShot includes a graphical user interface and is also export-controlled. ASTOS was originally developed by the German Aerospace Center (DLR) as launch trajectory optimization software , but it is now a commercial product and includes additional mission design features. ASTOS is commonly used by the European Space Agency , but it has not been widely adopted in the United States. Another software package, ZOOM, was created by an independent developer and is available for free, but it has not been widely used in the literature. 0 50 100 150 200 Du ra tio n, s Mesosphere Stratosphere Troposphere Above 3,000 ft Troposphere Below 3,000 ft
Commercial Space Vehicle Emissions Modeling 24 Table 5. Selected software packages for trajectory design and optimization. Software Developer Availability Ref. Program to Optimize Simulated Trajectories II (POST2) NASA Langley Research Center Export-controlled  Optimal Trajectories by Implicit Simulation (OTIS4) NASA Glenn Research Center Unavailable  Marshall Aerospace Vehicle Representation in C (MAVERIC-II) NASA Marshall Space Flight Center Restricted or unavailable  Simulation and Optimization of Rocket Trajectories (SORT) NASA Johnson Space Center Restricted or unavailable  Trajectory Analysis and Optimization Software (TAOS) Sandia National Laboratories U.S. government and contractors  QuickShot SpaceWorks Commercial and export-controlled  Analysis, Simulation, and Trajectory Optimization Software for Space Applications (ASTOS) Astos Solutions GmbH Commercial  ZOOM David F. Williams Free  The trajectory design and optimization software packages listed in Table 5 could be leveraged by end users of the commercial space vehicle emissions model to design detailed trajectories for specific launch vehicles and missions. However, altitude profiles from historical trajectory data are likely sufficient for many academic and research use cases. Additionally, for environmental analyses, nominal trajectories are typically provided by launch vehicle manufacturers.