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178 This appendix supplies the technical details supporting the assessment of the cable-based arrestor in Section 7.7. D.1. Mechanical Parameters The mechanical input parameters considered in the cable- based arrestor sensitivity analysis and associated output param- eters are shown in Table D-1. The geometry parametersâ distance between the brake units and slack in the cableâ influenced the loading on the main landing gear by changing the angle θ. The limiting lateral and longitudinal loads were determined from FAR part 25 for a Boeing 737-800 (44). D.2. Dynamics Figure D-1 shows a cable-based arrest in which the tension in the cable is Tc1. Figure D-2 is a detail of the main landing gear engaged by the cable with tension Tc1. The load in the cable between the main gear struts is Tc2. The lateral load on the land- ing gear strut is the transverse resultant of Tc1 and Tc2, and the transverse resultant depends on the coefficient of friction between the cable and the strut. As the distance from the arrest- ing engines increases, the angle θ decreases. As θ decreases, the projection of Tc1 on the transverse axis decreases, causing more of the load from Tc2 to be resisted only by the strut. D.3. Calculation Methodology The cable arresting simulations were performed using Microsoft Excelâ¢, in a time-marching transient calculation. After an assumed transient, linear increase in the tension of the arresting cable, the tension in the cable was determined by taking the equilibrium of one of the struts (Figure D-2). The longitudinal load on the strut was assumed to be the FAR 25 limiting load. The aircraft was stepped through the arrest length in 0.5-ft increments, and the tension in the cable was determined by equilibrium at each position. The tension in the cable decreased as the aircraft stepped through the arrest length because θ decreased with each arrest length increment. Equi- librium of the entire aircraft provided the deceleration of the aircraft at each step. That deceleration was used to determine the speed at each step. This iterative process was continued until the speed of the aircraft was zero. This iterative process was performed for numerous cases of the inputs listed in Table D-1. Of particular interest was the effect of the coefficient of friction between the cable and the strut on the lateral load applied to the strut. The lateral load was determined using the equilibrium of the strut and the bearing friction equation. D.4. Interface Friction Study A simulation was developed to determine whether, for a typ- ical arrest case, the lateral load on the landing gear would reach a limiting value. Preliminary simulations showed that if the maximum tension in the cable were kept below a critical value, the lateral load on the landing gear remained below the limiting lateral load, implied by FAR part 25, regardless of the strut-cable coefficient of friction (44). This fact is illustrated in Figure D-3. For a braking coefficient of 0.25 and no reverse thrust, simula- tions were run for a B737-800 in which the strut-cable coeffi- cient of friction was varied and the maximum lateral load on the landing gear was recorded. These maximum lateral loads were normalized by the limiting lateral load. As shown in Fig- ure D-3, the maximum lateral load nearly reached 90% of the limiting lateral load for a strut-cable coefficient of friction of approximately 0.7. Therefore, on the basis of preliminary investigation, if the maximum tension in the cable is limited to the critical value, lateral collapse of the landing gear can be prevented. D.5. Load and Deceleration Histories For a given set of input parameters, the speed and deceler- ation profiles for the aircraft were determined in the follow- ing way. A limiting deceleration of the aircraft was assumed. A P P E N D I X D Active Arrestor Calculations
179 Table D-1. Cable-based arrestor sensitivity analysis parameters. Input Parameters to Vary Output Parameters from Models Exit speed â arbitrary Geometry ⢠Distance between brake units ⢠Slack in cable Maximum tension in cable Strut-cable coefficient of friction Aircraft type â B737-800 ⢠Limiting lateral load ⢠Limiting longitudinal load Aircraft braking condition ⢠Braking ⢠Skidding ⢠Free-rolling Reverse thrust â arbitrary Stopping distance Max lateral load Max longitudinal load Primary Tension Primary Tension Landing Gear Braking Unit Braking Unit Figure D-1. Cable-based arrest of aircraft with tension in cable Tc1. Tc1 Tc2 Figure D-2. Detail of cable and lateral loads on main gear strut. Two sources of limiting deceleration were the commonly assumed 1-g deceleration to prevent occupant injury and the limiting longitudinal load on the main gear, caused by both the engaged cable and braking. Preliminary investigation revealed that the limiting longitudinal load controlled. Once a limiting deceleration was inferred, dynamic equilibrium was imposed on the aircraft, and the tension in the cable was determined. A reasonable limit was then imposed on the maximum tension in the cable. Linear interpolation from a tension of zero at the runway exit point to the point of max- imum tension was used to generate a resultant tension in the cable. The resultant curve for tension in the cable is shown in Figure D-4 (a). All forces in the plots were normalized by
180 the MTOW of the aircraft. Thus, the primary vertical axis is labeled âForce Ratio.â Figure D-4 (b) shows the normalized forces of Tc2, the ten- sion in the cable between the main gear landing struts as illus- trated in Figure D-2, and the lateral and longitudinal loading on the main gear. Tc2 was obtained from Tc1 using the bearing friction equation. The lateral and longitudinal loads were obtained by taking the equilibrium of the strut. The force ratios shown in Figure D-4 (b) were obtained using a strut- cable coefficient of friction of 0.40 to illustrate force ratio trends. Furthermore, the braking coefficient was 0.25 with no reverse thrust. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 N or m al iz ed L at er al L oa d Strut-Cable Coefficient of Friction Braking Coefficient = 0.25 R/T = 0 0 10 20 30 40 50 60 70 80 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 0 50 100 150 200 250 300 350 Sp ee d [kt s] Fo rc e R at io Nose Gear Travel [ft] Tc1 Resultant Tc2 Lateral Longitudinal Speed 0 10 20 30 40 50 60 70 80 0.0 0.4 0.8 1.2 1.6 2.0 0 50 100 150 200 250 300 350 Sp ee d [kt s] Fo rc e R at io Nose Gear Travel [ft] (b)(a) Tc1 Equilibrium Linear Tc1 Resultant Speed Figure D-4. (a) Resultant tension Tc1 in the cable (b) lateral and longitudinal loads. Figure D-3. Dependence of lateral load on strut-cable coefficient of friction.