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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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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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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.
