Motorcycle and Cars: Wheelies, the physics behind them.

[michaelwoodco]

Ok so I got in a HUGE argument with some people over on a car forum. They say that cars with longer wheelbases are harder to wheelie. I disagreed. I said it not only depends on the wheel base since that is an oversimplified way to look at it, it depends on where the center of gravity is in relation to the rear axle and the contact patch.

I believe you can calculate the amount of forward thrust a car can handle without doing a wheelie by looking at it this way:

the red dot is it's center of gravity, pulling down, providing a torque on the axle. Whereas the horizontal line is the distance from the contact patch to a vertical line drawn through the COG. I believe that if you use a similar triangle it could enter a wheel stand when the bottom leg's value is great enough that the other vertical leg would have a value that exceeds the weight of the vehicle.

Anyways any comments, advice, or equations on this?

Thanks,

Michael Woodcock

 

[Drakkith]

I'd say that in general, longer wheelbases are harder to wheelie. The weight of the front is multiplied the further it is from the rear wheel due to leverage. Given similar weights, power, ETC, a longer wheelbase is harder to wheelie than a shorter one.

 

[michaelwoodco]

Yes, but what if your wheel base is 10,000,000 feet long, but your center of gravity is right over your rear axle? coudn't it wheelie with even 1 horsepower and 1 foot pound of torque?

 

[Drakkith]

Yes, but what if your wheel base is 10,000,000 feet long, but your center of gravity is right over your rear axle? coudn't it wheelie with even 1 horsepower and 1 foot pound of torque?

I'm not disagreeing with you. The center of gravity would have a lot to do with how easy it is to wheelie. I'm simply pointing out that in GENERAL a vehicle with a longer wheelbase also has its center of gravity further away from the rear axle. That is why people are telling you that it is easier to do a wheelie with a shorter wheelbase.

 

[michaelwoodco]

Yes, but many sports cars now a days are designed to have such a low center of gravity. Obviously if the center of gravity were as low as the contact patch the car could never wheelie, (unless it came upon a bump or hill) So the center of gravity seems to play an undeniably large role to me. More so than the wheel base.

 

[pallidin]

For a "wheelie" it is ideal that the COG exists above the applied pivot point.

 

[Drakkith]

Yes, but many sports cars now a days are designed to have such a low center of gravity. Obviously if the center of gravity were as low as the contact patch the car could never wheelie, (unless it came upon a bump or hill) So the center of gravity seems to play an undeniably large role to me. More so than the wheel base.

Sure. But like I said before, the wheel base will determine the COG in most cases. Or at least play a significant part. Both you and the guys on the other forum are correct depending on how you look at the problem.

 

[jack action]

michaelwoodco, you are correct, length does not play a role; only ratio. The wheelbase is the reference length and all others are compared to it (CG height and distance between the CG and the rear axle).

When the wheelbase is increased on a motorcycle for hill climbing, the rear axle is pushed rearward. The true effect is that the static weight is more on the front axle than the rear one, thus less chance of flipping over.

When the wheelbase is increased on a motorcycle for drag racing, the front axle is pushed forward. The true effect is that the static weight is more on the rear axle than the front one, thus more traction available for a RWD.

Just to show how wheelbase length is not that important, here is a picture of a funny car who's wheelbase was lengthen (by pushing the front axle forward) and another one who's wheelbase was shorten (by setting the rear axle closer to the CG). Both have the same objective: Put more weight on the rear axle.

[PLAIN]http://www.airheartsales.com/images/AirheartFunnyCarLG.jpg

[URL]http://www.redcelery.com/www_redcelery_com/Alt_wh_base_SS/IMAG002.JPG[/URL]

All the equations (and a calculator, see bottom right graph) can be found on http://hpwizard.com/car-performance.html" (At the bottom of the page see Theory»Longitudinal acceleration»Accelerating» Traction limited & Axle load distribution).

 

[rcgldr]

No one has mentioned the effect of angular momentum with a longer wheelbase. Given everything else is the same (including cg distance from rear axle) a longer wheelbase will reduce the rate of pitch (up) in a wheelie.

 

[russ_watters]

Yes, but many sports cars now a days are designed to have such a low center of gravity. Obviously if the center of gravity were as low as the contact patch the car could never wheelie, (unless it came upon a bump or hill) So the center of gravity seems to play an undeniably large role to me. More so than the wheel base.

Low doesn't mean far back, though, does it?

Usually with this kind of question, I try to isolate properties. So you would want to say 'all else being equal, a car with a longer wheelbase is tougher to wheelie'. That means if the center of gravity is in the same relative location, but one car has a longer wheelbase, it'll be tougher to wheelie.

 

[russ_watters]

michaelwoodco, you are correct, length does not play a role; only ratio. The wheelbase is the reference length and all others are compared to it (CG height and distance between the CG and the rear axle).

That's not correct. Torque depends on the actual length of a lever arm, not the relative length. So with the same relative position of the cog, a longer wheelbase means the cog is further from the back wheel and therefore requires more torque to lift. Ie, if two cars have the cog centered, the one with the longer wheelbase is tougher to wheelie.

And your two motorcycle examples argue against your point for exactly that reason: they are moving one wheel specifically so they can move the cog further forward or backwards with respect to the wheel that matters.

 

[michaelwoodco]

The wheelbase is the reference length and all others are compared to it (CG height and distance between the CG and the rear axle).

Thanks, makes sense to me!

No one has mentioned the effect of angular momentum with a longer wheelbase. Given everything else is the same (including cg distance from rear axle) a longer wheelbase will reduce the rate of pitch (up) in a wheelie.

If the rear wheel has the same relation to the CoG? Basically, to maintain a wheelie at low speeds, the CoG has to be right over the contact patch. I think the relation of the center of gravity to the pivot point gives it angular momentun, and not where the front wheels are, right?

That's not correct. Torque depends on the actual length of a lever arm, not the relative length. So with the same relative position of the cog, a longer wheelbase means the cog is further from the back wheel and therefore requires more torque to lift. Ie, if two cars have the cog centered, the one with the longer wheelbase is tougher to wheelie.

And your two motorcycle examples argue against your point for exactly that reason: they are moving one wheel specifically so they can move the cog further forward or backwards with respect to the wheel that matters.

Yeah Torque as far as I know depends on the length of the leverage arm. Ok so how about I throw in what I think this would look like as an equation:

so here's a basic illustration I found online

I'm going to guess that when the resultant vector of all the forces on the COG is behind the contact patch you can get a wheelie.

This is the maximum acceleration I think a motorcycle with this weight at that point can withstand continuously:

While this one will probably wheelie:

Does that math/reasoining work out?

 

[jack action]

That's not correct. Torque depends on the actual length of a lever arm, not the relative length. So with the same relative position of the cog, a longer wheelbase means the cog is further from the back wheel and therefore requires more torque to lift. Ie, if two cars have the cog centered, the one with the longer wheelbase is tougher to wheelie.

And your two motorcycle examples argue against your point for exactly that reason: they are moving one wheel specifically so they can move the cog further forward or backwards with respect to the wheel that matters.

I'll partially agree with you. But it still a ratio thing and the wheelbase has nothing to do with it.

In the end of it, here is the condition to make a wheelie (meaning vertical force on the front axle is zero):

Wd = Fh

Where W is the weight of the car, F is the traction force at the rear tires, h is the CG height and d is the horizontal distance between the CG and the rear axle. If this condition is met, it does not matter how long the wheelbase is. The horizontal distance between the CG and the front axle can be as long or as short as you want, it won't change a thing: the front axle will begin to lift.

So, it is not how long the wheelbase is that counts, but where the CG is with respect to the rear axle. And the important ratio is h/d; the bigger it will be, the easier it will be to do a wheelie.

 

[jack action]

so here's a basic illustration I found online

I'm going to guess that when the resultant vector of all the forces on the COG is behind the contact patch you can get a wheelie.

This is the maximum acceleration I think a motorcycle with this weight at that point can withstand continuously:

While this one will probably wheelie:

Does that math/reasoining work out?

That seems to go with the equation I gave in my previous post.

 

[Ranger Mike]

great points ..jack action ..

 

[Lsos]

Ok so I got in a HUGE argument with some people over on a car forum. They say that cars with longer wheelbases are harder to wheelie. I disagreed. I said it not only depends on the wheel base since that is an oversimplified way to look at it, it depends on where the center of gravity is in relation to the rear axle and the contact patch.

Both you and the people on the car forum are right. There should be no argument here. Let me guess, somebody said "NO YOU ARE WRONG!" or something to that effect. Testosterone then kicked in and then everybody started arguing, name calling, threatening violence, about what amounts to the same viewpoint.

ALL ELESE BEING EQUAL, a longer wheelbase WILL make it harder to do a wheelie. You are simply going deeper into it and specifying that the location of the center of gravity is what matters. Sure, you are right, but the center of gravity depends to a large extent on the wheelbase, which makes them simultaneously right.

There are of course other factors involved, and you could very well lengthen the wheelbase while skewing every other factor the other way just to prove your point, but it won't change the fact that the longer wheelbase still hurt you in your quest to do a wheelie.

Given enough thrust, you could make a brick fly in order to prove that larger wings don't increase lift. But guess what, they do.

Unfortunately, while both viewpoints are correct, the fact that there is an argument about this makes everybody wrong.

 

[michaelwoodco]

Both you and the people on the car forum are right. There should be no argument here. Let me guess, somebody said "NO YOU ARE WRONG!" or something to that effect. Testosterone then kicked in and then everybody started arguing, name calling, threatening violence, about what amounts to the same viewpoint.

ALL ELESE BEING EQUAL, a longer wheelbase WILL make it harder to do a wheelie. You are simply going deeper into it and specifying that the location of the center of gravity is what matters. Sure, you are right, but the center of gravity depends to a large extent on the wheelbase, which makes them simultaneously right.

There are of course other factors involved, and you could very well lengthen the wheelbase while skewing every other factor the other way just to prove your point, but it won't change the fact that the longer wheelbase still hurt you in your quest to do a wheelie.

Given enough thrust, you could make a brick fly in order to prove that larger wings don't increase lift. But guess what, they do.

Unfortunately, while both viewpoints are correct, the fact that there is an argument about this makes everybody wrong.

Well name calling hasn't started yet, just a couple of bets
so to sum everything up:

All else being the same, the car or bike with a longer wheel base will be harder to wheelie
all else being the same, a car or bike with a lower center of gravity will be harder to wheelie
all else being the same, a car or bike with a more forward weight distribution will be harder to wheelie

 

[jack action]

ALL ELESE BEING EQUAL, a longer wheelbase WILL make it harder to do a wheelie.

With a statement like that, you have to define «all else». That is a source of argumentation. Because, as I said in my earlier post, if you increase the wheelbase without changing the h/d ratio, you can increase the wheelbase as long as you want, it won't affect the wheelie capabilities of the vehicle.

If you scale up a car, increasing its wheelbase but also its CG height-to-wheelbase ratio, and weight distribution («all ratios being equal»), h/d is still the same.

If you modify a car by increasing the wheelbase, but keeping the CG height and the weight distribution the same («some length equal, some ratios equal»), h/d is not the same.

If you modify a car by increasing the wheelbase, but keeping the CG height and the front axle-to-CG distance the same («all lengths being equal except rear axle-to-CG distance»), h/d is not the same.

If you modify a car by increasing the wheelbase, but keeping the CG height and the rear axle-to-CG distance the same («all lengths being equal except front axle-to-CG distance»), h/d is still the same.

It is not a wheelbase thing it's a h/d thing.

 

[russ_watters]

With a statement like that, you have to define «all else». That is a source of argumentation.

Agreed.

Because, as I said in my earlier post, if you increase the wheelbase without changing the h/d ratio, you can increase the wheelbase as long as you want, it won't affect the wheelie capabilities of the vehicle.

If you scale up a car, increasing its wheelbase but also its CG height-to-wheelbase ratio, and weight distribution («all ratios being equal»), h/d is still the same. [emphasis added]

Well I would define "all else" to be all else. So if you change the wheelbase and you increase the height of cog (in order to keep that ratio the same), then you're changing something else besides just the wheelbase.

You're also changing (but not saying you're changing) every other physical specification of the vehicle in your "scale up" example: including the weight and engine torque*. So let me state the two cases another way:

1. A car with all the same physical specs as another except a longer wheelbase will have a harder time popping a wheelie.
2. A car with a longer wheelbase than another and a higher cog, larger weight and larger engine will wheelie the same. In other words, if you change everything about a car in proportion, it will have the same likelihood of being able to wheelie.

*[edit] That is kind of key: you can extend the front and back suspension of a motorcycle somewhat without substantially increasing its weight (or, at least, increasing it much less proportionally than the wheelbase length increase), but you can't make the bike physically larger in all dimensions including height without also increasing the weight. With cars, it is even easier to change just the wheelbase, since the wheels are not all the way on the front and back ends.

 

[russ_watters]

Obviously if the center of gravity were as low as the contact patch the car could never wheelie, (unless it came upon a bump or hill)...

Well...that's not quite 100% true. Your diagram and the equation Jack Action posted ignore the torque between the wheel and the car. The moment of inertia of the wheel coupled with its angular acceleration provides a torque that rotates the car up and back. So the reaction vector isn't straight back, it is also slightly up.

Now how big of a deal that is, I'm not sure, but the larger the wheel and faster the acceleration (ie, on a dragster), the bigger the impact.

 

[sophiecentaur]

I can't imagine how anyone can have a "huge argument" about something that is so amenable to straightforward calculations. Give the dimensions, the available torque, the performance of tyres and some information about the masses involved the answer is there for all to see.
If someone wants to over-generalise then there is no point arguing.

 

[michaelwoodco]

Well...that's not quite 100% true. Your diagram and the equation Jack Action posted ignore the torque between the wheel and the car. The moment of inertia of the wheel coupled with its angular acceleration provides a torque that rotates the car up and back. So the reaction vector isn't straight back, it is also slightly up.

Now how big of a deal that is, I'm not sure, but the larger the wheel and faster the acceleration (ie, on a dragster), the bigger the impact.

True, I forgot about that. I suppose it's kindof like motocross. If you're in the air and your bike is rotating to far back you can hit the brakes. If it's rotating to far forward you can nail the gas. It's a pretty small effect, but I suppose it depends on the "polar moment of inertia" of the wheel, if that is the correct term to use in this case.

 

[Lsos]

With a statement like that, you have to define «all else». That is a source of argumentation. Because, as I said in my earlier post, if you increase the wheelbase without changing the h/d ratio, you can increase the wheelbase as long as you want, it won't affect the wheelie capabilities of the vehicle.

I see what you're saying, but I'm sure any experimenter would know better than holding the h/d ratio constant. It would be like trying to tune an engine for power, while keeping the "torque x rpm" ratio constant. You're not going to make much progress. You break it up into it's fundamental constituents and tweak each one individually, not three, ten, or two (h/d) at once.

That said, since we're trying to isolate the effect of a linear dimension (the wheelbase) on wheelie capability, it would make sense that "all else equal" would mean holding all other linear dimensions the same. It IS possible to do, even if only on paper.

It's as basic as we can get. If we pick a convenient ratio and try to hold it equal at the expense of having to change many other dimensions, we're not going to effectively answer the question "what effect does wheelbase have on wheelie capability".

If out out of the infinite ratios and mathematical functions, we could pick anyone and try to hold it constant, what's stopping us from holding "wheelie capability" constant...and then changing all other dimensions in order to see if they have an effect on wheelie capability.

 

[michaelwoodco]

Well...that's not quite 100% true. Your diagram and the equation Jack Action posted ignore the torque between the wheel and the car. The moment of inertia of the wheel coupled with its angular acceleration provides a torque that rotates the car up and back. So the reaction vector isn't straight back, it is also slightly up.

Now how big of a deal that is, I'm not sure, but the larger the wheel and faster the acceleration (ie, on a dragster), the bigger the impact.

I see what you're saying, but I'm sure any experimenter would know better than holding the h/d ratio constant. It would be like trying to tune an engine for power, while keeping the "torque x rpm" ratio constant. You're not going to make much progress. You break it up into it's fundamental constituents and tweak each one individually, not three, ten, or two (h/d) at once.

That said, since we're trying to isolate the effect of a linear dimension (the wheelbase) on wheelie capability, it would make sense that "all else equal" would mean holding all other linear dimensions the same. It IS possible to do, even if only on paper.

It's as basic as we can get. If we pick a convenient ratio and try to hold it equal at the expense of having to change many other dimensions, we're not going to effectively answer the question "what effect does wheelbase have on wheelie capability".

If out out of the infinite ratios and mathematical functions, we could pick anyone and try to hold it constant, what's stopping us from holding "wheelie capability" constant...and then changing all other dimensions in order to see if they have an effect on wheelie capability.

What he said though kindof makes sense. Because by changing the wheel base, and leaving all else the same, you need to define in what ways you leave all else the same. Do you leave the weight distribution the same, the H/D ratio (angle to the CoG from the rear wheel) or do you leave the CoG with the same relation to the front wheel it had before you extended the wheelbase.
There is no way to change the wheelbase and leave all else the same, you can leave almost everything. For example with the same weight distribution you have to move the CoG back. Then you change the angle from the contact patch to the CoG

 

[Lsos]

I would think that unless it was explicitly stated that we want to keep h/d or CoG the same, then we would keep as many fundamental properties of the design the same as possible.

CoG and h/d can be based on many, many, many variables, and hence they are not fundamental.

Arbitrarily holding CoG or h/d constant would require changing lengths in two if not three dimensions. It would require changes in size, mass, weight, possibly in materials and who knows what else.

To illustrate my point, we could theoretically design both a car or an entire universe to have the same h/d and CoG. Clearly it doesn't make sense to compare a 1.5m wheelbase average car, and a 2m wheelbase universe-sized car in their wheelie capabilities. Yet it is being suggested that unless I clarify not to do so, this is a possibility.

So while I agree to an extent, I think when doing a back-to-back comparison of the effect of wheelbase on wheelies, anybody in their right engineering mind would know what variables to keep constant and what not to.