Worked Example 1

In Chapter 1, the primitive helicopter built by Paul Cornu has been described. Each rotor of his machine was approximately 19.7 ft in diameter and the machine had a net gross weight (with pilot) of about 575 lb. Cornu claimed from experiments that 13 hp was required for the rotors to lift this weight. Use momentum theory to verify the power requirements for flight free of the ground.

Assuming each rotor lifted half of the total aircraft weight, then the momentum theory gives a result for net minimum possible power (or ideal power) required to drive both rotors using

0

2((W/2)W

ideal_4 -ДрА )’

where the total take-off weight W — 575 lb and where each rotor had a swept disk area, A = 304 ft2. Assuming sea level air density, this gives the ideal shaft power (in horsepower) required to drive both rotors of Cornu’s machine as

Therefore, an installed power of at least 14.7 hp would be required for free flight, but only if the rotors were aerodynamically 100% efficient and there were no transmission

losses. Realistically, with the primitive types of rotors used by Cornu, we could expect the aerodynamic efficiency of the rotors to be no more than 50% (a figure of merit of 0.5) and so leading to a power required of about 30 hp. Remember that Cornu also used an inefficient belt and pulley system to drive the rotors from an engine that produced only 24 hp. Therefore, taking into account the aerodynamic efficiency of the rotors and with a conservative estimate of transmission losses, for Cornu to hover his machine free of the ground the installed power required would need to have been about 40 hp. Using an engine with a power output of only 24 hp it is highly unlikely that Paul Cornu’s machine ever flew freely in sustained flight, even when accounting for the benefits of ground effect (see Section 5.8) and discounting the losses in efficiency that would be encountered with the slippage of the belt transmission.