Trim Analysis

The simplest trim concept is portrayed in Figs 4.2(a)-(c). The helicopter, flying forward in straight trimmed flight, is assumed to consist of a main and tail rotor with a fuselage experiencing only a drag force. The rotor is assumed to be teetering in flap, with no moments transmitted through the hub to the fuselage, and the centre of mass lies on the shaft, below the rotor. Assuming the fuselage pitch and roll attitudes are small, the following elementary model of trim can be constructed.

The balance of forces in the vertical direction gives the thrust approximately equal to the weight

(4.18)

This condition actually holds true up to moderate forward speeds for most helicopters. Balancing the forces along forward fuselage axis gives the approximate pitch angle as the ratio of drag to thrust

Since the thrust remains essentially constant in trimmed straight flight, the pitch angle follows the drag and varies as the square of forward speed. In our simple model, the absence of any aerodynamic pitching moment from the fuselage or tail requires that the hub moment is zero, or that the disc has zero longitudinal flapping.

From Fig. 4.2(b), the tail rotor thrust can be written as the main rotor torque divided by the tail arm

Qr

Tt (4.20)

lT

The tail rotor thrust therefore has the same form as the main rotor torque, with the bucket at minimum main rotor power. In practice, the vertical fin is usually designed to produce a sideforce in forward flight, hence reducing the thrust required from the tail rotor. Figure 4.2(c) then shows the balance of rolling moment from the main and tail rotors, to give the lateral disc flapping

Thus, the disc tilts to port, for anticlockwise rotors, and the disc tilt varies as the tail rotor thrust.

The balance of sideforce gives the bank angle

tt h _ %

Mag hR

If the tail rotor is located at the same height above the fuselage reference line as the main rotor, then the required bank angle is zero, for this simple helicopter design. In practice, the two terms in the numerator of eqn 4.22 are of the same order and the neglected in-plane lift forces have a significant influence on the resulting bank angle.

From the force and moment balance can be derived the required control angles – main/tail rotor collectives producing the required thrusts and the lateral cyclic from the lateral disc tilt.