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178 APPENDIX D Active Arrestor Calculations This appendix supplies the technical details supporting the because decreased with each arrest length increment. Equi- assessment of the cable-based arrestor in Section 7.7. 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 D.1. Mechanical Parameters until the speed of the aircraft was zero. The mechanical input parameters considered in the cable- This iterative process was performed for numerous cases of based arrestor sensitivity analysis and associated output param- the inputs listed in Table D-1. Of particular interest was the eters are shown in Table D-1. The geometry parameters-- effect of the coefficient of friction between the cable and the distance between the brake units and slack in the cable-- strut on the lateral load applied to the strut. The lateral load was influenced the loading on the main landing gear by changing determined using the equilibrium of the strut and the bearing the angle . The limiting lateral and longitudinal loads were friction equation. determined from FAR part 25 for a Boeing 737-800 (44). D.4. Interface Friction Study D.2. Dynamics A simulation was developed to determine whether, for a typ- Figure D-1 shows a cable-based arrest in which the tension ical arrest case, the lateral load on the landing gear would reach a limiting value. Preliminary simulations showed that if the in the cable is Tc1. Figure D-2 is a detail of the main landing gear maximum tension in the cable were kept below a critical value, engaged by the cable with tension Tc1. The load in the cable the lateral load on the landing gear remained below the limiting between the main gear struts is Tc2. The lateral load on the land- lateral load, implied by FAR part 25, regardless of the strut-cable ing gear strut is the transverse resultant of Tc1 and Tc2, and the coefficient of friction (44). This fact is illustrated in Figure D-3. transverse resultant depends on the coefficient of friction For a braking coefficient of 0.25 and no reverse thrust, simula- between the cable and the strut. As the distance from the arrest- tions were run for a B737-800 in which the strut-cable coeffi- ing engines increases, the angle decreases. As decreases, the cient of friction was varied and the maximum lateral load on projection of Tc1 on the transverse axis decreases, causing more the landing gear was recorded. These maximum lateral loads of the load from Tc2 to be resisted only by the strut. were normalized by the limiting lateral load. As shown in Fig- ure D-3, the maximum lateral load nearly reached 90% of the D.3. Calculation Methodology limiting lateral load for a strut-cable coefficient of friction of approximately 0.7. Therefore, on the basis of preliminary The cable arresting simulations were performed using investigation, if the maximum tension in the cable is limited Microsoft ExcelTM, in a time-marching transient calculation. to the critical value, lateral collapse of the landing gear can be After an assumed transient, linear increase in the tension of prevented. the arresting cable, the tension in the cable was determined by taking the equilibrium of one of the struts (Figure D-2). The D.5. Load and Deceleration longitudinal load on the strut was assumed to be the FAR 25 Histories limiting load. The aircraft was stepped through the arrest length in 0.5-ft increments, and the tension in the cable was For a given set of input parameters, the speed and deceler- determined by equilibrium at each position. The tension in the ation profiles for the aircraft were determined in the follow- cable decreased as the aircraft stepped through the arrest length ing way. A limiting deceleration of the aircraft was assumed.
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179 Table D-1. Cable-based arrestor sensitivity analysis parameters. Input Parameters to Vary Output Parameters from Models Exit speed arbitrary Stopping distance Geometry Max lateral load · Distance between brake units Max longitudinal load · Slack in cable Maximum tension in cable Strut-cable coefficient of friction Aircraft type B737-800 · Limiting lateral load · Limiting longitudinal load Aircraft braking condition · Braking · Skidding · Free-rolling Reverse thrust arbitrary Braking Unit Primary Landing Gear Tension Primary Tension Braking Unit Figure D-1. Cable-based arrest of aircraft with tension in cable Tc1. T c1 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 T c2 maximum tension in the cable. Linear interpolation from a Figure D-2. Detail tension of zero at the runway exit point to the point of max- of cable and lateral imum tension was used to generate a resultant tension in the loads on main gear cable. The resultant curve for tension in the cable is shown in strut. Figure D-4 (a). All forces in the plots were normalized by
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180 Braking Coefficient = 0.25 R/T = 0 1.0 0.9 0.8 Normalized Lateral Load 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Strut-Cable Coefficient of Friction Figure D-3. Dependence of lateral load on strut-cable coefficient of friction. the MTOW of the aircraft. Thus, the primary vertical axis is friction equation. The lateral and longitudinal loads were labeled "Force Ratio." obtained by taking the equilibrium of the strut. The force Figure D-4 (b) shows the normalized forces of Tc2, the ten- ratios shown in Figure D-4 (b) were obtained using a strut- sion in the cable between the main gear landing struts as illus- cable coefficient of friction of 0.40 to illustrate force ratio trated in Figure D-2, and the lateral and longitudinal loading trends. Furthermore, the braking coefficient was 0.25 with no on the main gear. Tc2 was obtained from Tc1 using the bearing reverse thrust. 2.0 80 1.0 80 Tc1 Equilibrium Tc1 Resultant Linear 70 Tc2 70 Tc1 Resultant 0.8 Lateral 1.6 Speed 60 Longitudinal 60 0.6 Speed 50 50 Force Ratio Force Ratio 1.2 Speed [kts] Speed [kts] 40 0.4 40 0.8 30 30 0.2 20 20 0.4 0.0 10 10 0.0 0 -0.2 0 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 Nose Gear Travel [ft] Nose Gear Travel [ft] (a) (b) Figure D-4. (a) Resultant tension Tc1 in the cable (b) lateral and longitudinal loads.