AC 23-8C

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20000 18000 16000 14000 12000 10000 8000 6000 4000 2000 11/16/2011 AC 23-8C Figure A1-1 – Brake Horsepower Versus Pressure Altitude A1-4

PRESSURE ALTITUDE ­

IN FEET

SEA LEVEL 20 22 24 26 28 3018 MANIFOLD PRESSURE - IN.H.g.

240 280 320 360 400 BRAKE HORSEPOWER - BHPc

FULL THROTTLE MANIFOLD PRESSURE vs

PRESSURE ALTITUDE

FULL THROTTLE, TEST MANIFOLD

PRESSURES AT VY (OBTAINED FROM COOLING CLIMB

OR CLIMB PERFORMANCE DATA)

FULL THROTTLE ZERO

RAM CHART MANIFOLD PRESSURE 2650 RPM

FULL THROTTLE

INSTALLED CHART BRAKE HORSEPOWER 2650 RPM

FULL THROTTLE ZERO RAM

CHART BRAKE HORSEPOWER 2650 RPM

~- Calculated Test Day BHPc for the AFM Expansion:

For the Same Conditions as Test Day,............................................335 BHP BHP (from Figure A1-1)........................................................................335 BHP Correcting for Inlet Temperature, expansion 460  44.7 ..............................................................329.1 BHP BHP – 335 460  63

4. Turbocharged Engines with Constant Speed Propellers.

a. Manifold Pressure Versus Altitude. From flight tests, it is appropriate to plot manifold pressure versus pressure altitude used to demonstrate satisfactory cooling and climb performance demonstrations. The engine manufacturer’s chart brake horsepower should be entered at these manifold pressure values. The result is the chart br ake horsepower to be utilized in data expansion.

For some installations, the manifold pressure and fuel flows are limited by the airplane manufacturer’s design schedule. For these, the full th rottle values must be identified. Whenever the manifold pressures and fuel flows must be manually set to a schedule, corresponding limitations must be established.

b. Horsepower. Refer to Figure A1-2 for an illustration of manifold pressure and horsepower versus pressure altitude. It is rare for the horsepower values to be constant below the critical altitude. The horsepower ratings are not necessarily limited and it is common to observe chart horsepower values at the intermediate altitudes higher than rated power. As with normally aspirated engines, the term chart brake horsepower indicates that the horsepower values have yet to be corrected for inlet temperature conditions. The corrections for temperature are usually greater for turbocharged than normally aspirated. A 1 percent decrease in power for each 10 ºF increase in temperature above standard temperature conditions at a constant specific fuel consumption (SFC) is common. The apparent effects for a particular installation could be more or less than this. Manufacturer’s data for the particular engine should be used.

c. Example Calculation. The overall corrections to determine installed test brake horsepower and brake horsepower to be used in the expansion of performance would be as follows (refer to Figure A1-2):

Known: Pressure Altitude.....................................................9,500 feet Manifold Pressure...................................................44.3 in. Hg.

Outside Air Temperature........................................53.0 ºF Compressor Inlet Temperature...............................67 ºF Engine Speed..........................................................2,575 r.p.m.

Engine Calibration..................................................+1.7% Engine Tolerance....................................................±2 1/2%

A1-5

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I ~) 24000 22000 20000 18000 16000 14000

PRESSURE ALTITUDE - 12000 FEET 10000 8000 6000 4000 2000 SEA LEVEL MANIFOLD PRESSURE vs PRESSURE ALTITUDE MANIFOLD PRESSURE - In.H.g.

BRAKE HORSEPOWER vs PRESSURE ALTITUDE BRAKE HORSEPOWER - BHPc 36 37 38 39 40 41 42 43 44 45 46 290 300 310 320 330 340 350 360

FULL THROTTLE

MANIFOLD PRESSURE OBSERVED

DURING COOLING CLIMBS AND

PERFORMANCE CLIMBS

INSTALLED CHART

BRAKE HORSEPOWER 2575 RPM 11/16/2011 AC 23-8C Appendix 1 Figure A1-2 - Turbocharged Brake Horsepower Versus Altitude A1-6

Appendix 1 Calculated Test Day BHP for a Calibrated Engine:

Standard Temperature @ 9,500 ft.....................................................25.1 ºF Power Correction Due to Temperature at 1%/10 ºF........................................................................................-4.2% (Temperature rise = 67º -25.1 ºF) Installed Chart Brake Horsepower (from Figure A1-2)...................................................................................351 BHP Engine Calibration Correction (351)(.017).......................................+5.97 BHP Test BHP = (351 + 5.97) - (.042)(356.97)......................................332.1 BHP Calculated Test Day BHP for an Uncalibrated Engine:

Standard Temperature @ 9,500 ft.....................................................25.1 ºF Power Correction at 1%/10 ºF...........................................................-4.2%

Installed Chart Brake Horsepower351

(from Figure A1-2) Test BHP = 351 - (351)(.042) + 351(.025)......................................335.3 Calculated BHPc for Test Day Density Altitude (Hd):

Hd at 9,500 ft and 53 ºF....................................................................11,280 ft Installed BHPc (from Figure A1-2).........................................................350 BHP Power Correction Due to Inlet Temperature Rise at 1%/10 ºF (temperature rise = 14 ºF)..................................................................-1.4% BHPc = 350-(350)(.0233)..................................................................341.8 BHP Calculated BHPc for the AFM Expansion:

For the Same Conditions as Test Day,...............................................351 BHP BHPc (from Figure A1-2)

Temperature Correction to BHPc =...................................................326.5 BHP 350-(.042)(351)

5. Normally Aspirated Engines with Fixed Pitch Propellers. (Reserved).

6. Turbopropeller Engines.

a. Power Measurement. Turbopropeller engines (turboprops) are gas turbine engines that drive a propeller. Power output is a function of the gas tu rbine airflow, pressure, and temperature. Power measurement is made by measurement of the propeller shaft speed and torque, from which the shaft horsepower can be obtained by a simple calculation. Torque is measured by an integral device that may be mechanical, hydraulic, or electrical and connects to the indicator required by Part 23, § 23.1305(m). Shaft horsepower is the same as brake horsepower, that is, the power developed at the propeller shaft. The total thrust horsepower, or e quivalent shaft horsepower (ESHP) is the sum of the shaft horsepower and the nominal horsepower equivalent of the net exhaust thrust.

A1-7

Appendix 1

b. Power Available. The prediction of power available is obtained from the engine manufacturer as a computer program. Each installation must be evaluated to identify:

Generator Loads (all engine and one engine inoperative) Bleed Air Extractions (with and without ice protection) Accessory Pad Extractions

Engine Air Inlet Efficiency (with and without ice protection) Engine Exhaust Efficiency Effect of Specific Humidity

With these values as input to the computer program, installed power available and fuel flows at various airspeeds, temperatures, and altitudes can be calculated.

A1-8

Appendix 2 Appendix 2. Climb Data Reduction

1. Drag Polar Method. This is one method to develop the airplane’s drag polar equation directly from climb flight test data. It is a simplified method that assumes climb speeds where the compressibility drag is negligible (usually Mach numbers below 0.6), climb angles of less than 15 degrees, and no propeller slipstream effects on the wing lift and drag characteristics.

a. Cautions. Propeller airplanes are susceptible to slipstream drag, and all airplanes are susceptible to trim drag. This is most noticeable on airplanes with wing-mounted engines and when one engine is inoperative. Care should be given so that drag results are not extended from one flight condition to another. Examples of this are:

(1) Drag obtained in level cruise configuration cannot be extended to a climb configuration.

(2) Two-engine climb data cannot be extended to the one-engine-inoperative case.

In summary, the power and trim conditions must remain very close to those existing for the actual test conditions. Drag results are only as accurate as the available power information and propeller efficiency information. The cooling airflow through the engine is also a factor.

b. Calculation of CD and CL. Flight test data for various climb airspeeds, weights, and altitudes should be used to calculate CD and CL. The equations are as follows:

TAT AF  R / CO WT  96209CD = BHP    T P  3 TAS 33,000  V  S  e  2  T AFR / C AT O295WT  1   101.27VC  TAS  CL = Ve 2 S

Where:

BHPT = test day horsepower (see Appendix 1) P = propeller efficiency (obtain from propeller manufacturer or may be estimated) TAT = test air temperature - ºKelvin TAS = standard air temperature - ºKelvin   A2-1

Appendix 2 R/CO = observed rate of climb - feet/minute WT = airplane test weight - pounds Ve = equivalent airspeed - knots S = wing area - square feet  = atmospheric density ratio (see Appendix 7, figure 1) AF = acceleration factor (may be insignificant at lower speeds) 2 3.5 1  0.2M 1 2AF =  0.133M  1 2 2.5 1  0.2M Where: M = Mach number VC is constant, altitude below 36,089 feet

c. Data Plotting. Once CD and CL2 are calculated from various climb tests at many altitudes, weights, and airspeeds, a plot is made of CD versus CL2. This choice of parameters reduces the parabolic drag polar (CL vs. CD) to a straight line relationship. These procedures should be used to establish CDP and e for each configuration where climb data is obtained.

Figure A2-1 - Coefficient of Drag Versus Coefficient of Lift .05 .06 .07 .08 CD CDP 0 .1 . 2 . 3 . 4 . 5 . 6 2CL From this plot, the profile drag coefficient (CDP) can be determined graphically and Oswald’s efficiency factor (e) can be calculated.

A2-2

Appendix 2 CL2 CL2 / CDe = or e =2 2    CD  CDP 3.1416 b  3.1416 b     S S    Where: b = wing span - feet S = wing area - square feet

d. Standard Day Correction. Since the CL 2 versus CD data was developed from test day conditions of weight, altitude, temperature, and power, calculations will be required to determine standard day conditions.

THPA  THPR 33,000 R/C = WC (AF) Where: THPA = thrust horsepower available THPR = thrust horsepower required WC = aircraft weight to which correction is to be made (pounds) AF = acceleration factor (see paragraph b) THPA = BHPc (  )P Where: BHPc = chart brake horsepower at test day density altitude (see Appendix 1)  = propeller efficiency P VT 3 CDPS 0.2883WC 2 THP R =  296209 eb V T Where:  = atmospheric density ratio VT = true airspeed - knots CDP = profile drag coefficient S = Wing area - square feet e = efficiency factor b = wing span - feet WC = aircraft weight to which correction is to be made - pounds

e. Expansion to Non-standard Conditions. The methods in paragraph “d” can be used to expand the climb data by choosing weight, altitude, temperature, and the corresponding power available.

A2-3

0 D 0 0 11/16/2011 AC 23-8C Appendix 2

f. References. The following references may be of assistance in cases where compressibility drag is a factor, climb angles are greater than 15 degrees, or if the reader wishes to review the basic derivations of the drag polar method:

(1) “Airplane Aerodynamics and Performance” by C. Edward Lan and Jan Roskam. Published and sold by:

Roskam Aviation and Engineering Corporation Route 4, Box 274 Ottawa, Kansas 66067

(2) Air Force Technical Report No. 6273, “Flight Test Engineering Handbook,” by Russell Herrington, et al., dated May 1951. Corrected and revised June 1964-January 1966. Refer to NTIS No. AD 636.392. Available from:

National Technical Information Service (NTIS) 5285 Port Royal Road Springfield, Virginia 22161

2. Density Altitude Method. This method is an alternate to the Drag Polar Method. The Density Altitude Method is subject to the same cautions as the Drag Polar Method. Item numbers 1, 2, 6, 9, 12, 17, 18, and 19 are observed during flight tests and the remaining items are calculated.

Item No. Item 1 Pressure Altitude (Hp) – feet 2 Outside Air Temperature – °F 3 Atmospheric Density Ratio –  .4699 4. Density Altitude (Hd) – feet. Hd = 145539 1   

5. Std. Temp. @ Hp (TS) – °F + 460

6. IAS – knots

7. CAS – knots

8. TAS = 7 3

9. Observed rate of climb – ft/min

10. T/T S = 2 + 460 ____ 5 A2-4

oO O 0 0- 00 0000 ) _ _________ 11/16/2011 AC 23-8C Appendix 2

11.

12.

13.

Wc Where WC = aircraft weight to which correction is to be made

14. q πeb2 = 7 2 πeb2 295 Where: b = wing span in feet e = Oswald's efficiency factor (0.8 may be used if a more exact value cannot be determined)

215. ΔD 8 = Wc  12  _______________

16. Δ(R/C) ΔD i WS

17. Calibrated RPM (reciprocating engine)

18. Calibrated MP (reciprocating engine)

19. Inlet air temperature

20. Test day BHP corrected for temperature from Appendix 1 at Hd

21. P -- propeller efficiency (obtain from propeller manufacturer or may be estimated)

22. ΔTHP = (

23. Δ(R/C) ΔP = WC

24. R/CSTD = 11 - 13 - 16 + 24 Actual R/C = * Test Weight, 2- lbs.

∆R/C∆W = (I - 9 10 11 12 = 101.27 _____________ ____ 14 15 8

-  X 33,000 ________ 22 21 20 23 Items 4, 7, and 24 are used to plot figure 25-2.

A2-5

I Appendix 3 Appendix 3. Static Minimum Control Speed Extrapolation to Sea Level

1. General. The purpose of this appendix is to identify one method of extrapolating minimum control speeds (VMC) observed during flight tests, to sea level, standard temperature conditions. There is a geometric relationship between the yawing moment about the c.g. caused by the operating engine, and the rudder deflection necessary to offset this tendency and cause an equilibrium.

2. Calculation Method. This method involves calculating a geometric constant (C2) for each observed test value, averaging the results, and calculating a sea level VMC. The equations are as follows:

1 VMC = [(C2 )(  )(THP)] 3 or;

3VMCC2  (  )(THP) Where: C2 = a geometric constant  = the square root of the density ratio THP = thrust horsepower (test shaft horsepower or brake horsepower times propeller efficiency)

3. Cautions and Assumptions. This method has the following associated cautions and assumptions:

a. This method is limited to airplanes with a VMC due to lack of directional control. Each test value of VMC must be observed with full rudder deflection. If, for example, the test conditions result in reaching the force limit (150 pounds rudder force) prior to achieving full rudder deflection, then observed VMC values would require special consideration.

b. The effects of wing lift in the 5 degree bank angle are ignored.

c. Do not use this method for fixed-pitch or windmilling propellers.

d. Any altitude effects that may result from drag on a rotating feathered propeller on the inoperative engine are ignored.

e. Computing a VMC value at sea level involves raising to the power of 1/3 (use 0.33333333). The number of significant digits used affects the resulting computations. For this reason, use at least 8 significant digits.

A3-1

r Appendix 3

f. Propeller efficiencies should be reasonable. They may be obtained from propeller efficiency charts provided by the propeller manufacturer, or from other acceptable sources.

4. Sample Calculations. Test data from two-engine turbopropeller airplanes have been used for illustration. Observations for one ta keoff flap setting are presented. The procedures should be repeated for each additional approved takeoff flap setting. Table A3-1 presents five data points that were collected at various altitude and temperature conditions, and the resulting C2 values that were calculated. For these tests, the inoperative propeller was feathered (auto-feather available).

Table A3-1 – Flight Test Data RUN

PRESSURE

ALTITUDE (FEET) O.A.T.

(°F) TORQUE (FT-LB)

PROPELLER RPM VMC (KCAS)  SHAFT HORSE- POWER p

(2) C2 1 3500 86.3 3219 1700 91.2 .914243 1041.95 .590 1349.657 2 4200 88.3 3219 1700 91.2 .900795 1041.95 .585 1381.516 3 4800 87.3 3219 1700 90.7 .891588 1041.95 .580 1384.786 4 5500 85.2 3219 1700 90.7 .881668 1041.95 .575 1412.544 5 6300 83.2 3219 1700 90.7 .870083 1041.95 .570 1443.907

(1) Calculated from observed torque and propeller rpm

(2) Obtained from propeller manufacturer The propeller efficiencies were obtained from power coefficient versus advance ratio map, which was obtained from the propeller manufacturer. The 4-blade propellers were assumed for these calculations to have an activity factor = 80; and an integrated lift coefficient = 0.700.

The five C2 values from Table A3-1 were averaged as 1394.482. The sea level, standard temperature maximum shaft horsepower was 1050. At low speeds, the propeller efficiency changes fairly significantly with speed. For this reason, it is appropriate to determine propeller efficiencies at several speeds near the estimated sea level VMC value. Table A3-2 presents the thrust horsepower values determined for calibrated airspeeds of 90, 95, 100, and 105 knots and the VMC values calculated using these thrust horsepower values and the average C2 (1394.482).

Figure A3-1 illustrates the plot of airspeed versus thrust horsepower. One curve is of thrust horsepower available versus airspeed. The other represents the calculated VMC values versus thrust horsepower available at sea level. The intersection of the two curves represents the VMC value associated with sea level, standard temperature conditions. These calculations resulted in a final VMC value of 98.8 knots calibrated airspeed.

A3-2