OK. I put the car on jackstands and measured the motion ratios. Astonishing results are in!

How I did it
I put the car on jack stands. Remove wheels. Use a scissor jack to jack the lower ball-joint bolt to stock ride-height. Measure distance between certain points on upper and lower spring perch. Measure distance from a certain point on the hub to a marked point on the fender lip (chosen such that the point I chose on the hub travels toward this point on suspension compression). Since the point chosen on the hub for measurement has not too much horizontal offset from the lower ball-joint, any camber change from the camber curve is negligble. I then jack up the suspension at various points and re-measure upper-to-lower spring perch distance and fender-to-hub distance to double check my numbers. I keep jacking and measuring until the scissor jack race the whole front (or rear) off the jack stands.

The results
The front motion ratio is EXACTLY as I measured from SpitfireS' drawing -- 0.70!
The rear motion ratio is 0.667 which is lower than I estimated. I double-checked everything and I'm pretty sure these numbers are correct.

F = 0.70 +/-0.01
R = 0.67 +/-0.01

I did a closer look at the suspension and noticed that the lower mounting point for the shock absorber is not as far out on the lower arm (in terms of percentage) than the front. Also, the front shocks don't lean much more than the rears. Those explain why the rear has lower motion ratio than the front.

 

Thanks for doing that!

Since we're after wheel rates, though, wouldn't it also be valuable to try to measure those directly? Just disconnect swaybars and put a scale between the jack and suspension (maybe put the wheel and tire back on!). For stock springs, a bathroom scale might suffice since the wheel rates are pretty low (only measure the first 2 or 3 inches of travel).

Then compare to the quoted stock spring rates (220/290) and see if there's any correlation.

 

The rule of thumb does not suggest particular spring rates that are ideal. Instead, it suggests suspension frequency for certain application. This frequency is mostly determined by the ratio of wheel rate to corner weight. For a street/autox/track car, high 1.X to low 2.X Hz are good start. For more performance-oriented streetable car, start at low 2-ish Hz. High 2-ish becomes bone-jarring and 3Hz is a bit too much for the streets IMO. Sways do affect roll-stiffness and in fact, they contribute more than springs in most if not all cases. The fact is it's the wheel rate with respect to corner weight that determines the natural frequency of a suspension which should be the starting point when setting up suspension. Sways are then used to fine-tune roll-stiffness. Shocks are then used to fine-tune damping for the chosen spring rates. I've ridden in many FWD cars that they run so much rear spring rates for the light rearend that it basically keeps bouncing off the pavement. That's not the way to set up suspension.

Take some easy number to start with. Say for the S with 2800lb with driver and 50/50 weight distribution. Corner weight is ~700lb. For low 2-ish suspension frequency, that works out to about 260lb wheel rate. Since you don't want exactly the same frequency front to back to avoid "resonance", you want to lower the wheel rate for one end by at least 15%. It's always favorite to lower the wheel rate on the drive axle for better drive traction. So with our RWD nature, you want 15% less wheel rate for the rear, another rule of thumb. With my measured motion ratio, that works out to 530lb/in front and 490lb/in rear. Don't these numbers sound familiar to us?

 

I didn't get to do it. I think someone will kill me if I use the fancy glass-platform digital scale, but it sounds like a good idea if someone would like to do it.

 

This is an awesome thread! Thanks for you valuable input Race Miata. Makes me want to do some math to decide which springs before I reinstall the Motons . Or maybe I should let you decide for me. And John, don't tell me that this doesn't make you want to keep those JRZ's so you can tune to your delight!

 

Just remember a lot of other things go into picking spring rates. AKA most formula fords these days run wheel rates about equal to corner weights. DSR (which has some downforce) is about 1.75x the corner weight!

Bill

 

I'm glad my inputs can be useful. Keep in mind my illustration above with numbers is to show the correlation between suspension frequency and spring rates and provide some good base numbers to start with for a streetable RWD 50/50 weight-distributed track car without downforce, aiming at equal tire-size front and back (which I've always been thinking to do on the S if I'm to start working on the suspension from ground up ultimately). The effect of downforce will require stiffer springs accordingly. The choice of sways/shocks/tire-stagger will need more testing/tuning and repeat, and perhaps spring rates also need to be revised in the process.

Agree with blackey that FF runs much higher suspension frequency even without downforce. That's why I mentioned the low 2-ish frequency is applicable to streetable cars, regardless of gross weight of the car. Suspension frequency is like a magic number that tells you how stiff the ride is for a street car. I recall reading now and then on the Internet and suspension tuning books with charts of suspension frequency range for different applications (e.g., street car, streetable car, closed-wheel track car, open-wheel track car, car with downforce, etc.).

 

Chris, could you give the formula you are using to define "suspension frequency"?

 

I kind of cut corner when I came up with my suspension frequency numbers. I used my miata and BMW data (try to recall as much as I could) to estimate the case for the S so my numbers above could be off.

Let me try dig out the actual formula. The base idea is that suspension frequency is proportional to square root of wheel-rate-to-corner-weight ratio (IIRC).

EDIT: Found the equation. It's good that you asked, Mike.

SF = 187.8 x SQRT(WR/SW)

where

SF = suspension frequency in CPM (divide by 60 to get Hz)
WR = wheel weight (effective spring rate at the wheel)
SW = sprung weight (corner weight minus roughly half of the suspension weight for that corner, there's a general rule of thumb for the number to use for street car's suspension weight, I think something like 15% of the weight of the car)

With some easy numbers to do calculations, say a 2800lb lightened car with the driver and 50/50 weight distribution, corner weight is 700lb. Subtracting 7.5% unsprung weight, that's 647.5 SW. With WR of 260lb/in, SF = 119 CPM or 1.98 Hz.

EDIT: Oops, forgot 187.8 in the equation.

 

OK, I would appreciate it. I'm trying to figure out what the time dependence is at all (since frequency is measured in Hz which is time^-1). Does it assume some velocity of the car (or more directly, some time duration for the application of the force on the suspension)? Or does the time component come from the damping?