Minimum spring force required to keep a car level

[at570]

Oh I get it. By axle I was thinking the assembly that has the rotating piece that connects to the wheels inside of it. I think youre asking me about the rotating piece right? Or asking if the whole wheel/axle area acts like a pivot joint
So if the springs are pivoted at the bottom then the front one can move farther under relative to the body and the back one can move farther out. I think there would be force opposing gravity and I think it would be different for each one. You can find them by dividing the distance from one to the center of gravity by the distance of the other one to the center of gravity * mg. But I am not quite sure where to go from here. Mostly about how to find the spring compression

 

[at570]

Saw your edit. So I guess you do treat the wheels as moving freely then. I am still trying to figure out how to get the spring compression with the springs angled

 

[at570]

I don't think you can do it the same way anymore because of the wheels now being included and the springs angled. Make a triangle at the connection of one of the springs to the body. The angle the body is at is θ. The angle of the triangle at the spring connection is θ. The hypotnuse is the spring force and adjacent is the part of the spring force opposing gravity. All of the adjacents together have to equal the force of gravity. Should I do this by weight and would it be the amount of weight on each wheel since the wheel positions are also different because of the rotation, one has gone underneath and one has gone out, so that force transferred up the suspension to the spring, or by weight at the spring connection to the body? I would think it would be the force tranferred up the suspension. I wonder though if i did it by weight if youd always get zero rotational torque.
Or should I do it by angle, since the angle of rotation is θ. Id make a triangle halfway between the connections of the springs to the body to one connection of the spring to the body. The angle is θ, adjacent is half the distance between the connections of the springs to the body and the opposite is the spring compression from rotation. But the spring compression from rotation only isn't enough to equal gravity anymore because of the rotation of the springs. There needs to be some extra force and I am not sure if its distributed evenly or by percent of weight on each wheel or possibly another way.
Im also wondering because the wheels and body are both now angled, would the spring compressions and because of that the distance from the suspension to the bottom of the wheel for the two springs always be the same with that angle and mass? I would think so
Also has the roll center moved since the wheels and whole suspension is included now? Is it still halfway between the connections for the springs to the body or it it somewhere else mabey on the ground under the center of mass when level?
Can someone give me some ideas or comments on these ways of doing it?

 

[at570]

I saw that the rotation center of a car front to back is the pitch center. Make the first two triangles at level and then rotate it angle θ. Make a triangle from the pitch center to to connection between the body and the front spring. The height is s_o the height of the bottom of the body when level opposite is d₁ the distance from the center of the body to the connection to the front spring. Get the angle at the pitch center a and the hypotnuse p₁ the distance from the pitch center to the connection of the spring to the body. Make a triangle from the pitch center. The hypotnuse is p₁ and the angle at the pitch center is a + θ. The adjacent is l₄ the moment arm for the front spring force in the x direction and opposite is l₁ the moment arm for the front spring force in the y. Make another triangle from the pitch center to the connection of the back spring to the body. The adjacent is s_o and the opposite is d₁. Get the angle at the pitch center a and the hypotnuse p₂ the distance from the pitch center to the connection of the back spring to the body. Make a triangle from the pitch center. The angle at the pitch center is a - θ and the adjacent is l₂ the moment arm of the back spring force in the y and opposite is l₅ the moment arm of the back spring force in the x. Make a triangle from where the front spring connects to the body down. Angle is θ and adjacent is l₄. Get the hypotnuse s_f the length of the front suspension to the bottom of the wheel now. Make a triangle from the connection of the back spring to the body down. The angle is θ and adjacent is l₅. Get the hypotnuse s_b the length of the back suspension to the bottom of the wheel now. Do s_o - s_f = x_fd difference in spring compression for front spring from level. Do x_fd + x_o = x_f total front spring compression. x_o is original spring compression at level. Do s_o - s_b = x_bd difference in spring compression for back spring from level. Do x_bd + x_o = x_b total back spring compression. Do x_f * k = f_f front spring force. k is spring constant. Do x_b * k = f_b back spring force. Make a triangle. Angle is θ and hypotnuse is f_f. Get adjacent is f_fy front spring force in the y direction and opposite is f_fx front spring force in the x. Make a triangle. Angle is θ and hypotnuse is f_b. Get adjacent f_by back spring force in the y and opposite f_bx back spring force in the x. Do ( f_fy * 2 ) × l₁ = τ_fy front spring force in the y and ( f_by * 2 ) × l₂ = τ_by back spring torque in the y and ( f_fx * 2 ) × l₄ = τ_fx front spring torque in the x and ( f_bx * 2 ) × l₅ = τ_bx back spring torque in the x.
Make a triangle from the pitch center to the center of gravity. Angle is θ and hypotnuse is h the height of the center of gravity above the pitch center at level. Get the opposite l₃ moment arm of gravity. Do f_g = mg force of gravity. Do f_g × l₃ = τ_g torque from gravity.
Do τ_fy - τ_by - τ_fx - τ_bx = τ_s spring torque. Do τ_s - τ_g = τ overall torque
I tried it out a few times and if everythings good here with the right set up it has a place where gravity is stronger than the springs decreasing and then the springs are stronger than gravity increasing and it can get stuck there. I think the spring force increases because of the front wheel moving farther under the body. The set up is a small distance between the wheels and a high center of gravity compared to it.
Can someone confirm this is correct/the correct process?

 

[at570]

Thanks to everyone who helped out, esp. haruspex