Spring Deflection Calculator

# SPRING DEFLECTION

The following calculations resulted from a conversation I had one night with a friend over the phone.  I was talking about calculating the applied weight of my winch on the front bumper as applied to the front and rear springs and how much it actually changed the level of the vehicle.  I figured it would be fairly easy to determine based upon a seesaw effect on the springs.  The basic calculations were worked out by Chet Szymecki so he gets the original credit.  The below is his discussion with a few edits for fine tuning.

We will use the example of installing a winch on the front of the Jeep:
Note that even thought the winch is pulling down on the front it is also pulling up on the rear too.

For the sake of this argument we can assume:

* you have a 94" wheelbase (WB)
* the winch weighs 100lbs (XW)
* the center of mass for that winch is 24" forward of the front axle (XCOM)
* the front springs have a rate of 160lbs/in (FSR)
* the rear springs have a rate of 175lbs/in (RSR)
* front spring deflection in inches (FSD)
* rear spring deflection in inches (RSD)

OK...so;

FSD=(((-XW*XCOM)/WB)+(-XW))/(2*FSR)

FSD=(((-100lbs*24in)/94in)+(-100lbs))/(2*160lbsin)
FSD=(((-2,400lbsin)/94in)+(-100lbs))/(320lbsin)
FSD=((-25.5lbs)+(-100lbs))/320lbsin
FSD=-125.5lbs/320lbsin
FSD=-.39in

So your front bumper will compress front the springs .39 inches.

But how much will that same front bumper extend the rear springs?

RSD=((XW*XCOM)/WB)/(2*RSD)

RSD=((100lbs*24in)/94in)/(2*175lbsin)
RSD=(2,400lbsin/94in)/(350lbsin)
RSD=25.5lbs/350lbsin
RSD=.07in

edit - note that the compression (-125.5lbs) and extension (25.5lbs) leave you with only the additional force applied to the system by the new winch (100lbs). So -125.5lbs+25.5lbs=100lbs

*This same mathematical model can be used to calculate the change in compression/extension of springs due to the removal of the rear hardtop. What we need to know is the center of mass for the rear hardtop. If it is the  axles - then you would insert this number as a (-) for distance to the closest axle.

*When we look at the numbers above please keep in mind that these numbers represent compression or extension right at the spring - if you wanted to carry that number out to the front or rear bumper you can use the same basic mathematical model as above.

A simple way to figure this is tangent of spring deflection divided by 1/2 wheel base times distance from bumper to spring + 1/2 wheel base

Or TANH((FSD/(WB/2)))*(FBD+(WB/2))

FBD = Front Bumper Distance
RBD = Rear Bumper Distance

All you would need to do is swap out FSD and FBD with RSD and RBD to get the rear bumper.  Now this does not take in account the shift in Center of Gravity (COG).  Eventually I will work on fine tuning this a little bit more.  This is just a ballpark calculator for now.

CALCULATORS BASED ON THE ABOVE