How Does Varying Torque Affect Aircraft Rotation in Flight Simulations?

[AndreiStoian]

This is quite a tough one. I'm working on a flight simulation and aircraft are modeled as a rigid solid moving under drag. I'm making the AI system so I need to plan a path for the airplane - thus i need to spin it around so it points in the right direction.

Rotation is determined the usual way, by integrating torque twice. Torque is equal to the force applied using the flight stick to which a linear drag is applied.

Thus

T = max_rotational_velocity_konst * StickInput - w * C

StickInput is in [-1..1]

C is the drag constant and is calculated from the 'max_rotational_velocity_konst' constant and the 'time_to_reach_max_vel' constant - so that the designers can model a plane that achieves a certain angular velocity in a certain time (if the stick is kept at maximum during that time).

Next, the angular velocity is equal to the integral of Torque.

w = (T / (inv_mass * inertia)) * dt;

And finally, the angle of rotation is equal to

alpha = w * dt

Unfortunately, several stick movements need to be input each frame (so that behaviors can be tweened - ground avoidance for one should increase in priority as the plane gets closer to the ground) and I can't change this.

Thus my AI will input stick commands to make the plane roll to the right direction by measuring the angle between its current rotation and the desired rotation. I take the CrossProduct of the two 'Up' vectors so I get the sinus of the angle. I use this value as the StickInput value - thus it will achieve 0 input when its in the right angle.

Thus:

T = max_rot_speed * sin(alpha) - w * C
w = integral(T)
alpha = integral(w)

What I want is to find the angle as a function of time in order to determine the time it will take for the aircraft to achieve a certain rotation. I've already found a way to do it for constant force from here, but I don't know how to use it for a varying force.

Any ideas?

 

[LightHero]

The trick here is to use the integral of the torque equation. You can use integration to calculate the angular velocity as a function of time, then integrate again to calculate the angle as a function of time. In this case, the equation for the angular velocity as a function of time would be:w(t) = max_rot_speed * (1 - exp(-C*t/inertia)) + w0 * exp(-C*t/inertia)where w0 is the angular velocity at t = 0.To calculate the angle as a function of time, you simply have to integrate this equation once more:alpha(t) = max_rot_speed * t + w0 * (1 - exp(-C*t/inertia)) - (inertia/C) * exp(-C*t/inertia)This equation will give you the angle at any time, given the initial conditions.

 

[astrokreng]

I would suggest using a numerical integration method such as Euler's method or Runge-Kutta method to solve for the angle of rotation over time. These methods can handle varying forces and can provide a more accurate solution than a simple analytical approach.

Additionally, it may be helpful to consider the aircraft's dynamics and aerodynamics in your simulation, as these can also affect the rotation and response to varying torque. Consulting with aeronautical engineers or using a flight simulation software that takes these factors into account may provide more accurate results.

Overall, it is important to carefully consider and analyze all the variables and factors involved in the rotation of the aircraft in order to accurately model and simulate its behavior.