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174 Appendix C provides the technical details of calcula- tions supporting the EMAS sensitivity analysis discussed in Chapter 5. C.1. Data The data for the EMAS performance calculations were obtained from the manufacturer. Speciï¬cally, the manufac- turer conducted three simulations of an arrest using in-house software. The three cases were distinguished by the type of aircraft used. The three types of aircraft were a CRJ 200 ER, B737-800, and B747-400. For all cases, the exit speed was 70 knots; the compressive strength of the material was 60 psi; the setback was 35 ft; there was no reverse thrust; and there was a braking friction coefï¬cient of 0.25. Given these initial conditions, the length of the bed was minimized. Plots of air- craft speed with respect to nose-gear travel were provided. C.2. Calculations C.2.1. Performance of an EMAS In order to characterize the performance of aircraft within the EMAS bed, for each given design case, a total of 10 to 15 data points were extracted from the manufacturer plots once the aircraft had entered the bed. That is, the initial point in the plots was the point at which the aircraft entered the bed. These extracted data points were plotted discretely and a polynomial trend line was ï¬tted to the discrete data. The poly- nomial trend line was then used to generate points of aircraft speed and aircraft travel in the bed for an arbitrary aircraft travel step. Elementary kinematic relations were applied over each travel step to obtain deceleration of the aircraft. The data with a trend line and extracted deceleration proï¬le for the B737-800 are shown in Figure C-1 (a) and (b) respectively. Deceleration due to braking in the setback area and reverse thrust during the arrest were added to the deceleration due to the EMAS bed. Thus, it was possible to estimate the speed proï¬le for any setback, braking coefï¬cient of friction, and reverse thrust. Reverse thrust in such cases was simply taken as a lumped deceleration value. This value was varied to observe the sensitivity of the response and to determine the criticality of the assumed reverse thrust level. At 70 knots and lower, the reverse thrust contribution is generally minimal. Therefore, in all comparative calculations, the standard assumption of zero reverse thrust was used. A plot of exit speed with respect to stopping distance was obtained from a plot of the absorbed energy. That is, the force applied to the aircraft by braking, reverse thrust, and EMAS bed engagement was obtained from the resultant deceleration proï¬le of the aircraft and its MTOW. This proï¬le was then numerically integrated to obtain the energy absorbed during the arrest. For every quantity of absorbed energy there was a corresponding stopping distance. The absorbed energy was set equal to the kinetic energy of the aircraft at its exit from the runway, as shown in Equation C-1. In order to extend the domain of exit speed to 80 knots, the steady-state por- tion of the absorbed energy curve was linearly extended to an absorbed energy corresponding with 80-knot exit speed. The resultant absorbed energy proï¬le for the B737-800 is shown in Figure C-2. Figure C-3 shows stopping distance with respect to exit speed for the three design aircraft. m = mass of aircraft v = aircraft exit speed F(x) = instantaneous force applied to the aircraft as func- tion of position L = distance required to arrest the aircraft For a given bed width and setback, the cost of an EMAS was calculated as a function of stopping distance, or, put 1 2 2 0 mv F x dx L = ( )â« (Equation C-1) A P P E N D I X C EMAS Calculations
175 Figure C-1. (a) Speed and (b) deceleration profile of B737-800 in EMAS bed. Figure C-2. Energy vs. exit speed for B737-800. Figure C-3. Stopping distance vs. exit speed for three aircraft. 0 20 40 60 80 100 120 140 0 50 100 150 200 250 300 350 Sp ee d [ft/ s] Bed Nose Gear Travel [ft] Data Poly. (Data) 0.0 0.2 0.4 0.6 0.8 1.0 0 5 10 15 20 25 30 0 50 100 150 200 250 300 350 D ec el er at io n [g 's ] D ec el er at io n [ft/ s^ 2] Bed Nose Gear Travel [ft] (a) (b)
176 another way, minimum bed length. As discussed in Chap- ter 5, design cost numbers are reported in FAA Order 5200.9 (29) and were obtained as part of the Survey of U.S. Airport Operators (Chapter 3). Furthermore, as was also discussed in Section 4-4, DOT/FAA/CT-93/80 (5) and more recent ACRP research (24) provided data for relating exit speed to cumulative percentage of overrun occurrences. Therefore, for the three aircraft design cases, it was possible to generate several sets of curves where the paired param- eters were either stopping distance, cost, exit speed, and reli- ability. The resulting curves are shown in Figure C-4 through Figure C-8. Figure C-4. Cost vs. exit speed for three aircraft. Figure C-5. Cost vs. reliability for three aircraft using revised overrun probability curve. 0 2 4 6 8 10 12 14 16 18 20 0 10 20 30 40 50 60 70 80 Co st [$ M] Exit Speed [kts] B737 5200.9 B737 Survey B747 5200.9 B747 Survey CRJ200 5200.9 CRJ200 Survey 0 2 4 6 8 10 12 14 16 18 20 0% 20% 40% 60% 80% 100% Co st ($ M) Cumulative Percentage of Occurrences B737 5200.9 B737 Survey B747 5200.9 B747 Survey CRJ200 5200.9 CRJ200 Survey
Figure C-6. Cost vs. reliability for three aircraft using CT-93/80 overrun probability curve. Figure C-7. Stopping distance vs. reliability for three aircraft using revised overrun probability curve. Figure C-8. Stopping distance vs. reliability for three aircraft using CT-93/80 overrun probability curve. 0 2 4 6 8 10 12 14 16 18 20 0% 20% 40% 60% 80% 100% Co st ($ M) Cumulative Percentage of Occurrences B737 5200.9 B737 Survey B747 5200.9 B747 Survey CRJ200 5200.9 CRJ200 Survey 0 100 200 300 400 500 600 700 800 0% 20% 40% 60% 80% 100% St op pi ng D is ta nc e (ft ) Cumulative Percentage of Occurrences B737 B747 CRJ200 0 100 200 300 400 500 600 700 800 0% 20% 40% 60% 80% 100% St op pi ng D is ta nc e (ft ) Cumulative Percentage of Occurrences B737 B747 CRJ200