The key is to match the front and rear frequencies accounting for the travel time between wheels (tuning for a particular speed), with the front lower than the rear in order to minimize pitching motion. The Natural Frequency of the suspension should fall in the range of 1 to 2 cycles / sec. Lower limit is for soft sedans and upper limit for racing cars. I'm not sure what's recommended for a C3.

To calculate the Natural frequency of the existing front and rear wheels:
Disconnect the shock. Measure the ride height. Jack the car up until the load is completely off the springs. Measure the ride height. The difference between these two values is the static deflection (in inches).

Natural Frequency = 3.133 / (sqrt(static deflection)) (Eqn 1)

Wheel rate is defined as the amount of force required at the wheel to move the suspension one inch vertically. Sprung weight is the weight sitting on the springs.

Natural Frequency = 3.133 * Sqrt(Wheel Rate / Sprung weight per wheel) (Eqn 2)

If you calculate the Natl Freq using Eqn 1 and can approximate the weight / wheel then you can back out the wheel rate from the Eqn 2.

To go between Wheel Rate and spring stiffness you need to account for the mechanical advantage (or leverage). Consider an A arm with the wheel at the end and the spring exactly in the middle. If the wheel moves 2 inches, the spring only moves 1 inch. Also the FORCE on the spring changes due to the change in height, but also that force is transmitted to the wheel via the mechanical advantage, another reduction in 2, for a total of squaring the mechanical advantage.

Wheel Rate = (Spring Stiffness) / [(Mech. Adv)*(Mech. Adv)] (Eqn 3)

Mechanical Advantage is pure geometry. If you know either the Spring stiffness or the Mech Adv then you can calculate the other one. Later on if you're just changing springs and not geometry use Eqn 3 to get the new wheel rate. I'm not sure how to get mechanical advantage for the rear leaf springs, but I think for the spring's acting distance it's the center of the differential to the outer end of the leaf. And for the wheel distance it's from the center of the differential to the vertical line through the tire contact patch. The measurements are all made horizontally between the appropriate vertical places.

I think for the rear's the Mech. advantage should be a number like 2, whereas for the front it might be something like 1.75. I haven't measured mine yet.

To look at the Pitching motion you need to consider ONE speed and the wheelbase. Basically you calculate the the time for one full cycle of motion of the front and one cycle of the rear. You want the front period GREATER than the rear period by the time it takes your car to travel it's wheelbase length at the tuned Car Speed. Or conversely you want the rear period shorter than the front by the wheelbase travel time.

Time to travel wheelbase = .0568 * Wheelbase / (Car Speed) (Eqn 4)
Where Time is in seconds, speed is in MPH and wheelbase in inches.

Period Rear = period Front - Time to travel Wheelbase (Eqn 5)

Frequency = 1/Period and Period = 1/Frequency (Eqn 6)

OK, with this one can calulate period & frequencies considering the geometry of the car for the existing springs. How do you determine which springs to change to? Depends of course on what you're trying to do. The big variable here is the Natural Frequency (low=soft, high=stiff). Say you want to stiffen the car and have new front springs, but you're trying to decide which rear ones to go for:

1. Calculate what you have for the period in the front (Eqns 1 - 3 with front numbers).
2. Add the time to travel wheelbase for the speed you're tuning for (track lap speed or cruising speed whatever's appropriate) and get the Rear Period (Eqn 5)
3. Get rear frequency (Eqn 6)
4. Back out Rear Spring stiffnes (Eqn 1-3 with rear numbers)

I wonder what the numbers are for my car.... Anyone know theirs? We've already got some spring stiffness numbers posted in the Vettebrakes leaf spring post... Guess it's time for some applied research for me.

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~Juliet ...overlooking Mill Creek on the Chesapeake Bay...
Loaded Bridgehampton Blue on Blue '70 350/300Hp TH400 with a White Ragtop

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geeeyejo
Red 1974 4 spd l48 coupe
Rebuilt #'s matching drivetrain
Staten Island NY
Save The Wave!
Visit: [URL=http://geeeyejo.homepage.com/index.html
[img]http://geeeyejo.homepage.com/my74vette.jpg[/img]

I always thought it was simply The wheels on the bus go 'round and 'round

Good luck with the research project!

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Bill
Eastpointe, MI
1970 L46 Cortez Silver Convertible
www.ameritech.net/users/whardy/billscar.htm

The sprung weight per wheel is the weight distribution of the entire car. If you sat each of the tires of the car on 4 Jumbo bathroom scales, the sprung weight is what each would read. Yes, the tire & wheel weight will enter into the sprung weight, but it's a secondary effect.

The equations posted above from Puhn's book consider simple spring geometry and linear spring constants. In reality the natural frequency of the wheel is affected by the sprung to unsprung weight ratio. The simplified equations posted above assume in effect zero wheel weight and are neglecting any inertial effects of the wheel on the spring system. In reality this will have a real effect on the natural frequency, even if a minor effect on the unsprung weight. The bigger impact will be on the overall vehicle dynamics and the system damping ratios. I don't think that I'm going to get into vehicle dynamics here, it's a world unto it's own... A good reference book for this stuff is Competition Car Suspension by Staniforth. ~Juliet

Its so much easier to put a car on a $1 million kinematic and compliance machine and have the numbers spit out for you Unfortunately, I don't yet have one in my garage.

To corect one thing you said, Juliet, the sprung weight is notthe weight a (large) bathroom scale would read if placed under each wheel. That is the corner weight. The SPRUNG weight is that MINUS the weight that's unsprung. What's unsprung? Well, that is the wheel, tire, brake rotor, caliper assembly, etc... But what about the conrtol arms, you say? Well, in that case, 1/2 of the weight of the control arm is sprung and 1/2 is unsprung. Unfortunately, adding up all of those weights isn't the easiest thing to do if you're browsing through a catalog and you want to buy new springs.

The linkage ratio, or the inverse of mechanical advantage, is somewhere in the range of 60-80% I believe. That means that the spring is placed 60-80% of the way out from the lower control arm bushings (for the front). So in terms of mechanicaladvantage, this would be in the general range Juliet specified.

On Natural Frequency, the equation for the nat. freq. is correct relative to the static deflection of the spring. however, you cannot measure the static deflection by jacking up your car. Springs are pre-loaded, so there is always load on them. That's why you need to use a spring compressor to remove them. It sure would be nice if they were completely unloaded. Safer too. But that's not possible considering that its necessary to have a spring that doesn't fall out of place when the suspension drops, and the static deflections are so high that the suspension travel would have to be HUGE to accomplish that.

To clarify the different rates front to rear and the piocth balancing stuff, think of it this way. if you hit a bump with the front and then with the rear a short time later, the front will be coming back down when the rear is starting to go up. So the ends are going in opposite directions. This is rather unpleasant. To balance that out, you want to make the rear stiffer, so it bounces faster. Done correctly, it will essentially catch up with the front susspension, and the car will bounce up and down and not pitch fore and aft. A general rule of thumb, developed by Maurice Olley-the father of modern vehicle dynamics, is that the ride frequency for the rear of the car should be 10-20% higher than the front suspension.

Will: The frequency of a first order linear system is freq= sqrt(k/m) where k is the spring rate and m is the mass. So yes, a lower mass is effectively the same as a stiffer spring.

BUT!

The numbers that you mentioned for the wheel and tire weights are UNSPRUNG. "Yeah, so?" The unsprung mass does not figure into the ride rates and ride frequencies. It does factor into the wheelhop frequencies AND lower unsprung mass is better for ride.

geeeyego: It only gets more fun after Calculus!!

Thanks for the great thread, Juliet!

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Dave
White '69 Stingray Coupe
Brighton, MI
AIM: Sxty9Vtte
"Indecision may or may not be my problem"

e^(jwt) * cos (wt + bt)

which is a decreasing sinusoidal wave within the limits of the E function..

where w=angular freq
t= time
bt=phase angle

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76 daily driver
email: dreksler@ufl.edu
web: http://grove.ufl.edu/~dreksler

As far as determining the spring rate, the 'bathroom scale' method would work. The tire also has a spring rate that needs to be taken into consideration, bt that spring rate is much stiffer and can probably be neglected.

You hit the nail on the head with the comment about depending on how in-depth you want to get. One of these days I need to find or make a suspension model for a C3. if and when I do, I'll be sure to let everyone know what the basics are.

The rear leaf springs may or may not be preloaded. I have a VB glass springon mine and the preload on it determines the rear ride height. I'm not sure about the stock spring.

For those who are interested in reading more about the topic, I can recommend some decent Vehicle Dynamics books:

1)"Fundamentals of Vehicle Dynamics" by T. Gillespie. Tom is a professor of Mechanical Engineering at University of Michigan. His book is used at several universities in vehicle dynamics classes.

2) "Theory of Ground Vehicles" by Wong. Another book that's frequently used as a textbook. This book is used in a Graduate-level course at UofM. It contains more in depth theory than Gillespie's book.

3) "Race Car Vehicle Dynamics" by Milliken and Milliken. Don't let the title fool you. Aside from the race-car specific aerodynamics, most all of the info applies equally to any car. (I have an extra copy I'd be willing to sell if anyone is interested)

The book that Juliet mentioned and others like it, geared toward the weekend racer, are also good sources.

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Dave
White '69 Stingray Coupe
Brighton, MI
AIM: Sxty9Vtte
"Indecision may or may not be my problem"