Help with adding air resistance into my projectile trajectory function

[CraterHater]

Hey,

I am working on a video game in which there will be archers who have the ability to shoot at enemies. My game is two dimensional and I am trying to calculate the angle at which the archer, given an initial velocity, has to shoot in order to hit the target perfectly. I came up with the following equation:

α = ½ * asin (-(-G * S)/V0²)

Where α is the angle at which the archer has to shoot.
G is the gravitational constant.
S is the distance to the target.
and V0 the initial velocity of the target.

This function works to calculate the angle but it does not take into account several factors which I do want to take into account. These are:
- Air resistance.
- Differences in height between the archer and the target. Right now it assumes both are at the same height.
- Initial velocity of the target. The target is probably not stationary and so the formula should take the initial velocity into account in order to predict where the target will be on projectile impact.

I graduated high school last year and have never been the best at physics though I think this should be possible in a single equation. Can anyone help me out? Thanks!

 

[PeroK]

Summary:: Hey,

I am working on a video game in which there will be archers who have the ability to shoot at enemies. My game is two dimensional and I am trying to calculate the angle at which the archer, given an initial velocity, has to shoot in order to hit the target perfectly. I came up with the following equation:

α = ½ * asin (-(-G * S)/V0²)

I need to add the following conditions to make it work more realistically though:
- Air resistance
- Variable Height
- Target Initial Velocity

Hey,

I am working on a video game in which there will be archers who have the ability to shoot at enemies. My game is two dimensional and I am trying to calculate the angle at which the archer, given an initial velocity, has to shoot in order to hit the target perfectly. I came up with the following equation:

α = ½ * asin (-(-G * S)/V0²)

Where α is the angle at which the archer has to shoot.
G is the gravitational constant.
S is the distance to the target.
and V0 the initial velocity of the target.

This function works to calculate the angle but it does not take into account several factors which I do want to take into account. These are:
- Air resistance.
- Differences in height between the archer and the target. Right now it assumes both are at the same height.
- Initial velocity of the target. The target is probably not stationary and so the formula should take the initial velocity into account in order to predict where the target will be on projectile impact.

I graduated high school last year and have never been the best at physics though I think this should be possible in a single equation. Can anyone help me out? Thanks!

Adding all those factors would be very difficult. Having a difference in height is easy enough. But, for all three you'd need a very sophiosticated model.

 

[CraterHater]

Adding all those factors would be very difficult. Having a difference in height is easy enough. But, for all three you'd need a very sophiosticated model.

Mhm, how would you approach this problem? I learned some things about computational physics. Would that be a good approach?

 

[PeroK]

Mhm, how would you approach this problem? I learned some things about computational physics. Would that be a good approach?

I'm not sure about air resistance for an arrow. You'd need some data on how an arrow is affected. It's not just how to compute equations numerically but what sort of equations you would generate in the first place.

 

[A.T.]

Mhm, how would you approach this problem?

https://www.physicsforums.com/threa...-including-air-resistance.973732/post-6196581

 

[rude man]

Including air resistance, unless friction force is assumed proportional to velocity (which is a poor assumption; it's more like proportional to the square of the velocity), the equation of motion is non-linear so a closed-form solution is out. I'm guessing your only avenue would be some kind of numerical simulation to which I think post 3 alludes. You might amuse yourself trying that in Excel.

The other parameters you list can all be included in your (linear) equation of motion. Laborious but entirely doable.

 

[Lnewqban]

This function works to calculate the angle but it does not take into account several factors which I do want to take into account. These are:
- Air resistance.

These may help:
https://en.wikipedia.org/wiki/Projectile_motion#Trajectory_of_a_projectile_with_air_resistance

https://en.wikipedia.org/wiki/Drag_equation

https://sites.google.com/site/techn...rag-coefficients-of-bullets-arrows-and-spears

Best luck with your project!

 

[A.T.]

These may help:
https://en.wikipedia.org/wiki/Projectile_motion#Trajectory_of_a_projectile_with_air_resistance

https://en.wikipedia.org/wiki/Drag_equation

https://sites.google.com/site/techn...rag-coefficients-of-bullets-arrows-and-spears

Best luck with your project!

Quite frankly, this is such a standard problem in computer games, there should be tons of example code out there.

@CraterHater Have you tried googling "game physics ballistics" or simmilar?

 

[FactChecker]

In a video game, I would not worry about getting the physics exactly right. Just calculate a reasonably-shaped path to the target and have the arrow follow that path. The flight of an arrow is so fast that no player can tell if the physics is exactly correct.