Helicopter -- from Eric Weisstein's World of Physics

Helicopter

Helicopters fly by sucking air from above and forcing it downwards with a thrust equal to (for hovering) or exceeding (for climbing) the weight of the helicopter. The minimum engine power required to hover is called the "induced power." In an optimally designed helicopter, the extra power required to overcome drag from the rotors is only half as much as the induced power. Let the rotors have radius r so that they sweep out an area

(1)

Far above the helicopter, the air is at rest with a pressure . Just above the rotors, the velocity of air being sucked in is and the pressure is P. From Bernoulli's law,

(2)

Below the rotors, the pressure is and the velocity is . Far below, the pressure is again with velocity .

(3)

Thrust Coefficient

References

Gessow, A. and Myers, G. C. Aerodynamics of the Helicopter. New York: F. Ungar, 1967.

Johnson, W. Helicopter Theory. New York: Dover, 1994.

Stepniewski, W. Z. Introduction to Helicopter Aerodynamics. Morton, PA: Rotorcraft Pub. Committee, 1950.

Weisstein, E. W. "Books about Helicopters." http://www.ericweisstein.com/encyclopedias/books/Helicopters.html.