Slip Ratio calculations

I have a couple of questions about slip ratio used in vehicle grip calculations SR = (W*R - V) / V. First, why is it a ratio? If you have a W*R of 110 and a V of 100, the SR will be 10%. If you have a W*R of 1010 and a V of 1000, the SR will be 1%. This doesn't make sense to me since in both cases the relative speed difference between W*R and V is 10. Second, how do you handle it when V is 0? I've tried using this: if(V == 0) SR = 1; else SR = (W*R -V) / V; But I'm just not happy with it, there seems like there should be a more clever way of handeling it.

[email hidden] wrote: > I have a couple of questions about slip ratio used in vehicle grip > calculations SR = (W*R - V) / V. First, why is it a ratio? The short answer to this part of your question is because this type of model matches experiment results. - Matt

On Wed, 25 Dec 2002, Matt Jessick wrote: > [email hidden] wrote: > > I have a couple of questions about slip ratio used in vehicle grip > > calculations SR = (W*R - V) / V. First, why is it a ratio? > > The short answer to this part of your question is because this > type of model matches experiment results. And a slightly longer answer is that several other formulations are used. RCVD p. 39-40 lists 7 different definitions... http://www.millikenresearch.com/rcvd.html [yet another shameless plug -- order from SAE, best service & price, link on bottom of our page]. -- Doug Milliken Milliken Research Associates Inc.

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>> I have a couple of questions about slip ratio used in vehicle grip >> calculations SR = (W*R - V) / V. First, why is it a ratio? > >The short answer to this part of your question is because this >type of model matches experiment results. > >- Matt

The long answer (:-P) is due to where these longitudinal forces come from. This is a quick write up, so bear with me if it's a little shoddy :-D Following is a simplified example, but the same principle applies to real tires. Imagine a contact patch 1 foot long. When you have a "slip ratio," this simply means that the wheel is rotating at a different speed than it would be if it was rolling freely. First, let's paint a little dot on the tire tread: If the tire was rolling freely at a speed at which you could watch the little dot move the through contact patch at 1 foot per second (our camera is moving along with the wheel,) for the purpose of this post you could say the tire is moving at 1 foot per second. Now, let's apply a driving torque to the wheel so it's now running at a 0.1 slip ratio. As you know, this means that the wheel is rotating 10% faster than it would be if it was rolling freely. Meanwhile, we keep the tire moving along at 1 foot per second. The little dot will enter the contact patch and stick to the ground. It'll stay stuck to the ground of course because there's a vertical force on the tire. Since it's stuck to the ground, the little dot will move at 1 foot per second through the contact patch, matching the tire's free rolling speed (the axle speed.) However, the tire is rotating 10% more quickly than the free rolling velocity. The dot will not stay in the same position as it would if it was NOT stuck to the ground. In essence, the little dot *should* be moving through the contact patch at 1.1 foot / second instead of 1 foot per second. As a result, the tire of course flexes and some stress (force) is produced. When the dot first enters the front of the contact patch, it's exactly where it "should" be. The tire isn't distorted yet. However, as the dot moves through the patch, it is progressively pulled further and further away from where it should be. By the time it leaves the contact patch, it has been stretched 0.1 feet out of shape. The contact patch acts like a spring. If you stretch the "dot" out of place by 0.1 feet, you could basically multiply that by the tire's "longitudinal spring rate," or the stiffness of the tire, to find out how much force was produced. Of course, in a real tire, the rear of the contact patch slips, but this still serves the point. Now, what happens if the tire is moving 10 feet per second and also has a 0.1 slip ratio? The "slip velocity" is quite different, but the force remains basically the same. You're question is "why?" Let's follow the dot... The dot "should be" moving at 11 feet per second. It's stuck to the ground though, so it moves at the same speed as the axle: 10 feet per second. The contact patch is 1 foot long, so it will enter the front and leave the rear in only 1/10 = 0.1 seconds. How far will it be stretched out of the way at the end of the contact patch? The speed difference in the contact patch betwen actual and free-rolling is 1 foot/second. The dot is stretched out of place by 1 * 0.1 = 0.1 feet. It's the same amount of stretching, regardless of the velocity. The amount of stretching is proportional to the amount of force produced. So... The tire velocity doesn't matter in this example. The ratio causes the force, not the slip velocity. After all, if the contact patch is 1 foot long and try to make the dot go 10% "too far," it will be stretched out of place by .1 feet, regardless of the tire's speed. Todd Wasson --- Performance Simulations Drag Racing and Top Speed Prediction Software http://PerformanceSimulations.Com My little car sim screenshots: http://performancesimulations.com/scnshot4.htm

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>> [email hidden] wrote: >> > I have a couple of questions about slip ratio used in vehicle grip >> > calculations SR = (W*R - V) / V. First, why is it a ratio? >> >> The short answer to this part of your question is because this >> type of model matches experiment results. > >And a slightly longer answer is that several other formulations are used. >RCVD p. 39-40 lists 7 different definitions... > http://www.millikenresearch.com/rcvd.html >[yet another shameless plug -- order from SAE, best service & price, link >on bottom of our page]. > >-- Doug Milliken > Milliken Research Associates Inc. > >

Hehe :-D This is a really good book. I've relied pretty heavily on it in my own development work. It's a great read for the hardcore armchair reader too. Have a Merry Christmas, Doug Todd Wasson --- Performance Simulations Drag Racing and Top Speed Prediction Software http://PerformanceSimulations.Com My little car sim screenshots: http://performancesimulations.com/scnshot4.htm

On 25 Dec 2002, J. Todd Wasson wrote:

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> >> I have a couple of questions about slip ratio used in vehicle grip > >> calculations SR = (W*R - V) / V. First, why is it a ratio? > > > >The short answer to this part of your question is because this > >type of model matches experiment results. > > > >- Matt > The long answer (:-P) is due to where these longitudinal forces come from.

<snip> > It's the same amount of stretching, regardless of the velocity. The amount of > stretching is proportional to the amount of force produced. > > So... The tire velocity doesn't matter in this example. The ratio causes the > force, not the slip velocity. Nice to have good students, saves me a lot of typing<grin> Happy Holidays to all, -- Doug Milliken

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>> So... The tire velocity doesn't matter in this example. The ratio causes >the >> force, not the slip velocity. > > >Nice to have good students, saves me a lot of typing<grin> > >Happy Holidays to all, > >-- Doug Milliken >

Thank you, teacher :-D Happy Holidays to you as well, Todd Wasson --- Performance Simulations Drag Racing and Top Speed Prediction Software http://PerformanceSimulations.Com My little car sim screenshots: http://performancesimulations.com/scnshot4.htm