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18 x y Figure 18. X-Y origin for aircraft undershoots. length is adjusted for each type of aircraft according to MTOW and the EMAS bed length, according to the follow- ing steps: y 1. The maximum runway exit speed to hold the aircraft within the EMAS bed is calculated according to the Figure 19. Y origin for aircraft veer-offs. model presented below. The adjusted R2 for this model is 89%. For Table 5, the following are the parameters represented: v = 3.0057 - 6.8329 log (W ) + 31.1482 log ( S ) d = any given distance of interest; where: x = the longitudinal distance from the runway end; v = the maximum exit speed in m/s; P{d>x} = the probability the wreckage location exceeds dis- W = the maximum takeoff weight of the aircraft in kg; and tance x from the runway end; S = the EMAS bed length in meters. y = the transverse distance from the extended runway centerline (overruns and undershoots) or from the 2. The maximum runway exit speed estimated using the pre- runway border (veer-offs); and vious regression equation, along with the EMAS bed length P{d>y} = the probability the wreckage location exceeds dis- (SEMAS), is input in the following equation to calculate the tance y from the extended runway centerline (over- deceleration of the aircraft in the EMAS bed. runs and undershoots) or from the runway border v2 (veer-offs). aEMAS = 2S Figures 2229 illustrate the models presented in Table 5. 3. The runway length factor is then estimated as follows: EMAS Deceleration Model aEMAS RLF = a RSA The analysis tool developed in this research includes the capability to evaluate RSAs with EMAS beds. The details of 4. The runway length factor is then estimated as follows: the development are presented in Appendix E. The same location models for overruns are used when aEMAS RLF = EMAS beds are available in the RSA. However, the bed a RSA Probability location Probability location Exceeds y Exceeds x n m P{ Location x } e ax P{ Location y} e by P{Loc > x1} P{Loc > y1} rwy end x1 Distance x from runway end X rwy border y1 Distance y from runway border y Figure 20. Typical model for aircraft overruns. Figure 21. Typical model for aircraft veer-offs.

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19 Table 5. Summary of location models. Type of Type of Model R2 # of Accident Data Points LDOR X 0.00321x 0.984941 99.8% 305 P{d x} e Y 0.20983 y 0.4862 93.9% 225 P{d y} e LDUS X 0.01481x 0.751499 98.7% 83 P{d x} e Y 0.02159 y 0.773896 98.6% 86 P{d y} e LDVO Y 0.02568y 0.803946 99.5% 126 P{d y} e TOOR X 0.00109 x 1.06764 99.2% 89 P{d x} e Y 0.04282y 0.659566 98.7% 90 P{d y} e TOVO Y 0.01639 y 0.863461 94.2% 39 P{d y} e Prob=exp((-.00321)*X**(.984941)) R2=99.8% 1.0 Probability of Stopping Beyond X 0.8 0.6 0.4 0.2 0.0 0 400 800 1200 1600 2000 Distance X from Runway End (ft) Figure 22. Longitudinal location model for landing overruns. Prob=exp((-.20983)*Y**(.486)) R2=93.9% 1.0 Probability of Stopping Beyond Y 0.8 0.6 0.4 0.2 0.0 0 200 400 600 800 1000 1200 Distance Y from Extended Runway Centerline (ft) Figure 23. Transverse location model for landing overruns.

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20 Prob=exp((-.01481)*X**(.751499)) R2=98.7% 1.0 Probability of Touching Down Before X 0.8 0.6 0.4 0.2 0.0 0 400 800 1200 1600 2000 Distance X from Runway Arrival End (ft) Figure 24. Longitudinal location model for landing undershoots. Prob=exp((-.02159)*Y**(.773896)) R2=98.6% 1.0 Probability of Touching Down Beyond Y 0.8 0.6 0.4 0.2 0.0 0 200 400 600 800 1000 Distance Y from Runway Extended Centerline (ft) Figure 25. Transverse location model for landing undershoots.

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21 Prob=exp((-.02568)*Y**(.803946)) R2=99.5% 1.0 Probability of Stopping Beyond Y 0.8 0.6 0.4 0.2 0.0 0 200 400 600 800 1000 Distance Y from Runway Edge (ft) Figure 26. Lateral location model for landing veer-offs. Prob=exp((-.00109)*X**(1.06764)) R2=99.2% 1.0 Probability of Stopping Beyond X 0.8 0.6 0.4 0.2 0.0 0 400 800 1200 1600 2000 Distance X from Runway End (ft) Figure 27. Longitudinal location model for takeoff overruns.