How to Calculate Trajectory of Object Unity Without Physics

Calculating an object's trajectory in Unity without using the physics engine requires understanding basic projectile motion principles and implementing them with code. This guide explains the math behind it and provides a working calculator to visualize the results.

Introduction

When you need to simulate projectile motion in Unity but want to avoid the physics engine for performance or control reasons, you can calculate the trajectory mathematically. This approach gives you precise control over the motion and better performance for simple cases.

Projectile motion follows a parabolic path determined by initial velocity, angle, and gravity. By calculating position at each time step, you can animate an object along this path without physics.

Basic Trajectory Formula

The key formulas for projectile motion are:

Horizontal position: x(t) = v₀ * cos(θ) * t

Vertical position: y(t) = v₀ * sin(θ) * t - (1/2) * g * t²

Total time of flight: T = (2 * v₀ * sin(θ)) / g

Where:

v₀ = initial velocity
θ = launch angle in radians
g = acceleration due to gravity (9.81 m/s²)
t = time

These formulas give the position of the projectile at any time t. By calculating these values at small time intervals, you can animate the object's motion.

Implementing in Unity

To implement this in Unity C# script:

1. Create a GameObject with a SpriteRenderer or MeshRenderer

2. Attach this script to the object

3. Set the initial velocity and angle in the inspector

4. The script will calculate and animate the trajectory

The implementation involves:

Converting the angle to radians
Calculating the total flight time
Updating position at each frame using the formulas
Resetting when the projectile hits the ground

This approach gives you complete control over the motion while avoiding the physics engine.

Worked Example

Let's calculate a trajectory with:

Initial velocity = 20 m/s
Launch angle = 45°
Gravity = 9.81 m/s²

Using the formulas:

θ = 45° = 0.785 radians

Total time = (2 * 20 * sin(0.785)) / 9.81 ≈ 2.86 seconds

At t = 1 second:

x(1) = 20 * cos(0.785) * 1 ≈ 14.14 meters

y(1) = 20 * sin(0.785) * 1 - 0.5 * 9.81 * 1² ≈ 12.25 meters

This means after 1 second, the projectile will be at approximately (14.14, 12.25) meters from the launch point.

FAQ

Why would I use this instead of Unity's physics engine?

This method gives you more control over the motion and better performance for simple cases. It's useful when you need precise trajectory control or when working with many objects where physics overhead would be too expensive.

How accurate is this method compared to physics?

This method is mathematically precise for ideal projectile motion. Real-world factors like air resistance aren't accounted for, which is why physics engines are often preferred for complex simulations.

Can I use this for 3D trajectories?

Yes, you can extend this to 3D by adding a z-component to the position calculation. The basic principles remain the same, but you'll need to account for both horizontal and vertical components.

What if I want to add air resistance?

To add air resistance, you would need to modify the velocity calculation at each time step. This would make the implementation more complex but would provide more realistic results.