The following Cna vs CLsin φ plot shows the airframe curve, the standard day engine curve, and the test day curve:
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 0 0.05 0.1 0.15 0.2 0.25 CLsinφ Cna From the airframe/engine curve intersections:
Cnt = .052 Cns = .048 CLsinφt = .147 CLsinφs = .124 VMCAt = 82.4 kts VMCAs = 89.7 kts This is a thrust correction of approximately 8%. If the constant Cn method had been used, the test value of .052 would have applied, and the corresponding VMCAt would have been 85.7 kts, an error of 4 knots (5%) in the nonconservative direction.
Noting that the correction from test day to standard day is along the Cn vs CLsin φ curve, which is a straight line, and denoting the slope of the airframe curve as K β , the intersection of the standard day thrust line with the airframe curve as Cns and CLsin φs, and the intersection of the test day thrust line with the airframe curve as Cnt and CLsinφt, the following equation can be derived:
Given the point-slope form of a straight line, Y2 - Y1 = m(X2 - X1) Correspondingly, Cns - Cnt = Kβ ⋅ (CLsinφs - CLsinφt ) Cns - Kβ ⋅ CLsinφs = Cnt - Kβ ⋅ CLsinφt F l q S b na e s s ⋅ ⋅ ⋅ ⋅ - Kβ ⋅ W sinq Ss ss f⋅ = F lq S bna et t ⋅⋅ ⋅ − Kβ ⋅ W sinq St tt f⋅
Substituting q = V 295 e 2 and then multiplying through by V S 295 e 2 S ⋅ Fnas ⋅ lbe - Kβ ⋅ Ws ⋅sinφs = VVe 2 e 2 s t ⋅ F lb K W sinnat e t t⋅ − ⋅ ⋅ b f and finally, VMCAs = VMCAt ⋅ F lb K W sin F lb K W sin na e s s na e t t s t ⋅ − ⋅ ⋅ ⋅ − ⋅ ⋅ b b f f 1 2 for Turbojets VMCAs = VMCAt ⋅ 326 SHP V l b K W sin 326 SHPV lb K W sin S S S MCA e s s t t t MCAt e t t s ⋅ ⋅ ⋅ ⋅ − ⋅ ⋅ ⋅ ⋅ − ⋅ h s f h s f b b 1 2 for Turboprops In the simplified form of the lateral directional equations, Kβ is C Cn yb b which is the directional static margin .
The value of Kβ typically varies from approximately 0.14 to 0.19, depending on the lateral/directional characteristics of the airplane being tested. As with the graphical method, if Kβ is determined by flight test, 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 thrust correction to VMCA. A somewhat conservative default value of 0.20 for Kβ may be used if flight test data is not available; however, in this case, any thrust extrapolation is limited to 10% of the test day 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 CLsinφ that is greater than CLMAX ⋅sin5°.
APPENDIX 4
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 V MCA , see Appendix 3.
Given the static lateral/directional equations of motion for straight line, unaccelerated flight:
Fy∑ = 0 Cy b b⋅ + C y aad d⋅ + Cy rrd d⋅ = CL · sinφ (1) M x∑ = 0 Clb b⋅ + Cl aad d⋅ + Cl r rd d⋅ = 0 (2) ΣMz = 0 Cnb b⋅ + Cn aad d⋅ + Cn rrd d⋅ = Cna (3) For a reversible control system, rudder force versus deflection is:
FR = GR · q · SR · cR · Ch Rd · δR and δR = kR · F V R e 2 Substituting for δR in equations (1) through (3), and solving, results in an identity of the form:
FR = A·Fna - B·Wsinφ 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 thrust, weight, and bank angle. If asymmetric 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 V e2), but the same force would be required (varies directly with V e2).
When a force limited V MCA is determined during flight test, the variation in rudder force with airspeed results solely from the change in net thrust with speed, and if an airspeed (thrust) is reached at which the rudder force is 150 lbs, there is no way to correct this force limited V MCA to any other thrust level. Therefore, if V MCA is rudder pedal force limited, takeoff thrust at all flight conditions must be limited to the test value of asymmetric thrust.
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 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 FAR limit (i.e., 135 lbs after Amendment 25-42; 162 lbs prior to Amendment 25-42).
1. At any convenient airspeed (typically 1.2V s 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 Wsinφ for each of the test points.
3. Calculate Wssin 5°, where W s 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 Wsinφ and the curve from step (2). For example:
Fnat = 2600 lbs V = 1.2Vs Ws = 9000 lbs FR=166 lbs Wsinφ = 784 lbs -50 0 50 100 150 200 250 400 800 1200 1600 Wsinφ − lbs Rudder Pedal Force (FR) - lbs
4. Determine the maximum allowable asymmetric thrust from the relationship:
F Fna namax t= ⋅ 150FRs * *( 180FRs prior to Amendment 25-42) Assuming a 180 lb force limit: F 2600 180 166namax = ⋅ = 2820 lbs
5. Plot 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 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 150 140namax = ⋅ = 2686 lbs 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 must be derated to a level which provides a maximum asymmetric thrust value of Fnamax 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 must be limited to a value which results in a pedal force no greater than 150 lbs (180 lbs prior to Amendment 25-42).
APPENDIX 5
ONE-G STALL COMPLIANCE BASIS
1. APPLICABLE REGULATIONS .
§ 25.103 Stalling speed.
§ 25.201 Stall demonstration.
§ 25.203 Stall characteristics.
§ 25.207 Stall warning.
2. EXPLANATION.
a. Section 25.201 provides the regulatory defi nition of airplane stall. In particular, § 25.201(d)(1) defines the aerodynamic stall as existing "at an angle of attack measurably greater than that for maximum lift. . .." The resulting stall speed is defined in § 25.103 as the minimum speed (V S MIN) attained in the maneuver. For many high speed swept wing transport category airplanes this has resulted in the V S MIN stall speed being defined with a flight path load factor considerably less than one, which has led to inconsistent and non repeatable reference stall speeds.
Additionally, because the minimum speed in the maneuver typically occurs near the point at which the airplane spontaneously pitches nose down or where the pilot defines the level of buffet as deterrent, inconsistencies can also be introduced into the definition of the minimum speed by pilot technique and judgment. Since 14 CFR part 25 defines operating speeds as multiples of the V S MIN stall speed, the resulting operating speed margins to stall are not representative of the actual lift margin available (i.e., the margin to the speed at which wing lift alone can support the weight of the airplane in 1-g flight); the net result of this inadequate lift margin being inconsistent operating speed margins and maneuvering margins. To remedy this situation, procedures and requirements that are interpreted as being equivalent to the current part 25 stall-related regulations have been developed to define a reference stall speed that exists when the wing is generating maximum usable lift in a 1-g flight condition; this speed is referred to as the 1-g stall speed (V S -1g).
b. Service history has not indicated any safety problem from the use of V S MIN stall speeds and their related operating speed factors as currently defined in part 25. A survey of various swept wing transport category airplanes was conducted to establish what load factor existed at V S MIN; the average load factor was determined to be 0.88, which equates to the V S MIN speed being 94 percent of the speed at which the wing lift is equal to the weight of the airplane (i.e., VS -1g). Since service history indicates the existing operating speeds have provided an acceptable level of safety, the existing part 25 operating speed factors were factored by the ratio VS MIN/VS -1g = 0.94, thereby resulting in essentially the same operating speeds, regardless of the basis used for determining reference stall speeds.
c. The 1-g stall speed criteria has been applied to most type certification projects since the mid-1980s by making a finding of equivalent safety. The FAA Issue Paper process, as described in Order 8110.4A, "Type Certification Process" and Order 8100.5, "Aircraft Certification Directorate Procedures," has been used to document the equivalent safety finding and resolve any airplane-specific issues related to the application of the 1-g stall speed methodology.
3. PROCEDURES.
a. A generic Issue Paper is presented in this appendix that presents equivalent interpretations of the affected part 25 regulations to enable application of the 1-g stall speed compliance basis.
b. The following generic Issue Paper contains the necessary equivalent interpretations for making a finding of compliance for airplanes having stall defined by inherent aerodynamic characteristics (e.g., uncommanded nose down pitching moment) or by a system that provides an abrupt nose down pitch (e.g., a stick pusher). Because
airplanes with systems such as stick pushers would realize a considerable reduction in operating speeds and operating speed margins from stall with the basic 1-g stall speed criteria, the design characteristics of such airplanes and their systems should be evaluated with regard to providing a satisfactory level of safety.
c. For airplanes that have stall defined by a system that provides an abrupt nose down pitch (e.g., a stick pusher) that do not gain a significant increase in wing lift with power on, it may not be feasible to permit full reduction of the operating speed factors as contained in the 1-g stall speed criteria. Other factors such as susceptibility of the wing to stall angle of attack variability due to leading edge contamination should also be investigated before applying the full 1-g stall operating speed reductions to these airplanes. Such investigations may be accomplished by review of analytical data and in conjunction with other certification testing (e.g., windtunnel and icing flight test data could be used to investigate the effects of leading edge contamination). For assistance in determining allowable operating speed factor reductions for these airplanes, the FAA Transport Standards Staff of the Transport Airplane Directorate should be contacted.
ISSUE PAPER PROJECT: Generic Airplane Company ITEM:
ANM-110-XXX STAGE:
REG.REF.: § 1.2 (Abbreviations and symbols); All FAR 25 sections, except structural, dealing with stall speeds and related factors; and FAR 36 Noise standards (Appendix C) DATE:
Generic IP Revised 11/14/97
NATIONAL POLICY REF.: NONE ISSUE STATUS: OPEN SUBJECT: Use of 1-g Stall Speeds Instead of Minimum Speed in the Stall as a Basis for Determining Compliance BRANCH ACTION: -160x
COMPLIANCE TARGET: Pre-TC
EQUIVALENT SAFETY FINDING STATEMENT OF ISSUE:
Generic may elect to use 1-g stall speeds, rather than “traditional” V SMIN stall speeds, as the reference datum for regulatory compliance. Use of 1-g stall speeds as the performance basis requires changes to related abbreviations and symbols in FAR 1, and speeds based on multiples of stall speed presented in Subparts B, D, E, and F of FAR 25, and FAR 36. Speed factors in Subpart C of FAR 25 remain unchanged, since they have been applied historically to 1-g stall speeds, not V SMIN stall speeds.
If Generic elects to use the traditional V SMIN to define stall speed, the FAA will require the ratio of V SMIN/VS1-G to be greater than or equal to 0.94 to ensure that application of the subsequent operating speed margins will provide adequate protection from stall. With this additional limitation on allowable V SMIN, all associated operating speed margins will be calculated based on current FAR 25 requirements (e.g., V 2MIN = 1.2VSMIN).
BACKGROUND:
An equivalent safety finding for the use of 1 -g stall speeds, instead of the minimum speeds obtained in the st alling maneuver, as the basis for showing compliance with certain FAR 25 performance, and FAR 36 noise requirements, was established for several past type certification projects. Pilot objectivity on stall identification has become a key factor in decisions on flying technique, especially where deterrent buffet or excessively low load factors are developed during stalls to V SMIN. To avoid these problems, and to become consistent with recent certification practice, the application of 1-g stall speed criteria is being expanded to include most areas of the transport-related regulations that use stall speed as a factor.
The 1-g stall requirements were derived to provide a more realistic and consistent basis for the definition of stall speed as the minimum speed at which wing lift alone can support the weight of the airplane in level flight. Service history has not indicated a safety related deficiency in existing operating speeds that typically have their minimum
allowable values defined as a multiple of the V SMIN stall speed. Consequently, the 1-g stall Issue Papers have applied reduced operating speed factors for determining the minimum operating speeds in order to compensate for the 1-g stall speeds being higher than V SMIN speeds. The net result was little or no change in operating speeds for airplanes with aerodynamic stall, thus leading to a finding of equivalent safety.
FAA POSITION:
The following constitutes the FAA Equivalent Safety Finding for the Generic Model XYZ airplane:
CFR 14 Reference Equivalent Interpretations for Generic Model XYZ Part 1 (Definitions and abbreviations)
1.1 Add the following new definitions:
“Final takeoff speed means the speed of the airplane that exists at the end of the takeoff path in the en route configuration with one engine inoperative.”
“Reference landing speed means the speed of the airplane, in a specified landing configuration, at the point where it descends through the landing screen height in the determination of the landing distance for manual landings.”
1.2 Add the following new abbreviations:
“VFTO means final takeoff speed.”
“VREF means reference landing speed.”
“VSR means reference stall speed.”
“VSR0 means reference stall speed in the landing configuration.”
“VSR1 means reference stall speed in a specific configuration.”
“VSW means speed at which onset of natural or artificial stall warning occurs.”
Part 25 (Airworthiness Standards:
Transport Category Airplanes)
25.103(a) Change to read: “The reference stall speed , VSR, is a calibrated airspeed defined by the applicant. V SR may not be less than a 1- g stall speed. VSR is expressed as:
V V n SR CLMAX zw ≥ where___ VCLMAX = Calibrated airspeed obtained when the load factor-corrected lift coefficient ( n W qS zw ) is first a maximum during the maneuver prescribed in paragraph (c) of this section. In addition, when the maneuver is limited by a device that abruptly pushes the nose down at a selected angle of
attack (e.g., a stick pusher), VCLMAX may not be less than the speed existing at the instant the device operates;
nZW = Load factor normal to the flight path at VCLMAX;
W = Airplane gross weight;
S = Aerodynamic reference wing area; and q = Dynamic pressure.
VCLMAX is determined with:”
25.103(a)(1) Change to read: “Engines idling, or, if that resultant thrust causes an appreciable decrease in stall speed, not more than zero thrust at the stall speed;”
25.103(a)(2) Change to read: “Propeller pitch controls (if applicable) in the takeoff position;”
25.103(a)(3) Insert a new paragraph that reads: “The airplane in other respects (such as flaps and landing gear) in the condition existing in the test or performance standard in which V SR is being used;”
25.103(a)(4) Renumbering of the old § 25.103(a)( 3) and change “V S” to “VSR.”
25.103(a)(5) Change to read: “The center of gravity position that results in the highest value of reference stall speed; and”
25.103(a)(6) Insert a new paragraph that reads: “The airplane trimmed for straight flight at a speed selected by the applicant, but not less than 1.13 VSR and not greater than 1.30 V SR.”
25.103(b) Change to read: “Starting from the stabilized trim condition, apply elevator control to decelerate the airplane so that the speed reduction does not exceed one knot per second.”
25.103(b)(1) Remove this paragraph.
25.103(b)(2) Remove this paragraph.
25.103(c) Insert a new paragraph that reads: “In addition to the requirements of paragraph (a) of this section, when a device that abruptly pushes the nose down at a selected angle of attack (e.g., a stick pusher) is installed, the reference stall speed, V SR, may not be less than 2 knots or 2 percent, whichever is greater, above the speed at which the device operates.”
25.107(b)(1) Change “1.2 VS” to “1.13 VSR.”
25.107(b)(2) Change “1.15 VS” to “1.08 VSR.”
25.107(c)(3) Insert a new paragraph that reads: “A speed that provides the maneuvering capability specified in § 25.143(g).”
25.107(g) Insert a new paragraph that reads: “V FTO, in terms of calibrated airspeed, must be selected by the applicant to provide at least the gradient of climb required by § 25.121(c), but may not be less than--
(1) 1.18 VSR; and
(2) A speed that provides the maneuvering capability specified in § 25.143(g).”
NOTE: Unless AOA protection system (stall warning and stall identification) production tolerances are acceptably small, so as to produce insignificant changes in performance determinations, the flight test settings for stall warning and stall identification should be set at the low AOA tolerance limit; high AOA tolerance limits should be used for characteristics evaluations.
25.111(a) Replace “a speed is reached at which compliance with §
25.121(c) is shown” with “V FTO is reached.”
25.119(b) Change to rea d: “A climb speed of not more than V REF.”
25.121(c) Change to read: “...for four engine airplanes, at V FTO and with – ”
25.121(d) Change to read: “In a configuration corresponding to the normal all-engines-operating procedure in which V SR for this configuration does not exceed 110 percent of the V SR for the related all-engines-operating landing configuration, the steady gradient of climb may not be less than 2.1 percent for twoengine airplanes, 2.4 percent for three-engine airplanes, and 2.7 percent for four-engine airplanes, with –”
25.121(d)(3) Change to read: “...but not more than 1.4 V SR; and”
25.121(d)(4) Add new paragraph as follows: “Landing gear retracted.”
25.125(a)(2) Change to read: “A stabilized approach, with a calibrated airspeed of not less than V REF, must be maintained down to the 50 foot height. VREF may not be less than ___
(i) 1.23 VSR0; and
(ii) VMCL established under § 25.149(f); and
(iii) A speed that provides the maneuvering capability specified in § 25.143(g).”
25.143(g) Insert a n ew paragraph that reads: “The maneuvering capabilities in a constant speed coordinated turn at forward center of gravity, as specified in the following table, must be free of stall warning or other characteristics that might interfere with normal maneuvering:
CONFIG-
URATION SPEED
MANEUVERING
BANK ANGLE IN A
COORDINATED TURN
THRUST/POWER
SETTING TAKEOFF V2 30° ASYMMETRICWAT-LIMITED.1 TAKEOFF V2 + XX 2 40° ALL-ENGINES-OPERATING CLIMB.3 ENROUTE VFTO 40° ASYMMETRICWAT-LIMITED.1 LANDING VREF 40° SYMMETRIC FOR-3° FLIGHT
PATH ANGLE
(1) A combination of weight, altitude and temperature (WAT) such that the thrust or power setting produces the minimum climb gradient specified in § 25.121 for the flight condition.
(2) Airspeed approved for all- engines-operating initial climb.
(3) That thrust or power setting which, in the event of failure of the critical engine and without any crew action to adjust the thrust or power of the remaining engines, would result in the thrust or power specified for the takeoff condition at V 2, or any lesser thrust or power setting that is used for all-engines-operating initial climb procedures.”
25.145(a), (a)(1) Change to read: “It must be possible, at any point between the trim speed prescribed in § 25.103(a)(6) and stall identification (as defined in § 25.201(d)), to pitch the nose downward so that the acceleration to this selected trim speed is prompt with-
(1) The airplane trimmed at the speed prescribed in § 25.103(a)(6);”
25.145(b)(1) - (4) Change “1.4 VS1” to “1.3 VSR1.”
25.145(b)(1) Change “40 percent” to “30 percent.”
Change “stalling speed” to “reference stall speed.”
25.145(b)(6) Change “1.4 VS1” to “1.3 VSR1.”
Change “1.1 VS1” to “VSW.”
Change “1.7 VS1” to “1.6 VSR1.”
25.145(c) Change “1.1 VS1” to “1.08 VSR1.”