# Unity aircraft physics

I want to make a simple aircraft controller, what looks like little realistic in unity. I watch some video from airplane physics. and make a simple script in unity, but if I start, my plane cant move or if I change drag to zero, it cant lift. I tried to use real data and get it from wiki(F22 Raptor). To my game object, I gave the rigidbody component mass = 19670 kg. Engine thrust = 2 * 116000.0f Newton.

    private void calculateEnginePower()
{
EnginePower = engineThrust * ThrottleInput;
}

private void calculateForces()
{
angleOfAttack = Vector3.Angle(Vector3.forward, rb.velocity);
angleOfAttack = Mathf.Clamp(angleOfAttack, 0, 90);

coefficient = Mathf.Pow(1225.04f * rb.velocity.magnitude, 2) - 1; //M^2-2 where: M is mach.

if (coefficient > 0.0f)
coefficientLift = (4 * angleOfAttack) / Mathf.Sqrt(coefficient);
lift = 1.2754f * 0.5f * Mathf.Pow(rb.velocity.magnitude, 2) * coefficientLift * 78.04f; // densy1.2754 kg/m3, speed m/s , (F22)Wing area: 840 ft² (78.04 m²)

coefficientDrag = 0.021f;
rb.drag = coefficientDrag * 0.5f * Mathf.Pow(rb.velocity.magnitude,2) * 1.2754f * 78.04f;

}


roll, pitch... inputs from keyboard and mouse, EnginePower, RollInput... are simple properties and I call the Move function in a controller inside void Update.


Move(float roll, float pitch, float yaw, float throttle)
{
// transfer input parameters into properties.s
RollInput = roll;
PitchInput = pitch;
YawInput = yaw;
ThrottleInput = throttle;
AirBrakes = false;
calculateEnginePower();
calculateForces();
calculateRotation();
}

used these formulas:

for Lift force: Lift formula for Lift coefficient: Cl formula for Drag: Drag formula and for Drag coefficient: I used data from wiki too (0.021f).

## Introduction

Ah no, I'm afraid that this won't work. You decided to get to an intriguing yet difficult realm. Calculating accurately $C_L$ and $C_D$ is not easy (there wouldn't be aerodynamic tunnels if it was).

Also I would suggest to try modeling much older aircraft (of the Cold war era like F-86 or Mig-17). Getting aerodynamic information for fighters like F-22 is virtually impossible (they are classified). I've heard that for some few of the older jets some aerodynamic figures have been declassified but I can't find any information right now. You can search in Aviation SE or ask if it's not already asked.

Having said that, let's look into your problems:

## Why can't I accelerate

You are setting the value you calculated for the aerodynamic drag to rb.drag. That won't work. Unfortunately the documentation isn't clear as in what drag represents. As I get it is aerodynamic drag which is dimensionless. You set newtons there so I guess drag will be so high that your aircraft is trying to swim not fly. So you have 2 options:

1. Set rb.drag to zero and call

float drag = coefficientDrag * 0.5f * Mathf.Pow(rb.velocity.magnitude,2) * 1.2754f * 78.04f;

2. or simply do rb.drag = coefficientDrag; and then let unity handle it.

The first gives you more control while the second relies on unity's computations that I am unfamiliar with.

## Why can't I takeoff

Well that's simpler: you use a formulae that applies to supersonic speeds

$$C_{L} = \frac{4α}{\sqrt{M^2 - 1}}$$

Clearly if $M < 1$ then the radicand becomes negative and the root can't be calculated. Your code ignores it. So coefficientLift will be 0 (I guess, you don't show the initialization). That means that you won't get any lift until you get supersonic. Ouch. You need a big runway for that.

One thing you can do, is to create a text file (in a format of your preference) that will represent a "typical" $C_L - AoA$ matching. One example you can use is from Wikipedia

You can have something like

#AoA  CL
-5    0
-3    0.25
-0.5  0.5
2     0.75


and so on, and then apply linear interpolation to get the values in between.

## Other remarks

You use rb.velocity.magnitude as both velocity and Mach number. You need to make conversions (from Wikipedia): $$M = \frac{u}{c}$$

where:
M is the Mach number
u is velocity of the moving aircraft and
c is the speed of sound at the given altitude


Hope the above helps. Good luck with your game.