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Hi all,

I'm writing a car simulation for a game engine, and this problem has me going bonkers. For a car with known mass and center of mass, how can you figure out the "share" of mass that each tire is supporting? For standard tire arrangements (4 tires on 2 axles) I know it's just a ratio based on distance to center of mass, no problem. And I can figure it out for most cases similar to this. But I want my users to be able to put ANY number of tires at ANY points on the chassis, and here I don't know how to figure out how much mass each tire should support.

Keep in mind that the simulation is completely rigid, including the tires.

The only solution I've come up with that both kind of makes sense and works out mathematically is to recursively subdivide the tires in the longitudinal direction like this:

1.) In 2d (top-down) Find out all the tires above and below the (x,y) center of mass and split them into two groups.

2.) For each group, find an imaginary "axle" by averaging the tires' distances to the center of mass. You'll end up with 2 axles and each will have a ratio describing the percentage of mass it's supporting.

3.) Treat each axle like another center of mass and repeat steps 1.) and 2.) until you can't subdivide anymore. By compounding the ratios on each subdivision, you'll know the percentage of mass each tire is supporting in the y direction. Multiply this ratio by the mass of the car divided by 2 and you have the longitudinal share of mass on each tire.

4.) Repeat above 3 steps in latitudinal direction.

Hope that makes sense. Thank you for any insight.

I'm writing a car simulation for a game engine, and this problem has me going bonkers. For a car with known mass and center of mass, how can you figure out the "share" of mass that each tire is supporting? For standard tire arrangements (4 tires on 2 axles) I know it's just a ratio based on distance to center of mass, no problem. And I can figure it out for most cases similar to this. But I want my users to be able to put ANY number of tires at ANY points on the chassis, and here I don't know how to figure out how much mass each tire should support.

Keep in mind that the simulation is completely rigid, including the tires.

The only solution I've come up with that both kind of makes sense and works out mathematically is to recursively subdivide the tires in the longitudinal direction like this:

1.) In 2d (top-down) Find out all the tires above and below the (x,y) center of mass and split them into two groups.

2.) For each group, find an imaginary "axle" by averaging the tires' distances to the center of mass. You'll end up with 2 axles and each will have a ratio describing the percentage of mass it's supporting.

3.) Treat each axle like another center of mass and repeat steps 1.) and 2.) until you can't subdivide anymore. By compounding the ratios on each subdivision, you'll know the percentage of mass each tire is supporting in the y direction. Multiply this ratio by the mass of the car divided by 2 and you have the longitudinal share of mass on each tire.

4.) Repeat above 3 steps in latitudinal direction.

Hope that makes sense. Thank you for any insight.

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