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 Motorcycle Safety
 Physics and the theoretical
 Roll Centre
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nb89
Starting Member
4 Posts


London, London
United Kingdom

(None)

Posted - 05/13/2011 :  6:43 AM                       Like
I understand how the front and rear roll centres of a car can be found using the suspension geometry. I was wondering how it is determined for a motorcycle though? I assume for a trike, the rear roll centre can be found using the same method used for cars, but what about the front roll centre? Thanks.

James R. Davis
Male Administrator
17279 Posts
[Mentor]


Houston, TX
USA

Honda

GoldWing 1500

Posted - 05/13/2011 :  7:50 AM Follow poster on Twitter  Join poster on Facebook as Friend  
First, welcome to the site.

Second, this is the LAST place you should be looking for racing hints.

Third, your motorcycle is a single-track vehicle, unlike a car. A 'roll angle' for a single-track vehicle is merely its 'lean angle'.

A bike's lean angle is a function of the square of its speed and the radius of the turn it is riding. In other words, it is a function of its lateral acceleration.

Further, the lean angle of the bike is modestly different than the lean angle of its CG, depending on the width of its tires. The wider the tire, the greater the bike's lean angle as compared to the lean angle of its CG.

Is that sufficient for your needs or do you need formulas?
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nb89
Starting Member
4 Posts


London, London
United Kingdom

(None)

Posted - 05/13/2011 :  8:13 AM
Thanks for the reply. Wouldn't a trike with 2 rear wheels have a roll centre that is dependent on the suspension setup?
I'm just trying to get my head around how a three wheeled vehicle would behave when going round corners. With the front wheel located at the centre, would the weight on the front wheel remain constant throughout a bend, with any weight transfer being applied only to the outer rear wheel? This seems to be the case when I do moment calculations as the front wheel is at the centre of the track width. But when I visualise it, it seems some weight should also be transferred to the front wheel also.
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staticattic
Male Senior Member
410 Posts


Tampa, FL
USA

Honda

Shadow Spirit 750

Posted - 05/13/2011 :  8:32 AM
OK, you got me. I had never even heard that term before, so I had to Google it. I came across the "official" definition:

The SAE's definition of the force based roll center is, "The point in the transverse vertical plane through any pair of wheel centers at which lateral forces may be applied to the sprung mass without producing suspension roll".

That didn't do much for me, so I had to keep digging. I found this website which gives a diagram and added a few lumens to the light inside my head:

http://f1-dictionary.110mb.com/roll_center.html


"The roll centre is an imaginary, but accurately defined, point on the centre-line of the car around which the car rolls on its suspensions. The roll centre can be high off the ground, low, or even underneath the ground (it's only imaginary, remember). A line connecting the rear suspension roll centre with that of the front is called the roll axis. If the axis runs nose-down, the car tends to oversteer. If the axis runs nose-up, the car tends to understeer.The roll center of a car is where the car will roll (when cornering) when looked at from the front (or behind)."

I never knew there was so much math and physics involved in transportation. I find it all interesting, but some of it is over my head. The closest example that would relate to me was given on Wikipedia:

http://en.wikipedia.org/wiki/Roll_center

"Load transfer is of critical importance for vehicle stability in vehicle such as SUVs. Ideally in high performance applications load transfer tends to be minimized as a tire's performance is directly affected by the amount of load that it has to transmit. In a steady state turn the final load transfer, summed across all the axles, is only related to the position of the center of mass above the ground, the track width and the lateral acceleration. SUVs must shift their center of mass lower or decrease their lateral acceleration to avoid tipping. To keep them from tipping many auto manufacturer use tyres with lower grip to reduce the vehicles cornering capacity, or the roll stiffness balance front to rear can be altered to encourage understeer or oversteer as necessary to limit the maximum lateral acceleration of the vehicle."

Now I have some interesting reading for the rest of the day...
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DataDan
Advanced Member
538 Posts
[Mentor]


Central Coast, CA
USA

Yamaha

FJR1300

Posted - 05/13/2011 :  11:13 AM
I think it's an interesting question, nb89.

I actually misspent high school class time figuring out how to graphically determine roll centers for various car suspension configurations. [I will not be answering questions about how long ago that was, or if pneumatic tires had yet been invented.]

As staticattic found, the roll center is the point about which the vehicle is free to rotate in roll (side to side). Find the front and rear roll centers, connect them, and you have the roll axis. This is an important design consideration because the roll center / mass center relationship influences vehicle behavior in roll. When NASCAR folks talk about a track bar adjustment, it's a roll center change that affects handling.

Wondering about rear suspensions on trikes, I learned a little just by searching for photos. Some conventional trikes (two wheels aft) are apparently hard-tails (no rear suspension), and some have solid rear axles located by trailing arms. More interesting are some of the Gold Wing conversions I found, which have independent suspension located by double A-arms pivoting from a bolt-on subframe. However, all the ones I found have conventional telescopic forks up front, with roll center at ground level.

The Can Am Spyder (two wheels in front) has a double A-arm front suspension and a typical motorcycle swingarm at the rear (also roll center at ground level).


Theoretical considerations aside, does anyone have practical knowledge about trike handling behavior? Are some designs generally regarded as better handling than others?


edit, 12:54 CDT: removed an unsupported assertion

Edited by - DataDan on 05/13/2011 12:57 PM
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tusome
Male Junior Member
97 Posts


St. Louis, MO
USA

Harley-Davidson

Rd King

Posted - 05/13/2011 :  11:44 AM
Interesting that 3 wheeled ATVs were outlawed several years ago. I believe they were outlawed because of roll over issues. Now all you see are 4 wheeled ATVs. So if you follow the logic of society will we end up with 4 wheeled "motorcycles"?
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scottrnelson
Advanced Member
6882 Posts
[Mentor]


Pleasanton, CA
USA

KTM

990 Adv, XR650L

Posted - 05/13/2011 :  12:40 PM
quote:
Originally posted by tusome

So if you follow the logic of society will we end up with 4 wheeled "motorcycles"?
Well, some of us don't think anything with three wheels should count, unless it's a bike with a sidecar which can be removed to turn it back into a proper two-wheel motorcycle.
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gymnast
Moderator
4260 Posts
[Mentor]


Meridian, Idaho
USA

Harley-Davidson

Sportster Sport

Posted - 05/13/2011 :  12:45 PM
The Harley Davidson G model, Servi Car used mainly for parking meter enforcement had some "interesting" handling charicteristics and "getting it up on two wheels" was a common problem for those not trained in the vehicles proper use and limitations. At speeds of 40 MPH or so a curvy road was "interesting" and handling was a bit "vague". The Motor Company abandoned production of the last vehicle in the line up to use the flat-head 45 cubic inch motor about 1970, perhaps because of a combination of obsolescence and product liability problems.

http://static.howstuffworks.com/gif...vi-car-5.jpg
Note the wood pole behind the seat used to mark the tires of vehicles in time limited parking zones. The poles held a piece of chalk in the end. Used for parking enforcement, a Servi-Car could pay for itself with parking enforcement fines in about three weeks and generate the the patrol officers monthly salary in about the first three days of the month. Maybe even faster in Downtown Chicago.





Edited by - gymnast on 08/11/2013 10:29 AM
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greywolf
Male Moderator
1484 Posts
[Mentor]


Evanston, IL
USA

Suzuki

DL650AL2

Posted - 05/13/2011 :  2:26 PM
I used to drive a Cushman truckster at work as a University of Illinois mail messenger. It wound up on its side twice. Once making a left turn too fast and once on a hard braking. A union grievance required the University to lease four wheeled vehicles some time after I was no longer on deliveries. This is as close as I could find to what it looked like. When it was loaded, the center of mass was insanely high for the wheel placement.

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Tedd
Male Starting Member
9 Posts


Surrey, BC
Canada

Triumph

Speed Triple

Posted - 08/11/2013 :  10:26 AM
nb89:

A motorcycle doesn't have roll centers, as such.

A roll center is what's formally called an "instant center," in mechanics. It's a method of calculating the force vector transmitted from one body of a linkage to another body of the same linkage without having to calculate the forces on all the individual links. For example, some of the cupboards in your home probably have those fancy, four-bar-link hinges. If you know the geometry of the hinge you can find the instant center between the door and the frame, which would allow you to calculate how a force vector you apply to the door resolves to a force vector on the frame, without bothering to calculate the forces transmitted by the individual links in the hinge -- handy!

Strictly speaking, the roll centers on a car's suspension would only be instant centers if the tires were linked to the ground by pivots at the contact path, forming a "linkage" between the ground and the sprung mass. But, for all practical purposes, they behave as though the tires are linked to the ground, so it's a reasonable approximation to use the center of the contact patch as a "pivot point" in a linkage system, giving you a method of calculating the force vector on the sprung mass based on the forces at the contact patch.

The closest thing on a motorcycle would be the instant center of the rear swing-arm geometry. This can be very important in a shaft-drive bike, to minimize the torque effects of the drive system.
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Tedd
Male Starting Member
9 Posts


Surrey, BC
Canada

Triumph

Speed Triple

Posted - 08/11/2013 :  10:29 AM
I guess another example would be the anti-dive characteristics of the BMW "telelever" front suspension, which can be analyzed by finding the instant center of the linkage.
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