Appendix F F.4.9 The intersection of the airframe and the engine curve shows values of:
F.4.10 Since the engine Cn curve was based on W = 9000 lbs, the standard day value of VMCA can be determined from:
F.4.11 If the airframe data is obtained from flight test, there are no assumptions or simplifications, and the value of VMCA derived from this method includes all the effects of bank angle, sideslip, adverse yaw, angle-of-attack, etc. Also, since the standard day value of Cna will always be less than the test value, no extrapolation is required, and there is no restriction on the value of standard day power or thrust that may be used.
F.5 Equation Method F.5.1 A single test day value of VMCA can also be corrected to standard conditions (using all the appropriate variables) without using this graphical method, provided either the slope of the Cna versus CL sin Ø relationship is known (from wind tunnel, or analytical estimates), or one is willing to use a default (conservative) value. Power or thrust extrapolation using slope values not based on flight test is limited to 10 percent of the test day power or thrust. The following analysis shows the derivation of this single-point correction equation:
F.5.2 If the test day engine Cna curve was added to the previous plot, it would be possible to see how far, and in what direction, the correction from test to standard day was made.
Assuming that a single value of VMCA was determined at 3000 feet at a weight of 9000 lbs, a test day engine Cna curve could be plotted using the same technique used for the standard day curve, except substituting the 3000-foot thrust values from the engine specification:
F-6
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AC 25-7D Appendix F Table F-2. Example Data for Typical Business Jet Engine at Altitude of 3,000 Feet Ve Fna Cna CLsin˜ 70 2,634 0.073 0.204 90 2,589 0.043 0.123 110 2,554 0.029 0.082 130 2,528 0.02 0.059 150 2,510 0.015 0.044 F.5.3 The following Cna versus CL sin Ø plot shows the airframe curve, the standard day engine curve, and the test day curve:
Figure F-4. Yawing Moment—Engine and Airframe at Altitude of 3,000 Feet (Test Day)
0 0.05 0.1 0.15 0.2 0.25 CLsin Airframe .048 .052 Standard Day Engine Test Day Engine .124 .147
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09 Cna F.5.4 From the airframe/engine curve intersections:
F.5.5 This is a thrust correction of approximately 8 percent. If the constant Cn method had been used, the test value of .052 would have applied, and the corresponding
would have been 85.7 KEAS, an error of 4 knots (5 percent) in the non-conservative direction.
F-7
Appendix F F.5.6 Noting that the correction from test day to standard day is along the Cn versus CL sin O curve, which is a straight line, and denoting the slope of the airframe curve as Kp, the intersection of the standard day thrust line with the airframe curve as Cns and CL sinØ, and the intersection of the test day thrust line with the airframe curve as Cnt and Cr sinØ, the following equation can be derived:
Given the point slope form of a straight line, ·2 - 41 = m (X2 - 81) Correspondingly, Cns - Cnt = Kp (CL sin Ds -Cisin Øt) Ins - Ap. CisinDs = Cnt - hp Cisin D;
Fras le -Wt sin Dt 95 ' 5 • - Kg • 9: • S Substituting q = 295 And then multiplying through by 295 And finally, Fnas (F) - KgW sin Os VMCA; = VMCAL for turbojets Fna; (%) - KeW: sin Dt] And 326 - SHPs x Novos. (g) - KoWe sin Ds VACA; = MCAL 326- SHP: X NeVer. (f) - KeWesin De VuCAt VMCAS for turboprops F.5.7 In the simplified form of the lateral directional equations, Kb is Cng/ Cys, which is the directional static margin. The value of Ko typically varies from approximately 0.14 to
0.19, depending on the lateral/directional characteristics of the airplane being tested. As F-8
Appendix F with the graphical method, if Kb is determined by flight test, power or thrust corrections to VMCA are based on an interpolation of flight test defined airframe capability, and there is no limit on the amount of the power or thrust correction to VMCA. A somewhat conservative default value of 0.20 for Kb may be used if flight test data is not available;
however, in this case, any power or thrust extrapolation is limited to 10 percent of the test day power or thrust. To assure that corrections for bank angle and weight do not result in standard day VMCA values at or below stall speed, the corrections made by either the graphical or equation method should not result in a VMCA, which is based on a CL sin Ø that is greater than CLMAX sin 5°.
F-9
Appendix G APPENDIX G. RUDDER
PEDAL FORCE-LIMITED AIR MINIMUM CONTROL SPEED G.1 One Acceptable Method.
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 F of this AC.
G.1.1 Given the static lateral/directional equations of motion for straight line, unaccelerated flight:
(1)
(2)
(3) G.1.2 For a reversible control system, rudder force versus deflection is:
G.1.3 Substituting for FR in equations (1) through (3), and solving, results in an identity of the form:
G.1.4 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 ), but the same force would be required (varies directly with
). When a force limited VMCA is determined during flight test, the variation in ru dder 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.
G.1.5 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 G-1
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AC 25-7D Appendix G percent of the part 25 limit (i.e., 135 lbs after amendment 25-42; 162 lbs prior to amendment 25-42).
G.1.5.1 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.
G.1.5.2 Plot the rudder force versus Wsin Ø for each of the test points. See figure G-1.)
Figure G-1. Rudder Force Versus WsinΦ
400 800 1200 1600 Wsinlbs FR=166 lbs Wsin = 784 lbs -50 0 50 100 150 200 250 Rudder Pedal Force (FR) - lbs G.1.5.3 Calculate WS sin 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 WS sin 5° and the curve from step (2). For example:
G.1.5.4 Determine the maximum allowable asymmetric thrust from the relationship:
G-2
Appendix G Framax = Frat' 150 Assuming a 180 1b force limit:
180 Framex = 2600 • = 2820 lbs 166 G.1.5.5 Plot the maximum scheduled AFM thrust versus airspeed (see ШИ OSTALE High pitch rate Stall In Ground Effect * with low climb rate a can result in stall → Examples of
- → with positive takeoff tests Stall Margin
- > Decreasing VIOF 0 On Ground 1 (Free Air) h/b (Wing reference height above ground / Wingspan) figure ), and determine VMCA at the intersection of this curve and F namax* '(Fx.,) prior to amendment 25-42.
G-3
Appendix G Figure G-2. Plot to Determine VMCA
Fna - lbs.
3000 2950 2900 2850 2800 2750 2700 2650 2600
80.5 KEAS 2820 lbs 60 80 100 120 140 160 Ve - kts.
G.1.6 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:
G-4
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AC 25-7D Appendix G G.1.7 Using the same maximum asymmetric thrust available versus airspeed as before:
Figure G-3. Plot to Determine VMCA for an Amendment 25-42 Airplane
3000 Fna - lbs.
2950 2900 2850 2800 2750 2700 2650 2600 172 KEAS 2686 lbs 60 80 100 120 140 160 180 200 Ve - kts.
G.1.8 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 that provides a maximum asymmetric thrust value of Fna MCAmax at the desired V (80 knots in this example). The amount of derate required can be determined from the following plot:
G-5
Appendix G Figure G-4. Plot to Determine VMCA for Derate Thrust
3000 Fna - lbs 2900 2800 2700 2600 2500 2400 Maximum Thrust Derated Thrust (5%) 80 KEAS 2686 lbs 50 100 150 200 Ve - kts G.1.9 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 that results in a pedal force no greater than 150 lbs (180 lbs prior to amendment 25-42).
G-6
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