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 Physics and the theoretical
 CoG Height and Flickability?
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scottrnelson
Advanced Member
6888 Posts
[Mentor]


Pleasanton, CA
USA

KTM

990 Adv, XR650L

Posted - 03/17/2009 :  2:56 PM
quote:
Originally posted by Andrew Dressel

Foale and Cocco only mention center of mass height in the context of braking and acceleration performance.

That right there would be the biggest reason why race bikes would be designed to keep the center of gravity as low as possible. If a bike can brake harder without lifting the rear wheel or accelerate harder without lifting the front, it will have enough of an advantage to win races.
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Andrew Dressel
Male Standard Member
244 Posts


Milwaukee, WI
USA

Moto Guzzi

California Special

Posted - 03/18/2009 :  8:58 AM
Here's more information that might be interesting. Cossalter describes a Koch Index; apparently defined by J. Koch in his 1978 disertation in Berlin, but not used much since; that is the ratio of peak steering input torque to the product of forward speed and the peak roll rate. Cossalter says it "is mainly influenced by center of mass height, front wheel intertia, front frame inertia with respect to steering axis, frame inertia with respect to rolling axis and yaw axis." Touring bikes have a Koch Index of about 3, sport bikes between 1.5 and 2, and scooters of about 0.5.
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Tedd
Male Starting Member
9 Posts


Surrey, BC
Canada

Triumph

Speed Triple

Posted - 08/11/2013 :  11:27 AM
I'm very happy to find this thread, because this subject was the reason I joined this forum in the first place!

I first started thinking about the question of center of mass height years ago, when I rode a Honda GL500 Silverwing Interstate -- a heavy bike (for its displacement) that had, I suspect, a high center of mass. One of the things I noticed about the bike was that if you really chucked it into a turn it had a tendency to want to keep rotating. I.e., when you dropped hard into a turn you had to consciously stop the bike from rotating when you got to the desired lean angle. I've never felt quite the same effect on any other bike.

This got me thinking about the bike's moment of inertia about the roll axis through the center of mass. When moment of inertia comes up, it most often seems to be talked about in terms of the moment of the bike's mass about a longitudinal axis at the ground plane. So, if you have a high center of mass you also have a high moment of inertia (about the axis at the ground plane). But its entirely possible for a bike to have a high center of mass but also a low moment of inertia about a roll axis through the center of mass. And it seems to me that this might actually be the desirable combination, at least for a sport or road-racing bike.

The high center of mass would mean that the front tire contact patch has a long moment arm for initiating roll into a turn. For those of you who, like me, have more of a background in racing cars than racing bikes, this is directly analogous to the way a mid-engine car has better "turn in" than a front-engine car because of the longer moment arm between the front wheels and the center of mass.

But a low moment of inertia about the roll axis through the center of mass is also desirable, because it makes the moment that the front tire generates more effective in rotating the bike into the turn and because, once the bike is rotating, it's easier to stop the rotation when you get to the desired lean angle. That, I think, is what the Silverwing did not do well. I believe that it had a high center of mass and a high moment of inertia, so you could get it started "chucking" into a turn but it was hard to stop the "chuck!"

However, at low speed it seems to me that a lot of the balancing is accomplished by the rider's body "english." Using the Silverwing as an example again, when I had to maneouvre at very low speed I would often stand up on the pegs, like a trials rider, to give my body's mass a greater moment arm relative to the bikes's center of mass. A lower bike center of mass would have made low-speed handling easier.

So it seems to me that the following basic rules apply:

1. A lower motorcycle center of mass height is better for (very) low speed handling.

2. A higher center of mass increases "flickability" once above the (very) low speed range, other things being equal.

3. A lower moment of inertia about the bike's center of mass is always better.

Comments?
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Tedd
Male Starting Member
9 Posts


Surrey, BC
Canada

Triumph

Speed Triple

Posted - 08/11/2013 :  11:30 AM
Just trying to avoid a potential counter-argument: Yes, I realize that a high center of mass has other drawbacks, such as load transfer during acceleration or braking. For my purposes here, I'm only trying to understand its effects on turning and initiating a turn.
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scottrnelson
Advanced Member
6888 Posts
[Mentor]


Pleasanton, CA
USA

KTM

990 Adv, XR650L

Posted - 08/11/2013 :  2:57 PM
quote:
Originally posted by Tedd

2. A higher center of mass increases "flickability" once above the (very) low speed range, other things being equal.
My KTM 990 Adventure is taller then the Ducati ST2 that I rode before it. It is close to the same weight, but a few pounds heavier. The biggest difference is that it's quite a bit taller and therefore the center of mass is higher.

The Ducati, with the lower center of mass, had better flickability than the KTM. It took me quite a while to adjust to riding the KTM on twisty roads because of the added height.

I guess I'm disagreeing with point 2, based on my own personal experience.
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greywolf
Male Moderator
1495 Posts
[Mentor]


Evanston, IL
USA

Suzuki

DL650AL2

Posted - 08/11/2013 :  3:45 PM
I'll disagree with #2 based on experience and the physics of moment arm torque. It takes less effort to move a shorter arm (lower CoG) with the same weight.
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gymnast
Moderator
4265 Posts
[Mentor]


Meridian, Idaho
USA

Harley-Davidson

Sportster Sport

Posted - 08/11/2013 :  4:13 PM
All other things being equal, let me add,

a. unsprung weight
b. fork rake angle
c. length of wheelbase
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JanK
Male Junior Member
76 Posts


Ljubljana, Ljubljana
Slovenia

BMW

F650CS

Posted - 08/11/2013 :  5:38 PM
I'd say 1 and 3 yes. But if you add the requirement that the mass remains the same, 2 cannot be true, assuming realistic motorcycles, whose tires touch the ground.

You mentioned moment of inertia. Generally it depends on the square of the length. E.g., for a point mass circling at a radius R, it is m*R^2. The square "overrides" the linear advantage, that is gained by the increase of height of the centre of gravity. Since bikes' tires remain on the ground, an increase in height does provide a longer moment arm, but the moment of inertia has increased relatively more and offsets any gains made. You still need to put some steel between the tires' contact patches and the centre of gravity, so the mass can merely get redistributed. So you cannot have both the same moment of inertia and the same mass.

You could reduce mass to compensate. So a light tall motorcycle should be as flickable as a heavy low one.

You do not need two different bikes to test this. Try flicking your own bike while holding your body as tall and as parallel to the bike's centeline as possible and as close to the tank as possible (with no fore-aft movement of the centre of gravity, if possible). The bike should be easiest to turn when you're the lowest.
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scottrnelson
Advanced Member
6888 Posts
[Mentor]


Pleasanton, CA
USA

KTM

990 Adv, XR650L

Posted - 08/11/2013 :  7:50 PM
quote:
Originally posted by JanK

You could reduce mass to compensate. So a light tall motorcycle should be as flickable as a heavy low one.
I also happen to have a tall light motorcycle (actually two of them now). Lighter weight definitely makes a difference in being able to throw a bike around between turns. But what happens with the tall bikes is that the tires need to go further out to the side to get the same lean angle. That adds time to "flicking" them into a corner making it a bit slower.
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Tedd
Male Starting Member
9 Posts


Surrey, BC
Canada

Triumph

Speed Triple

Posted - 08/11/2013 :  11:01 PM
Thanks everyone for the replies.

I think I couple of people missed the distinction I was making between the moment of inertia about the ground plane and the moment of inertia about the roll axis through the C of M. Yes, if the C of M is higher then the moment of inertia about an axis at the ground plane will be higher, too. The relationship is:

Ig = I + m*r^2

where Ig is the moment of inertia about the ground-plane axis, I is the principle moment of inertia (about the roll axis through the C of M), m is the bike's mass, and r is the center of mass height.

But, with respect to initiating rotation, it's I that matters, not Ig. Roll is initiated by the lateral countersteer force at the front tire contact patch acting, at distance r, to rotate the bike about the C of M. Once roll is initiated, then the gravity couple continues the angular acceleration. And that, too, is enhanced by a higher center of mass (longer moment arm for the couple).

But there's another factor: the bike is also dropping into the turn. I.e., the center of mass has to translate downward while the bike rolls. And a higher center of mass means a greater translation, and therefore slower rotation. I wasn't thinking about that later part of the roll-in when I wrote my point #2. I was thinking purely of that first instant when countersteer initiates the roll. In reality, that may not be as important as the second effect, where the higher C of M slows the rest of the roll into the turn. If you picture an absurd example, such as one of those ridiculously high clown bicycles in the circus, it's easy to see that a higher C of M is definitely going to slow your roll rate, once you're past that very early initial rotation. Scott, I think that's pretty much what you were talking about in your second post.

So I think it's probably true that my point #2 doesn't tell the important part of the story. I think it's true in a limited, theoretical sense, but probably not the important factor in determining "flickability."
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twowheelsbg
Male Junior Member
50 Posts


Burgas, Burgas
Bulgaria

Suzuki

Posted - 08/12/2013 :  7:16 AM
quote:
Originally posted by greywolf

I'll disagree with #2 based on experience and the physics of moment arm torque. It takes less effort to move a shorter arm (lower CoG) with the same weight.


Might be wrong, but I would balance the discussion supporting #2.
It takes less effort to move/wrench not a shorter arm, but longer one.
Having higher COM and certain lateral forces at contact patches we end up with higher roll moment and higher roll rate/flick ability. This seems true for me in case of initiating the turn by counter steering, and also in the case of initiating the lifting of the bike at the end of the corner. Such 'easiness' to disturb the bike both to, and from corner has other advantage especially in the slippery/ dirt surfaces - the necessary roll in/out moments could be produced by fewer lateral forces amendments, that could be crucial in extreme traction demand situations.

I also don't agree with the example of compromised flick ability when standing on the pegs - here we have not only COM lifting, but also increased roll inertia, so it is not correct to judge the COM lifting effect alone.
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Andrew Dressel
Male Standard Member
244 Posts


Milwaukee, WI
USA

Moto Guzzi

California Special

Posted - 08/12/2013 :  8:24 AM
quote:
Originally posted by Tedd

With respect to initiating rotation, it's I that matters, not Ig. Roll is initiated by the lateral countersteer force at the front tire contact patch acting, at distance r, to rotate the bike about the C of M. Once roll is initiated, then the gravity couple continues the angular acceleration. And that, too, is enhanced by a higher center of mass (longer moment arm for the couple).



I believe you are mistaken about angular acceleration being enhanced by a higher center of mass. A bike is pretty closely approximated by an inverted pendulum, and in the equation of motion for a pendulum, angular acceleration is inversely proportional to the length. Thus, the higher the center of mass, the more slowly gravity increases the lean angle. That is one reason given for why upright bicycles are easier to balance than most recumbent bicycles: the higher center of mass means slower lean rates, which means easier to control.

How that bears on the rest of this discussion, I haven't thought through yet.
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Tedd
Male Starting Member
9 Posts


Surrey, BC
Canada

Triumph

Speed Triple

Posted - 08/12/2013 :  9:01 AM
"I believe you are mistaken about angular acceleration being enhanced by a higher center of mass."

I want to reiterate that I have only proposed that the higher center of mass might lead to more rapid initiation of roll, during the initial countersteer. To use the hammer analogy that someone used earlier, it's quite true that when the hammer is inverted (i.e., sitting in your palm with the head down) the natural frequency of it as a pendulum will be higher than when it's upright. I don't think anyone is disputing that. But if you visualize the lateral force required to start it rotating, it's also not hard to see that less force is required when the hammer is upright (head at the top) than when inverted.

The hammer example is nice because in both cases the principal moment of inertia is the same. The discussion can easily get clouded if people start comparing cases where both C of M height and moment of inertia are different. (That's one reason it's hard to learn much about it only by the experience of riding different bikes.)
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James R. Davis
Male Administrator
17286 Posts
[Mentor]


Houston, TX
USA

Honda

GoldWing 1500

Posted - 08/12/2013 :  9:43 AM Follow poster on Twitter  Join poster on Facebook as Friend  
Though I have zero experience at racing, and there are at least three physics gurus walking this thread, I'd like to add a bit of perspective to this topic.

While arguments employing a vertical hammer have appeal in visualizing the concept, I think the idea of 'flickability' refers to how easily/quickly the tire contact patches can be driven out from under the rider - not to how fast the rider can be leaned away from the tire contact patches.

If that is so, then a bike with a higher COM, it seems to me, is more 'flickable'.

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greywolf
Male Moderator
1495 Posts
[Mentor]


Evanston, IL
USA

Suzuki

DL650AL2

Posted - 08/12/2013 :  11:05 AM
So it's moving the handle under the hammer head. That is a better description. Still, a higher CoM (I like mass better than gravity for that description) will necessitate moving the hammer head up and down farther for the same lean angle, requiring more energy.

Goldwings are renowned for being among the more flickable of the big tourers because of their boxer engines. Now we need to include how inline crank engined bikes are more flickable than transverse crank types due to gyroscopic forces.

I hesitated to join this thread because I'm much more of a practical physicist than a theoretical one. Having time on various bikes, I have difficulty believing the differences I've noticed were entirely placebo effects.

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Andrew Dressel
Male Standard Member
244 Posts


Milwaukee, WI
USA

Moto Guzzi

California Special

Posted - 08/12/2013 :  1:27 PM
quote:
Originally posted by Tedd
I want to reiterate that I have only proposed that the higher center of mass might lead to more rapid initiation of roll, during the initial countersteer.



That might be what you meant, but what you wrote is

quote:
Originally posted by Tedd
Once roll is initiated, then the gravity couple continues the angular acceleration. And that, too, is enhanced by a higher center of mass (longer moment arm for the couple).



At any angle, the angular acceleration is inversely proportional to the distance from the pivot to the center of mass.

I know it is a small detail, and probably far from the main point of this discussion, but I have seen the assertion that shorter bikes are easier to balance than taller ones now and then, and I try to correct it when I can.
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JanK
Male Junior Member
76 Posts


Ljubljana, Ljubljana
Slovenia

BMW

F650CS

Posted - 08/12/2013 :  4:26 PM
quote:
Originally posted by scottrnelson

But what happens with the tall bikes is that the tires need to go further out to the side to get the same lean angle. That adds time to "flicking" them into a corner making it a bit slower.



I agree.

quote:
Originally posted by Andrew Dressel


Thus, the higher the center of mass, the more slowly gravity increases the lean angle.



The front wheel "shoots out" from underneath you with a higher rate of fork extension at higher roll rates. Would smaller vertical speed of the centre of mass unload the shock absorbers more? Would it have a similar effect on handling as if the rebound damping setting of the forks were too low? The motorcycle would be more stable, it would require greater rider input because of the lengthening of the wheelbase and trail. It would be less "flickable" as opposed to when the fork is compressed. This would match my observation that this happens more readily if the body position is more vertical, as opposed to hugging the tank.
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DataDan
Advanced Member
541 Posts
[Mentor]


Central Coast, CA
USA

Yamaha

FJR1300

Peer Review: 1

Posted - 08/12/2013 :  8:42 PM
quote:
Originally posted by Tedd

But there's another factor: the bike is also dropping into the turn. I.e., the center of mass has to translate downward while the bike rolls. And a higher center of mass means a greater translation, and therefore slower rotation. I wasn't thinking about that later part of the roll-in when I wrote my point #2. I was thinking purely of that first instant when countersteer initiates the roll. In reality, that may not be as important as the second effect, where the higher C of M slows the rest of the roll into the turn.

quote:
Originally posted by Andrew Dressel

I believe you are mistaken about angular acceleration being enhanced by a higher center of mass. A bike is pretty closely approximated by an inverted pendulum, and in the equation of motion for a pendulum, angular acceleration is inversely proportional to the length. Thus, the higher the center of mass, the more slowly gravity increases the lean angle.

Is the contribution of gravity even relevant?

Once roll is initiated--by the countersteering input--the motorcycle will continue to roll. It isn't obvious to me that gravity contributes enough to make a difference in perceived "flickability". I.e., the work could be basically done after the steering input.

I have a paper, Accident Avoidance Capabilities of Motorcycles (PDF), with graphs produced on an instrumented motorcycle executing a lane change. Figure 11, PDF page 37, shows the data produced by a skilled rider who countersteers effectively to initiate the manuever (some of the other riders are pretty lame). The "steer angle" plot shows a sharp steering input, which produces a change in "roll angle" ("lean angle" refers to rider body lean). Note that roll rate is fairly constant after initiation, so gravity doesn't seem to accelerate roll.


The data in the paper linked above was also used in another paper, "Rider Skill Influences on Motorcycle Maneuvering", which was collected in the 1978 SAE publication "Motorcycle Dynamics and Rider Control". BTW, does anyone have similar data more recent than the 1970s???

Edited by - DataDan on 08/12/2013 8:48 PM
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