finding magnitudes such that they produce the max resultant vector in a certain direction?

2D
1

I’m working on a 2d spaceshooter game where the ship has boosters.
I want to determine how much force each booster needs to exert to move my ship with the maximum force in the direction it wants to go.

The ship may have any number of boosters but will probably be a small number like 2-10.
The rotations of the boosters are known but I can’t determine their magnitudes.
The magnitudes can be from 0(min) to lets say 5(max).

I got to a point where I made this equation:

directionToGo = ForceB1B1Direction + ForceB2B2Direction

But now that I’m getting more boosters I’m just thinking, ok to find what I want I have to brute force in min/middle/max forces for each direction to find the others I dunno.

So how would I go about doing this.

2

You can add the vectors together and look at the final vector.

For example, if you have a force (0, 1) on your ship, and another force (0, -2), the two force will add up to make (0, -1). As you can see, the stronger force overpowered the weaker force, but the resulting force (or rather the sum of the forces) has a smaller magnitude than the original forces because they were working against each other.

3

Hey I’m still unable to solve this =/

4

Can’t you just apply the force in the direction you need to the main object & animate the thrusters to make it look like they are firing? That way there’s no need to calculate the force of each thruster