Calculating tire rate without using tire data.

[moksharmywebber]

Dear fellow FSAEiates we made a car last year using passenger car tires.Since no tire data is available for the same we played with springs to get the desired ride height.But now since we already have a car ready we decided to calculate tire rates for our tires using reverse engineering. But there seems to be some problem with the calculations. We followed the following steps:
1.Calculate deflection of springs at static condition (say x). We have spring rate and IR for our system.Hence,
(sprung mass)*9.81/IR = Kspring*x (Using : force= Kx)
2.Calculate natural frequency using freq=188/root(x).
3.Using above natural frequency and corner weight calculate ride rate by freq =(1/2pi)*sq.root(Kride/sprung mass)
4.Calculate wheel rate using Kwheel=Kspring*(IR)^2
5.Calculate tire rate using ride and wheel rate as Ktire= (Kride*Kwheel/(Kwheel-Kride))

The problem which we encounter is, we are getting Kwheel<Kride ...due to which we get a negative value of Ktire.
Let me post some values supporting our calculations:
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Based on the car which is ready, we have following values:
Sprung mass = 94 kg
IR = 0.6
Kspring = 60N/mm

Now, following above steps we get values as
1.x=25.6mm
2.freq = 3Hz
3.Kride = 33.398N/mm
4.Kwheel = 21.6N/mm
5.Now since Kwheel<Kride ...BINGO! tire rate comes out to be a negative value !!

Can anybody please suggest us were exactly are we going wrong ?

P.S.WISHING EVERYBODY A HAPPY AND PROSPEROUS NEW YEAR!

[monoposto]

First off the F=Kx equation is a linear approximation, there is almost nothing linear about tires. Second, your tire spring rate seems low. Even for passenger tires i'm guessing... But the only thing I have to compare your tire spring rate to is 13 inch racing tires, so take what I said with a grain of salt.

I'm sure more knowledgeable people will chime in at some point but good luck!

[Zac]

A realistic vertical springrate for a passenger tire (at passenger pressures...) should be ~300-350 N/mm depending on size, construction, pressure, etc.

But I don't know why you're screwing around with these calculations (your method is lacking btw). If you want to know the springrate of something, measure it directly. It really isn't hard to load up a tire and measure the deflection.

[exFSAE]

The issue here is that the tire should have no influence on your spring deflection (assuming you are setting the car up to some fixed nose weight, cross weight, right side weight).

If your RF scale weight for example is 180 lbf, it doesn't matter if your tire rate is 100 lbf/in, 1000 lbf/in, or 10000 lbf/in - the spring deflection will be the same in all cases. Regardless of what the tire is doing, the spring has to support the hub load just the same.

Effectively you just aren't measuring enough information here, and you are following some sort of circular path to try to get to the tire rate.

[Adambomb]

Ditto to exFSAE. To put it another way, ride rate has no influence on tire rate, so Eq. 5 can't be right. Draw an FBD. Your ride spring will be connected to the ground in series with the tire spring. Directly measuring Ktire would not be terribly difficult to measure (roughly), although I really hope your car isn't heavy enough to get a good measurement.

There are two fundamental problems with trying to find Ktire from a ride measurement. First, as exFSAE mentioned, you just plain don't have information on what Ktire is doing to ride displacement. Neglecting that, even some sort of 4th-order voodoo approximation won't really tell you anything for a couple reasons: aside from being subject to many many sources of error, it is also (as you have mentioned) a good deal stiffer than Kride, so most of the displacement will occur in Kride, and the displacement from Ktire will probably be on the same order of magnitude as measurement noise (if not worse).

I presume you're using some type of standard bolt pattern? One method would be to use a known weight...say a heavy corner of a passenger car with the same bolt pattern as your car. Use race scales or something of at least moderate accuracy to get the corner weight. Set the tire to the pressure you're running on the car (should be a good deal less than what is run in its original application I would imagine).

Jack the car up so the tire is barely in contact with the ground, then measure the sidewall height, height to the hub, or other suitable reference point on the wheel. Then lower the car so the full weight is on the tire, then take the same measurement, and find the difference in measurements. Now you have a load and displacement, and I would imagine that while not completely precise or accurate, would be a "better than nothing" measurement that doesn't cost much time or money.

[wil oberlies]

Just bear in mind that camber will have an effect on your vertical tire rate as well, might be interesting to vary camber angle and see for yourself...I believe that recommended camber angles and inflation pressures are used to this effect in passenger cars.

[moksharmywebber]

Thank you everyone for your valuable help!!!
But Sir Adambomb, we got this equation in step.5 from sources like
1.RCVD(its given in ride and roll rates chapter)
2.then it is also discussed in topic- http://fsae.com/eve/forums/a/t...=795102272#795102272 (http://fsae.com/eve/forums/a/tpc/f/125607348/m/358107072?r=795102272#795102272).

And sir, we will calculate the rate practically as suggested by you!

This was just an attempt to calculate tire rate using maths.

[exFSAE]

Originally posted by moksharmywebber:
Thank you everyone for your valuable help!!!
But Sir Adambomb, we got this equation in step.5 from sources like
1.RCVD(its given in ride and roll rates chapter)
2.then it is also discussed in topic- http://fsae.com/eve/forums/a/t...=795102272#795102272 (http://fsae.com/eve/forums/a/tpc/f/125607348/m/358107072?r=795102272#795102272).

And sir, we will calculate the rate practically as suggested by you!

This was just an attempt to calculate tire rate using maths.

Your problem is basically at step 2, in that you're using spring load to try calculating a ride frequency (i.e. encompassing both spring and tire effects). Just can't be done. Not valid. You can calculate a WHEEL frequency or rate with knowledge of the spring and corner mass, but not RIDE.

[Zac]

Originally posted by Adambomb:
Ditto to exFSAE. To put it another way, ride rate has no influence on tire rate, so Eq. 5 can't be right. Draw an FBD. Your ride spring will be connected to the ground in series with the tire spring. Directly measuring Ktire would not be terribly difficult to measure (roughly), although I really hope your car isn't heavy enough to get a good measurement.

There are two fundamental problems with trying to find Ktire from a ride measurement. First, as exFSAE mentioned, you just plain don't have information on what Ktire is doing to ride displacement. Neglecting that, even some sort of 4th-order voodoo approximation won't really tell you anything for a couple reasons: aside from being subject to many many sources of error, it is also (as you have mentioned) a good deal stiffer than Kride, so most of the displacement will occur in Kride, and the displacement from Ktire will probably be on the same order of magnitude as measurement noise (if not worse).

I presume you're using some type of standard bolt pattern? One method would be to use a known weight...say a heavy corner of a passenger car with the same bolt pattern as your car. Use race scales or something of at least moderate accuracy to get the corner weight. Set the tire to the pressure you're running on the car (should be a good deal less than what is run in its original application I would imagine).

Jack the car up so the tire is barely in contact with the ground, then measure the sidewall height, height to the hub, or other suitable reference point on the wheel. Then lower the car so the full weight is on the tire, then take the same measurement, and find the difference in measurements. Now you have a load and displacement, and I would imagine that while not completely precise or accurate, would be a "better than nothing" measurement that doesn't cost much time or money.

A car doesn't really have to be "heavy" in order to get a good measurement. For FSAE tires/vehicles, you'll see about 10 mm of tire deformation as the vehicle goes through the full 50 mm of suspension travel. It really wouldn't be difficult or expensive to setup a test fixture for this. A car, floor jack, dial indicator, scale, and some ballast will get you there.