AC 25-7B

Appendix 3 A3-1

Appendix 3

Correction of Air Minimum Control Speed To Standard Conditions

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 7.

1. Theoretical Basis

a. Given the static lateral/directional equations of motion for straight line, unaccelerated flight:

Fy  Cy   ay aC   Cyrr  = CL · sin 

Mx  Cl   Claa    Clrr    

Mz  Cn  Cnaa   Cnrr  Cna   

where:

CL = 2952WVSe Cna = 2952 FlVS bna ee

W = weight - lbs

V e = equivalent airspeed - kts

S = wing area - ft 2

F na = asymmetric net thrust - lbs

F na = (Fn + Dw) for engine inoperative

F na = (Fn + Fi) for engine at idle

F n = net thrust of the operating engine - lbs

F i = idle engine net thrust - lbs

Appendix 3 A3-2 D w = windmill drag - lbs

l e = distance from aircraft center line to engine thrust line - ft

b = wingspan - ft

2. Constant C n Method

a. For the case where full rudder deflection is achieved, r is a constant, and the system of equations can be resolved to an identity which shows that Cna is a linear function of CL sin .

 Cna = A·CL  sin + B (4)

b. If it is assumed that test and standard day V MCA 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:

VMCAs = VMCAt · F F na na s t for Turbojets

VMCAs = VMCAt · THPTHPsstt  1 3 for Propeller driven

where:

THP s = Maximum AFM scheduled Brake/Shaft horsepower multiplied by standard day propeller efficiency.

THP t = Test day brake/shaft horsepower where VMCA was achieved multiplied by test day propeller efficiency.

 s = Atmospheric density ratio at standard conditions.

 t = Atmospheric density ratio at test conditions.

c. 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.

d. 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

Appendix 3 A3-3 VMCA due to variations in bank angle, weight, sideslip angle, or adverse yaw, its use is limited to corrections of 5% or less in asymmetric net thrust or power.

e. For corrections beyond 5%, the relationship shown in equation (4) should be used, and enough flight test data should be obtained to define the correlation between Cna and CLsin.

3. Graphical Method

a. In theory these data could be obtained by varying any combination of asymmetric 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 maximum asymmetric 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.

b. To maximize the spread between stall and minimum control speed, V MCA tests are normally done at the lightest possible weight, at the maximum allowable asymmetric thrust (even with a short duration overboost, if the engine manufacturer will agree). At typical test altitudes (2000-3000 feet) and prototype gross weights, it will usually still not be possible to define VMCA with the full 5° bank, because of stall buffet.

c. To obtain the data necessary for extrapolation to the 5° bank limit, and to maximum asymmetric thrust, testing at three bank angles is required for the definition of the Cna vs CL sin relationship. These data should be obtained by shutting down the critical engine (normally the left), setting maximum allowable 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° - 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° - 3° into the inoperative engine.

d. 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.

Appendix 3 A3-4

e. Data obtained using this method with a typical business jet and a large jet transport are shown in the following two graphs:

2-ENGINE BUSINESS JET 0

0.01

0.02

0.03

0.04

0.05

0.06 -0.04 0 0.04 0.08 0.12 0.16 CLsin C K=0.20

4-ENGINE TRANSPORT 0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08 0 0.05 0.1 0.15 0.2 CLsin C K=0.14

Appendix 3 A3-5

f. 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 CLsin is Ve. By choosing the appropriate values of Fn available versus Ve, a plot of Cna versus CLsin can be made which represents the applied yawing moments. If the weight chosen represents some standard minimum weight, and the available net thrust values represent the maximum allowable 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.

g. 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 CLsin values are based on a gross weight of 9000 lbs.

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

Plotting both the airframe and engine yawing moment curves on the same graph looks like:

Airframe .048 Engine .124 0

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 CLsin Cna

h. The intersection of the airframe and the engine curve shows values of:

Appendix 3 A3-6 C na = 0.048 C Lsin = 0.124

i. Since the engine C n curve was based on W = 9000 lbs, the standard day value of VMCA can be determined from:

C Lsin= 0.124 =  295 WVSe2 

0.12490000.1108V2e 

V MCA = 89.7 KEAS

j. 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 thrust that may be used.

Appendix 3 A3-7

4. Equation Method

a. A single test day value of V MCA can also be corrected to standard conditions (using all the appropriate variables) without using this graphical method, provided either the slope of the Cna vs CLsin relationship is known (from wind tunnel, or analytical estimates), or one is willing to use a default (conservative) value. Thrust extrapolation using slope values not based on flight test is limited to 10% of the test day thrust. The following analysis shows the derivation of this single-point correction equation:

b. If the test day engine C na 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 ft thrust values from the engine spec:

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

c. The following C na vs CLsin 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 CLsin Cna

From the airframe/engine curve intersections:

Appendix 3 A3-8

C nt = 0.052 C ns = 0.048

C Lsint = 0.147 C Lsins = 0.124

VMCAt = 82.4 kts VMCAs = 89.7 kts

d. This is a thrust correction of approximately 8%. If the constant C n 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 non-conservative direction.

e. Noting that the correction from test day to standard day is along the C n vs CLsin curve, which is a straight line, and denoting the slope of the airframe curve as K the intersection of the standard day thrust line with the airframe curve as Cns and CLsins, and the intersection of the test day thrust line with the airframe curve as Cnt and CLsint, the following equation can be derived:

Given the point-slope form of a straight line,

Y 2 - Y1 = m(X2 - X1)

Correspondingly,

C ns - Cnt = K (CLsins - CLsint )

C ns - K  CLsins = Cnt - K CLsint

Fl qS b na e s s   - K Ws i nqSsss   FlqS bna et t  K Ws i nqSttt 

Substituting q = V295e2 and then multiplying through by VS295e2S 

Fnas  lbe - KWs sins = VVe 2 e 2 s t  F lb KW s i nnat e tt    

Appendix 3 A3-9

and finally,

VMCAs = VMCAt  F lb KW s i n F lb KW s i n na e ss na e tt s t                       1 2 for Turbojets

VMCAs = VMCAt  326 SHPV lb KW s i n 326 SHPV lb KW s i n SS S MCA e ss tt t MCAt e tt s                             1 2 for Turboprops

In the simplified form of the lateral directional equations, K is CCny which is the directional static margin. The value of K 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 K 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 K 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 CLsin that is greater than CLMAX sin5.

Appendix 4 A4-1

Appendix 4

History of Jet Transport Performance Standards

1. When the first jet transport airplanes were certificated in the late 1950’s, the applicable transport category airworthiness regulations were contained in part 4b of the Civil Air Regulations (CAR 4b). The airworthiness requirements of CAR 4b were developed from years of experience with propeller-driven airplanes powered by reciprocating engines. The different powerplant operating principles, and expanded speed and altitude envelopes of the first generation jet-powered airplanes required comprehensive changes to the performance requirements of CAR 4b. Special Civil Air Regulation No. SR-422 was adopted in July 1957 as a supplement to CAR 4b, containing airworthiness and operational requirements that were applicable to transport category airplanes powered by turbine engines (turbojet and turbopropeller).

2. As experience was gained, SR-422 was amended in July 1958 (SR-422A) and July 1959 (SR-422B) to better reflect the operating environment of these new airplane designs. These special civil air regulations, presented in this appendix, formed the basis for the current transport category airworthiness and operating performance regulations of parts 25, 121, and 135. Though the number of operational airplanes that were certificated to these requirements is continually decreasing, these special civil air regulations, and the related preamble material, still provide a worthwhile perspective on many of the issues behind the development of today’s regulations, and are therefore preserved for future reference in this appendix.

Appendix 4 A4-2 Special Civil Air Regulation No. SR-422

Effective: August 27, 1957 Adopted: July 23, 1957

(Paragraphs numbered 1 to 18.a.(1) in pages A4-2 to A4-5 are for reference purposes only.)

Turbine-Powered Transport Category Airplanes of Current Design

1. Part 4b of the Civil Air Regulations contains rules governing the design of transport category airplanes. For a number of years, this part has established airworthiness requirements for this category of airplanes by prescribing detailed provisions to be met for the issuance of a type certificate. However, the advent of turbine-powered airplanes (jets, turbo-props, etc.) has brought about operations at considerably higher speeds and altitudes than those involving reciprocating engine airplanes. These higher speeds and altitudes as well as certain inherent characteristics of turbine engines have introduced numerous new technical and design problems and have necessitated re-evaluation and amendment of many provisions in part 4b.

2. In recent years the Board has amended part 4b by introducing numerous technical provisions more specifically applicable to turbine-powered airplanes. These were included in amendments pertaining to structural, flight characteristic, powerplant installation, and other provisions. It is believed that part 4b as now written is applicable to turbine-powered airplanes with but one exception; namely, airplane performance. In the future, further amendments to this part, other than those relating to performance, will be comparatively minor in nature mainly reflecting the latest experience in the certification and operation of these airplanes.

3. The performance requirements presently in part 4b were first promulgated almost twelve years ago. They are now considered by the Board to be in a form not suitable for direct application to turbine-powered airplanes.

4. The administrator of Civil Aeronautics is in receipt of a large number of applications for type certification of turbine-powered airplanes. However, the so-called “non-retroactive” clause of section 4b.11(a) of part 4b does not make applicable to a particular airplane type any amendment which is adopted after an application is filed by the manufacturer for type certification of that airplane. Thus, most of these airplanes are not now required to meet some of the latest effective provisions of part 4b unless the Board prescribes otherwise. With so many applications for type certificates pending, it is essential that the Board establish adequate requirements which will effectively apply to the type certification of turbine-powered transport category airplanes. This Special Civil Air Regulation is being promulgated for that purpose.

5. This Special Civil Air Regulation is being made effective with respect to all turbinepowered transport category airplanes not yet certificated. In essence, it prescribes a revised set of performance requirements for turbine-powered airplanes and incorporates such of the recent amendments to part 4b as the Administrator finds necessary to insure that the level of safety of turbine-powered airplanes is equivalent to that generally intended by part 4b.

Appendix 4 A4-3

6. The performance requirements contained herein include not only the performance requirements necessary for the certification of an airplane, but also the complementary performance operating limitations as applicable under Parts 40, 41, and 42 of the Civil Air Regulations. In promulgating this new performance code, the Board intends that the resulting level of safety will be generally similar to the level of safety established by the performance code as expressed by the provisions now contained in Parts 4b and 40 (or 41 or 42 as appropriate) for reciprocating engine airplanes. To attain this, many of the performance provisions have been modified for better applicability to turbine-powered airplanes, some in the direction of liberalization, others in the direction of improvement in the required performance.

7. A significant change being made is the introduction of full temperature accountability in all stages of performance, except the landing distances required. The introduction of full temperature accountability will insure that the airplane’s performance is satisfactory irrespective of the existing atmospheric temperature. The performance requirements heretofore applicable did not give sufficient assurance in this respect.

8. The reason for omitting the direct application of temperature accountability in the requirement for landing distances is that this stage of performance always has been treated in a highly empirical fashion whereby temperature effects are taken into account indirectly together with the effects of other operational factors. Long range studies on rationalization of airplane performance so far have not yielded a satisfactory solution to the landing stage of performance.

The Board hopes, however, that continued studies will result in a solution of this problem in the near future.

9. The introduction of full temperature accountability has necessitated a complete reevaluation of the minimum climb requirements. Since the prescribed climb must now be met at all temperatures rather than to be associated with standard temperature, the specific values of climb have been altered. In each instance, the change has been in the downward direction because, although the previous values were related to standard temperature, a satisfactory resultant climb performance was attained at temperatures substantially above standard. While values of minimum climb performance specified in the new code will tend to increase the maximum certificated weights of the airplane for the lower range of temperatures, they will limit these weights for the upper range of temperatures, giving adequate assurance of satisfactory climb performance at all temperatures.

10. In considering the various stages of flight where minimum values of climb have been heretofore established, the Board finds that in two of the stages (all-engines-operating en route and one-engine-inoperative en route) the establishment of minimum values of climb is unnecessary because, in the case of the all-engines-operating stage, it has been found not to be critical and the case of the one-engine-inoperative stage is now more effectively covered by the en route performance operating limitations.

11. Considering that the minimum climbs being prescribed affect mainly the maximum certificated weights of the airplane but not the maximum operating weights, the Board, in adopting the new performance code, places considerable emphasis on the ability of the airplane to clear obstacles on takeoff and during flight. To this end, criteria for the takeoff path, the en