# tyre wear index to lateral g force - a magic formula!

23 replies to this topic

### #1 mariner

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Posted 07 June 2021 - 14:22

Looking for new road/trackday tyres for my car I came across lots of references to numbers like "120" , "180" basically in describing the  compound softness.

Apparently   its an index developed in the USA. to measure grip in standardised way.. Relying on Wiki as ever its here   https://en.wikipedia...Quality_Grading

In the treadwear section the methodology of using a special control tyre and the candidate tyre  is explained.

The interesting bit is the formula to convert the index , 100, 180 etc, to actual grip. It is mu=2.25/TW^0.15. where TW is the treadwear index

So going from a TW of 180 to 100 in the formula suggests a 9% increase in grip , or at least  friction co - efficient..

That is huge grip increase just from compound change. Some tyres in the  MSAUK list 1b, i.e "road " tyres for racing, sold in  UK come in compounds of 100 to 180 so , if it is true I gain 9% extra grip by buying a variant of the same tyre?

This seems a bit too good to be true?? a clue might be here in the Wiki article "The assigning of UTQG grades is done solely by the tire manufacturer. In many cases, this has resulted in the UTQG grading system to be more of a marketing tool than was originally intended".

### #2 gruntguru

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Posted 07 June 2021 - 20:53

There is some evidence of treadwear ratings being gamed by tyre makers. Some classes of motorsport specify a minimum treadwear number eg autocross in the US have a category where tyres used must be at least 200 TW. Guess what - there are some pretty grippy tyres out there with TW200 on the sidewall.

Interesting, the formula converges to a mu of 2.25. I wonder if that is close to the mu for a top fuel drag slick.

Edited by gruntguru, 07 June 2021 - 20:57.

### #3 Greg Locock

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Posted 07 June 2021 - 23:54

Have a read of SAE 942484. Back then (1994) the actual mu of a dragster tire was only 1.5, but the vehicle could accelerate at 3-4 g because of some weird stuff, which I am less than convinced by. I think the paper is on the right track, but i don't see how you can exert a vertical force into the ground greater than the axle weight for very long.

I've measured instantaneous longitudinal mu of 1.2 on very boring tires in an ABS stop. Perhaps some of that unexpected grip was the mechanism in that paper. For boring tires on the Flattrac machine long mu and lat mu are often the same or close enough, crude explanation being that when the patch of rubber is sliding it doesn't really care whether it is moving forward or sliding sideways.

### #4 gruntguru

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Posted 08 June 2021 - 04:20

I will have a read of that paper thanks.

TF dragsters have ~1000 lb of downforce from exhaust jet effect alone. Some of the jet effect is used for forward thrust by angling the nozzles (pipes). When you add in the inertial spike as the CG is lifted by tyre growth there is temporarily a lot of "DF" at launch. At higher speeds the wing takes over with reputedly 12,000 lb of DF at 325 mph. (car weighs 2,330 lb)

Edited by gruntguru, 08 June 2021 - 04:24.

### #5 Fat Boy

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Posted 08 June 2021 - 22:32

Have a read of SAE 942484. Back then (1994) the actual mu of a dragster tire was only 1.5, but the vehicle could accelerate at 3-4 g because of some weird stuff, which I am less than convinced by. I think the paper is on the right track, but i don't see how you can exert a vertical force into the ground greater than the axle weight for very long.

I've measured instantaneous longitudinal mu of 1.2 on very boring tires in an ABS stop. Perhaps some of that unexpected grip was the mechanism in that paper. For boring tires on the Flattrac machine long mu and lat mu are often the same or close enough, crude explanation being that when the patch of rubber is sliding it doesn't really care whether it is moving forward or sliding sideways.

It was a good day when I realized that camber was not just something used to optimize tire temps. It was a way for me to compromise lateral and longitudinal grip to provide the biggest benefit for a given situation.

### #6 mariner

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Posted 09 June 2021 - 11:41

I am not an SAE member so I can only read the synopsis of 942484, but it seems to indicate that a drag car can pull 4 g while the " natural" tire grip is only 2g.

As I cant read it I have question - does the way a top fuel car leaps up and sort of arches its back on launch act a spring which as it unwinds can push the rear ned down beyond pure  weight.?

A bit like peak loads form vibrations in an assembly far exceeding the static load ?

### #7 gruntguru

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Posted 09 June 2021 - 21:43

4G is average acceleration over the course. Launch acceleration is 8G (due to the effect you describe plus tyre growth at launch). Acceleration would then reduce (to perhaps 2.5 - 3.0 G?) then climb again as the wing builds DF.

Accelerometer graph here https://dragnews.com...te-the-hardest/ doesn't confirm the high launch acceleration.

Edited by gruntguru, 09 June 2021 - 21:50.

### #8 Canuck

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Posted 09 June 2021 - 21:59

I thought the exhaust thrust issue was taken apart here some time ago and found to be wanting.

### #9 desmo

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Posted 09 June 2021 - 23:57

I think we determined via simple Newtonian calculation that the massflows through the exhausts were never going to merit the grandiose DF claims being made.

### #10 gruntguru

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Posted 10 June 2021 - 02:07

I recall doing a calculation and 1,000 lb was the right order of magnitude. Can't recall the thread.

I think mass flow is about 10 kg/s so exhaust velocity would need to be 500 m/s to produce 5,000 N  - about 1,000 lb.

### #11 desmo

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Posted 10 June 2021 - 05:56

That 500 m/s velocity is of course well above speed of sound. DOHC did some quick maths and came up with a much lower number here. He uses 300 m/s.

The thrust of a jet is massflow*jet velocity. The massflow is the weight of the exhaust volume produced per time unit:

rho*V*revs/2,

where rho is the exhaust density and V the engine capacity. The jet velocity v is the speed by which the exhausts exit the pipe, so the thrust is

rho*V*revs/2*v.

Just to get a rough estimate, use rho = 1.23 kg/^m^3 (density of air, exhaust is heavier, but not by a lot with gas as the fuel), V = 0.003 m^3, revs=300/sec, and v=300 m/s and multiply.

Then you get

1.23*0.003*150*300 = 170 N.

So the peak thrust is on the order of 200 N or so (corresponding to a "20 kg" or "40 lbs" downforce), which is not a lot.

With nitromethane fuel things are a bit different as the mass flow is much larger (the fuel contains extra oxygen for the combustion). Also, the enormous engines increase mass flow as the engine capacity goes up. On the other hand, those engines might not run at 18,000 rpm.

In any case, the claim of "2,000 lbs" downforce seems to be a bit exaggerated. A calculation as rough as the one above would let's say use 5x the density rho (use of compressor and more fuel), 3x engine capacity V, but reduce revs by a factor of 2. I'd be surprised if the downforce vastly exceeded 1-2 kN, which is about "200-400 lbs" of downforce.

### #12 Ross Stonefeld

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Posted 10 June 2021 - 11:07

That link tries to take us to the moderator panel and includes some IP info

### #13 mariner

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Posted 10 June 2021 - 13:29

Thank you Gruntguru for the G force track.

On the exhaust downforce thing one point I would ad which may be relevant is that the shattering noise of Top Fuel  car is partially  due to the excess nitro burning off in the exhausts. Hence the huge sheets of white flame seen in a night run.

That means a simple cubic capacity*revs* VE calculation may not be correct.

I know sometime ago the relative low power of extra F1 noise was discussed but Top Fuel noise is very different, it literally shakes your whole body if you are within 100 ft.

### #14 Greg Locock

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Posted 10 June 2021 - 23:57

The point about the speed of sound is valid. You'd also get mach choking at the tailpipe, I doubt they'd risk that just to get downforce.

### #15 Ross Stonefeld

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Posted 11 June 2021 - 11:40

I know sometime ago the relative low power of extra F1 noise was discussed but Top Fuel noise is very different, it literally shakes your whole body if you are within 100 ft.

I went to an NHRA event when I was about 5 years old and hated it, purely because of the sensory experience. It was unpleasant for my tiny body.

### #16 Fat Boy

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Posted 11 June 2021 - 23:55

The point about the speed of sound is valid. You'd also get mach choking at the tailpipe, I doubt they'd risk that just to get downforce.

You don't know many Top Fuel guys, do you?

### #17 Greg Locock

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Posted 12 June 2021 - 07:31

You'd be right there - it is one the motorsports I've never seen in real life. So now you've got me thinking, do they dyno their engines? Or is the cost of engine per run so high that they do all their development on the track?

### #18 mariner

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Posted 12 June 2021 - 09:17

Nobody has ever sucessfuly dyno'ed a Top Fuel engine. Long ago somebody tried to hook on up to a aero engine dyno that could take up to 4,000 bhp but it didn't really work and Top Fuel power soon soared up to 8,00o bhp.

So most power was estimated using acceleration vs weight with a guess at drag - as getting coast down data is hard with a big chute on the back!

Then modern strain gauge technology was applied to teh drive shaft and real data could be captured. This led to finding out they really can deliver 11,000 bhp.

Here

I am an addict of Top Fuel and Funy Cars , the rest of drag racing doesn't grab me that much but the sheer mechical violence of a Top Fuel run is awesome. TV or the  internet cannot describe actually being there and feeling the noise. Not wise to watch without ear plugs but just once it is worth it.

.

Edited by mariner, 12 June 2021 - 09:19.

### #19 desmo

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Posted 12 June 2021 - 14:25

You don't know many Top Fuel guys, do you?

So is the exhaust velocity in the pipes supersonic or not?

### #20 MatsNorway

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Posted 12 June 2021 - 16:02

A top fuel dragster runs a 2" fuel line. If that helps narrowing down the flow calculations (mostly what it can not be above due to Reynolds number) The compressor uses 600hp at full chat if that helps narrow down the amount of air getting stuffed in there.

The Air/fuel ratio can be as low as 1.7/1 so if they do not get ignition they usually go hydraulic and lift the head of.

Top Fuel is a must see once in a life time for anyone interested in racing/engines/wild sports/sound

Edited by MatsNorway, 12 June 2021 - 16:16.

### #21 Greg Locock

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Posted 13 June 2021 - 00:11

Do you see mach diamonds in the exhaust? If not then it isn't supersonic. http://www.aerospace...ion/q0224.shtml

### #22 Joe Bosworth

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Posted 13 June 2021 - 09:03

I have some old karting data that shows lateral G forces of 1.4G. This has to be about the max limit for pure force through tyres.  Though my data is old I seriously doubt whether there has been any further tyre development between then and now.

This is for full slicks mounted on wheels that optimise the rubber usage including wheel width that about limits tread walking under load so true mu values result.  Needless to say there are no aero tricks or exhaust loadings that can affect G loads.  Karts frame/seat locations are also optimised so as to get the best tyre temperatures across treads and right to left.

I used to have some good F Ford on track data but that is too long ago for me to go find but I recall that data pretty much validating, but not equaling the kart data.

There was a recent tyre comparison published in Oz that gave volumes of good data for DOT approved road car tyres. The best dry braking tyres were Maxxis Premtra 5 that showed 1.04 G forces from 100 kph to full stop.  There were six tyre makes that all were above .96G.  The test Vehicle was a Hyundai Tucson so you can expect better test numbers from tyres mounted on higher performance vehicles with less compliant suspensions. At least these are real life numbers.

Regards

### #23 gruntguru

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Posted 13 June 2021 - 21:41

Some dynomometer testing has been done using one cylinder of a top fuel engine.

With combustion occuring in the exhaust pipes, you would expect the exhaust temperature to be at least 1000*C and the speed of sound more than 700 m/s.

I think mass flow is about 10 kg/s so exhaust velocity would need to be 500 m/s to produce 5,000 N  - about 1,000 lb.

### #24 Fat Boy

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Posted 13 June 2021 - 23:32

So is the exhaust velocity in the pipes supersonic or not?

That question is well out of my wheelhouse. I have no idea, although I believe I have seen pics of Fuel cars with compression diamonds visible in the exhaust.

My comment was more as to whether or not they would risk the test. If those guys have an inkling it will pick up 0.001 sec they'll try it. If you're not blowing things up on a fairly regular basis, you're probably not trying hard enough.

As far as I know, all of their full power running is on track. I don't believe there is a dyno built that could actually measure the power of a TF engine. The flow bench work that they do on *everything* is damned impressive.