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
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-,/ " I.)" \ / V 11/16/2011 AC 23-8C Appendix 3 Table A3-2 - Tabulated Thrust Horsepower Available and Calculated VMC VC (KCAS) SHAFT HORSEPOWER P THRUST
HORSEPOWER
AVAILABLE AT
SEA LEVEL
CALCULATED VMC C2 = 1394.482 90 1050 .610 640.5 96.3 95 1050 .640 672.0 97.9 100 1050 .665 698.3 99.1 105 1050 .688 722.4 100.2 Figure A3-1 - Thrust Horsepower at Sea Level 85 90 95 100 105 VCAS KNOTS
SEA LEVEL STD. DAY VMC
CALCULATED
VMC VALUES
THRUST HORSEPOWER
AVAILABLE AT SEA LEVEL 620 640 660 680 700 720 740
THRUST HORSEPOWER AT SEA LEVEL A3-3
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