Appendix E E.2.5 Figure E-3 provides guidance for determining the probability of occurrence associated with being in a particular portion of the flight envelope (Xe), in a particular atmospheric disturbance level (Xa), and with a particular flight control failure state (Xc). It also describes how the flight envelope probability (Xe) should be modified for interrelationships with the atmospheric condition.
Figure E-3. Probability of Occurrence Guidelines
A. Flight Envelope (Xe) Probability of occurrence (at flight envelope boundary) Normal Flight Envelope Generally associated with routine operational and/or prescribed conditions, either all engines operating or one engine inoperative.
100 Operational Flight Envelope Generally associated with warning onset; outside the normal flight envelope.
10-3 Limit Flight Envelope Generally associated with airplane design limits or EFCS protection limits.
10-5 Refer to this figure and figures E-4 and E-5 for more detail on determining which flight envelope is applicable.
It may be necessary to consider several of the pertinent flight parameters together to determine which flight envelope a given flight condition is in. For the more influential flight parameters, such as angleof-attack (AOA), speed, and load factor normal to the flight path (Nz), the choice of which flight envelope a condition is in may be determined by as few as one of the parameter values. Since the flight envelopes cover ranges of parameters (e.g., for Flaps UP, Nz in the LFE can be from 1.6 to 2.5), the above target probabilities for OFE and LFE might vary slightly depending on the expected airplane behavior and the assigned task.
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AC 25-7D Appendix E Figure E-3. Probability of Occurrence Guidelines (continued)
B. Atmospheric Disturbance Level Probability of occurrence (at flight envelope boundary) Light: Turbulence that momentarily causes slight, erratic changes in altitude and/ or attitude (pitch, roll, yaw). Crosswinds up to 10 knots.
100 Moderate: Turbulence that is similar to light turbulence, but of greater intensity. Changes in altitude and/or attitude occur. Usually causes variations in indicated airspeed. Crosswinds up to 25 knots.
10-3 Severe: Turbulence that causes large, abrupt deviations in altitude and/or attitude. Usually causes large variations in indicated airspeeds.
Crosswinds substantially in excess of the minimum required crosswind to be demonstrated safe for takeoff and landing.
10-5 C. Flight Control System Failure State Probability of occurrence (at flight envelope boundary) 100 Normal Operation:
100 - 10-5 Probable Failures:
10-5 - 10-9 Improbable Failures:
D. Modifying the Flight Envelope Probability for Interrelationships with Atmospheric Conditions The above probability of occurrence values apply when considered separately. When obvious interrelationships exist due to the design or the intended or expected operation of the airplane, the way to address this within HQRM is to modify the flight envelope probability value. For example, a severe windshear event may result in a flight envelope probability of 100, not 10-3 or 10-5 as shown above for the OFE or LFE, since the operational procedure for escape would be to pull toward the AOA limit in windshear. Similarly, an airplane may experience overspeed, from VMO cruise, into the OFE due to a gust, in which case the modified flight envelope probability would be 100, not 10-3 . This probability adjustment concept would also apply to EFCS failure cases where, for example, loss of warnings or exposure to reduced airplane stability might contribute to excursions outside the normal flight envelope (NFE) or OFE, in which case the flight envelope probability should be appropriately increased.
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AC 25-7D Appendix E E.2.6 Three different flight envelopes (or portions of the airplane’s flight envelope), called the normal, operational, and limit flight envelopes have been defined as a function of various flight parameters. These flight envelopes are shown for flaps up and flaps down configurations in figures E-4 and E-5, respectively.
Figure E-4. Flaps UP Flight Envelopes
E-7
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AC 25-7D Appendix E Figure E-5. Flaps DOWN Flight Envelopes
E.2.7 Figure E-6 presents the method for combining the various flight condition parameter probabilities to determine the minimum acceptable handling qualities rating for each combination of these parameters. This method is shown graphically in Figure E-7.
E-8
Appendix E Figure E-6. Combining Values
A. Analyze Failures/Determine Flight Control System Failure Probability (Xc).
Predicted failure rates/check failure co-dependence Equipment Inoperative Dispatch under MEL Service Difficulty Records (continuing airworthiness) B. Determine Flight Envelope Probabilities (Xe) and Atmospheric Probabilities (Xa) for the Flight Condition.
C. Modify the Flight Envelope Probability if Inter-related with the Atmospheric Condition.
(See Figure E-3, Section D.)
D. Repeat Process to Identify All Cases Where Xc * Xa * Xe 10-9 E. Determine: “Flight Condition” (Xc * Xe) Probable Flight Condition: 10-5 (Xc * Xe) < 0 Improbable Flight Condition: 10-9 (Xc * Xe) < 10-5 E-9
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AC 25-7D Appendix E Figure E-7. Probability Guidelines to Determine HQ Requirements
E.2.8 Table E-2 shows the minimum acceptable FAA handling qualities rating for a given flight condition, defined as a combination of the flight envelope conditions and the level of atmospheric disturbance, relative to the probability of the failure condition being evaluated. Table E-2 is not meant to imply that every atmospheric disturbance level and every flight envelope combination must be tested. It simply shows the minimum acceptable handling qualities rating for a handling qualities task conducted in a specific environmental state (i.e., atmospheric disturbance level), in a specific segment of the flight envelope, and in a specific system failure state.
E-10
Appendix E Table E-2. Minimum HQ Requirements
Flight Condition Atmospheric Disturbance (Xa) (Xc*Xe) Light Moderate Severe Flight Envelope (Xe)
NFE OFE LFE NFE OFE LFE NFE OFE LFE Probable Condition
S S A A C C C C C Improbable Condition
A A C C C C NFE = Normal Flight Envelope OFE = Operational Flight Envelope LFE = Limit Flight Envelope S = Satisfactory A = Adequate C = Controllable E-11
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AC 25-7D Appendix F
APPENDIX F. CORRECTION OF AIR MINIMUM CONTROL SPEED TO
STANDARD CONDITIONS F.1 Overview.
The following analysis presents three methods of correcting a flight test derived value of air minimum control speed to standard conditions. These methods are applicable only to rudder deflection limited VMCA, for 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 pedal force limited VMCA, see appendix G of this AC.
F.2 Theoretical Basis.
Given the static lateral/directional equations of motion for straight line, unaccelerated flight:
(1)
(2)
(3) Where:
W = Weight (lbs) Ve = Equivalent airspeed (kts) S = Wing area (ft2) Fna = Asymmetric net thrust (lbs) Fna = (Fn + Dw) for engine inoperative Fna = (Fn + Fi) for engine at idle Fn = Net thrust of the operating engine (lbs) Fi = Idle engine net thrust (lbs) Dw = Windmill drag (lbs) le = Distance from aircraft center line to engine thrust line (ft) b = Wingspan (ft) F-1
Appendix F F.3 Constant Cn Method.
F.3.1 For the case where full rudder deflection is achieved, r is a constant, and the system of equations can be resolved to an identity that shows that Cna is a linear function of CL sin Ø.
(4) F.3.2 If it is assumed that test and standard day VMCA occur at the same angle-of-attack and bank angle, the asymmetric yawing moment coefficient will be constant, and VMCA can be corrected to standard conditions by the relationship:
Where:
THPs = Maximum AFM scheduled brake/shaft horsepower multiplied by standard day propeller efficiency.
THPt = Test day brake/shaft horsepower where VMCA was achieved multiplied by test day propeller efficiency.
Atmospheric density ratio at standard conditions.
Atmospheric density ratio at test conditions.
F.3.3 Windmilling shaft horsepower is not considered because the current part 25 takeoff requirements for propeller driven airplanes result in such large performance penalties with a windmilling propeller that all part 25 turboprops to date have had autofeather installed.
F.3.4 Since both net thrust and shaft horsepower vary with speed, use of these equations will require an iterative solution. Because this constant Cn method does not consider the effect on VMCA due to variations in bank angle, weight, sideslip angle, or adverse yaw, its use is limited to corrections of 5 percent or less in asymmetric net thrust or power.
F.3.5 For corrections beyond 5 percent, the relationship shown in equation (4) should be used, and enough flight test data should be obtained to define the correlation between Cna and CL sin Ø.
F.4 Graphical Method.
F.4.1 In theory this data could be obtained by varying any combination of asymmetric power or thrust, airspeed, weight, and bank angle that would provide a representative variable set. However, since VMCA and stall speed are nearly coincident for most airplanes, there are some severe constraints on most of the variables. Typically, any reduction in F-2
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AC 25-7D Appendix F maximum asymmetric power or thrust will cause VMCA to decrease below stall speed, and any increase in weight will cause stall speed to increase above VMCA. Therefore, the only parameter that can reasonably be varied is bank angle.
F.4.2 To maximize the spread between stall and minimum control speed, VMCA tests are normally done at the lightest possible weight, at the maximum allowable asymmetric power or thrust (even with a short duration overboost, if the engine manufacturer will agree). At typical test altitudes (2000 to 3000 feet) and prototype gross weights, it will usually still not be possible to define VMCA with the full 5° bank, because of stall buffet.
F.4.3 To obtain the data necessary for extrapolation to the 5° bank limit, and to maximum asymmetric power or thrust, testing at three bank angles is required for the definition of the Cna versus CL sin Ø relationship. This data should be obtained by shutting down the critical engine (normally the left), setting maximum allowable power or thrust on the operative engine, and slowing down while maintaining constant heading until full rudder deflection is achieved. The first point, a wings level condition, is easy to set up, and results in a speed well above stall buffet. A second point, at zero sideslip, will be achieved at approximately 2° to 3° bank (flown with a yaw string, or instrumented sideslip vane) and will provide an intermediate speed, still above buffet. The third data point is flown with as much bank angle that can be used without excessive buffeting (no more than would be accepted as the minimum level of stall warning). If necessary, an additional point can be obtained by banking 2° to 3° into the inoperative engine.
F.4.4 To use this method, instrumentation is necessary for the determination of net thrust/shaft horsepower, and an accurate calibrated airspeed system is required, as well as engine/propeller charts for windmill drag, charts for propeller efficiency, and the ability to measure bank angle to at least a tenth of a degree.
F.4.5 Data obtained using this method with a typical business jet and a large jet transport are shown in figures F-1 and F-2, respectively:
F-3
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AC 25-7D Appendix F Figure F-1. Two-Engine Business Jet
2-ENGINE BUSINESS JET -0.04 0 0.04 0.08 0.12 0.16 CLsin 0
0.01
0.02
0.03
0.04
0.05
0.06 C K=0.20 Figure F-2. Four-Engine Transport
4-ENGINE TRANSPORT
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01 0 K=0.14 0 0.05 0.1 0.15 0.2 CLsin C F.4.6 These plots represent the capability of the airframe to produce yawing moment by a combination of rudder deflection (full, in this case), and the sideslip which results from the bank angle. In order to determine the limiting condition for VMCA, it is necessary to know what the applied yawing moment is (due to the engine-out moments), and to plot the applied moments on the same plot, in a similar form. It is possible to do this by choosing a gross weight to be used to calculate CL, and since standard bank angle will be 5°, the only remaining variable in CL sin Ø is Ve. By choosing the appropriate values F-4
Appendix F of Fn available versus Ve, a plot of Cna versus CL sin Ø can be made which represents the applied yawing moments. If the weight chosen represents some standard minimum weight, and the available net power or thrust values represent the maximum allowable power or thrust scheduled in the AFM, the intersection point of the airframe curve and the engine curve will be the desired standard day values, which can be used to calculate VMCA.
F.4.7 As an example, the following values of net thrust plus windmill drag have been extracted from a typical corporate jet engine spec. The data represent a maximum thrust engine, and have been corrected for ram drag and minimum accessory bleed and electrical load. The CL sin Ø values are based on a gross weight of 9000 lbs.
Table F-1. Example Data for Typical Business Jet Engine Ve Fna Cna CLsin˜ 70 2,846 0.079 0.204 90 2,798 0.047 0.123 110 2,764 0.031 0.082 130 2,737 0.022 0.059 150 2,710 0.016 0.044 F.4.8 Plotting both the airframe and engine yawing moment curves on the same graph looks like:
Figure F-3. Yawing Moment—Engine and Airframe
0 0.05 0.1 0.15 0.2 0.25 CLsin Airframe .048 Engine .124 0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09 Cna F-5