A Mathematical Model of a Single Main Rotor Helicopter for ... - Read

(B, is defined as zero if VH = UH = 0.) Finally the cyclic pitch must be expressed
in the hub-wind axis system. The expressions are:
A = Als cos $ - Bls sin Bw
1c W
Blc =
sin Bw + Bls COS Bw
Transformation T2
The rotor forces and moments calculated in the hub-wind axes system must be
expressed in the body-c.g. system as inputs to the six-degree-of-freedom rigid-body
equations of motion. To accomplish this, the forces and moments are first expressed
in the hub-body system of axes and then tranferred to the body-c.g. system.
The forces and moments in the x-y plane are modified by the first transforma-
tion as follows:
HH = H cos 8, + Yw sin B,
W
YH = -H sin f3 + Y cos 6,
W W W
% = Mw cos Bw + Lw sin BW
= -Mw sin €3 + L cos Bw
LH W W
The transformation to the body-c.g. system accounts for the shaft-tilt and the moment
about the c.g. caused by the rotor forces.
system are:
The forces expressed in the body-c.g.
= T sin i - cos i
S
S
Ym = YH
The moments in the body-c.g. system are:
= -T cos i - sin i
‘MR S S
- ST+) - %(mH - WL
= I’$ - Zm(STA c.g. c.g.
= Q cos i + L
NMR s H +
sin is + % R(~~c. g.
22
YMR(STAc.
g . - ST+)