Saturday, March 19, 2011

Spring Rate vs Wheel Rate


Spring Rate vs Wheel Rate



Spring rate is the amount of force it takes to compress a spring 1-inch.   Wheel rate is the spring rate actually measured at the wheel.   Both are expressed in lb/in.



In order to calculate wheel rate, you need to know the spring rate, the motion ratio and the spring angle, as shown above.   Then you can solve the following equation.





Wheel Rate = ( ( MotionRatio^2) * SpringRate ) * sine(Spring Angle)

When a spring is mounted in its stock position on the front of a 1979-2004 Mustang (shown on the right side, above) the motion ratio is about 0.50, and the wheel rate is about 0.25 x the spring rate.   That is, a 600 lb/in spring produces a wheel rate of about 150 lb/in.

If coilover springs are installed (shown left side, above) the spring is moved close to the wheel, the motion ratio becomes about 0.95, and the wheel rate is about 0.90 x the spring rate.   A much lighter 167 lb/in spring produces the same 150 lb/in wheel rate.

The chart below provides motion ratios and wheel rate factors that can be used to calculate an approximate wheel rate for a spring installed on a 1979-2004 Mustang.   To obtain the wheel rate, multiply the spring rate by the factor that corresponds to the spring type and position on the car (stock or coilover, front or rear).


1979-2004 MustangFrontRear
Spring TypeStockCoiloverStockCoilover
Motion Ratio0.500.950.701.05
Wheel Rate Factor0.250.900.491.10


Note: These numbers are approximations and this discussion omits some variables in the interest of simplicity.


What you have to do is first measure your suspension and weigh your corners. Get D1 and D2, spring angle (this is the angle of the shock to the lower control arm) and the coner weights from individual scales. Then pick a spring, this will be a ballpark spring rate.

Motion ratio = D1/D2

(motion ratio^2 x ballpark spring rate) x sine(spring angle) = wheel rate

"You want your wheel rate to be about 1/2 the unsprung corner weight at the corner. The unsprung weight is the corner weight minus the wheel, tire, brake system, hub (upright), coilover lower mount and 1/2 the lower control arm.
First: it should be clear at this point that there is a boatload of research that goes into suspension design. Use other people's efforts who have gone before you and buy at the very least "Competitiong Car Suspension" by Allan Staniforth and "Engineering to Win" by Carroll Smith. If you really want to know what's going on and you want to do all the math then buy "Race Car Vehicle Dynamics" by Milliken and Milliken, it's published by the SAE.
Secondly: what might not be so obvious is your new $300 camber plates just allowed you to change your spring angle, which changes your motion ratio and effectively makes your springs "softer" for a given spring rate. This is another reason you can't take someone elses spring rates and have them work directly for you.
Thirdly: That stiffer roll bar you just installed, yup, it changes your spring rate too.
Your spring rate is the amount of distance the spring compresses at a given weight. If you have a spring that compresses 1" with a weight of 250 lbs then it's a 250lbs/inch spring. If installed at the center of the wheel at 90 degree (impossible but makes the math easy) then the suspension spring rate is 250lbs/inch. If you add an anti roll bar then in roll it exerts a force from one corner to the other which increases the effective weight that the suspension can resist per inch. 
Sorry if this is odd sounding I'm on a phone and can't read what I wrote.
Think of it this way. If you have a bar, and it is one half of an anti roll bar, so it's a big L and it's connected to the suspension of one side like an anti roll bar but rather than held in a bushing on the chassis it's welded to the chassis then it will also resist suspension movement, It will act sort of like a big butterfly clip on it's side. It's just a different way to build a spring. In the case of the anti roll bar however it doesn't resist suspension movement if the other wheel is moving in the exact same way. So if you go over a curb with one wheel then the other wheel being connected resists the curb wheel's action. However if you go over a speed bump the anti roll bar doesn't really resist movement at all because both wheels are moving together.
--This is one reason you see big anti roll bars on luxury cars, you can get away with much lighter springs and still deal with road irregularities if you have a beefy anti roll bar. This makes the ride softer when you are just lumbering along on smooth roads or on the freeway.
--This is also why you see such small anti roll bars on F1 cars. They run such heavy springs that chassis flex and pneumatic tire deformation happens before the spring compresses, so anti roll bars don't really add much."  ~ milotrain


Source: http://www.miracerros.com/mustang/t_wheel_rate.htm

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