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 Physics and the theoretical
 CoG Height and Flickability?
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Pike Bishop
Male Junior Member
55 Posts


Norfolk, Virginia
USA

Suzuki

DualSport DR650SE

Posted - 12/31/2008 :  6:34 AM                       Like
I've been reading an interesting discussion about how the height of a bike's center of gravity (CoG) affects its stability and steerability here:

http://www.advrider.com/forums/show...php?t=419105

Does anyone here have any thoughts on how, all other things being equal, a bike with a higher CoG behaves in comparison to a bike with a lower CoG?

There doesn't seem to be any agreement or even consensus about it on the other thread, and I don't have any real-world experience to form an opinion.

scottrnelson
Advanced Member
6883 Posts
[Mentor]


Pleasanton, CA
USA

KTM

990 Adv, XR650L

Posted - 12/31/2008 :  7:41 AM
It is more important that the mass be centralized than how high it is off of the ground. Sometime in the late 70's or early 80's there was a race bike made by Elf that put the fuel tank under the engine. The idea was to keep the center of gravity low. That was good for acceleration and braking, but very bad for getting the bike to lean into a turn. They quickly realized their error and put the fuel closer to the middle to improve handling.

I can't give you any facts on this subject, only my own experience. I just purchased a bike with a higher center of gravity and the stability is fine but it also has very quick steering. It's not like the tires stay in one place while the rest of the bike leans into the turn. The tires go out to one side while the bike leans to the other to initiate a turn, so a higher center of gravity doesn't seem to be a drawback.

The bigger difference for how quick a bike steers is its weight. My Honda is supposed to be 100 pounds lighter than my Ducati, but it feels like a bigger difference than that. But there are so many other variables between the two bikes that it is hard to know if any one thing makes the difference in handling.
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James R. Davis
Male Administrator
17286 Posts
[Mentor]


Houston, TX
USA

Honda

GoldWing 1500

Posted - 12/31/2008 :  8:34 AM Follow poster on Twitter  Join poster on Facebook as Friend  
quote:
It's not like the tires stay in one place while the rest of the bike leans into the turn. The tires go out to one side while the bike leans to the other to initiate a turn, ...

What a wonderfully insightful observation! Just as was discussed a few days ago here, at any meaningful speed it is easier for the contact patch to move laterally than it is for the mass of the motorcycle while at slow speeds just the opposite is true.

At least one world-class racing bike designer, Aprilia's Gaetano Cocco, is so convinced that height of the CG is of fundamental importance in a bike's 'flickability' that for a couple of years the racing bikes used by their factory team were designed with adjustable engine mounts that allowed the engine to be raised or lowered a few inches so that the individual racer could dial in exactly the feel he desired. Substantial controversy resulted from that design in that Mr. Cocco's belief that a higher CG would result in quicker leans was thought to be 'obviously' wrong by many. Could be, (I don't know!), but the Aprilia team certainly did spectacularly well on the circuit.

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scottrnelson
Advanced Member
6883 Posts
[Mentor]


Pleasanton, CA
USA

KTM

990 Adv, XR650L

Posted - 12/31/2008 :  9:56 AM
quote:
Originally posted by James R. Davis

[quote]At least one world-class racing bike designer, Aprilia's Gaetano Cocco, is so convinced that height of the CG is of fundamental importance in a bike's 'flickability' that for a couple of years the racing bikes used by their factory team were designed with adjustable engine mounts that allowed the engine to be raised or lowered a few inches so that the individual racer could dial in exactly the feel he desired.
The Aprilia RSV4, which they will be racing for the first time in World Superbike this year, also has adjustable engine mounts allowing it to be moved up and down about an inch as well as forward and back about an inch. They only wanted it on the race bike, but had to put it on all of the ones sold to the public to be allowed to use it in racing.
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greywolf
Male Moderator
1484 Posts
[Mentor]


Evanston, IL
USA

Suzuki

DL650AL2

Posted - 12/31/2008 :  11:18 AM
Flickability and stability can be on opposite sides of the fence. Today's super maneuverable military jets need computer controls on fly by wire inputs just to keep them in the air. Lose the computers on an F-117 and you need to punch out. Low CoG fans need to remember Weebles wobble. The easier it is to get a bike to lean, the harder it is to maintain an upright straight line. CoG height has similar comparisons to changes in rake and trail.
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BossMan
Male Starting Member
3 Posts


Cincinnati, OH
USA

Suzuki

SV650s

Posted - 03/16/2009 :  9:54 AM
Sorry to bring up an old thread, but does anyone have a definite answer? I mean isn't a motorcycle an inverted pendulum? wouldn't a lower CoG be better?
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James R. Davis
Male Administrator
17286 Posts
[Mentor]


Houston, TX
USA

Honda

GoldWing 1500

Posted - 03/16/2009 :  10:03 AM Follow poster on Twitter  Join poster on Facebook as Friend  
I don't know the answer to the question but it seems to me that the higher the CG is, the easier it is (and quicker) to steer the contact patches out from under it and, thus, the more 'flickable' it is.
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BossMan
Male Starting Member
3 Posts


Cincinnati, OH
USA

Suzuki

SV650s

Posted - 03/16/2009 :  10:09 AM
Ok, that makes sense, but do you have any more info about steering the contact patches out from under the bike? I can't visualize it without thinking of the rear tire slipping.
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James R. Davis
Male Administrator
17286 Posts
[Mentor]


Houston, TX
USA

Honda

GoldWing 1500

Posted - 03/16/2009 :  10:13 AM Follow poster on Twitter  Join poster on Facebook as Friend  
Counter-steering (indeed, any steering input) changes the location of the contact patches relative to the CG. You drive out from under your CG - and the bike leans.

Your impression of the tires being stuck in place while the CG moves is the problem. Inertia tries to keep the CG in place while traction allows horizontal forces to move the contact patches with ease.

The question is about how the high the CG must be for a fast lean to occur. Imagine that your CG was a tiny fraction of an inch above the ground and you will see that you can never get the contact patches very far away from being directly underneath it. But a higher CG allows you to drive quite far - horizontally - away from being directly below it and that means that you must be able to cause a bigger lean, more quickly, with a taller CG (at least to my mind).
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Geotiggy
Male Standard Member
247 Posts


Tonawanda, New York
USA

Aprilla

Atlantic

Posted - 03/16/2009 :  10:41 AM
quote:
Originally posted by James R. Davis

Imagine that your CG was a tiny fraction of an inch above the ground and you will see that you can never get the contact patches very far away from being directly underneath it. But a higher CG allows you to drive quite far - horizontally - away from being directly below it and that means that you must be able to cause a bigger lean, more quickly, with a taller CG (at least to my mind).



So if I'm imagining this correctly a bike with a low CoG wants to stay straighter up in a turn than a bike with a high CoG??? Worded differently, the bike with a high CoG will be able to lean into a turn further because it can sustain a contact patch that is further away from vertical???

(I got a 'D' in physics, so these things take time to percolate )
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James R. Davis
Male Administrator
17286 Posts
[Mentor]


Houston, TX
USA

Honda

GoldWing 1500

Posted - 03/16/2009 :  10:46 AM Follow poster on Twitter  Join poster on Facebook as Friend  
quote:
So if I'm imagining this correctly a bike with a low CoG wants to stay straighter up in a turn than a bike with a high CoG???

Absolutely not. The lean angle is determined by the speed and the radius of the turn and is not affected in any way by how high the CG is.

The question is about how quickly a bike can be put into that lean angle - and it seems to me that a higher CG can be put into a designated lean more quickly than can a lower CG.
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scottrnelson
Advanced Member
6883 Posts
[Mentor]


Pleasanton, CA
USA

KTM

990 Adv, XR650L

Posted - 03/16/2009 :  10:57 AM
quote:
Originally posted by BossMan

Ok, that makes sense, but do you have any more info about steering the contact patches out from under the bike? I can't visualize it without thinking of the rear tire slipping.
I get the impression that you're trying to think of what would happen when the bike is not moving. At slow speeds, it takes a while to move the tire contact patches away from the center of gravity. However at higher speeds, like maybe 30 mph, you're traveling 44 feet per second. If I can steer the wheels out of line far enough to achieve the desired lean angle in 10 feet, that means that I got it leaned over in less than one fourth of a second. In real world riding I wouldn't dare turn in that quickly.

----- End of answer to your question - start of additional thoughts -----

This has all caused me to think a bit more about turning dynamics and what it takes to get a bike settled. Let's say that the center of gravity of my XR650 is two feet high and I want to lean it 45 degrees. The center of gravity would have to drop down to about 1.4 feet before achieving stability. If I were to turn the wheels out to the side quickly enough the suspension would have to extend a bit before the weight dropped, due to gravity, to the correct height. But at a 45 degree lean there would be about 1G of cornering force, so the suspension would actually have to compress more before reaching equilibrium.

The ultimate result of the turning and changing of suspension forces is that during part of the turn there would be lesser forces on the tires available for acceleration or braking and during some part of the transition the forces would be greater for some small amount of time.

This just reinforces to me the advice of Keith Code in his book A Twist Of The Wrist II about how smooth you want the control inputs to be so that you don't upset the traction any more than absolutely necessary.
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James R. Davis
Male Administrator
17286 Posts
[Mentor]


Houston, TX
USA

Honda

GoldWing 1500

Posted - 03/16/2009 :  11:06 AM Follow poster on Twitter  Join poster on Facebook as Friend  
While my answer 'feels' right there is an obvious problem with the logic. The lower the CG is, the less lateral distance must be traveled by the contact patches to result in the same lean angle.

As I said in the beginning, I don't know the answer, I have a 'feeling' that my answer is right, but this is a physics forum and 'feelings' don't count for much here.
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(Deleted or Lost)

Posted - 03/16/2009 :  2:31 PM
Apart from the Aprilia bikes, with and adjustable COG, the only other way I can think of to evaluate the effect of different COG height while everything else remains as close to the same as possible, is with lighter and heavier riders on the same bike.
As an anecdotal sample, I can report that substantially lighter riders than me report that my BMW is 'heavy to steer, while I find it 'flickable' (but not 'very flickable'). This tends to support James' expectation, FWIW.


Edit:
After further thought, that really doesn't satisfy - too much subjective rider judgment.
Anyone willing to strap a 50 pound sack of rice to their torso and try riding their bike?

Edited by - The Meromorph on 03/16/2009 2:53 PM
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Andrew Dressel
Male Standard Member
244 Posts


Milwaukee, WI
USA

Moto Guzzi

California Special

Posted - 03/16/2009 :  2:32 PM
quote:
Originally posted by James R. Davis

I don't know the answer to the question but it seems to me that the higher the CG is, the easier it is (and quicker) to steer the contact patches out from under it and, thus, the more 'flickable' it is.



I thought I'd give this a try in my bike simulation, and the results seem to suggest that the short bike is faster. I set up a short bike with a center of mass at 0.6 meters and a tall bike with a com at 1.72 meters. I then generate an optimal LQR controller for each configuration and ask it to snap to a 5 degree lean (I need to keep the angles small because this is a linearized model and the linearization depends in part on small angles). At 50 mph, the controller applies nearly identical torque to the handlebars (4.5 ft-lbs) which causes nearly identical steering angles (0.5 degrees). The short bike crosses 3.0 degrees in 1.186 seconds, 4.0 degrees in 1.31 seconds, 4.9 degrees in 1.73 seconds, 4.99 degrees in 2.14 seconds and 4.999 degrees in 2.55 seconds. The tall bike crosses 3.0 degrees in 1.25 seconds, 4.0 degrees in 1.345 seconds, 4.9 degrees in 1.78 seconds, 4.99 degrees in 2.2 seconds, and 4.999 degrees in 2.62.

As already suggested, this could be more a product of smaller moment of inertia than lower center of gravity. To move the center of gravity, I merely moved the rider up and down. Moving the rider up while leaving the bike center of mass alone increases the total bike moment of inertia.
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James R. Davis
Male Administrator
17286 Posts
[Mentor]


Houston, TX
USA

Honda

GoldWing 1500

Posted - 03/16/2009 :  2:59 PM Follow poster on Twitter  Join poster on Facebook as Friend  
Oh great. We have another useful model for 'proving' reality. No doubt the algorithms within it are sound and properly interconnected, and it does not violate any obvious physics laws, so by manipulating it we can determine that a lower CG falls into a turn faster than a higher CG - or maybe even determine if global warming is man made.

I respect the fact that you did not claim to have learned a fact from the use of the simulator or that its results categorically or absolutely resolved the question.
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Andrew Dressel
Male Standard Member
244 Posts


Milwaukee, WI
USA

Moto Guzzi

California Special

Posted - 03/16/2009 :  3:51 PM
quote:
Originally posted by James R. Davis

Oh great. We have another useful model for 'proving' reality.



Ha! No, I don't expect models to prove reality. They can, however make some experimentation a lot easier, faster, and safer. Also, anything that is as dependent on operator skill as motorcycle performance seems to be is ripe for a numerical simulation to cut through the human factor.

quote:
Originally posted by James R. Davis
No doubt the algorithms within it are sound and properly interconnected, and it does not violate any obvious physics laws, so by manipulating it we can determine that a lower CG falls into a turn faster than a higher CG.



Well, the underlying equations of motion have been published in a peer-reviewed journal, and initial experimentation seems to agree with them.

quote:
Originally posted by James R. Davis
or maybe even determine if global warming is man made



Alas, that's a much harder problem, as would be predicting how quickly a particular bike would reach a particular roll angle. It is at least as sensitive to measured data as to the model used.

quote:
Originally posted by James R. Davis
I respect the fact that you did not claim to have learned a fact from the use of the simulator or that its results categorically or absolutely resolved the question.



That's the easy part. I've made enough mistakes in the past to know better, at least most of the time.
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greywolf
Male Moderator
1484 Posts
[Mentor]


Evanston, IL
USA

Suzuki

DL650AL2

Posted - 03/16/2009 :  5:12 PM
I love under 500lb middle displacement bikes and have owned my share. At steady speeds, nothing would bank faster than my BMW R90S. Flat twins have great roll rates with all that weight down low. You won't see any tall road racers either. It may not be scientific, but a look at competition bikes will have a lot to say about Physics. My vote is for bikes with a short moment arm from contact patch to C/G. I'll agree that centralized mass is a huge deal, but it's better centralized low.
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BossMan
Male Starting Member
3 Posts


Cincinnati, OH
USA

Suzuki

SV650s

Posted - 03/17/2009 :  12:36 PM
quote:
Originally posted by greywolf

I love under 500lb middle displacement bikes and have owned my share. At steady speeds, nothing would bank faster than my BMW R90S. Flat twins have great roll rates with all that weight down low. You won't see any tall road racers either. It may not be scientific, but a look at competition bikes will have a lot to say about Physics. My vote is for bikes with a short moment arm from contact patch to C/G. I'll agree that centralized mass is a huge deal, but it's better centralized low.



Don't most race bikes have a much higher CoG and seat height? It seems like a higher CoG is beneficial then.

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scottrnelson
Advanced Member
6883 Posts
[Mentor]


Pleasanton, CA
USA

KTM

990 Adv, XR650L

Posted - 03/17/2009 :  1:11 PM
quote:
Originally posted by BossMan

Don't most race bikes have a much higher CoG and seat height? It seems like a higher CoG is beneficial then.

Race bikes have a higher seat height than most cruisers and might even have a higher center of gravity than the typical cruiser, but that is required to fit everything into a much shorter wheelbase. They still go for the lowest rider position they can on those bikes. They try to put as much weight as close to the center of gravity as possible rather than trying to get the lowest center of gravity.
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Andrew Dressel
Male Standard Member
244 Posts


Milwaukee, WI
USA

Moto Guzzi

California Special

Posted - 03/17/2009 :  1:12 PM
quote:
Originally posted by BossMan

Don't most race bikes have a much higher CoG and seat height? It seems like a higher CoG is beneficial then.




Yes, but that could be just to provide enough ground clearance to lean in turns are far as they do.

Not surprisingly, given the lack of a solid answer so far, I cannot find much about it in any of my favorite references. Foale and Cocco only mention center of mass height in the context of braking and acceleration performance. Cossalter goes a little further, discussing the effect of center of mass height on various instability modes, but not mentioning its effect on handling, as far as I can tell. It seems to be either not important, compared to other factors such as the ground clearance I mentioned above, or hard to analyze.
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