Calculating Lead For Projectiles

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Since this is a snippet this isn't a cut and paste job. It's meant as a pointer so you can integrate this easily into your own code. All the examples are in C#.

Aiming Code


// how fast the projectile will go (this might be the magnitude of targetQ also) float projectileSpeed = 40;

// aliases for where we are Vector3 selfPosition = transform.position; Vector3 targetPosition = target.transform.position;

// aliases for where we are going Vector3 targetQ = (target.rigidbody!=null) ? target.rigidbody.velocity :; Vector3 selfQ = (rigidbody!=null) ? rigidbody.velocity :;

// assuming that the projectile moves, and the target is moving add some lead to the target if(targetQ.sqrMagnitude !=0 && projectileSpeed > 0)

 targetPosition = targetPosition + targetQ * relativeTimeToTarget(selfPosition, selfQ, targetPosition, targetQ, projectileSpeed);

// from here on in you assume that by the time your projectile collides with the target the target will be at the location stored in targetPosition!

// ... your tracking/movement code here </csharp>

Calculating the time to target

Here's the rocket science bit. But actually it isn't. I shan't bore you with the details, but a solution to the same problem is [here] which takes you through a thorough description of the problem, but solved in a rather more complex manner.


// if we're moving, and they're moving we need to and origin isn't at 0,0,0 we need to use the difference // of "this" and "target" position/velocities

public static float relativeTimeToTarget( Vector3 originPosn, Vector3 originVel,Vector3 targetPosn, Vector3 targetVel, float pVel) {

 Vector3 diffPosn = originPosn - targetPosn;
 Vector3 diffVel  = originVel  - targetVel ;
 if(targetVel.sqrMagnitude == 0)
    diffVel =originVel;
 return Mathg.timeToTarget(diffPosn, diffVel,pVel);


// This is the meat of the code - the quadratic solver // and to think you thought this was rocket science! Solved by high school maths! // thanks to Ed (idevgames) for the original idea, and JohnJ of JJFFE for fixing my lame attempt at 3difying it public static float timeToTarget(Vector3 vTargetPosn, Vector3 vTargetVelocity, float projectileVelocity) {

 float a = Vector3.Dot(vTargetVelocity,vTargetVelocity) - (projectileVelocity*projectileVelocity);
 float b = 2*Vector3.Dot(vTargetPosn, vTargetVelocity);
 float c = Vector3.Dot(vTargetPosn,vTargetPosn);
 float d = b*b - 4*a*c;
 float t = 0;
 float u = 0;
 float tt = 0;
 float tu = 0;
 float r = 1; // add one second of lead if we're unsolvable
 if (d >= 0)
   tt = (-b + Mathf.Sqrt(d)) / (2*a);
   tu = (-b - Mathf.Sqrt(d)) / (2*a);
   // This portion picks the smallest nonnegative root.
   t = (tt < 0) ? System.Single.PositiveInfinity : tt;
   u = (tu < 0) ? System.Single.PositiveInfinity : tu;
   r = Mathf.Min(t,u); 
 return r;



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