Losses of the Real Rotor

We have been examining the operation of an ideal main rotor, i. e., a rotor in which all the power obtained from the engine was converted into work

in accelerating the air downward or in creating thrust.

We have assumed that the entire area swept by the rotor participates in creating thrust. This means that the increased air pressure below the rotor and the reduced air pressure above the rotor (Figure 25a) acts on the entire main rotor area. In reality, as will be shown later, the entire swept area does not participate in creating thrust. The ideal rotor accelerates a uniform air jet downward with the same induced velocity for all the blade elements. The real rotor provides a swirling jet, and the induced velocities will vary markedly along the radius for the different blade elements (Figure 25b).

The ideal rotor does not expend energy in overcoming friction forces, while the real rotor experiences profile drag forces resisting rotation, and considerable power is expended in overcoming these forces. Moreover, the real rotor has the so-called tip and root losses. The essence of these losses lies in cross-flow of the air from the high-pressure region below the rotor into the low-pressure region above the rotor. This cross-flow takes place through the ends of the blades (tip losses) and through the root sections of the blades near the main rotor hub (root losses), where the structural part of the blade (spar) does not have a lifting surface. The concept of the end loss coefficient x has been introduced to account for the tip and root losses. With account for this coefficient, the actual area participating in creation of thrust is defined by the formula

For most main rotors x = 0.90 – 0.92.

Since for the real rotor varies along the radius, we take as the induced velocity its value at the radius r = 0.7

To account for the influence of the profile drag forces, we assume that the real rotor power required for creating thrust is greater on the average than the ideal rotor power required by 25%.

With account for these losses, the thrust of the real rotor can be found from the formula

T~2yFoVl

Hence, it is easy to find the induced velocity in the hovering regime

7

2/Fp *

Knowing that

T = CTF-^-u

we obtain

For most main rotors, the induced velocity in the hovering regime is V«8—10 m/sec, and Cx« 0.003.

An important characteristic of the main rotor is the relative efficiency Ni

The main rotor relative efficiency is the ratio of the power required to create the thrust of the ideal rotor to the total power supplied to the rotor. For modem rotors, the efficiency is 0.6-0.75.