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# How to calculate the angle of a trajectory to hit the target

Hi everyone,

How do I calculate the angle of a trajectory to hit the target, without knowing the velocity. I only know the max height, offset height and the distance to the target.

This is what I got so far (I don't know how to calculate offset height ):

```
float GetAngle(Vector3 startLocation, Vector3 endLocation, float maxHeight)
{
float distance = Mathf.Sqrt(Mathf.Pow(startLocation.x - endLocation.x,2) + Mathf.Pow(startLocation.z - endLocation.z,2));
float offsetHeight = endLocation.y - startLocation.y;
//how do I calculate offset height in this equation ?
return -Mathf.Atan (4 * maxHeight/ distance ) + Mathf.PI;
}
```

I use this to calculate the velocity (works fine I only need the correct angle):

```
float LaunchVelocity (Vector3 startLocation, Vector3 endLocation, float angle)
{
float range = Mathf.Sqrt(Mathf.Pow(startLocation.x - endLocation.x,2) + Mathf.Pow(startLocation.z - endLocation.z,2));
float offsetHeight = endLocation.y - startLocation.y;
float gravity = Physics.gravity.y;
float velocity = range * range * gravity;
velocity /= range * Mathf.Sin(2 * angle) + 2 * offsetHeight * Mathf.Pow(Mathf.Cos(angle),2);
return Mathf.Sqrt(velocity);
}
```

Is it mandatory that the projectile reaches the maximum height?

To establish the Offset height, you could use Pythagoras... The hypotenuse can be determined by Vector3.Distance(start, target); which leaves one side remaining.

For theta, there's a similar post here, but its for 2D:

Sorry Agorichyrich but I do not fully understand what you what you mean. Can you finish my GetAngle function?

Use quanternions or something like that. I can't remember much about it, but it worked for me in many cases.

Quaternions just represent angles. They are not intuitive and I imagine that calculating trajectories would be easier in Euler.

**Answer** by koray1396
·
Nov 27, 2014 at 05:09 PM

first, you should need to complete your code, otherwise you will always face similar problems.

I think there is no need to deal with complex formulas, I find simple steps helpful;

VerticalSpeed = Mathf.Sqrt(2*gravity*MaxHeight)

TravelTime = Sqrt(2*(MaxHeight - OffsetHeight) / g) + Sqrt(2*MaxHeight / g)

HorizontalSpeed = Distance / TravelTime

So your speed vector would be VerticalSpeed + HorizontalSpeed.

You can calculate the angle by Mathf.Atan2. Speed would be Magnitude of FinalVector.

This is the correct answer. But, if the projectile doesn't have to reach the MaxHeight, there will be infinite angles to hit the target.

```
void TrialShootByMaxHeight(Rigidbody rigid)
{
Vector3 originOfLaunch = Vector3.zero;
Vector3 targetPositionForLanding = Vector3.forward * 10;
//Made these points up. Hope you change them!
float maxPermittedHeight = 10f;
//Not only does the code below find a trajectory...
//The curve never goes higher than a provided height.
//See the original question:
//http://answers.unity3d.com/questions/841870/how-to-calculate-the-angle-of-a-trajectory-to-hit.html
float heightDifference =
originOfLaunch.y - targetPositionForLanding.y;
float verticalSpeed =
Mathf.Sqrt
(2 * -Physics.gravity.y * maxPermittedHeight);
float trialAndErrorFudgeICouldNotRemove = 0.06f;
float expectedTravelTime = 0f;
if (Mathf.Sign(heightDifference) == -1)
{
expectedTravelTime =
Mathf.Sqrt
(2 * (maxPermittedHeight - heightDifference) /
-Physics.gravity.y)
+
Mathf.Sqrt
(2 * maxPermittedHeight /
-Physics.gravity.y);
}
else if (Mathf.Sign(heightDifference) == 1)
{
trialAndErrorFudgeICouldNotRemove *= -1;
expectedTravelTime =
Mathf.Sqrt
(2 * (maxPermittedHeight + heightDifference) /
-Physics.gravity.y)
+
Mathf.Sqrt
(2 * maxPermittedHeight /
-Physics.gravity.y);
}
float horizontalSpeed =
Vector3.Distance
(originOfLaunch, targetPositionForLanding)
/ expectedTravelTime;
Vector3 facingTargetWithNoY =
(targetPositionForLanding - originOfLaunch);
facingTargetWithNoY.y = 0f;
Vector3 normalizedForwardDir = facingTargetWithNoY.normalized;
Vector3 launchVector = new Vector3
(normalizedForwardDir.x * horizontalSpeed,
verticalSpeed,
normalizedForwardDir.z * horizontalSpeed);
//quote from the question page linked at the top.
// If you want, "You can calculate the angle by Mathf.Atan2.Speed would be Magnitude of FinalVector." ???
//Now to add force. Make sure it has none already.
rigid.AddForce(-rigid.velocity, ForceMode.VelocityChange);
//Launch
rigid.AddForce
(launchVector, ForceMode.VelocityChange);
//And add some of that fudge!
rigid.AddForce
(launchVector * trialAndErrorFudgeICouldNotRemove, ForceMode.VelocityChange);
}
```

Got it working by adding a bit of fudge force, messing with the sign of gravity in the equation, but above all: I had to add an if statement that uses "heightDifference" (the offset) with a different sign if it is positive (meaning the origin is above the landing spot).

Hate to say, I actually have to go play with this link for a few hours now. http://answers.unity3d.com/questions/49195/trajectory-of-a-projectile-formula-does-anyone-kno.html Because I don't need to keep to a certain MAX HEIGHT. I need to keep to a certain LAUNCH VELOCITY

But yeah, if you just need a trajectory, or need to keep below a certain height... my script interpretation of Koray's theory works OK

(You might also consider adding a "min range" for this whole function. If target is damn close - why lob when you can shoot right at it??)

With the appropriate algorithm, there's no need for an *if statement* checking whether there is a height difference.

You might want to check out this answer (http://answers.unity3d.com/questions/1087568/3d-trajectory-prediction.html#comment-1343095) I gave on the subject a while back. Specifically, there are examples included for multiple means of generating an optimal trajectory, including a fixed speed for the initial launch velocity.

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