I am analyzing the landing of an aircraft with the following assumptions:(adsbygoogle = window.adsbygoogle || []).push({});

- I consider the main and the nose landing gear wheels as skids, in order to ignore the tyre deflection;

- I have a 3 DOF aircraft model, with X and Y-axis indicating the forces acting respectively horizontally and vertically and the theta angle positive clockwise. This frame of reference is referred to the center of gravity;

- I assume that the plane has already touched the ground, so I don't consider the gliding phase towards the runway.

Now the summation of moments aroung the c.g. gives:

ƩM_{cg}= I_{yy}[itex]\ddot{\vartheta}[/itex]= R_{NLG}* L_{n}- R_{MLG}* L_{m}- h_{cg}* [itex]\mu[/itex]F_{vert}

Where:

[itex]\ddot{\vartheta}[/itex] is the angular acceleration of the pitch moment;

R_{NLG}and R_{MLG}are the vertical reactions of the nose and of the main landing gear shock absorber;

L_{n}and L_{m}are the distances respectively of the nose landing gear and of the main landing gear from the c.g.;

[itex]\mu[/itex] is the friction coefficient;

h_{cg}is the vertical distance between the runway and the c.g.;

F_{vert}is the resultant of the vertical forces.

Knowing the value of I_{yy}, which is the airplane pitch moment of intertia I can then compute [itex]\ddot{\vartheta}[/itex].

From this angular acceleration of the pitch angle I want to find the angle of attack, which is the difference from the pitch angle and the flight path angle:

A.o.A. -> α = θ - γ

My questions are:

1) Can I assume γ = 0 (flight path angle), since the plane has already touched the ground when I start my computations?

2) If so, how do I integrate [itex]\ddot{\vartheta}[/itex] in order to get the picth angle? What are my intitial conditions?

I hope that everything is clear and sorry for the long post.

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# Angle of attack from pitch angle acceleration

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