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Lean Angle == Turn Radius?


tweek
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I like to think of scenarios at extremes. So, What about negative trail? I mean ALOT lets say 50-70 mm behind the steering head.

 

I'm not sure I am clear about what you mean here. Do you mean the contact patch is behind the steering head itself or a line drawn through the steering head... ? That is what I call "normal" trail. "Negative" trail to me would be having the contac patch lead the steering axis.

 

To my understanding, "normal" trail puts the contact patch behind the point where an imaginary line extended from the steering axis meets the ground meaning the wheel will tend to self-correct into line with the direction of motion. Even when leaned over, there is a point or angle where the wheel will naturally balance or trail to. And I am proposing that, due to the compression of the suspension altering the rake/trail, the balance point or angle will be affected by more cornering force compressing the suspension. And, the more trail, the longer the lever that force has to act on. Actually, even if the suspension doesn't compress more, like with a bicycle, I think more downward force may still force the wheel to turn more outward.

 

I tested this idea on my associate's pro level racing mountain bike with disc brakes in the parking lot after work today and promptly crashed his bike... hard. He was not happy as he is training for the 24 hour endurance race at Big Bear next week and I tweeked the front wheel a bit...andy way...The left handle bar dug into my gut so hard that it tore a hole in my abdomen that is bleeding as I type this. No... really. I wish I had a video. I've never ridden a bicycle with disc brakes until today. I didn't stop to think that this guy routinely runs down mountains at like 60-70 mph or so and that his brakes might be different than mine. Me... I barely break 40 mph on my way to work everyday on my old road race bicycle... so there I was playing games trying to make the bike "run wide": around th parking lot and I barely touched the front brake, like a whisper of a hint of adding a microgram of pressure... like I laid my finger on the lever and the front wheel locked so hard I was over the handle bars and tangled up so fast my head spinning and I couldn't get untangled... not a dignified position for a man in his mid-forties. Anway... I just want you to understand my level of dedication to, er... stuff like this and to know just how much I have already sacrificed in pursuit of "the answer"... lol

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WOW! I hope you're alright. That is dedication!!!! Thanks for take one for the team.

When I said negative trail, I meant actually behind the steering head. But when I read "shopping cart" the light came on. All it would become is a shorter wheel base. So, never mind my thought.

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Right, moving the contact patch further back is further back on the same side of the steering axis. More trail, shorter wheel base.

 

Im still trying to figure out how the "rear wheel steers the bike" thing fits into my theory.

 

And if the front wheel is turning out, won't THAT counter steer the bike down more? Argh.

 

 

Edit: Maybe the tendency for the bike to lift up with more velocity is sort of balanced by the tendency to countersteer it down again...

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Alright, I need to conduct an experiment on a bike that has a throttle. The bicycle in the parking lot just isn't going to get it.

 

I don't currently have access to a motorcycle, so, anyone out there who cares to assist, please try this at your own risk... run into a corner (not hanging off) and take your hands off the bars (roll out of the gas). The bike will run wider. But, I want to know if it will actually stand up as well merely by rolling out of the gas (with no steering input), or merely run wider.

 

Taking your hands off the bars should isolate the "self-countersteering" theory.

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I was reading over some material and I think I might have been mistaken wrt the theory of a bike counter-steering up by simply being off the gas... as opposed to braking while leaned over.

 

That would fit in better. Still mulling the rear being responsible for steering while leaned over. I get the idea that the front is merely following along... as long as you are on the gas. But I can't get away from the idea of the front taking over off the gas, ie the steering follows the weight. And maybe that is the rub.

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I see your thought process. So, I played with the hands off idea for the last three days and really paid attention to not only the bike running wide, but how it is running wide. At speed above 30 MPH the bike runs wide (which we know it will do) and felt as if it was rotating around its center mass to stand up, but plowing the front. Almost as if it would lean all the way to the other side if something else wasn't pulling it back down (very slight). Automatic "pick-up" counter steering? Tire bite? gravity? . Now, at speeds below 30 MPH or when my bike would slow beyond that, it would stand up, but pull / turn to the inside of the corner the more it slowed. I tried this on all types of corners, tight, slow, fast, banked, off camber ect and the result was the same and only varied slightly.

 

I started to think about the rear and how it plays in steering the bike (off the gas). The rear tire wants to go to the outside of the corner and uses the steering head as a pivot point. I kept thinking the front contact patch may play a part in the pivot point, but if that was the case, a bikes tendency to self correct during a rear wheel slide would not happen. The rear is pivoting around the steering head.

 

I also thought of hard braking. If on the brakes hard with the rear wheel in the air, the bike will not lean in. If the wheel in touching the ground it will follow the front wheel

Now, lets say you're using a slipper clutch (at speed) , the bike will lean in, but pivot around the steering head like a flat tracker. I guess that brings up the question we're talking about. At what point does the rear want to go to the out side or track the front wheel.

And of course rear end chatter while leaning in is SCARY. Rear end chatter has it all. Grip, no grip, tracks the front, then doesn't track the front, will lean in, then will not lean in.

 

I'm sure glad the laws of physics still work even if you cant understand them. :)

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Wow. Thank you for all of that. I'm gonna need some time to digest it all. But all of it is familiar.

 

What sort of lean angles were you using? Did you ever try letting go at steep(er) lean angles? How tight were you turning at 30 mph? How leaned over?

 

PS - I am not encouraging you to have an (-other) accident here... lol. I'm sure your ribs are still sore.

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I cant wait for saturday. all my stuff is packed and the plane leaves tomorrow morning. I plan to spend some quality time in Mr. Barber's museum and watch my friends who are doing the two day camp.

 

anyway - I'll get to work on the stuff this thread has been about from the beginning: turning the bike like a wild man.

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I was riding a BMW 1150RT. The corners I used the most were freeway clover leaf style on ramps posted at a "cautionary" speed of 25 MPH and 30 MPH. You know, the ones you try to double. :)

I was leaning around 30 to 35 degrees and not hanging off. I think the beemers max lean is 42 (ish) degrees before scraping pegs.

Thanks for the safety concerns. If anything, having my hands off the bars keeps me from placing any undue pressures on the bars and tucking the front (again) ha! . ;)

 

The funny thing about this link is Keith did all this for YEARS to research his books. (And still does) I'm sure he could easily shed some light on the question we're trying to answer. But that would take all the fun out of it.

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The funny thing about this link is Keith did all this for YEARS to research his books. (And still does) I'm sure he could easily shed some light on the question we're trying to answer. But that would take all the fun out of it.

Exactly!

 

I'm glad you understand. ;)

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I cant wait for saturday. all my stuff is packed and the plane leaves tomorrow morning. I plan to spend some quality time in Mr. Barber's museum and watch my friends who are doing the two day camp.

 

anyway - I'll get to work on the stuff this thread has been about from the beginning: turning the bike like a wild man.

 

Have a safe journey and great time, tweek! We'll be expecting an Earth shattering Ka-Boom of riding epiphanies upon your return!

 

I really envy you getting to ride Barber, dude. It looks like an AWESOME track on the AMA race tape I've been watching. I suppose I'll just have to settle for being patient while waiting for my birthday... at Mid-Ohio in August.

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OK, it's quite late and I am fading fast, but... to review...

 

I have been attempting to isolate downward force at the front to use as an analogy for increased downward force on the suspension in general due to increased cornering force when carrying more speed through a corner. And also attempting to define and isolate a state of equilibrium (from the forces of forward acceleration), ie we are not increasing speed or acceleration through the corner. We are still at 60/40 r/f weight distribution... just at a higher speed. 60/40 at 75 mph compared to 60/40 at 60 mph. (60/40 @ 75 mph should carve a wider arc than 60 mph.)

 

We have a given from tweek that lean angle remain the same as velocity and radius increase. The bike is not standing up with less lean angle to describe a wider radius arc.

 

With ice skates and snow skis, this lean angle vs radius is mechanically determined and tweek's original idea (the title of the thread) holds true. Lean angle determines radius. Whether discussing the ice skate's "rocker" or the side cut of the ski, the radius is predominantly pre-determined by lean angle and the relationship between lean and radius is directly proportional for all speeds. The faster you go, the more you must lean to balance and the tighter your line will be. Not so with a motorcycle. While lean angle and radius are mechanically related, that relationship is affected by speed. You can go faster at the same lean angle and vary the radius of your turning arc.

 

So... the question is why does the bike run wide merely from a higher speed and consistent lean angle?

 

If we start with the fact that the rear is responsible for stabilizing the bike and/or the direction of travel while leaned over... then we probably should not ignore this as a source for what causes the bike to run wide under increased cornering force.

 

So, when the tire is leaned over, the contact patch is not symmetrical. It is conical (cone shaped) like a styrofoam cup rolling on its side. The base is smaller than the top lip hence it rolls in a circle. So, does a styrofoam cup roll in a wider radius circle the faster you roll it? I don't think so.

 

The bike is not standing up but what could make it act as if it were? Might the tire deform more under the increased cornering force... the faster you go the conical shape of the contact patch changes thereby altering the path? How would the contact patch change? Bigger? Would the tire carcass actually set or roll further up toward the center of the tread creating the same effect as if at less lean angle?

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Alright, even though there is more cornering force applied to the suspension and at the contact patch, if the bike is accelerating, the suspension actually extends rather than compressing as the chain pulls the swingarm down like a lever forcing the rear to rise. And the front gets light and tries to rise under acceleration as well (the beginning of the wheelie process).

 

So, the front fork does not compress under acceleration in a corner, even at relatively low acceleration of 60/40 and higher relative cornering forces.

 

So... the wheelbase gets a tad longer and the fork gets longer so maybe the front wheel turns out due to the geometry ... but the front is still merely trailing under acceleration. The rear wheel is in control.

 

Could it be gyroscopic precessional forces? The rear wheel will try to turn opposite the direction of the lean if it is lifted... or merely torque attempting to lift the lean angle is applied at the rear axle. Nah.

 

The rocker, the sidecut... it has to be a physical matter of the effective radius of the rear tire. Has to be. Or it is slightly sliding, ie. not tracking precisely.

 

OK... the rear wants to stand up, is trying to stand up more at higher speed. Newton's laws and all. So, as the bike is accelerating, we have to apply pressure at the bars to maintain the same lean angle. But when we are merely carrying more speed to start with and maintaining the same rate of acceleration (60/40) at the same lean angle, what is different?

 

Either the tire is "creeping" or semi-sliding and tracking less precisely or the contact patch is effectively a larger radius. If the front does not affect the direction at a stable lean angle, I don't know what else it could be.

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An instructor at a local riding school recently told me that a rider must apply slight pressure to the bars to maintain lean angle under acceleration (to prevent the bike from standing up?) and that hanging off with your upper body just the right amount will create equilibrium without applying pressure to the bars. I have not had the opportunity to play with this. And I don't know if it has any bearing on the question at hand.

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Either the tire is "creeping" or semi-sliding and tracking less precisely or the contact patch is effectively a larger radius. If the front does not affect the direction at a stable lean angle, I don't know what else it could be.

 

Does nobody else have any thoughts on this?

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Either the tire is "creeping" or semi-sliding and tracking less precisely or the contact patch is effectively a larger radius. If the front does not affect the direction at a stable lean angle, I don't know what else it could be.

 

Does nobody else have any thoughts on this?

 

I believe that is a true statement. Kinda. What about rotating mass in the front wheel. IE A loooong wheelie. During a long wheelie, the front tire will stop spinning, which causes the bike to become unstable and more difficult to maintain an upright / straight line. Can still be done, but it harder to do.

Is this the same principle as the bike being leaned over (on the gas) with the front wheel off the ground maintaining the same radius? IE corner exit.

 

You mention skis. Now that makes sense. The lead edge followed by the trailing edge because it's a solid piece. Turn that leading edge and the rear edge must pivot around the lead edge, thus pushing snow away from it.

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You mention skis. Now that makes sense. The lead edge followed by the trailing edge because it's a solid piece. Turn that leading edge and the rear edge must pivot around the lead edge, thus pushing snow away from it.

 

I'm not sure I am following you here.

 

Snow skis have a curved edge or sidecut (when viewed from above) that allows the ski to bend when leaned over on edge creating a curved edge that carves the snow. The more you lean the ski, the more the ski bends and the sharper the curve of the edge in contact with the snow, hence, the tighter the ski turns.

 

Mogul skis are softer with a deeper sidecut to allow really sharp turns between the bumps.

 

It's a less precise process in powder than on hardpack, but, still the same basic action.

 

If the ski does not track precisely, say on ice, in powder or during less aggressive or lazy skiing, or with "beginner" skis with less sidecut performing a "snow plow" into a "step turn" or "christie" or simply more of a sliding style, the rear may tend to slide and "rotate" around until it catches and the ski begins to carve. This sliding technique is useful in many situations, but, I guess I am thinking of really good skiers (like racing in good conditions) who utilize the sidecut to really carve the ski.

 

Anyway... if one is sliding more than carving the ski, then more velocity will cetainly increase the radius of a turn. But if the ski is carving, then the lean angle determines the radius. And the faster you go, the more you lean and the sharper the ski turns... until you slide.

 

Is this what you are thinking of?

 

 

Anyway, the rear tire may be tracking "off radius" or off center on a tangent so to speak that might account for the increased turn radius or maybe the tire is squishing or rolling the carcass away from the edge effectively creating a larger rolling radius... these seem to be the best two ideas I can come up with. I'm about ready to throw in the towel and do some research on Google.

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Alright, even though there is more cornering force applied to the suspension and at the contact patch, if the bike is accelerating, the suspension actually extends rather than compressing as the chain pulls the swingarm down like a lever forcing the rear to rise. And the front gets light and tries to rise under acceleration as well (the beginning of the wheelie process).

 

So, the front fork does not compress under acceleration in a corner, even at relatively low acceleration of 60/40 and higher relative cornering forces.

Upon further consideration, I realize that I don't know this for certain. Can cornering forces "overpower" the tendency for acceleration to extend the (front) suspension? For instance, under mild acceleration rates such as will effect a 60/40 weight distribution, will some level of increased velocity create enough cornering force to balance or even counter-act the lifting effect (at the front) of that relatively mild acceleration?

 

 

So... the wheelbase gets a tad longer and the fork gets longer so maybe the front wheel turns out due to the geometry ... but the front is still merely trailing under acceleration. The rear wheel is in control.

Or not?

 

Is it true that a small amount of force must be applied to the inside bar to maintain lean angle (unless hanging off)?

 

Would this mean that in fact the front is constantly controlling or affecting lean angle as the bike is attempting to stand up under acceleration?

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I cant wait for saturday. all my stuff is packed and the plane leaves tomorrow morning. I plan to spend some quality time in Mr. Barber's museum and watch my friends who are doing the two day camp.

 

anyway - I'll get to work on the stuff this thread has been about from the beginning: turning the bike like a wild man.

 

Have a safe journey and great time, tweek! We'll be expecting an Earth shattering Ka-Boom of riding epiphanies upon your return!

 

I really envy you getting to ride Barber, dude. It looks like an AWESOME track on the AMA race tape I've been watching. I suppose I'll just have to settle for being patient while waiting for my birthday... at Mid-Ohio in August.

 

I wrote up about 4 pages worth of stuff - but my hosting company is servicing the database server so my Blog is down. at least that is what I hope is going on. I'll know tomorrow.

 

Anyway - a great time was had by all. Especailly the 11 yo kid who was ripping up the track. I'm seriously impressed with how well Keith and his crew worked with him. Then again, maybe I shouldnt be - they're used to dealing with kids - just bigger ones.

 

While I wait on my server to come back to life here are a few videos -

Me doing the level 3 knee to knee drill - http://www.livevideo.com/video/8962177B497...-barber-08.aspx

Dylan showing how its done - http://www.livevideo.com/video/46B7908D536...-barber-08.aspx

View of turn 7 from the Museum - http://www.livevideo.com/video/85A24AE112F...useum-turn.aspx

 

I should start a new thread about this - I'm still agog at how great level 3 is. The hook turn is wild and the knee to knee drill is NOT what I thought it was.

 

And really - Lean Angle != Turn Radius. Seriously. I was sooo wrong. sooo very very wrong. I could go on but I'd end up being rude about how wrong I was. Just learn to hook turn and quick turn together and the fun will never stop!

 

Oh - get reference points. Unless you like to see Keith's eyebrows climbing up his forehead as you answer his questions about what you are looking at.

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Welcome back, tweek!

 

It sounds like you had a great time. I'm really looking forward to reading your blog.

 

I can't tell from the video what the "knee to knee" drill is about. What are you trying to do there?

 

Also, I'm not clear what your symbols mean here: "Lean Angle != Turn Radius". Is the exclamation point like a slash through the equal sign meaning that lean angle does NOT equal turn radius?

 

Thanks,

 

racer

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"Everybody knows that the faster you go, the steeper you have to lean to get around a turn. Right? Okay I agree. The more speed you have, the more centrifugal force is generated pushing you to the outside and steering to a steeper lean angle compensates for that force and allows you to hold your line."

 

~ Keith Code, A Twist of the Wrist II, page 67

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!= er equals "not equal too"

 

== is the C/C++/Java/C# token for equality

= is for assignment.

 

Silly programming stuff.

 

 

oo00oohh... now i get it.

 

thanks

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Saw this discussion and had some thoughts.

 

Just wanted to jump in here with a possible idea on the same lean angle describing a wider arc at a higher rate of speed thing. I know squat about physics, but from thinking about this:

 

This happens with cars too right? for a given front wheel steering angle the car will cut a wider arc at a higher speed. With a car the front turned in wheels move the front of the car inside the path (turns the car) at a given rate (unless it slides). If you increase the speed the vehicle travels farther for the same given rate of inward movement (turning) therefore a wider arc for the same steering input.

 

Now with the bike's wheels do they not create an inward turning from rolling on a cone shape (inside of tire smaller diameter than outside of contact patch area, creating a cone shaped rolling object, creating an inward (turning) force that is (like a car's turned wheels) constant. Then with an increase in speed and a constant inward turning force, the vehicle travels farther for a given amount of inward turning force from the cone, naturally describing a wider arc to the turn.

 

In addition to that often a bike will steer a small bit into the turn once countersteering in is finished, more so at slower speeds, less at higher speeds, but if the bike is tracking and not sliding there is some amount of front wheel turn in is there not? While the rear may take the bulk of the turning on, I wouldn't be surprised to find the front contributing something. Sure you can wheelie mid turn, but that doesn't mean the front won't contribute a percentage if it's on the ground. It may be following along, but to contribute nothing it would have to be weightless. So perhaps the turned in front wheel also generates a small inward (turning) force as well, which also would be constant in rate, meaning speed would effect what radius arc it helped generate. If the front contributed nothing to cornering you couldn't lose the front in a turn.

 

Make sense?

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I'm thinking of this as happening over time. A certain amount of inward turning from the cone shaped tire over half a second say, much more distance traveled in a half of a second at a high rate of speed than at a low rate of speed.

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