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32 RSA will encompass approximately 80 percent of all landing exist. In other words, a statistical analysis was necessary to overruns. evaluate if greater longitudinal distances for wreckage loca- The probability that the point of first impact is beyond a tion can lead to greater transverse distances. certain distance for landing undershoots is depicted in The correlation between the longitudinal and lateral dis- Figures 22 and 23, for raw distances, and in Figures 24 and 25, tance for each type of event is shown in Table 12. for normalized distances. For nearly 13 percent of landing Although the correlation between x and y locations is not undershoots, the aircraft point of first impact will occur at zero for LDOR and LDUS (P < 0.05), the level is relatively distances greater than 1000 ft from the runway threshold. low; it was assumed that the correlation is not important. The raw location probability trend for takeoff overruns is This leads to the assumption that the transverse location dis- depicted in Figures 26 and 27. From the raw, unweighted tribution of accidents is fairly constant along the longitudinal accident and incident data, close to 20 percent of takeoff locations from the threshold. overruns will occur beyond a 1000 ft distance from the threshold. The normalized distance models for takeoff over- runs is presented in Figures 28 and 29. Consequences For each set of location models, one model was developed As described earlier, accident costs were used to integrate with the raw distance locations and one model used normal- consequences related to injuries and property loss into a single ized distances relative to terrain type, runway elevation, and parameter. The initial intent was to relate the consequences, the air temperature during the accident/incident. Tables 10 represented by the accident cost, with the wreckage distance for and 11 show the location models developed in this study. the accident. The relationship could be used to estimate the The sample sizes available to develop the models shown in consequences of accidents based on the wreckage location, Table 11 were smaller than those used for the models shown providing a link between the location and consequences mod- in Table 10. A number of investigation reports provide only els. Unfortunately these relationships were found to be quite the distance from the threshold, but not the lateral distance. Sample sizes for normalized models also are smaller than poor, as consequences depend not only on the speed when the those developed with raw data. For a few cases in each acci- aircraft departs the runway, but also the nature and location of dent group there was no information on the terrain type used existing obstacles, as well as the type and size of aircraft. to normalize the distance. Additional analysis attempted to relate accident location with aircraft damage. Four categories of damage--none, minor, substantial, and hull loss--were correlated to accident Analysis of RSA Geometry location. The use of raw distances proved to hold very low The correlation between the overrun and undershoot dis- correlations between wreckage path distance and the aircraft tances to the lateral distance relative to the runway axis was damage. However, there was an improvement when normal- evaluated to define the geometry of the safety areas. RSA are ized distances relative to terrain, elevation, and temperature normally rectangular-shaped areas, but it was possible that a were used. The correlations are quite reasonable, as shown in strong correlation between longitudinal and lateral could Table 13. Raw Distances Model for Landing Undershoots 100% Actual Data Alt Model 80% P{d>x}=exp(-0.024445*C4^0.643232) Prob{distance > x} R2=98.5%; n=82 60% 40% 20% 0% 0 500 1000 1500 2000 2500 Distance x to Threshold Figure 22. LDUS location model using raw (nonnormalized) distances.

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33 Raw Lateral Distances Model for LDUS 100% Actual Data Model 80% Probaility{distance > y} P{d>x}=exp(-0.409268*Y^0.351851) R2=92.0%; n=48 60% 40% 20% 0% 0 200 400 600 800 Distance Y from Extended Runway Axis (ft) Figure 23. LDUS lateral location model using raw (non-normalized) distances. Normalized Distances Model for Landing Undershoots 100% Actual Norm Data Norm Model Raw Model 80% P{d>x}=exp(-0.022078*X^0.585959) Prob{distance > x } R2=99.1%; n=69 60% 40% 20% 0% 0 2000 4000 6000 8000 10000 12000 Distance x to Threshold (ft) Figure 24. LDUS location model using normalized distances. Normalized Lateral Distances Model for LDUS 100% Actual Data Model Probaility{distance > y} 80% P{d>x}=exp(-0.19539*Y^0.433399) R2=90.3%; n=41 60% 40% 20% 0% 0 200 400 600 800 1000 1200 1400 Distance Y from Extended Runway Axis (ft) Figure 25. LDUS lateral location model using normalized distances.

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34 Raw Distances Model for Takeoff Overruns 100% Actual Data Model 80% P{d>x}=exp(-0.001033*x^1.065025) R2=99.0%; n=76 Prob{distance > x } 60% 40% 20% 0% 0 500 1000 1500 2000 2500 Distance x from Threshold (ft) Figure 26. TOOR location model using raw (nonnormalized) distances. Raw Lateral Distances Model for TOOR 100% Actual Data Model 80% Probaility{distance > y} P{d>x}=exp(-0.182098*Y^0.448346) R2=95.6%; n=44 60% 40% 20% 0% 0 200 400 600 800 1000 1200 1400 Distance Y from Extended Runway Axis (ft) Figure 27. TOOR lateral location model using raw (nonnormalized) distances. Normalized Distances Model for Takeoff Overruns 100% Actual Data Norm Model Raw Model 80% P{d>x}=exp(-0.003364*x^0.807138) Prob{distance > x } R2=98.5%; n=72 60% 40% 20% 0% 0 1000 2000 3000 4000 5000 6000 Distance x from Threshold (ft) Figure 28. TOOR location model using normalized distances.

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35 Normalized Lateral Distances Model for TOOR 100% Actual Data Model 80% Probaility{distance > y} P{d>x}=exp(-0.181046*Y^0.406544) R2=97.1%; n=42 60% 40% 20% 0% 0 500 1000 1500 2000 2500 3000 Distance Y from Extended Runway Axis (ft) Figure 29. TOOR lateral location model using normalized distances. Both Spearman R and Kendal Tau correlation coefficients accident, as previously done to model frequency and location. provide an indicator of the degree of co-variation in the vari- However, a rational probabilistic approach is suggested to ables. Both tests require that variables are represented at least evaluate the probability of accidents or serious accidents. in ordinal scale (rank), which is the case for aircraft damage. The basic idea is to use the location model to estimate the While Spearman R has an approach similar to the regular incident occurrences when the aircraft will have high energy Pearson product-moment correlation coefficient, Kendall resulting in serious consequences. Figure 30 can be used to Tau rather represents a probability. illustrate and help understand this approach. Despite these reasonable correlations, a more rational The x-axis represents the longitudinal location of the approach to model consequences was preferred to assess the wreckage relative to the threshold. The y-axis is the probabil- effect of different obstacles at various locations in the vicinity ity that the wreckage location exceeds a given distance "x." of the RSA. Examples of such obstacles include fences, drops The location distance can be normalized or not, according to and elevations in the terrain, existing facilities, culverts, ALS, the criteria selected. and ILS structures, trees, etc. In this example, an obstacle is located at a distance "D" from the threshold and the example scenario being analyzed is an aircraft landing overrun incident. The figure shows an Modeling Approach exponential location model developed for the specific acci- The main purpose for modeling consequences of aircraft dent scenario, in this case, landing overrun. accidents is to quantify the risk based on the probability of There are three distinct regions in this plot. The first region occurrence and the results in term of injuries and property (medium shaded area) represents those occurrences that the loss. It was not possible to develop one model for each type of aircraft departed the runway, but the exit speed was relatively Table 10. Summary of X-location models. Type of Type of Model Eq.# R2 # of Accident Data Points 0.955175 LDOR Raw P{d x} e 0.003871x (12) 99.8% 257 0.824513 Normalized P{d x} e 0.004692 x (13) 99.5% 232 0.643232 LDUS Raw P{d x} e 0.024445 x (14) 98.52% 82 Normalized 0.022078 x 0.585959 (15) 99.1% 69 P{d x} e 1.065025 TOOR Raw P{d x} e 0.001033x (16) 99.0% 76 Normalized 0.003364 x 0.807138 (17) 98.5 72 P{d x} e where P{d > x} is the probability the wreckage location exceeds distance x from the threshold, and x is the longitudinal distance from the threshold.

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36 Table 11. Summary of Y-location models. Type of Type of Model Eq.# R2 # of Accident Data Points 0.489009 LDOR Raw P{d y} e 0.20174 y (18) 94.7% 141 0.388726 Normalized P{d y} e 0.243692 y (19) 93.4% 138 0.351851 LDUS Raw P{d y} e 0.409268 y (20) 92.0% 48 0.433399 Normalized P{d y} e 0.19539 y (21) 90.3% 41 0.448346 TOOR Raw P{d y} e 0.182098 y (22) 95.6% 44 Normalized 0.181046 y 0.406544 (23) 97.1% 42 P{d y} e low, and the aircraft came to a stop before reaching the exist- presence of obstacles. This is a conservative assumption be- ing obstacle. The consequences for such incidents are expected cause there are events when the pilot will avoid some obsta- to be none to minor as the aircraft may hit only frangible ob- cles if he has some control of the aircraft. The database jects (e.g., threshold lights) within these small distances. contains a number of cases when the pilot avoided ILS and The rest of the curve represents events that the aircraft Approach Lighting System (ALS) structures in the RSA. exited the runway at speeds high enough for the wreckage A second assumption is that the aircraft follows a path near path to extend beyond an existing obstacle. However, a por- parallel to the extended runway axis. Again, this assumption tion of these accidents will have relatively higher energy and will lead to calculations of higher than actual risk and is con- should result in more severe consequences, while for some servative. The aircraft may hit or avoid obstacles in paths that cases the aircraft will be slow when hitting the obstacle so that are nonparallel to the runway axis. catastrophic consequences are less likely to happen. The shaded area in Figure 31 represents the area of analy- Using this approach, it is possible to assign three scenarios: sis. Accident data was considered relevant when wreckage the probability that the aircraft will not hit the obstacle (re- location challenged an area of 2000 2000 ft beyond the sulting in none or minor consequences); the probability that threshold. The example shown in the figure depicts an over- the aircraft will hit the obstacle with low speed and energy run example. (with substantial damage to aircraft but minor injuries); and Obstacle 1 is located at a distance xo, yo from the threshold the probability that the aircraft will hit the obstacle with high and has dimensions W1 L1. When evaluating the possibility energy (with substantial damage and injuries). of severe consequences it is possible to assume this will be the For events with low energy when impacting the obstacle, it case if the aircraft fuselage or a section of the wing close to is possible to assume that if no obstacle was present the aircraft the fuselage hits the obstacle. Thus, it is possible to assume would stop within a distance from the location of the obsta- the accident will have severe consequences if the y location cle. The problem is to evaluate the rate of these accidents hav- is between Yc and Yf, as shown in the figure. Based on Equa- ing low speeds at the obstacle location and this is possible based tion 11 for transverse distance, the probability the aircraft axis on the same location model. This probability can be estimated is within this range can be calculated as follows: by excluding the cases when the speed is high and the final - bym m e - byc -e f wreckage location is significantly beyond the obstacle location. Psc = (24) A similar approach was developed to combine the longitu- 2 dinal and transverse location distribution with the presence, where type, and dimensions of existing obstacles. The basic approach is represented in Figure 31 for a single and simple obstacle. Psc = the probability of high consequences; A few simplifying assumptions were necessary when devel- b, m = regression coefficients for y-location model; oping this approach. One simplification is to assume the Yc = the critical aircraft location, relative to the obstacle, lateral distribution is random and does not depend on the closest to the extended runway axis; and Table 13. Correlation between normalized Table 12. Correlation between lateral and wreckage location and aircraft damage. longitudinal overrun/undershoot distances. Type of Event Sample Size Spearman R Kendall Tau Type of R R2 CI 95% p n LDOR 224 0.62 0.49 Event LDOR 0.320 10.2% 0.20 - 0.43 < 0.0001 235 LDUS 68 0.30 0.23 LDUS 0.316 10.0% 0.11 - 0.50 0.0040 81 TOOR 67 0.55 0.44 TOOR 0.113 1.3% -0.12 a 0.33 0.3430 73 All 359 0.56 0.44