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Hanging Off Mathematically Quantified!


Thielert
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One last assumption, the weight shift was purely lateral whereas it is possible to move over and downward, thus lowering the combined CG slightly. My intuition is telling me that if I add in these extra variables, the equations are going to become much more difficult to derive yet have little effect on the actual outcome.

 

I've posted my equations on several other forums and it has created a shitstorm of controversy. 500 years ago everyone knew the world was flat, if you believed otherwise you were a lunatic or a heretic. If you transported someone from the 15th century to modern day and told them the earth was actually round, they would not believe you because it would require a massive paradigm shift in the way they perceived their world.

This is the problem I'm running into with the whole weight shift thing. Riders are so convinced that weight shift is the key to fast cornering, that when I show them that it accounts only for about 4% of their cornering speed, the rest being attributable to lean angle, they don't or won't believe it.

 

I think the majority of riders believe that leaning off actually increases their cornering grip. It doesn't increase grip at all, your tires decide how much grip you have and not where you put your body weight. The only thing that leaning off does is reduce the required lean angle for any given corner. I have no technical data or even track time to back this up but 4% seems about right to me. I've experimented with hanging off of corners that I've been through a hundred times before at the same speed and leaning off simply reduces the bikes lean angle by a little bit (but a noticeable amount).

 

That 4% is a HUGE difference when it comes down to race terms. 4% at 80mph is an extra 3.2mph. That means if ground clearance is whats limiting your corner speed like it is for professional riders that means you'll be going through that corner at 83.2mph instead of being LIMITED to 80mph. That is a difference of 5 feet per second!!!!!! That means you'll be losing plus or minus 5 feet per second, every second through every corner that you rode through on the race track. At higher speeds that distance will be even greater while it will be shorter at lower speeds. Not only will you be losing distance on your competitors through every corner but you'll be losing that much more time down every single straight away because your corner speed and exit speed will be slower. By not leaning off in a race you could very well be down a full lap by the end of a race.

 

I'm not much of a math guru anymore so maybe Centurion can crunch the numbers and give us some more info on how much time you'll actually be losing. I can quote this from my twist of the wrist 2 book where Keith mentions that going through a corner at 60mph instead of 59mph is a 3/100ths of a second difference which is about 2.6 feet. On a 9 turn track that 1mph is nearly a full 24 feet per lap that separates you from the person that's only going 1mph through every corner.

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Fajita Dave, I couldn't agree more with you, you need to use every advantage on a race track and even a 4% increase in speed through a turn will give you a big advantage. Maybe my logic is off here but I'm also thinking that if you're not leaning the bike to near it's cornering limits then the hang off is not really gaining you much...you could achieve the same thing by simply leaning more until you either start dragging hardparts or run out of corner grip.

 

My statement that you have to learn to lean the bike first before you can get a big payoff from hanging off really stirred up some guys on the ZX-10R forum. They weren't getting the part about corner speed being roughly 96% attributable to lean angle and the last 4% from the hang off. They were thinking it was the other way around.

 

I told them to try this simple experiment, go to their local track or favorite twisty road and take the first corner at their normal entry speed without leaning the bike, using hangoff only to see if they can make the corner. That ended it, no more discussion after that.

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Great videos Eirik, man those guys look bolt upright compared to the modern style, it was all about lean angle back then but they seem to be going pretty darned fast despite.

 

That's amazing that there is only a three second lap difference at Phillip Island between Gardner and Hayden despite 20 years of development, the bikes back then were bucking broncos compared to what they have today and look how the lead kept changing hands. Those guys were real riders back in the day compared to the processions we have today. Seems like with all of the electronics and smooth power delivery we have now, there is only one really fast line around the track and everyone is on it.

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Fajita Dave, I couldn't agree more with you, you need to use every advantage on a race track and even a 4% increase in speed through a turn will give you a big advantage. Maybe my logic is off here but I'm also thinking that if you're not leaning the bike to near it's cornering limits then the hang off is not really gaining you much...you could achieve the same thing by simply leaning more until you either start dragging hardparts or run out of corner grip.

 

My statement that you have to learn to lean the bike first before you can get a big payoff from hanging off really stirred up some guys on the ZX-10R forum. They weren't getting the part about corner speed being roughly 96% attributable to lean angle and the last 4% from the hang off. They were thinking it was the other way around.

 

I told them to try this simple experiment, go to their local track or favorite twisty road and take the first corner at their normal entry speed without leaning the bike, using hangoff only to see if they can make the corner. That ended it, no more discussion after that.

 

One other consideration here is effectiveness of the suspension. If you are going around a corner that has bumps or rough pavement, you are counting on your suspension to keep the tire on the road, and the more you are leaned over, the less effective the suspension is at doing that. So even if you aren't at the lean angle limit for your bike, you can still get some benefit from hanging off to reduce the lean angle.

 

(To be clear, I agree that there is not a lot of point in hanging off you aren't near lean angle limits, especially if it compromises your vision or wears you out physically, but this is another consideration and a rider might use the hang-off technique in a particular corner to help the bike work better over bumps.)

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especially if it compromises your vision or wears you out physically

 

Yes, I have noticed that last part, it is much more physically demanding to move your body mass from one side of the bike to the other rather than just staying centered and leaning.

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Fajita Dave, I couldn't agree more with you, you need to use every advantage on a race track and even a 4% increase in speed through a turn will give you a big advantage. Maybe my logic is off here but I'm also thinking that if you're not leaning the bike to near it's cornering limits then the hang off is not really gaining you much...you could achieve the same thing by simply leaning more until you either start dragging hardparts or run out of corner grip.

 

 

You are absolutely right but there are other benefits of leaning off. Like hotfoot said the suspension works much more efficiently when the bike is as close as possible to vertical. I think another potential advantage of using body position is tire wear (again this is more for pros than the much more useful answer that hotfoot gave :P). If you spend a lot of time on one part of the tire it will surely wear out much faster than if you spread that wear over a wider area. So you can use body position to spread the wear over a larger area on the rear tire while your exiting corners. It wouldn't be a big deal at the start of a race but it could give you a big advantage by the end. If you watched motorcycle racing you may have noticed that the guys who keep it leaned over longer in every corner tend to fade back by the end of the race because their tires have fallen off quicker than their competitors who spent less time at maximum lean angle.

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mgp_2012_03_23_jerez_caseystoner_2644.jpg

 

That's Stoner, what do you estimate his lean angle is here? I'm guessing 55% minimum which would put him at a coefficient of friction of around 1.40 which is entirely plausible for sticky racing tires. Our sport tires for the street are good for 1.20.

 

I plugged the numbers for Casey in to the equation , assuming a suited weight of about 140 lbs, hang off of about 300 mm or about 12", bike weight of 350 lbs wet and a CG height of around 600 mm and I get a lean advantage of about 4.3 degrees and a speed advantage of almost 9 %. Not bad, pick up almost 9mph in a 100 mph turn, that's about 12 to 13 ft/sec.

 

I'm hoping to find someone who has data acquistion to prove my equations validity.

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Been flat out doing schools, so coming to this thread late...but my total seat of the pants is that hanging off vs not is worth more than 4.3 degrees. Would be nice to have some back up on this, I'm going to see if I can chase some data down.

 

Would have to have same rider, same bike, same turn as a minimum for this test.

 

CF

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Been flat out doing schools, so coming to this thread late...but my total seat of the pants is that hanging off vs not is worth more than 4.3 degrees. Would be nice to have some back up on this, I'm going to see if I can chase some data down.

 

Would have to have same rider, same bike, same turn as a minimum for this test.

 

CF

 

I thought I saw saw this is the twist 2 DVD .. same guy with different body position at the same turn and speed

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Would be great to see some hard data on this, theory is great but not worth much until you can validate it under real world conditions.

 

One thing I haven't crunched numbers on is lowering the CG by hanging off and down to the inside, my equation is all horizontal weight shift, might make a difference.

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In 1990, Gardner did a 1:33.9 race lap around PI on the NSR500. That is roughly 3 seconds off the fastest race lap ever, set in 2008 by Hayden IIRC. If you consider the billions spent on developing tyres, suspension, chassis, electronics, brakes plus the extra power and driveability of the modern 4-strokes, it's a pretty slim improvement.

 

 

I checked and your right, Hayden set the all time lap record of 1:30.06 almost 18 years after Gardner, 3.84 seconds difference or about a 4% decrease in lap time. Gardner had a distinctively old school, centered on bike style, Hayden is definitely a hang off type guy.

 

With the improvements in technology and riding style it begs the question, why such little payoff after 18 years of intense R & D in motorcycle technical development and changes in rider position?

 

My equation would predict a 4% drop in lap time from the changes in body position alone.

 

Food for thought and I don't pretend to have the answers.

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Been flat out doing schools, so coming to this thread late...but my total seat of the pants is that hanging off vs not is worth more than 4.3 degrees. Would be nice to have some back up on this, I'm going to see if I can chase some data down.

 

Would have to have same rider, same bike, same turn as a minimum for this test.

 

CF

 

I thought I saw saw this is the twist 2 DVD .. same guy with different body position at the same turn and speed

 

Guess I better go and watch that again!

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mgp_2012_03_23_jerez_caseystoner_2644.jpg

 

That's Stoner, what do you estimate his lean angle is here? I'm guessing 55% minimum which would put him at a coefficient of friction of around 1.40 which is entirely plausible for sticky racing tires. Our sport tires for the street are good for 1.20.

 

I plugged the numbers for Casey in to the equation , assuming a suited weight of about 140 lbs, hang off of about 300 mm or about 12", bike weight of 350 lbs wet and a CG height of around 600 mm and I get a lean advantage of about 4.3 degrees and a speed advantage of almost 9 %. Not bad, pick up almost 9mph in a 100 mph turn, that's about 12 to 13 ft/sec.

 

I'm hoping to find someone who has data acquistion to prove my equations validity.

 

Based on Centurion's picture, I have drawn a schematic in AutoCAD in order to estimate angles and forces.

 

I have assumed that the camera view was perfectly horizontal, that he was accelerating at the recommended 0.2 g, and that he was not supporting any weight on his right knee.

 

Note that Stoner may have felt his own weight grow from the assumed 140 lb up to 257 lb.

 

The magenta line of the picture shows the angle that the bike would have to be at if the rider wouldn't have hung off the assumed 300 mm.

 

Note as well that when the rider hangs off he doesn't change the location of the system's CG, but rather pushes the CG of the bike in the opposite direction (86 mm in this case, which means approximately 5 degrees of leaning saving).

 

That relocation of the bike's CG is as many times smaller than the hang off distance as times is smaller the weight of the rider respect to the weight of the system; hence, for lighter bikes and/or heavier riders, the hang off technique is more effective.

post-23333-0-35443700-1333741278_thumb.jpg

post-23333-0-17816500-1333741457_thumb.jpg

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Notice that he's not only off the side about 300 mm but also lowered his and the entire systems CG, I guessed 150 mm. I Plugged that in to the equation and got 5.11 degrees saved for a 10.4% net increase in speed through the corner, very close to what you measured graphically.

 

I'm convinced the equation is accurate and also that hanging off is a worthwhile endeavor. I'm in the process of tweaking my body position to take advantage of this effect.

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Note as well that when the rider hangs off he doesn't change the location of the system's CG, but rather pushes the CG of the bike in the opposite direction (86 mm in this case, which means approximately 5 degrees of leaning saving).

 

 

There are two ways to look at this but I prefer to look at that 5 degrees as a speed bonus. Casey would have to lean his bike to 62 degreees (impossible on current tire technology) to achieve the corner speed he is getting at 57 degrees lean.

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Note as well that when the rider hangs off he doesn't change the location of the system's CG, but rather pushes the CG of the bike in the opposite direction (86 mm in this case, which means approximately 5 degrees of leaning saving).

 

 

There are two ways to look at this but I prefer to look at that 5 degrees as a speed bonus. Casey would have to lean his bike to 62 degreees (impossible on current tire technology) to achieve the corner speed he is getting at 57 degrees lean.

 

The centripetal force for a given speed and curvature doesn't change with the lean angle of the bike, it is given by Fc = MCv^2. There is no "speed bonus" simply from the bike's reduced lean angle.

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Hanging off allows the bike to take the same radius corner with the same lean angle but at a higher velocity since the additional moment created by hanging off one side has to be balanced by some additional force on the other side. In this case , that additional force is an increase in the MV^2/R component (centripetal force) but since M and R are held constant, V has to rise to create the new equilibrium condition.

 

Simply stated, hang off the inside without changing turn radius or lean angle and your speed has to go up.

 

You can call it whatever you want but I call that a speed bonus.

 

 

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Hanging off allows the bike to take the same radius corner with the same lean angle but at a higher velocity since the additional moment created by hanging off one side has to be balanced by some additional force on the other side. In this case , that additional force is an increase in the MV^2/R component (centripetal force) but since M and R are held constant, V has to rise to create the new equilibrium condition.

 

Simply stated, hang off the inside without changing turn radius or lean angle and your speed has to go up.

 

You can call it whatever you want but I call that a speed bonus.

Provided the tire is capable of the increased centripetal force - If you are already at the traction limit, hanging off the inside does not guarantee an increase in speed.

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Correct, the maximum attainable speed through a turn of given radius is determined solely by the tires coefficient of static friction, the advantage in hanging off at that point is a reduction in the required lean angle and the attendant positive effects on suspension compliance.

 

So, at least In theory, two riders on identical machines with identical tires, one hanging off and the other centered, could take the same corner at the same maximum speed as long as ground clearance wasn't a factor.

 

Maybe it's the angle but I think this photo illustrates the point, at maximum lean, these guys seem to be staying more centered on their bikes but you know they are traveling very fast!

 

1967.jpg

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