Rotor Speed Decay

The entry into autorotation is usually an emergency—or at least a simulated emergency—maneuver, so there is a finite time delay between the power loss and the pilot’s corrective action. The decay of rotor speed during this period is a function of the power required and of the rotor’s level of kinetic energy. If the rotor were on a whirl tower, the decelerating torque could be assumed to be proportional to the square of the instantaneous rotor speed. Measurements of rotor speed decay during simulated power failures in flight such as those in references 5.11, 5.12, and 5.13, however, indicate that the actual rate of decay is somewhat less than would be predicted by this assumption. The reasons are several:

1. During a simulated failure using a throttle chop, the engine torque decays at a finite rate rather than instantaneously.

2. In some helicopters, the engine supplies a small amount of torque even after a throttle chop.

3. At low speeds, the helicopter immediately begins to descend, thus decreasing the power required.

4. At high speeds, the loss of rotor speed increases the tip speed ratio, which makes the rotor flap back, thus decreasing the power required.

The use of the assumption that the decelerating torque is proportional to the Square of the rotor speed is therefore somewhat conservative, but the degree will depend on the conditions existing at the time of the engine failure. Using the assumption anyway, the equation for the rotor speed decay is:

wherb the subscript 0 refers to conditions at the time of the power failure, and J is thfe total effective polar moment of inertia of the drive system, including the main rotor, the tail rotor, and the transmission referred to the main rotor speed; that is,

For the example helicopter, this gives:

An equation for the rotor speed time history an be derived by integrating the equation for the rate of deay:

f" — <m = –

ci0 Cl2 Л Jdl

Carrying out the integration gives:

ft 1

It is convenient to rewrite this as a function of the time during which all the rotor’s kinetic energy would be dissipated at the initial horsepower and rotor speed:

550 h. p.0

Using this definition, the rotor decay equation becomes:

ft 1

u 1 +—————

2^k. e.

The equation has been evaluated for several values of t^ and the results are plotted in Figure 5.4. The figure applies to any flight condition from hover to maximum speed. The example helicopter has a value of /KE of 1.2 seconds with full engine power. Thus for flight in this condition, the rotor speed would deay 30%

in the first second following a sudden failure of both engines. Failure of one engine from a full power condition would result in a decay of 17% in the first second if the other engine did not increase its power.