mep wrote:... Can somebody put this into a physical formel to calculate the amount the spring is compressed.
I tried this once but failed immediately.
I can give you the simplified form civil engineers use to calculate the IRI (International Roughness Index) wich measures how many millimeters you move up and down while you move one millimeter along a road: it's the old and well known "Quarter Car Model". I don't have at hand the equations (I made once a program to solve the integral you have to make, but I was young and did not have children asking me to play outside, like today
). Perhaps someone can give you his own program or you can google for it. There is also a "Half Car Model" we discussed at some thread here, more complicated, which is more accurate if you want to reproduce the pitch sensitivity of the aerodynamic components of the car.
This is the model:
The car chassis is the "sprung mass" ms.
The wheel assembly is the "unsprung mass" mus.
The spring is ks and the damper is bs, placed between the car body and the wheel assembly
The spring kt is the tyre.
The variables xs, xus, and r are the car body travel, the wheel travel, and the road disturbance or bump.
The force fs, kN, applied between the sprung and unsprung masses, is controlled by feedback and represents the active component of the suspension system. If your car has not active suspension, omit it.
In that condition (no active suspension) if you define x1:=Xs', x2 = d(Xs), x3:=Xus and x4:=d(Xus), were d() means the derivative, then this are the equations that describe the behaviour of the quarter car dynamics (the dot on top of variables means the derivative):
Typical values for IRI calculation are:
ms = 290 kg
mus = 59 kg
bs = 1000 N/m/s
ks = 16182 N/m
kt = 190000 N/m
Hope this helps. If I have time (sorry, I have to play football with my 8 years old kid AND he is tugging my arm while I write this!
) I'll check my old class notes to look for the solution to the equations.
What you're looking for is the difference between X1 and X3 (or Xs and Xus) wich shall give you the spring compression, BTW. The solution I have somewhere buried gives you only X1, that is, how much the chassis moves up and down.
You have to integrate to solve the differential equations. I'm sure someone has to have the equation solved. Perhaps Reca? Or you can use Mathematica, if you have it.