# Frictional accelerations greater than one G

LareeRudi
I see it all the time; engine powered [not jet] dragsters getting EASILY over 1.5 - 2.0 G's, and then sometimes MORE.

And their most rapid accel is in the first part of the race. I know they can increase the downward force on their tires because of wind pushing down on them, but at the beginning the gain is zero to negligible.

[my kids would come home from High School and tell me these "outrageous" times and velocities for the dragsters and I flat out DIDN'T BELIEVE it [1972=1988]...then I saw it on TV with my own eyes, .......... and NOW it's even higher.

I was taught [College Physics in 1955] that the greatest f [frictional] factor is 1.00000000 and thus greatest accel is 1.000000 G.

I've got a couple of ideas/opinions, but can't find evidence that I'm right, and even if I AM, I can't see that much gain [from my ideas].

What is the secret? People that don't even KNOW Physics are out there doing it RIGHT NOW............. WONDERING.

thx,

LarryR : )

## Answers and Replies

Mentor
I see it all the time; engine powered [not jet] dragsters getting EASILY over 1.5 - 2.0 G's, and then sometimes MORE.

And their most rapid accel is in the first part of the race. I know they can increase the downward force on their tires because of wind pushing down on them, but at the beginning the gain is zero to negligible.

[my kids would come home from High School and tell me these "outrageous" times and velocities for the dragsters and I flat out DIDN'T BELIEVE it [1972=1988]...then I saw it on TV with my own eyes, .......... and NOW it's even higher.

I was taught [College Physics in 1955] that the greatest f [frictional] factor is 1.00000000 and thus greatest accel is 1.000000 G.

I've got a couple of ideas/opinions, but can't find evidence that I'm right, and even if I AM, I can't see that much gain [from my ideas].

What is the secret? People that don't even KNOW Physics are out there doing it RIGHT NOW............. WONDERING.

thx,

LarryR : )

I believe it's over 4g:

http://hypertextbook.com/facts/2007/AnamAhmed.shtml

I'm not sure of the math (and don't have time at the moment to figure it out), but keep in mind that the dragster's tires are spinning much faster than it is moving. This is likely the source of the extra capability to generate forward force. If the tires were just barely not slipping, then it does seem like the limit in acceleration might be 1g.

LareeRudi
I believe it's over 4g:

http://hypertextbook.com/facts/2007/AnamAhmed.shtml

I'm not sure of the math (and don't have time at the moment to figure it out), but keep in mind that the dragster's tires are spinning much faster than it is moving. This is likely the source of the extra capability to generate forward force. If the tires were just barely not slipping, then it does seem like the limit in acceleration might be 1g.

but I was taught [1955 College Physics] that kinetic friction [spinning] is LESS then static friction [tires NOT spinning]................ and yes, I DID see the greater than 4.0 accel but was too shy to post that; it is almost beyond belief for me, ha.

Opinion; I believe that it is BEYOND "friction"; I have an idea and have relayed it to a friend [for a witness] but don't wanna state it right now, as I value "cold thoughts" from ya'll more then thoughts that you get from MY thoughts, know what I mean? NOT being "secretive"........... I just wanna know; it's academic, but isn't that what we love?

LarryR : )

thx,

LarryR : )

dacruick
if the had wheels spinning faster than the motion it would switch to kinetic friction and there would be less acceleration. I assume that they have the exhaust shooting upwards conserving momentum and pushing the car down against the ground. That would be the only plausible source for that kind of friction I think.

dacruick
They also could have wheels that create some sort of vacuum under them, im sure its possible.

Mentor
I don't think the downforce from the exhaust or any vacuum effects at the tires are significant. I'm still thinking about it, but Figure 3 in this paper sure shows that the 4g acceleration of a top fuel dragster is near constant from the launch all the way down the track:

http://www.inds.co.uk/education/ChrisButlin/Vernier%20LabQuest%20Investigating%20the%20motion%20of%20a%20model%20dragster.doc [Broken]

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LareeRudi
I don't think the downforce from the exhaust or any vacuum effects at the tires are significant. I'm still thinking about it, but Figure 3 in this paper sure shows that the 4g acceleration of a top fuel dragster is near constant from the launch all the way down the track:

http://www.inds.co.uk/education/ChrisButlin/Vernier%20LabQuest%20Investigating%20the%20motion%20of%20a%20model%20dragster.doc [Broken]

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Nice chart Figure 3............. but my old eyes cannot read the GREEN numbers; anybody's computer fine enough to read them? I think I got the other colors.

thx,

LarryR : )

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Mentor
The green numbers (Hayabusa) are about the same as the red ones (600hp Escort). Here are the green numbers:

Code:
MPH      Sec.
0-60     3.13
0-100    5.87
0-150    11.46
Max      182.1

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LareeRudi
...................... I'm still thinking about it, but Figure 3 in this paper sure shows that the 4g acceleration of a top fuel dragster is near constant from the launch all the way down the track:

http://www.inds.co.uk/education/ChrisButlin/Vernier%20LabQuest%20Investigating%20the%20motion%20of%20a%20model%20dragster.doc [Broken]

.

I did a calc on all the 9 pcs of data that I COULD read, and he accel DOES IN FACT DECREASE as the velocity increases [kinduv normal in my opiniion] ............ NOT approx constant as you had suspected.

Good graph tho.

LarryR : )

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Mentor
I did a calc on all the 9 pcs of data that I COULD read, and he accel DOES IN FACT DECREASE as the velocity increases [kinduv normal in my opiniion] ............ NOT approx constant as you had suspected.

Good graph tho.

LarryR : )

The leftmost graph for the top fuel dragster shows almost constant acceleration, IMO. Air resistance is increasing with speed, but so is downforce from the rear wing.

Mentor
Besides, the point is that the initial acceleration is basically the same as when there is more downforce available. That's the non-intuitive part that I believe is your original question.

LareeRudi
The green numbers (Hayabusa) are about the same as the red ones (600hp Escort). Here are the green numbers:

Code:
MPH      Sec.
0-60     3.13
0-100    5.87
0-150    11.46
Max      182.1

Thanks for doing that so quickly; so I made this chart and if I DID make errors, pls let me know. So yes, the first two DO keep their accel rate up, in fact it INCREASES during the trip, but the second two are more like I'd expect; decreasing accel with progression down the track.

Published et's
0 to 60 1.03 2.58 2.87 3.13
0 to 100 1.72 3.87 6.18 5.87
0 to 150 2.53 5.78 13.63 11.46

G's for Figure 3; if errors, pls let me know
0 to 60 2.6555 1.0601 0.9530 0.8738
0 to 100 2.6503 1.1779 0.7376 0.7766
0 to 150 2.7027 1.1830 0.5017 0.5967

LarryR : )

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Gold Member
Frankly, I never heard of such a statement that friction coeff can't be greater than 1. I can confirm that even the friction coeff of today's tourism tires reach easily 0.95, high perf tire can go slightly higher then 1. Racing tire vary from 1.3 to 1.7. Dragster tires reach easily 3. One engineer from a tire company even told me about dragster tire that in the dynamic deformation at launching, the friction coeff could be as high as 5.

Anyhow, I search on the web where this theory of µ < 1 came from and found nothing. But I found http://mathforum.org/library/drmath/view/51493.html", that might help you understand why it is possible to have friction coeff greater than 1.

All I can think for this theory is that under its own weight, the maximum friction force produced cannot exceed the equivalent of the object's weight.

But the force present at the tire contact patch can be A LOT more than the weight of the car.

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LareeRudi
Frankly, I never heard of such a statement that friction coeff can't be greater than 1. I can confirm that even the friction coeff of today's tourism tires reach easily 0.95, high perf tire can go slightly higher then 1. Racing tire vary from 1.3 to 1.7. Dragster tires reach easily 3. One engineer from a tire company even told me about dragster tire that in the dynamic deformation at launching, the friction coeff could be as high as 5.
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LarryR comment: Aha, THIS would explain then, the possibility of accels = 4.0 g's, but I've never been exposed to this kind of info, thus my original question in post one....... hmmmmmm
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Anyhow, I search on the web where this theory of µ < 1 came from and found nothing. But I found http://mathforum.org/library/drmath/view/51493.html", that might help you understand why it is possible to have friction coeff greater than 1.

All I can think for this theory is that under its own weight, the maximum friction force produced cannot exceed the equivalent of the object's weight.
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[LarryR comment: hmmmm, THAT/THIS was/is my ORIGINAL presumption and belief, but......................... now you say f can be 5.
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But the force present at the tire contact patch can be A LOT more than the weight of the car.
qqqqqqq
Yes, but only with SOMETHING adding the downward Force, right? like wind downward force on the slanted surface?
qqqqqqq

LarryR thanks ya'll........... does anybody else know about these tires that have f=5?

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Gold Member
qqqqqqq
Yes, but only with SOMETHING adding the downward Force, right? like wind downward force on the slanted surface?
qqqqqqq

LarryR thanks ya'll........... does anybody else know about these tires that have f=5?

First, the dragster tires don't have a friction coeff of 5. It's just when the tire deforms itself at launching. It lasts for a fraction of a second and it won't really show on the car's performance. 3 is a more appropriate value (That's high enough isn't it?).

The maximum acceleration of a car, in g's, is equal to the tire friction coeff (if it is a 4WD) or less (if it is a 2WD). If you add downforce, then the normal force increases, but not the weight of the car so the maximum acceleration will also increase (hence the 4 g's acceleration even if the dragster tire has f = 3).

But downforce DOES NOT modify the friction coefficient.

All I can think for this theory is that under its own weight, the maximum friction force produced cannot exceed the equivalent of the object's weight.

With that last statement, I was trying to find an explanation for where that theory of f < 1 came from. After re-reading it, it doesn't make sense. Probably because the statement f < 1 doesn't make sense either: Friction coeff greater than 1 have been measured (and not only car tires on asphalt), so it is possible!

Just re-read Doctor Ian's answer in http://mathforum.org/library/drmath/view/51493.html" I gave you.

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LareeRudi
Well, you guys have helped a lot, and tho we don't agree on EVERYTHING, you provide VERY GOOD thought provoking stuff, and it gives me incentive to look even further, so you've got answers AND you're a catalyst. Thx.

I'd love to see documentation on those tires with f=5 [I believe you, just wanns see more; because THAT is a major part of the answer to my "puzzlement"].

But here is what I found 20 mins ago and I'll share it with you if you're interested. A 159 page paper prep'd by a student in 1998 that concentrated on dragsters, their tires AND their rear wing. He actually [to me it seems] concentrated on the wing more than the tires, and tho that IS of interest to me, I was wanting to learn about the "phenomena" that I was inquiring about; f.

But here it is [it's been there all the time waiting for me to find it, and I've been puzzling on this since 1972-ish.

www.caselab.okstate.edu/pubs/tmb_thesis.pdf

Thanks again, and don't stop NOW........... if you've still got thoughts, I'm really anxious to hear them.

LarryR : )

LareeRudi
.........................................

With that last statement, I was trying to find an explanation for where that theory of f < 1 came from. After re-reading it, it doesn't make sense. Probably because the statement f < 1 doesn't make sense either: Friction coeff greater than 1 have been measured (and not only car tires on asphalt), so it is possible!

Just re-read Doctor Ian's answer in http://mathforum.org/library/drmath/view/51493.html" I gave you.
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My response:
Oh yes, I was typing while you posted this, so it'll seem that my post "ignored" yours, not so, I just NOW found yours after writing mine one minute ago. Yes, that Dr Ians thing was helpful and I DID read it, yes. And yes, I acknowledged that f CAN be more than ONE, but I didn't learn that until yesterday evening; thus my puzzlement.

I don't know if you saw it, buy MY College Physics was in 1955, and I'd LOVE to go back and see IF they said what I said, becuase I've kinda blamed it onto THEM, didn't I, huh?

But this is 65 years later, and I'm still learning, and AGAIN, I thank ya'll, but don't stop now if you have more to say.

LarryR : )

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tvavanasd
One engineer from a tire company even told me about dragster tire that in the dynamic deformation at launching, the friction coeff could be as high as 5.

All I can think for this theory is that under its own weight, the maximum friction force produced cannot exceed the equivalent of the object's weight.

But the force present at the tire contact patch can be A LOT more than the weight of the car.

Perhaps you have already implied the answer...

More explicitly, the tires expand at such a high rate (fully expanded within a fraction of a second I expect) that they act as springs accelerating the CofG of the wheels and eventually the car upward.

Accelerating your car upward from a standstill by spinning your tires will increase the normal force on the contact patch, making it appear as though the coefficient of friction is much higher than it is.

Therefore it is advantageous to spin up your tires quickly, and maximize the diameter difference (change in potential wheel centre height) to maximize the normal force (effective car weight).

Obviously drag racing isn't only about horizontal acceleration.

LareeRudi
Perhaps you have already implied the answer...

More explicitly, the tires expand at such a high rate (fully expanded within a fraction of a second I expect) that they act as springs accelerating the CofG of the wheels and eventually the car upward.

Accelerating your car upward from a standstill by spinning your tires will increase the normal force on the contact patch, making it appear as though the coefficient of friction is much higher than it is.

Therefore it is advantageous to spin up your tires quickly, and maximize the diameter difference (change in potential wheel centre height) to maximize the normal force (effective car weight).

Obviously drag racing isn't only about horizontal acceleration.
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For a very SHORT time indeed; yes, but the normal force you refer to is for, as you say, a "fraction of a second", so the moment the dia stops changing, now we don't HAVE that "additional normal force", as the rising axle has STOPPED accelerating upwards; no acceleration upwards, no force downwards.

And your LAST sentence, I certainly agree with wholeheartedly.

LarryR : )

tvavanasd
Time for vertical accel must be greater than the time of wheel spin up. Chassis mass must also be accelerated.

Homework Helper
For a better example than drag racing slicks, the coefficecient firction between a table tennis ball and high end rubber on a table tennis paddle is over 5. A video showing the grip using a comb instead of a ball to demonstrate the amount of friction:

Mentor
Obviously drag racing isn't only about horizontal acceleration.

That's probably a typo.

mender
The exhaust adds a substantial amount of downforce, between 800 and 1000 lbs. Given a total vehicle weight of 2300 lbs, that increases the acceleration rate by over 40%. Also, during the burnout, the tires are laying down fresh sticky rubber that the driver makes use of on the run. That allows 0-100 mph in .7 seconds and 0-280 mph in 660 feet.

And finally, the object is to not spin the tires, because the one who does is usually (almost always) the loser.

Homework Helper
I remember the discussion from my high school physics: If the friction force does not depend on surface contact area, then why do dragsters have such wide tires? Of course, in retrospect the high school viewpoint was quite naive. Just because you use F = mu N to solve a few homework problems in high school doesn't mean that that formula is absolutely correct. Anyway, I will share the high school physics answer that I was told: The tires supposedly heat up and get "gooey", i.e. sticky, and that apparently does depend on surface contact area. That was also the justification for why they spin their tires at the starting line with all that smoke; to heat them up and make them sticky.

EDIT: sorry, mender; I somehow missed your post. Also, opposite of what I had hear about the spinning.

Gold Member
I see it all the time; engine powered [not jet] dragsters getting EASILY over 1.5 - 2.0 G's, and then sometimes MORE.
And their most rapid accel is in the first part of the race. I know they can increase the downward force on their tires because of wind pushing down on them, but at the beginning the gain is zero to negligible.

I wonder whether for the horizontal force generated in the first meters a comparison with tractor pulling is relevant. (That is, the kind of pulling that is done by the special rigs for tractor pulling competition.)

Interestingly, tractor pulling is not friction pulling; the massive tires are spinning furiously all along the track. It follows logically that tractor pulling must be reaction pulling. The spinning tires cause soil to be accelerated rearward. By the action-reaction principle the force required to accelerate the soil mass is the forward force that the tractor is generating.

I wonder: maybe the tire-spinning of the drag cars ablates so much rubber, ejecting that rubber rearward, that the reaction force is significant. How much rubber do the tires lose in the first few meters?

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xxChrisxx
OH god thing again.

OK the max friction coefficient of 1 due to the equations mu = F/N only applies to rigid objects that don't deform.

Rubber materials, such as tyres, have many other eays of generating grip. Mechancial keying is one of the largest. This is where the surface of the tyre deforms to fit the roughness of the road (like a key in a lock). This allows grip coefficiencts higher than 1.

On the size of the tyres. They aren't acutally wide as a matter of design. The idea for a drag tyre to get good accelearation is to be very tall (to get a long contact patch), however a tall thin tyre would overheat and destroy itsself. They make it wide to get suitable temperature characteristics.

Homework Helper
Gold Member
Don't dragsters have rear wheel drive? Due to the vehicle's location of its center of gravity, the car tends to rotate during acceleration, which, for a level surface, reduces the normal force on the front tires, but increases the normal force on the rear tires.

xxChrisxx
Don't dragsters have rear wheel drive? Due to the vehicle's location of its center of gravity, the car tends to rotate during acceleration, which, for a level surface, reduces the normal force on the front tires, but increases the normal force on the rear tires.

A perfect launch on a dragster will have just enough weight transfer to lift the fronts off the floor.

It's also interesting to note that as the tyre temp and rpm increases, the rear wheels expand, effectively gearing the car up.

Gold Member
I think the 'max 1g' idea must be a myth, in practice.
After all, if you had splines cut across the track and had gear teeth on your wheels, you could get pretty much any forward force you wanted.
Once the tyres get sticky and come in contact with the tarmac of the track, you aren't dealing with simple, conventional, linear contact forces.

Gold Member
I think the 'max 1g' idea must be a myth, in practice.
After all, if you had splines cut across the track and had gear teeth on your wheels, you could get pretty much any forward force you wanted.
Once the tyres get sticky and come in contact with the tarmac of the track, you aren't dealing with simple, conventional, linear contact forces.

Ha ha! That was precisely the visual aide I was going to use as I read through this thread.

I was also going to ask the question: "What is the coefficient of friction of duct tape stuck to something, and how much force is required to peel it from the surface?"
Dragsters almost always do a burn out before the race, heating up the tires, making their surfaces fly paper sticky.

Gold Member
On the lines of 'duck tape', I could suggest that, in order to get higher than g friction forces, you probably need even more engine power - to do the 'unsticking' as well as the accelerating.
There may be figures which show this. It's a bit like the 'design speed' idea with boat hulls; over a certain speed, a displacement hull needs wildly increasing powers to go faster and faster.

Gold Member
I was also going to ask the question: "What is the coefficient of friction of duct tape stuck to something, and how much force is required to peel it from the surface?"
Dragsters almost always do a burn out before the race, heating up the tires, making their surfaces fly paper sticky.

Then again, dragsters don't actually use that stickyness in the first meters.
In the first meters the tires are spinning furiously. In all other forms of car racing you lose acceleration if you have wheel spin at the start.

Are dragster tires shredded after a single run?

xxChrisxx
Q

Then again, dragsters don't actually use that stickyness in the first meters.
In the first meters the tires are spinning furiously. In all other forms of car racing you lose acceleration if you have wheel spin at the start.

Are dragster tires shredded after a single run?

Yeah, considering the engine basically needs a rebuild after each run (for a top fuel dragster) the life of a tyre is 1 run.

The aim is to get a slight amount of wheel spin on all starts, this is becuase if you don't the tyre can bite and it bogs the engine down.

Gold Member

Yeah, considering the engine basically needs a rebuild after each run (for a top fuel dragster) the life of a tyre is 1 run.

The aim is to get a slight amount of wheel spin on all starts, this is becuase if you don't the tyre can bite and it bogs the engine down.

So tyre = clutch, effctively?

xxChrisxx

So tyre = clutch, effctively?

Err, the line isn't as sharp as that. They usually have torque converters that are designed to lock up in a specific way to just make the tyre have a certain amount of wheel spin for best acceleration. This is so the driver can lauch at/close to full thottle.

If they get the clutch wrong for the conditions, the engine will either bog down (revs will drop off) or the tyres will just spin away. You can see when they get it wrong as the tyre screws itsself up, and the car bounces around wildly.

A drag tyre really is an amazing peice of kit. It not only has to act like a tyre, but acts like a secondary clutch and a gearing system as well.

Heres a nice viedo demonstating what i'm decribing.