By Kuethe A.M., Chow C.-Y.
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Additional resources for Foundations of aerodynamics
The figures show: – The response of the airplane as pitch angle (θ) as a function of time. – The response of the airplane as attitude angle (α) as a function of time. For a step input of the elevator command, the pitch angle response displays an integration mode as a function of time (linear increase mode), while the pitch angle mode displays an almost constant response without integration. Before the application of the elevator step input the airplane moves freely at an attitude angle α0, which is the attitude angle obtained after the very slow angular motion, called “phugoid”, is stabilized.
So, for: β<0 → MXβ = q0. S . 2. Roll due to ailerons’ angular displacement CLδl The lateral motion of the control stick acts on the ailerons’ angular displacements. When the control stick moves to the left, the left aileron goes up and the right aileron goes down, creating a control torque which enables the plane to make a left roll. So for: δL < 0 → MXδL = q0. S . 19. 3. S. 24] This torque, which is proportional to an angular velocity, becomes a damping torque, with a stabilizing tendency. Its property is to be increased with the aspect ratio of the wing (and horizontal stabilizer).
Effect of gravitational forces As the airplane moves through the atmosphere it is submitted to a uniform gravitational field. The resulting effect of this field on the airplane is a unique vertical force applied in a downward direction to the center of the airplane’s mass. We will now evaluate the components of this force by the airplane reference (GXYZ). We consider the pitch angle (θ) and the roll angle (φ) which position the airplane reference in relation to the Galilean reference (Gx0y0z0).