Appendix 7 A7-1
Appendix 7
Rudder Pedal Force-Limited Air Minimum Control Speed
The following analysis presents one method of addressing rudder pedal force limited air minimum control speed. This method is applicable to either jet or propeller driven airplanes.
The effect of banking into the operating engine is accounted for, and the method will work with either fixed pitch or constant speed propellers, including the effects of windmilling drag. For rudder deflection limited VMCA, see Appendix 6.
Given the static lateral/directional equations of motion for straight line, unaccelerated flight:
Fy = 0 yC + Cy aa + Cy rr = CL · sin
Mx 0 lC + a laC Cl r r = 0
Mz = 0 Cn + Cn aa Cn rr = Cna
For a reversible control system, rudder force versus deflection is:
FR = GR · q · SR · cR · C h R · R
and R = kR · F V R e 2
Substituting for R in equations (1) through (3), and solving, results in an identity of the form:
FR = A·Fna - B·Wsin
All the airspeed terms cancel, indicating that the engine-out rudder force required for straight flight is not a function of airspeed, but only of asymmetric power or thrust, weight, and bank angle. If asymmetric power or thrust did not vary with airspeed, it would be possible to stabilize at any airspeed with the same rudder force. At higher speeds, less rudder deflection would be required (varies inversely with Ve2), but the same force would be required (varies directly with Ve2). When a force limited VMCA is determined during flight test, the variation in rudder force with airspeed results solely from the change in net power or thrust with speed, and if an airspeed
(i.e., power or thrust level) is reached at which the rudder force is 150 lbs, there is no way to correct this force limited VMCA to any other power or thrust level. Therefore, if VMCA is rudder pedal force limited, takeoff power or thrust at all flight conditions should be limited to the test value of asymmetric power or thrust.
Appendix 7 A7-2
In some cases, it is possible to achieve full rudder deflection at the test altitude without reaching a pedal force limit, but with the higher power or thrust at standard conditions, a force limit would exist. To preclude missing this crossover effect, the following analysis should be performed whenever test day rudder pedal forces are greater than 90 percent of the part 25 limit (i.e., 135 lbs after amendment 25-42; 162 lbs prior to amendment 25-42).
1. At any convenient airspeed (typically 1.13 VSR with minimum takeoff flaps), shut down the critical engine, and leave it windmilling (propeller feathered if autofeather is required), apply maximum available power/thrust to the operating engine, and while maintaining constant heading, vary the bank angle from 10° to less than 5° in approximately 2°-3° increments, noting the rudder force at each stabilized bank angle.
2. Plot the rudder force vs Wsin for each of the test points.
3. Calculate Wssin 5°, where Ws is either the average test weight, or the lightest weight scheduled in the AFM, and define standard day rudder force (FRs) as the intersection of this value of Wsin and the curve from step (2). For example:
Fnat = 2600 lbs V = 1.13 VSR Ws = 9000 lbs FR=166 lbs Wsin = 784 lbs -50 0 50 100 150 200 250 400 800 1200 1600 Wsinlbs Rudder Pedal Force (FR) - lbs
Appendix 7 A7-3
4. Determine the maximum allowable asymmetric thrust from the relationship:
F Fna namax t 150 FRs * *( 180 FRs prior to amendment 25-42)
Assuming a 180 lb force limit:
1661802600F maxna 2820 lbs
5. Plot the maximum scheduled AFM thrust vs airspeed, and determine VMCA at the intersection of this curve and Fnamax :
80.5 KEAS 2820 lbs 2600 2650 2700 2750 2800 2850 2900 2950 3000 60 80 100 120 140 160 Ve - kts.
Fna - lbs.
If the force limited VMCA value is high enough to adversely impact the takeoff speed schedule, it can be reduced to an acceptable value by derating takeoff power or thrust. For example, if the standard day rudder force (FRs) was 140 lbs on an amendment 25-42 airplane, the maximum allowable asymmetric takeoff thrust would be:
F 2600 150140namax 2686 lbs
Appendix 7 A7-4 Using the same maximum asymmetric thrust available vs airspeed as before:
172 KEAS 2686 lbs 2600 2650 2700 2750 2800 2850 2900 2950 3000 60 80 100 120 140 160 180 200 Ve - kts.
Fna - lbs.
Because of the shallow thrust lapse rate with airspeed, the force limited VMCA for these conditions would be 172 knots, which is obviously unacceptable. To reduce this value back to 80 knots (or any other speed), takeoff thrust should be derated to a level which provides a maximum asymmetric thrust value of F at the desired VMCA (80 knots in this example).
The amount of derate required can be determined from the following plot:
Maximum Thrust Derated Thrust (5%) 80 KEAS 2686 lbs 2400 2500 2600 2700 2800 2900 3000 50 100 150 200 Ve - kts Fna - lbs
For a given weight and bank angle, rudder pedal force is determined solely by asymmetric thrust;
consequently, takeoff thrust should be limited to a value which results in a pedal force no greater than 150 lbs (180 lbs prior to amendment 25-42).
na max