24 replies to this topic

[Nathan]

Hello!

 

I circle track race and have often wondered about where the C of G is on a vehicle in a banked corner relative to where it is when the car is on flat ground.  I can't help but think when a vehicle with a heavy left side weight bias enters a banked corner, the vehicles true C of G should lower.  Am I correct?

 

Thanks for any help.

[Greg Locock]

I don't know if there is a general rule of thumb. The truck I'm working on at the moment jacks up in corners which I'm not very pleased about. Also do you mean height or x and Y?

[Kelpiecross]

Hello!
 
I circle track race and have often wondered about where the C of G is on a vehicle in a banked corner relative to where it is when the car is on flat ground.  I can't help but think when a vehicle with a heavy left side weight bias enters a banked corner, the vehicles true C of G should lower.  Am I correct?
 
Thanks for any help.

The centre of gravity stays in the same spot no matter what. It is the vertical line through the CoG that matters. If the car or object is tilted so this line falls outside the base of the object - it falls over. Going around a corner makes the vertical line move outwards - if it again goes outside the object it falls over (a car would probably slide first). Having a tilt on the corner means that it becomes increasingly difficult for the line through the CoG to go outside the base of the car - the ultimate limit being when the track is vertical where the line can never fall outside the base so the corner speed can never be too high.
So I think the answer is that moving the CoG to the inside of the car means that the line though the CoG must swing to a greater angle before the car goes over - thus allowing a higher speed through the corner.

Edited by Kelpiecross, 15 February 2017 - 07:07.

[thegforcemaybewithyou]

Hello!

 

I circle track race and have often wondered about where the C of G is on a vehicle in a banked corner relative to where it is when the car is on flat ground.  I can't help but think when a vehicle with a heavy left side weight bias enters a banked corner, the vehicles true C of G should lower.  Am I correct?

 

Thanks for any help.

 

I think you're correct. In a banked corner the suspension gets compressed more compared to a non banked corner. Although the normal load from gravity should reduce a bit with the cosine of the angle.

 

Extreme case: You're going around in a vertical cylinder, normal load from gravity is zero. Load from the the "banking" is m*v^2 / r.

[Bloggsworth]

The centre of gravity stays in the same spot no matter what. It is the vertical line through the CoG that matters. If the car or object is tilted so this line falls outside the base of the object - it falls over. Going around a corner makes the vertical line move outwards - if it again goes outside the object it falls over (a car would probably slide first). Having a tilt on the corner means that it becomes increasingly difficult for the line through the CoG to go outside the base of the car - the ultimate limit being when the track is vertical where the line can never fall outside the base so the corner speed can never be too high.
So I think the answer is that moving the CoG to the inside of the car means that the line though the CoG must swing to a greater angle before the car goes over - thus allowing a higher speed through the corner.

"The centre of gravity stays in the same spot no matter what. It is the vertical line through the CoG that matters."

Really? I thought the centre of gravity moved around, depending on whether you are talking about static or dynamic, how fast the vehicle is moving. If the car was static on the banking dropping a vertical would move the CofG towards the inside of the banking - So it doesn't stay the same, the centre of mass would...

[Kelpiecross]

"The centre of gravity stays in the same spot no matter what. It is the vertical line through the CoG that matters."

Really? I thought the centre of gravity moved around, depending on whether you are talking about static or dynamic, how fast the vehicle is moving. If the car was static on the banking dropping a vertical would move the CofG towards the inside of the banking - So it doesn't stay the same, the centre of mass would...

I would have thought the centre of mass and the CoG were essentially the same for most practical purposes. The CoG doesn't (can't) move.

Edited by Kelpiecross, 16 February 2017 - 01:53.

[Greg Locock]

It certainly moves, relative to the contact patches.  Or vice versa if you prefer

[HP]

http://study.com/aca...n-examples.html

 

This definition also has an example on a banked corner.

[Kelpiecross]

http://study.com/aca...n-examples.html
 
This definition also has an example on a banked corner.

The picture of the red bus is the idea I am writing about. The line of action through the CoG either from gravity alone or in combination with sideways cornering forces moves about relative to the contact patch - but the CoG itself remains fixed.

[imaginesix]

I think he means the projection of the forces acting on the CoG where they cross the ground plane, and this assuming a fixed speed in the banked corner.

[Catalina Park]

I would have thought the centre of mass and the CoG were essentially the same for most practical purposes. The CoG doesn't (can't) move.

The vehicles I drive the centre of gravity can move a couple of feet in a few seconds even when stationary.

[saudoso]

Known to be actually capable of moving the COG around are sloshing liquids.

[Nathan]

I will try and get some illustrations made later to explain my thinking..

[Allan Lupton]

http://study.com/aca...n-examples.html

 

This definition also has an example on a banked corner.

 

 

The picture of the red bus is the idea I am writing about. The line of action through the CoG either from gravity alone or in combination with sideways cornering forces moves about relative to the contact patch - but the CoG itself remains fixed.

 

Sorry no, the bus in the diagram is parked on a sideways slope.

On a correctly banked corner the resultant of the centripetal acceleration due to cornering and the 1 g. vertical acceleration gives an arrow perpendicular to the road surface. Depending on the radius of the corner and the peripheral speed the bank angle of the track can get quite extreme - e.g. "wall of death" motorcycles on a near-enough vertical surface.

As has been said, the CofG of a vehicle is a fixed point, apart from second order effects from fluid in part-filled tanks.and no amount of muddled thinking can alter that.

 

Edited by Allan Lupton, 16 February 2017 - 17:17.

[munks]

First off, let's clear up "center of gravity" vs "center of mass". According to the Internet: "The center of mass is the mean position of the mass in an object. Then there's the center of gravity, which is the point where gravity appears to act. For many objects, these two points are in exactly the same place. But they're only the same when the gravitational field is uniform across an object." (http://study.com/aca...of-gravity.html) I think for a car, we can safely consider the gravitational field to be pretty uniform, so these terms are identical.

 

Second, any time you ask for a position, you need to ask relative to what. If you're asking for the CofG of a car, relative to itself, then yes Allan Lupton is essentially correct that it doesn't really move. But if you're asking if for the CofG relative to the ground surface, then it most certainly changes in a banked corner. The suspension would compress, lowering it, but as Greg says that could be somewhat counteracted if the vehicle jacks itself from the cornering forces. If you're asking relative to the tire contact patches, check Greg's other answer above.

 

BTW, I think in general it will lower relative to the ground surface regardless of the left-right weight bias. Although changing that bias might affect the amount for various reasons (non-symmetrical suspension setup, etc.).

[Nathan]

I guess another part I need to understand is, when I'm cornering what is relative to the center of gravity; the track surface, or the horizontal plane of the earth?

 

If we had a car with a 60% left weight bias, and let's say that 20% difference was ballasted in the left rocker panel. If we measured the CofG as we normally would with all four wheels flat on the ground, would we get the same CoF height and location if the same car had its CofG miraculously measured with it's right side tires 1 foot (300mm) off the ground?

Edited by Nathan, 17 February 2017 - 00:14.

[thegforcemaybewithyou]

Are you using the same springs on the left and right side of the car you imagine?

[munks]

I guess another part I need to understand is, when I'm cornering what is relative to the center of gravity; the track surface, or the horizontal plane of the earth?

 

If we had a car with a 60% left weight bias, and let's say that 20% difference was ballasted in the left rocker panel. If we measured the CofG as we normally would with all four wheels flat on the ground, would we get the same CoF height and location if the same car had its CofG miraculously measured with it's right side tires 1 foot (300mm) off the ground?

 

No. Take a piece of paper and draw your car from the rear (flat on a level surface). Draw a single point somewhere to represent the CofG - let's say it is slightly left of center and maybe a foot above the underbody. Now in order to get your right side tires 1 foot off the ground, you need to rotate the car around the left side tire contact, right? Go ahead and stab a pencil at the bottom of the left tires and rotate the whole paper. Notice that the CofG goes up and to the left. So it is now higher and with more bias to the left, relative to the flat ground.

 

But wait, what if the right side tires are 1 foot higher because the ground itself is banked? You'll still have more bias to the left, but height above the banked ground will be approximately the same as it was when the car was sitting on flat ground!

 

This is just a static analysis of a parked car, though, where the force of gravity is pointed straight down. If you're actually cornering and want to know the dynamic left/right bias, that's another level of complexity.

 

Are we getting your question answered here? It's difficult to gauge if we're giving you too much or too little information.

[Greg Locock]

There is a good reason why both Gillespie and Milliken kick off their respective Vehicle Dynamics books with a chapter on coordinate systems. It is less than thrilling reading (I've never made it all the way through)

[Kelpiecross]

Sorry no, the bus in the diagram is parked on a sideways slope.
On a correctly banked corner the resultant of the centripetal acceleration due to cornering and the 1 g. vertical acceleration gives an arrow perpendicular to the road surface. Depending on the radius of the corner and the peripheral speed the bank angle of the track can get quite extreme - e.g. "wall of death" motorcycles on a near-enough vertical surface.
As has been said, the CofG of a vehicle is a fixed point, apart from second order effects from fluid in part-filled tanks.and no amount of muddled thinking can alter that.

Sorry, no, What? I think during circle track racing the resultant is not perpendicular to the track surface. If it were this would imply that the cars were just cruising around the corners with no sideways g being resisted by the tyres - clearly in racing there is sideways g on the cars - so the resultant is not perpendicular to the ground but has swung towards the outside of the corner.
The aim of a banked highway turn may be to allow cornering at zero sideways g - but that is not the aim in racing.

[Allan Lupton]

The aim of a correctly banked corner is, indeed, that there should be no sideways load no matter if it is on a racing track or a public road. I have never suggested that when racing one has to use the speed for the banking to be correct. I have witnessed the use of the Milbrook test circle for record-breaking where the design speed of the outer (or Upper) lane is 100 m.p.h. and the speeds being achieved were some 30% above that. The easily visible angle to the track that the car made, showed the level of cornering force being generated.

My point in the above quotation is that the diagram shows the 'bus to be parked, as the arrow is vertically downwards (i.e. no dynamic component).

[Bloggsworth]

The aim of a correctly banked corner is, indeed, that there should be no sideways load no matter if it is on a racing track or a public road. I have never suggested that when racing one has to use the speed for the banking to be correct. I have witnessed the use of the Milbrook test circle for record-breaking where the design speed of the outer (or Upper) lane is 100 m.p.h. and the speeds being achieved were some 30% above that. The easily visible angle to the track that the car made, showed the level of cornering force being generated.
My point in the above quotation is that the diagram shows the 'bus to be parked, as the arrow is vertically downwards (i.e. no dynamic component).

Surely no sideways load only applies to parabolic bankings...

[Greg Locock]

What do you mean by parabolic banking? As a practical observation it is easy to drive right around the outer lane of our constant speed track at 180 kph using less than one finger's width of steering input. 180 kph is the designed neutral speed.

 

https://www.google.c...935,2554m/data=!3m1!1e3!4m5!3m4!1s0x6ad6a01e7bd833f3:0x27937b5120b2ceb7!8m2!3d-37.9327778!4d144.4319444!5m1!1e4

 

The comparison with MIRA's track is hilarious, the transitions from straight to curve were incorrectly calculated so the car does some rather nasty things on entry and exit from the banked corners. Their's is a nicer shape though, it's the curvy triangle

 

https://www.google.c...394,2778m/data=!3m1!1e3!4m5!3m4!1s0x487751974882bc0b:0xc2a35df50e30b0e1!8m2!3d52.553776!4d-1.462883!5m1!1e4

 

.

[Kelpiecross]

When considering the sideways forces on the tyres on a banked track: the horizontal sideways g loading through the CoG is always the same no matter what the angle of the banking is - it is dependent only on the radius of the corner and the speed of the car. What the banking does is split this sideways g force into two components - one along the surface of the road (which the tyres have to resist) and one vertically. So if the corner force is 1g and the bank angle is 30degrees the tyres have only to resist .86g (cos30), 60 degree bank - .5g (cos60) and on a vertical bank there is no sideways force at all (cos90).

[Fat Boy]

There is a good reason why both Gillespie and Milliken kick off their respective Vehicle Dynamics books with a chapter on coordinate systems. It is less than thrilling reading (I've never made it all the way through)

 

As far as this thread goes, everyone should just just look at Race Car Vehicle Dynamics (Milliken and Milliken). It's chapter 18, section 6 in my (pretty old) edition. If there are any questions past that, we can rejoin the conversation.