ABSTRACT
Symbol Definition Units ݐ௦ sea level temperature ሺݐ݁݉݁ݎܽݐݑݎ݁ሻ ܶ thrust ሺ݂ݎܿ݁ሻ ܶ jet engine thrust ሺ݂ݎܿ݁ሻ
ܶ ሺሻ corrected net thrust ሺ݂ݎܿ݁ሻ ܶ ሺ௦௩ௗሻ observed net thrust ሺ݂ݎܿ݁ሻ
ܶܵܨܥሺሻ corrected thrust specific fuel consumption ሺݓ݄݁݅݃ݐሻ
ሺ݂ݎܿ݁ሻ · ሺݐ݅݉݁ሻ
ܶܵܨܥሺ௦௩ௗሻ observed thrust specific fuel consumption ሺݓ݄݁݅݃ݐሻ
ሺ݂ݎܿ݁ሻ · ሺݐ݅݉݁ሻ ݒ velocity ሺ݈݁݊݃ݐ݄ሻ ሺݐ݅݉݁ሻ⁄
ݒஶ free stream velocity ሺ݈݁݊݃ݐ݄ሻ ሺݐ݅݉݁ሻ⁄ ݒ exhaust velocity ሺ݈݁݊݃ݐ݄ሻ ሺݐ݅݉݁ሻ⁄
ݒ effective velocity ሺ݈݁݊݃ݐ݄ሻ ሺݐ݅݉݁ሻ⁄ ݓሶ ሺሻ corrected weight flow rate of air ሺݓ݄݁݅݃ݐሻ ሺݐ݅݉݁ሻ⁄
ݓሶ ሺ௦௩ௗሻ observed weight flow rate of air ሺݓ݄݁݅݃ݐሻ ሺݐ݅݉݁ሻ⁄ ݓሶ ௨ ሺሻ corrected weight flow rate of fuel ሺݓ݄݁݅݃ݐሻ ሺݐ݅݉݁ሻ⁄
ݓሶ ௨ ሺ௦௩ௗሻ observed weight flow rate of fuel ሺݓ݄݁݅݃ݐሻ ሺݐ݅݉݁ሻ⁄
ߙ angle between effective velocity and chord line ሺ݈ܽ݊݃݁ሻ
ߚ angle between plane of rotation and chord line ሺ݈ܽ݊݃݁ሻ
߶ angle between lift and net thrust ሺ݈ܽ݊݃݁ሻ ߟ propeller efficiency ‐‐‐‐‐‐‐‐ ߟ propulsive efficiency for jet engines ‐‐‐‐‐‐‐‐ ߩ density of air ሺ݉ܽݏݏሻ ሺ݈݁݊݃ݐ݄ଷሻ⁄ ߱ propeller angular velocity Radian ሺݐ݅݉݁ሻ⁄
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Net Thrust ܶ ൌ ܮ · ܿݏሺ߶ሻ െ ܦ · ݏ݅݊ሺ߶ሻ
Revolutions per Unit Time
݊ ൌ ߱2 · ߨ
Advance Ratio
ܬ ൌ ݒ݊ · ݀
Propeller Efficiency
ߟ ൌ ܶ · ݒ ௦ܲ௧
Power Coefficient
ܥ ൌ ௦ܲ௧ߩ · ݊ଷ · ݀ହ
Thrust Coefficient
ܥ் ൌ ܶߩ · ݊ଶ · ݀ସ
Torque Coefficient
ܥொ ൌ ܳߩ · ݊ଶ · ݀ହ
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Pr op
el le r E
ff ic ie nc y
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Thrust Equation
ܶ ൌ ൫ ሶ݉ ሶ݉ ௨൯ · ݒ െ ሶ݉ · ݒஶ ሺ െ ஶሻ · ܣ
Assuming ሶ݉ ௨ ا ሶ݉ ܶ ൌ ሶ݉ · ሺݒ െ ݒஶሻ ሺ െ ஶሻ · ܣ
Propulsive Efficiency ߟ ൌ ܶ · ݒஶ
ሶ݉ · ൮ ൬1 ሶ݉ ௨ሶ݉ ൰ · ሺݒሻ
2 െ ሺݒஶሻଶ2 ൲
Assuming ሶ݉ ௨ ا ሶ݉ and ൎ ஶ
ߟ ൌ ܶ · ݒஶ൫ ܶ · ݒஶ൯ ሶ݉ · ሺݒ ଶ െ ݒஶଶሻ2
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ܶ ሺሻ ൌ ܶ ሺ௦௩ௗሻߜ
Corrected Fuel Flow
ݓሶ ௨ ሺሻ ൌ ݓሶ ௨ ሺ௦௩ௗሻ
ߜ · ߠ௫ ݔ ൎ 0.5
Corrected Thrust Specific Fuel Consumption ܶܵܨܥሺሻ ൌ
ܶܵܨܥሺ௦௩ௗሻ ߠ௫ ൌ
ݔ ൎ 0.5
Corrected Air Flow ݓሶ ሺሻ ൌ
ݓሶ ሺ௦௩ௗሻ ߜ · ߠ
௫ ݔ ൎ 0.5
Corrected Exhaust Gas Temperature
ܧܩ ሺܶሻ ൌ ܧܩ ሺܶ௦௩ௗሻ
ߠ௫ ݔ ൎ 1
Corrected Rotor Speed
ሺܰሻ ൌ ሺܰ௦௩ௗሻߠ௫ ݔ ൎ 0.5
Corrected Shaft Power
௦ܲ௧ ሺሻ ൌ ௦ܲ௧ ሺ௦௩ௗሻߜ · ߠ௫ ݔ ൎ 0.5
Note: ߜ ൌ ௦⁄ and ߠ ൌ ݐ ݐ௦⁄ , ݐ conditions: ambient or stagnation at engine inlet
The exponent of ߠ is a function of the engine cycle and is developed
from theoretical and empirical data.
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