Mathematics for Car Suspension System

Hi, I was wondering what mathematics I would need to know to get started with a car suspension system (Like the ones from jailbreak). I already saw a few posts about this but they all had calculus and deriving equations which I don’t understand fully. The scripts on the threads automated springs without actually needing spring constraints which is something I would like to do. Is there any way I can made a suspension system without high level mathematics or any links that could help explain it? Thanks.


Could you include the articles you’ve tried in your post? To get a better understanding of where you sit and what we should be avoiding in addressing a helpful solution to your problem?
The Jailbreak cars use the same suspension method as the freemodel jeep in the toolbox. It’s been discussed many times and uses a force inversely proportional to the distance of the wheel well to the ground.
There’s unique caveats too, like keeping the thrusters inside the hitbox / collision boundary of the full vehicle to avoid them clipping through terrain (as they are often not colliders) and applying the force to drive the vehicle into the ground.
To give a rough answer I would say it’s not too mathematically intensive, you just have to decide how your going to apply that force given the variable distance, which I think can be done with just an inverse square function.

Here are a few articles I looked at:

And I also took a look at the free model jeep as one of the threads mentioned it could help, but I couldn’t make much sense of any of it. Also, in the first post OseDay had commented with a formula which used hookes law in a second order problem (which I don’t really understand that well). Also I don’t really understand what you meant when you said use a inverse square function at the end of your reply and how I could apply it to my solution. This is my first time really dealing with cars so you’ll have to bear with me if I don’t understand some of the terms your using.

It’s Oseday, not OseDay.

Here’s a script for you to implement it:

local Engine = ... --main part of the car

local WheelDistanceFromGround = 1.75
local WheelRayDistance = 3.5
local Rigidity = 0.35

local CarMass = ...
local CarCenterofMass = ...  --in object space of the engine

Engine.TorqueAttachment.Position = CarCenterofMass

local Wheels = {} 
do --Create wheels
	local WheelCount = 0
	for _,Wheel in pairs(Car.Wheels:GetChildren()) do
		if Wheel:IsA"Part" then
	for _,Wheel in pairs(Car.Wheels:GetChildren()) do
		if Wheel:IsA"Part" then
			Wheels[#Wheels + 1] = {
				CFrame = Engine.CFrame:inverse() * Wheel.CFrame,
				Stiffness = 1/WheelCount,
				Rigidity = Rigidity,
				dx = 0,
				d2x = 0,

	local EngineCF = Engine.CFrame
	local EnginePos = EngineCF.Position
	local CarCOM = EngineCF * CarCenterofMass
	local ForceTotal =
	local TorqueTotal =
	--do suspension per wheel
	for i,Wheel in pairs(Wheels) do
		local WheelCF = EngineCF * Wheel.CFrame
		local WheelPos = WheelCF.Position
		local raycastResult = workspace:Raycast(WheelPos, WheelCF.UpVector * -WheelRayDistance, rayParams)
		if raycastResult then
			local x = (raycastResult.Position - WheelPos).magnitude
			x = (WheelRayDistance - x)/(WheelRayDistance - WheelDistanceFromGround)
			local F = x*Wheel.Stiffness + Wheel.Rigidity*(x-Wheel.dx) + Wheel.Rigidity/2*(x-Wheel.d2x)
			F *= workspace.Gravity * CarMass
			F *= WheelCF.UpVector
			Wheel.d2x = Wheel.dx --store the past values
	 		Wheel.dx = x
			local NormalF = F:Dot(raycastResult.Normal)*raycastResult.Normal - F
			ForceTotal += F + NormalF
			TorqueTotal += F:Cross(CarCOM - WheelPos) + NormalF:Cross(CarCOM - raycastResult.Position)

	Engine.Force.Force = ForceTotal --in world space
	Engine.Torque.Torque = TorqueTotal --in world space

Not trying to be rude or anything but if you had read my initial post, I asked if it was possible to make a suspension system without any high level mathematics like calculus. What I’m trying to do is understand what formulas I’m using in my scripts, not just copy them down. (also sorry for mistyping your name earlier)

Then use constraints. I use constraints and they work out very well! Remember that constraints exist for a reason :wink:

I’m working on realistically simulating cars at the moment :slight_smile:

Oh, sorry for the late response (haven’t been able to access my PC for other reasons). Right now I’m trying to make it without anything that already does the suspension for me (so that I can use scripts). Do the constraints your talking about need scripting for them to work?

Not the constraints themselves, but for the vehicle to move, naturally yes.

A suspension is a damped spring, you cannot create a suspension without damped springs therefore you need to know the physics and math of a damped spring to create a suspension which includes the “high level mathematics”. Obviously those are the mathematics you need to know which were said and explained in the article.

It’s literally just: F = ma = -kx -cv

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