Factors affecting rotor speed decay

2.12.1.1 Minimum rotor speed and rotor inertia

It is vital that the RRPM does not decay too far following a loss of power as it may then be impossible to establish the aircraft in a stabilized autorotation. The rate of rotor speed decay is therefore a very important factor, and the minimum rotor speed below which recovery is impossible is of critical concern to the rotor system designer. It is rather difficult to determine the minimum rotor speed accurately but by making some reasonable assumptions it is possible to get a basic understanding of the issue. Suppose the minimum allowable rotor speed ()min) corresponds to the maximum mean lift coefficient achievable by the rotor (CLmax). Now the rotor thrust, T, is given by [2.25]:

T = 2 pV 2bcRCL

If the thrust is assumed to remain constant during the initial phase of the power failure [2.25] and the inflow velocity is small compared with the rotor speed, then:

P )2»m bcR3CLnom =

p nmin bcR3cL

max

Thus:

L nom

) = ) “min “nom

L max

where )nom = rotor speed at instant of power failure and CLnom = average lift coefficient at instant of power loss.

In addition if the torque coefficient remains unchanged [2.25], then:

where Qnom = torque required at instant of power failure and Qmin = torque required at minimum rotor speed.

Hence the torque required to drive the rotor at any instant following the power failure will be given by:

2

Q = Q

nom

In the absence of any shaft power from the powerplants the torque requirement will tend to cause the rotor speed to decay. Thus:

Q

I

Reorganizing, integrating and applying the initial condition that at t = 0, ) = )nom, gives:

t = I)2m /1 _ 1

Qnom V ^ ^nom /

Therefore, the time taken for the rotor speed to reduce to the minimum permissible value can be obtained from:

Thus we see that tmin is dependent on the rotor inertia, the rotor speed and torque requirement at the instant of power loss and the ratio of the thrust required to the maximum thrust the rotor can produce. Consider the effect of changing some of these variables on a 4-bladed rotor of 6.5 m radius and 0.4 m chord with a lift curve slope of 6 per radian operating in the hover, see Table 2.1. Note that from the simplistic analysis detailed above the minimum rotor speed for this example helicopter is 18 rad/s based on a nominal mass of 5000 kg. The data in Table 2.1 indicates that the decay time can be lengthened by increasing the rotor inertia, increasing the nominal rotor speed or by reducing the thrust that the rotor has to produce under normal power-on conditions.

Rotor speed )nom(rad/s)	Mass (kg)	Torque Qnom (Nm)	Rotor inertia I (kg/m2)	Lift coefficient C v_’Lnom	Maximum lift coefficient C ‘-‘L max	Time to minimum rotor speed ^min (s)
35.0	5000	23 087	6000	0.2640	1.0024	8.63
35.0	5000	23 087	5400	0.2640	1.0024	7.76
35.0	5000	23 087	6600	0.2640	1.0024	9.49
31.5	5000	22923	6000	0.3258	1.0411	6.49
38.5	5000	23712	6000	0.2183	0.9586	10.67
35.0	4500	21036	6000	0.2377	1.0024	10.52
35.0	5500	25 242	6000	0.2904	1.0024	7.14

Table 2.1 Examples of decay time (based on conditions at 75% rotor radius).