# Measuring the Motion Ratio

Motion Ratio | Spring and Shock Rate Spreadsheet

Here's how to measure the motion ratio at the tire contact patch. This is what the tire actually sees. As Doug says, "with any other method there are too many possibilities for error."

#### Taking the Measurements

1. With the car sitting on the ground, determine the position of the suspension at ride height. Our wheels don't have hub covers, so I measured from the top of the fender lip to the center of the axle cap.
2. Jack the car up and put it on jackstands.
3. Loosen the spring collar on the spring/shock unit and spin the collar away from the spring far enough so the suspension can move freely. You'll need at least 1" travel above ride height.
4. Put the wheel back on and put a jack under it.
5. Jack the wheel/suspension up until it is at ride height.
6. Measuring at the center of the contact patch, lower the wheel one inch.
7. Measure the distance between the spring perches, and write this down.
8. Again measuring at the center of the contact patch, raise the wheel two inches. It should now be 1 inch above ride height. The spring should still not be contacting the upper spring perch. If it is, unwind the collar some more and start again at step 5.
9. Measure the distance between the spring perches, and write this down.

Be as accurate as you can about these measurements, because small errors get multiplied and can have a large effect.

#### Making the Calculations

Now you can calculate the installation ratio:

`Installation ratio = (Db - Da) / 2"`

Where

```Db = distance between spring perches at 1" below ride height
Da = distance between spring perches at 1" above ride height```

The 2" on the right side of the equation is the distance we moved the wheel between our two spring perch measurements.

Now calculate the motion ratio, which is simply the square of the installation ratio:

`Motion ratio = Installation ratio x Installation ratio`

And finally we can calculate the wheel rate for a given spring:

`Wheel rate = Spring rate x Motion ratio`

Here's an example:

```Db = 10.125"
Da = 9.0"
Spring rate = 450 lb.

Installation ratio = 10.125" - 9.0" / 2"
Installation ratio = 1.125" / 2"
Installation ratio = .5625
Motion ratio = .5625^2 = .3164
Wheel rate = 450 lb. x .3164
Wheel rate = 142 lb.```

#### What?? Why Do We Square It?

Yes, the motion ratio is the square of the installation ratio! This is because the spring has a disadvantage in two ways:

1. It's operating in the middle of the lever, and the wheel is operating at the end, so the spring has a mechanical disadvantage.
2. It only moves a fraction of what the wheel moves.

I know, this isn't really intuitive at first. I didn't believe it either until I thought about it.

In fact, when I actually made the measurements, I didn't believe those either. It just didn't seem possible that we should need to use springs as stiff as the resulting calculations called for. We measured our car and another car several times until we were convinced that our measurements were correct.

#### Independent Opinion

Bruce Allen is a COMSCC instructor. He is also COMSCC's fastest driver. He gets FTD at almost every COMSCC event in his old Crossle FF.

Bruce is also winning races in SCCA Club Ford with the same car. If you know about SCCA and Formula Ford, you know what that means! Bruce is very quick, and he knows what he's doing.

Bruce drove our car and his analysis was that the front bar was too stiff and the front springs (800 lb) were too soft, allowing the front suspension to intermittently bottom. He felt this caused inconsistent gross understeer.

Bruce wasn't aware of any of the controversy over the FFR's front motion ratio, so his analysis was based solely on his own reactions to the way the car handled.

#### References

If you're interested, here are some books that may help you understand these concepts and encourage you to do your own measurements and calculations:

Race Car Vehicle Dynamics, William F. and Douglas L. Milliken. This is the "bible" of race car engineering. It's expensive, and loaded with equations, but it's worth the money and the effort it takes to understand it. Chapter 16 deals with installation ratio and calculating spring rates from desired chassis frequencies (which are related to wheel rates).

Note: Doug Milliken tells me that Amazon and Barnes and Noble don't stock his book, so it can take a long time to get it if you order from them. He recommends ordering directly from the Milliken Research Associates site or from the SAE. He also notes that many other good racing books are available from the SAE site.

Going Faster, Carl Lopez. The Skip Barber Racing School textbook. Carl does a brilliant job of explaining just about every aspect of driving a race car, including some fundamentals of car setup. See page 211 for Carl's excellent explanation of how suspension geometry and spring rate determine wheel rate.

How to Make Your Car Handle, Fred Puhn. See pages 138 - 139 for the discussion of spring rate vs. wheel rate, and how to determine the relationship for a given suspension. This and Going Faster are the only references I've found which explicitly recommend you make this determination by actually measuring the wheel movement and the resulting spring movement (in a manner similar to what I've described above) although Carroll Smith implies this in Tune to Win, as do the Millikens in Race Car Vehicle Dynamics.

Tune to Win, Carroll Smith. See page 66 for discussion of spring rates, wheel rates, and motion ratio.

Mustang Performance Handbook, William R. Mathis. See page 84 for suggested spring rates for the Mustang 5.0.

Advanced Race Car Suspension Development, Steve Smith, from Steve Smith Autosports. Excellent distillation of the concepts into brief summaries and easy to use equations. Beware, however, that Smith uses the less reliable measure-the-control arm technique of determining motion ratio.

The Racer's Math Handbook, Bob Emmons. Also from Steve Smith Autosports, and also uses the measure-the-control arm technique of determining motion ratio. Good discussion of racing-related math, though.

Other good booksg:

Drive to Win, Engineer to Win, and Prepare to Win, Carroll Smith.

Race Car Engineering and Mechanics, Paul Van Valkenburgh