# Car Suspension Force Equations

So I have found this equation:

$F_\mathrm{suspension} = Kx + F_\mathrm{damper}V_\mathrm{contact}$

Where:

• $K$ = spring stiffness
• $x$ = the contact depth of spring(also known as spring compression)
• $F_\mathrm{damper}$ = damper strength
• $V_\mathrm{contact}$ = the speed at which the spring is compressing/decompressing

My questions are:

• Is this accurate equation for calculating car suspension force?
• What are the different factors in equations for different types of suspension setups found in multiple cars? This is meant that trucks and old cars use leaf springs while new cars mostly has coil springs, some cars has multiple springs or dampers etc.
• I have answered the first part of your question but I would suggest that you ask the second part (coil vs leaf springs) as a separate question. It is interesting but not directly related to the rest and would benefit from a separate answer. – Chris Johns Mar 4 '16 at 21:27

This equation will give you the static force for any given displacement but on its own it may not tell you that much as suspension systems are by their nature dynamic.

For starters this adds an additional inertia term to the RHS of the equation F = ma where m is the unsprung mass (wheel, hub etc) and a is the acceleration.

Also any serious analysis of suspension behaviour needs to consider frequency response.

To give you an overview of the problem vehicle suspension has two distinct but interrelated functions the first is to isolate vibration in the wheels from bumps and irregularities in the road surface from the chassis of the vehicle for comfort and to stop it from shaking itself to bits. This aspect is broadly covered by the above equation.

The second function is handling ie to control the weight distribution of the vehicle and the orientation of the tyre contact patch to the road as the vehicle brakes, accelerated and turns. Here the detailed geometry of the suspension and transmission of forces between all four wheels becomes very important.

In general, coil, leaf and torsion springs can be modelled by this equation. The choice of spring type for a particular vehicle depends on a wide variety of factors. In particular left springs may be non-linear and/or self damping.

• At the second part do you mean weight transfer? If I apply force at wheel positions which equals current load on the wheel will it work like you expect in the end of your answer? – Adrians Netlis Mar 4 '16 at 22:09
• Broadly yes, the equation is perfectly valid in itself to model the behaviour of a spring/damper unit under known forces, The caveat is that knowing what those forces are is the tricky bit. – Chris Johns Mar 4 '16 at 22:13
• OK! Later I will need to implement what's known as aerodynamical downforce, will need to get equations for that aswell, right? Oh, and as this is for a game, this could be a good approximation, right? However, could you edit the question and add some short explanation and maybe additional equation(similar to mine one) for few other suspension types(as much as you know)? – Adrians Netlis Mar 5 '16 at 7:47