A Mathematical model of a gyroplane can be created that has fidelity up to the same level as helicopter modeling. A nonlinear gyroplane model should at least include all body, rotor speed, teeter, and inflow degrees of freedom. It would also be prudent to include the torsional effects of rotor blades. Gyroplane structures are typically not that streamlined. Therefore it is not sensitive to changes in Reynolds numbers. This fact is significant in any attempts for subscale testing. This model is an extension of the longitudinal equations for fixed-wing aircraft.
$$x=
\begin{bmatrix}
u \\ w \\ q \\ \theta \\ \Omega
\end{bmatrix}$$
$$u=[\eta_s]$$
$$A=
\begin{bmatrix}
X_u & X_w & X_q & X_\theta & X_\Omega \\
Z_u & Z_w & Z_q & Z_\theta & Z_\Omega \\
M_u & M_w & M_q & M_\theta & M_\Omega \\
0 & 0 & 1 & 0 & 0 \\
Q_u & Q_w &Q_q & Q_\theta & Q_\Omega
\end{bmatrix}$$
$$B=
\begin{bmatrix}
X_{\eta_s} \\ Z_{\eta_s} \\ M_{\eta_s} \\ 0 \\ Q_{\eta_s}
\end{bmatrix}$$
If the longitudinal hub tilt is decreased with an increasing airspeed, that is indicative of a forward tilt of the disc. This reduces the pitch attitude of the gyroplane.
| Derivative Parameter | Influenced By |
| \(M_w\) \(M_\Omega\) | Vertical location of the CG |
| \(M_w\) | Pod and tailplane aerodynamics (dominated by pod) |
| \(Q_\Omega\) | proportional to the blade drag coefficient |
| \(X_u\) \(Z_w\) | modeling of physical phenomenon unique to gyroplanes |
[[Gyroplane Stability]]
- CAAPaper2009
Backlinks:
[[Aerodynamic Stability Derivatives]]
[[Gyroplanes]]
[[Longitudinal Flight Dynamics]]
[[Pitch Rate Tracking Control Example]]
[[Rotorcraft Models]]
[[State-Space Model]]