# Hanging Off

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I was wondering if anyone could quantify the reduction in lean angle at a given cornering speed or conversely the increase in cornering speed possible for a given lean angle while hanging off the inside versus a more upright riding position.

There are a lot of variables here I realize, so not looking for hard numbers, just a ballpark idea.

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This picture has been posted before (I believe by Kai but my memory is suspect) and I thought it gave a nice impression of the effect of body position and lean angle. As you mentioned there are quite a few variables so this is the best I can offer. Maybe Hotfot can do the math for us.

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I still have reservations with that display.

Look at the rider position in picture 1 and 5 and explain the 5 degree difference in bike lean.

Look at the rider position in picture 1 and 4 and explain why the bike leans over the same.

Picture #2 seems reasonable compared to picture 5.

My biggest gripe is with picture number 3. I cannot see how that should save you 13 degrees compared to #1 and #4. For me it doesn't compute. 44 degrees of bike lean, yes, but not 39.

However, I would love to have somebody point out exactly why it is like we see it, preferably backed up by calculations. Because I do not know for a fact, I simply state what seems and looks logical to me. And my logic can be wrong

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I still have reservations with that display.

Look at the rider position in picture 1 and 5 and explain the 5 degree difference in bike lean.

Look at the rider position in picture 1 and 4 and explain why the bike leans over the same.

Picture #2 seems reasonable compared to picture 5.

My biggest gripe is with picture number 3. I cannot see how that should save you 13 degrees compared to #1 and #4. For me it doesn't compute. 44 degrees of bike lean, yes, but not 39.

However, I would love to have somebody point out exactly why it is like we see it, preferably backed up by calculations. Because I do not know for a fact, I simply state what seems and looks logical to me. And my logic can be wrong

I'm having the same problem, I come from an engineering/technical background and would like to see the math. That is a great picture however for showing the different riding styles.

My biggest problem is with pictures 4 and 5. I've looked at the physics and from a statics and dynamics standpoint raising or lowering the CG should not affect the lean angle. The weight of the bike/rider combination, MG, is acting verticaly downward through the C of G, while the centripetal force that creates an equlibrium, MV2/R acts horizontally through that same C of G. Raising or lowering the C of G along the centerline of the machine at a constant lean angle,changes the moment arms of the two equilibriuim forces but their ratio remains constant (similiar triangles).

Expressed another way, if the rider suddenly were to raise himself upright in a corner, his C of G would also be raised causing him to flop to the inside of the turn but the centripetal force acting on his raised C of G would exactly counterbalance this with an opposing moment tending to move him back towards the vertical. The equilibrium would not change.

Maybe I'm missing something here in my analysis, I don't know but there is an easy way to find out. Simply ride at a constant speed/lean angle through a constant radius turn positioned as in picture 4, then suddenly raise your body up as in picture 5. I've actually tried this and there appeared to be no affect on my lean angle.

Please excuse my symbols, I cannot find a way to express Mass x Velocity squared divided by Radius on my keyboard except by MV2/R, I hope this doesn't confuse anyone.

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I still have reservations with that display.

My biggest gripe is with picture number 3. I cannot see how that should save you 13 degrees compared to #1 and #4. For me it doesn't compute. 44 degrees of bike lean, yes, but not 39.

Eirik, I did try to crunch the numbers, there is very little on the internet available on this subject so I treated it as a simple statics problem and made several determinations. Unless my logic is off, whilst hanging off the inside of the bike in a turn, not only the displacement of the riders weight horizontally is of importance but also the ratio of the riders mass to the total mass of the bike/rider combination appears to be of significance.

Intuitively, a very light rider on a massively heavy machine is going to have minimal affect on the lean angle of the bike/rider combination by hanging off the inside while conversely a heavy rider is going to have a rather large affect by hanging off the inside of a light weight machine. This is born out by the math calculations but I, like you, have failed in my logic occasionally.

Running the numbers with a 225 lb rider (suited up) displaced 6 inches to the inside of centerline on a 450 lb literbike, gave a rider mass to total mass ratio of 225/675 or .333 to 1. Plugging those numbers into a static equilibrium problem, I came up with a reduction in radial acceleration of right at .165 due to hanging off. That is significant and gave reductions in lean angles very close to what is shown in figures 1 and 3.

Once again, a disclaimer, I may have failed in my logic and in these cases, peer review is always necessary to reach a consensus.

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I still have reservations with that display.

Look at the rider position in picture 1 and 5 and explain the 5 degree difference in bike lean.

Hello Eirik, it appears that the only difference in pictures 1 and 5 is that in picture 5 the rider has displaced his entire body towards the inside of the turn which would reduce the lean angle for a given corner speed.

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I ride a touring bike, mostly locked into the tank with both knees. When I lean my upper body IN, leaning as far as comfortable, with my head betwean the windshield and the inside mirror, my internal protractor tells me I'm saving about 5-degrees. The above pictures back me up. I am pictures 1(usually) or picture 5 (when I want to feel like Tommy Hayden). Five degrees is actually a LOT of lean angle--on my bike, it is easily the difference btwean scraping pegs and scraping hard parts.

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This picture has been posted before (I believe by Kai but my memory is suspect) and I thought it gave a nice impression of the effect of body position and lean angle. As you mentioned there are quite a few variables so this is the best I can offer. Maybe Hotfot can do the math for us.

thankyou for that awesome pic .. I had felt that but I was unsure whether to say it coz everyone says you should hug the tank rather than sit upright .. woot woot

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Thank you for your efforts, Centurion - much appreciated! The reason why a higher CoG require less lean comes from the tyre width; if tyres had zero width, your math would be correct.

I still find it strange that leaning out only add 3 degrees of lean compared to neutral and that laying down on the fuel tank add 5 degrees of lean compared to errect, and that minutely leaning in compared to sitting in line save 5 degrees from neutral. And if hanging off to the inside save 13 degrees of lean from neutral, Hailwood should not have been able to win races in the 1978-80 era, or?

But I guess I'll have to accept the pictures as truth until (if) I can prove them wrong

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Thank you for your efforts, Centurion - much appreciated! The reason why a higher CoG require less lean comes from the tyre width; if tyres had zero width, your math would be correct.

OK Eirik, now you've gone and lost me.

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My point of confusion on the whole lean angle versus CG thing is that even the experts can't seem to agree and form a consensus. Please read the article above by James R. Davis, a recognized expert on motorcycle dynamics and especially the part where he claims motorcycle/ rider Center of Gravity has no effect on angle of lean in a turn. He may consider the effects of tire width on the argument to be of little significance.

Another article I read on motorcycle dynamics introduced the tire width argument and claimed low CG = higher lean angle, high CG=lower lean angle. An opposing view.

Ok, I watch MotoGP racing and the riders all seem to have this cornering thing down pretty well and all of them seem to be getting a low as possible CG. Spies seems to drag his elbows quite frequently. This low CG increases required lean angle for a given speed/ radius turn so that they can....... run out of corner grip sooner? I'm either missing something here or their are advantages of the lower CG that somehow outweigh the disadvantages.

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Due to tyre width, the contact point on the road doesn't sit in the direct line in the centre of the bike. The creates leverage and all sort of stuff that I cannot explain other than that because of this, height matters. And the wider the tyres, the more impact height re CoG matter.

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Due to tyre width, the contact point on the road doesn't sit in the direct line in the centre of the bike. The creates leverage and all sort of stuff that I cannot explain other than that because of this, height matters. And the wider the tyres, the more impact height re CoG matter.

OK, thanks Eirik, I'll try a Google search on the subject, if I can see some math on it it will make more sense. Right now it's going against my intuition which bothers me.

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Ahhhh got it, I drew a free body diagram and it's now quite easy to see the effect. The effective lean angle between the combined motorcycle/rider CG and point of tire contact is less than the actual lean angle through the centerline of the machine depending upon the ratio of CG height to tire width.

Skinny tires and a high CG would have little or no effect (think racing bicycle here) and the opposite extreme would be a long, low custom with a 300 mm rear tire and extreme low CG. Explains why they need an area the size of Texas to turn one of those things around ....lol!

Basically this answers my previous question, as in most things there is a compromise involved. The positive effects of shifting body weight low and to the inside of the turn is going to have a greater impact on turn rate than the lowering of the CG will have a negative impact.

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Here we go, I found this diagram that perfectly illustrates the point, the effective lean angle through the tire contact patch is less than the real angle measured through the centerline of the machine, hence the bike must be leaned further for a given turn radius/speed combination. The lower the CG the less the effective lean angle meaning you gotta really crank it over on it's side to make that turn. Learn something new everyday.

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1. 125 cc machine with a 130mm rear tyre and CoG 650mm off the floor. With a speed that theoretically required 40.5 degrees of lean would take an actual 45 degrees of lean.

2. 600 cc machine with a 180mm rear tyre and CoG 600mm off the floor. For the same cornering speed 47.5 degrees of actual lean is needed.

3. 1800cc cruiser with a 240mm rear tyre and CoG 500mm from the ground. For the same cornering speed 53 degrees of actual lean would have to be achieved. Not easy with a bike that cannot go past 38 degrees ;-)

Note: All examples with rider sitting bolt upright. Also, this was all theoretical, not from actual testing.

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Hanging off!! why do racers hang off? So that they can keep the bike as upright as possible to maintain more grip to put the power down earlier to get better drive out of a corner thereby making them faster? Would that sound about right? Personally I'm not too fussed about how many degrees my bike is at I just ride the bloody thing. I'm guessing you guys dont ride with a protractor attached to your bikes so you are at 47.25647859 degrees max lean angle, you know when your exceeding it cause your sliding along the track personally I know that when I'm over too far I feel the bike getting loose and wanting to push out from the front, stepping out in the rear or I'm tucking my elbow in and knee back in to the tank because its dragging too much . If I wasnt locked into the tank and had a good body position, head to mirror etc I wouldnt be going faster than I did prior to doing CSS where I learnt these skills.

Fact: Hanging off has definatley made me quicker plus it also looks very very cool!!!

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I stumbled across the book Motorcycle Dynamics on Amazon - might be worthwhile read of the resident math and physics geeks (count me out, even though I'm an engineer).

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Hanging off!! why do racers hang off? So that they can keep the bike as upright as possible to maintain more grip to put the power down earlier to get better drive out of a corner thereby making them faster? Would that sound about right?

No argument there OZFireblade, we were just discussing the magnitude of the effect and whether it could be mathematically derived.

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I was wondering if anyone could quantify the reduction in lean angle at a given cornering speed or conversely the increase in cornering speed possible for a given lean angle while hanging off the inside versus a more upright riding position.

There are a lot of variables here I realize, so not looking for hard numbers, just a ballpark idea.

You can have an exact idea by hanging off your bike while moving in a straight line rather than in a turn.

By relocating the CG of your body away from the vertical line that goes down between the contact patches, you are relocating the CG of the bike alone away from the same line in the opposite direction.

That last angle is what you are saving the bike from leaning in any turn.

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The lower the CG the less the effective lean angle meaning you gotta really crank it over on it's side to make that turn.

I would say that the combined CG (bike + rider) height and lean angle are independent.

http://forums.superb...indpost&p=26514

The big change comes from the angular relocation of both CG's respect to the line that joints front and rear contact patches.

The mass of the rider is several times smaller than the mass of the bike and it is concentrated a little higher than his belly button when seated (that is why relocating his rear end and upper body has more effect than leaning the upper body alone.

The angular displacement of the rider's CG respect to the combined CG must be as many times higher as his mass is smaller.

If the mass ratio is 1:3, such must be the ratio of angular deviation of each individual CG respect to the combined CG (just like a jigsaw with an asymmetric fulcrum and loads) .

Hanging off or not, the tires feel the same skidding forces; however, the suspension works at least a little better.

That happens because the axis of liberty of each suspension system is perfectly aligned with the vertical axis of the bike, while the reactive forces from the asphalt imperfections are perpendicular to the road surface.

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Yes, oh great owl. If you set up for the corner while you are in the straight, you can see how much lean you will save. First time I saw it happen was pretty cool.

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The lower the CG the less the effective lean angle meaning you gotta really crank it over on it's side to make that turn.

I would say that the combined CG (bike + rider) height and lean angle are independent.

http://forums.superb...indpost&p=26514

The big change comes from the angular relocation of both CG's respect to the line that joints front and rear contact patches.

The mass of the rider is several times smaller than the mass of the bike and it is concentrated a little higher than his belly button when seated (that is why relocating his rear end and upper body has more effect than leaning the upper body alone.

The angular displacement of the rider's CG respect to the combined CG must be as many times higher as his mass is smaller.

If the mass ratio is 1:3, such must be the ratio of angular deviation of each individual CG respect to the combined CG (just like a jigsaw with an asymmetric fulcrum and loads) .

Hanging off or not, the tires feel the same skidding forces; however, the suspension works at least a little better.

That happens because the axis of liberty of each suspension system is perfectly aligned with the vertical axis of the bike, while the reactive forces from the asphalt imperfections are perpendicular to the road surface.

you should write a book IMHO... its so hard to make something hard sound simple and be understood so well too imho...

PS. will bikes with "soft" frames or thin suspension cores (um, the metal rod at the center of the suspension) benefit much more if hanging off? ?

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