racer
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THE REASON YOU NEED A DIFFERENT RADIUS AT DIFFERENT SPEEDS for the SAME LEAN ANGLE, is that is necessary or the bike cannot keep either a constant arc or a constant lean angle. That is because speed and turn sharpness forces must combine to equal the force of the lean angle used. The ONLY way the bike can vary the radius is by following the direction the front tire is pointed in, and there is only ONE CONSTANT radius possible for any given speed and lean angle combination.
Well, call me pedantic, but, the "bike" doesn't do anything, only the rider does.
Hence, the bike can not "vary the radius", only the rider can. That said...
You have done a good job of outlining forces that control the direction of the front wheel while a bike is leaned over, but, I do not believe you have demonstrated that the front wheel is responsible for the lean angle or direction of the bike (aside from rider input at the bars).
The way I see it, under acceleration, weight is biased to the rear, hence, without rider input at the bars, the rear dictates the lean angle of the bike and the front wheel is "forced" along for the ride.
Here is Keith Code's take on this from pages 58 and 59 of Twist of the Wrist II:
According to the laws of physics and engineering principles, the following is true: As long as you apply force to the bars, the bike continues to lean further over. However, once the bike is fully leaned into a corner, the rear end "steers" the machine. The front end "turns" the bike or changes the lean angle but the moment the motorcycle is leaned over and stable, the main mass of the bike--from the steering head back--determines the lean angle it will hold.[snip]
If your throttle control is standard, the only things that will change the lean angle of the bike to any great degree are a slide/catch action or steering input. The most convincing illustration of this is doing a wheelie while coming off a corner. The lean angle of the bike remains the same even though the front wheel has left the ground!
Front-End Duties
Once leaned over in a turn, the front end is no longer steering the bike: It helps stabilize it but does not steer it. But the front end's function is still important. The 30 or 40 percent of the cornering load it is carrying accounts for about that same percentage of cornering speed. In other words, if you added 30 or 40 percent more load on the rear wheel at speed, you would certainly slide it.
So, when the rider turns the throttle more at a stable lean angle, increased cornering force causes the radius to increase. But I believe that the angle of the front wheel changes because the radius increases, not vice versa. IMO, by your own description of the forces involved, it is the forces applied to the front wheel caused by the changing radius that turns the front wheel wider after the fact.
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I'm sorry but my brain hasn't digested the info in your previous posts yet, so there is no room for new information. I thought we we're coming to a conclusion, and you just keep on adding new aspects (contact patch) to the scenery.. Argh, my head hurts!
Conclusion? Where's the fun in that? Besides, we've barely scratched the surface in any meaningful scientific way.
As for conclusions... the gyro vs gravity vs angular momentum debate has been going on since physics first looked at two-wheeled vehicles. From counter-rotating gyro-canceling wheels to equations of motion, each side claims experimentally and mathematically supported victory on a regular basis.
In fact, each side claims the counter-rotating wheeled bicycle proves their theory. Can you believe that? Two groups of people ride the same machine. One group claims it is virtually as easy to balance and ride as a normal bike, the other claims it is virtually impossible to balance or ride at all.
Um... right. Somebody is full of spit... lol.
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OK, I decided to read Leftlaner's suggested wiki link.
And, whaddya know...
"Tires
Because real tires have a finite contact patch with the road surface that can generate a scrub torque, and when in a turn, can experience some side slipping as they roll, they can generate torques about an axis normal to the plane of the contact patch.
One such torque is generated by asymmetries in the side-slip along the length of the contact patch. The resultant force of this side-slip occurs behind the geometric center of the contact patch, a distance described as the pneumatic trail, and so creates a torque on the tire. Since the direction of the side-slip is towards the outside of the turn, the force on the tire is towards the center of the turn. Therefore, this torque tends to turn the front wheel in the direction of the side-slip, away from the direction of the turn, and therefore tends to increase the radius of the turn.
Another torque is produced by the finite width of the contact patch and the lean of the tire in a turn. The portion of the contact patch towards the outside of the turn is actually moving rearward, with respect to the wheel's hub, faster than the rest of the contact patch, because of its greater radius from the hub. By the same reasoning, the inner portion is moving rearward more slowly. So the outer and inner portions of the contact patch slip on the pavement in opposite directions, generating a torque that tends to turn the front wheel in the direction of the turn, and therefore tends to decrease the turn radius.
The combination of these two opposite torques creates a resulting yaw torque on the front wheel, and its direction is a function of the side-slip angle of the tire, the angle between the actual path of the tire and the direction it is pointing, and the camber angle of the tire (the angle that the tire leans from the vertical).[17] The result of this torque is often the suppression of the inversion speed predicted by rigid wheel models described above in the section on steady-state turning.[14]
Because the front and rear tires can have different slip angles due to weight distribution, tire properties, etc., bikes can experience understeer or oversteer. Of the two, understeer, in which the front wheel slides more than the rear wheel, is more dangerous since front wheel steering is critical for maintaining balance.[17]"
...there's even more going on at the contact patch than I thought.
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I think the smart chioce would be CSS + AMA at Mid-Ohio and watch Motogp on tv
Yeah, I think I'd have to agree.
Ben Spies is ridind the Suzuki here at Donington park this weekend in place of Caparossi which Ithink will be very interesting as this will give him time to get used to the bike and setup in preperation for his wildcard rides at Laguna and Indy, though I would like to see Nicky Hayden get back on the podium.Indeed. I'd really like to see Nicky back on top of the podium again. I think he has another good chance at his "home track" Laguna. Indy will be a new track for everyone.
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In any case, framing the angle change of the front wheel at increased speed as due to the centripetal force of the pavement applied tangentially or orthogonally to the circular path of the trailing contact patch really helped me to "feel" the "why" of the front turning out more at increased speed better.
I thought I had a good grip with my experiments with the trail bikes and framing the angle as dependent on the centrifugal or cornering force applied down through the forks which describes the same action from the opposite "node" back on page two of this thread, but, this really helps complete the picture.
Thanks for that guys.
That said, I'm still not ready to back off the idea of the rear being responsible for the radius and the front turning out as an effect, rather than a cause.
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I'm with you on the whole gyro effect thing, I see how the rear will turn outwards if you apply a force to decrease lean angle (and vice versa). But how does this apply to real life riding? How would you apply that force to change the lean angle of the rear tyre?
I had the idea late last night that increased centrifugal force, regardless of a stable lean angle (ie. even if the lean angle didn't change), would apply increased upward torque to the rear wheel (whether enough to overcome gravity or not) and cause a wider radius or arc due to gyroscopic forces. I wasn't so sure when I woke up. I played with the bicycle wheel over coffee and decided to run with it anyway. I am afraid I am going to need to "cheat" a bit and brush up on gyroscopes and angular momentum, etc. to confirm or falsify this theory.
In the light of a new day, it seems just as reasonable that increased centrifugal "force" simply forces the rear wheel to "track wider" due to tangential force applied to the conically steering contact patch, hence, the contact patch rolling off center or off angle ... so to speak... if you know what I mean.
In any case, before I began doubting my latest theory, I was going to say...
You don't apply "that force" to change lean angle. You apply it to increase velocity (and rpm of the gyro). Higher velocity at the same lean angle applies increased centrifugal "force" as the bike travels through the corner. Regardless of whether the lean angle remains balanced or stable, that force still translates to vertical torque applied to the gyro of the rear wheel.
Or at least that is where I was thinking before. Oh well.. back to the drawing board.
BTW, I was just thinking about how this phenomenon also affects the FRONT wheel as you turn on the bars. Interestingly, it seems that the "gyro effect" will contribute to leaning the bike to the left when countersteering to the right. So the front wheel actually "helps" the top end of the bike to lean over to the left when the lower end is turning right. Kind of like a team work between inertia and gyro forces.Yep!
PS. That gyro phenomenon only applies when the bike is "unstable" due to the rider giving steering inputs. It doesn't affect anything when the bike is trailing happily at perfect balance (straight forward or at a constant lean angle)..This is where I am hung up. I'm not sure this is true, but, I'm also not sure it matters. The more I think this theory through, the less realistic it seems and the more I am reverting to my original two possiblities of expansion of the contact patch imitating a contact patch higher up the crown of the tire or simply a degree of sliding or rolling off-angle. The last one really seems most plausible to me at the moment.
Hence, that would mean there is some validity to carl's original idea of the wheel traveling further forward for each measure of distance traveled inward on the circle.
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I removed the front wheel from my bicycle this morning to conduct this test against for myself and I am more convinced than ever now. Hodling the wheel at some degree of lean angle and attempting to reduce the angle of lean forces the wheel to turn outward with significant force.
Also, re-reading pages 58-59 of TOTW II, the points made in the "Steer for the Rear" chapter are much clearer and make more sense to me now.
I've run out of time to find the page where Keith discusses the gyro force and countersteering, but, I will find it later.
High ho, off to work I go!
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Anyway, I remember doing that experiment with the bicyle wheel once. I sat in an office chair (one of those chairs that turn around), spun the wheel, and tried to "lean" the wheel over (that would be the z axis?). What happened was that the office chair would turn around (on the y axis, right?). I assume that you're moment of EUREKA has something to do with this phenomenon. Looking forward to hearing the full story from you. Sleep tight
Yeah, that's the one! Try it just standing still and holding the wheel in your hands. Turn the wheel right and left and feel the wheel wants to lean over. Lean the wheel over and it wants to turn left and right. Rotate the whole experiment so that the wheel is nleaned over and try to un-lean it with the wheel turning. The wheel turns outward wrt the corner! So...
If centrifugal (cornering) force tries to make the rear wheel stand up (or lean less), gyro forces will make the wheel turn outward.
Possibly even if the wheel doesn't actually change lean angle but merely has force applied in that direction.
It still feels like the right answer in my gut.
PS - Also try tying a string to the axle of the wheel and hanging it from the ceiling or some form of truss and play with setting it at different lean angles. It will seem to defy gravity as it maintains degrees of vertical orientation while its only support is the string in the center.
Pretty freaky, dude!
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I fell asleep on the couch watching a DVD called The Doctor, The Tornado and The Kentucky Kid. (Story of 2005 Laguna Seca GP) I just woke up at 2:45 am here. Turned off the TV and came to turn off the computer to go to the bedroom and now I'm not so sure about my theory anymore... lol.
I was afraid of that. I knew I shouldn't get so excited.
The key I recall to those gyro moves is that the wheel deflects or precesses a given amount for torque applied... even if the torque doesn't cause motion in its own plane. At least that is what a NASA engineer told me once. But now I'm not so sure. What if the rear wheel has to actually stand up to be deflected or turn outward... ???
Hmm... back to the laboratory and my bicycle wheel tomorrow night...
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Keith Code also talks about it in TOTW II.
I don't have the page number right now but I will find it tomorrow.
Good night my friend!
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and and and... here it is... holy ######.... it's the precessional forces that turn the rear outward due to the torque applied to the moment arm defined by the wheel itself!!!
Aaaahh!! Now I get it..! ....not
You totally lost me, dude. When you find the time, please explain this concept in English (layman's words)..
OK, I will. But I don't think tonight, I have to get to bed and I want to do a good job of it.
In a nutshell, when a torque is applied to the axle of a spinning wheel or gyroscope, the wheel tries to turn 90 degrees in the next plane of rotation. It's part of what makes a motorcycle lean over in the first place.
When you turn the front wheel right, the wheel tries to lean to the left which is a different plane x, y, z. Vertical, horizontal, and depth. Yaw, pitch and roll. Three dimensions or degrees of freedom.
In the meantime, this is where I learned most of my basic physics:
http://www.glenbrook.k12.il.us/gbssci/Phys/Class/BBoard.html
I also have some really good gyroscopic websites with some really cool experiments around here somwhere, I'll get them together for you too. In the meantime.... get the front wheel off your bicycle and hold the axle in your fingers and spin the wheel. Now try to move the wheel left and right and see what happens.
This effect is the basis of precession!
Google gyroscopes and precession and do some digging.
Be back soon.
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I went to the moto gp at Catilunia in spain last week and watched thomas luthi and his style is very smooth and fast, the whole weekend was great!
Wow... MotoGP at Catalunya. I am so envious.
I'm hoping to find a way to attend the MotoGP at Indianapolis this year. I'm afraid I'll have to choose between CSS and AMA Superbikes at Mid-Ohio and the GP at Indy.
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I am really excited to come back out and the fact that I can play a small role in helping the CSS is a VERY proud thing for me.
I know exactly what you mean.
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HA HA HA HA HA HA HA HA!!!
that's hysterical!
and it looks like the best is yet to come.... got wings?
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This is the greatest forum on the internet...
isn't it tho?
when i think about most of the other forums out there (motorcycle or otherwise)... i'm really proud of what we're doing here.
i give the website to every new rider i meet (about 2-3 everyday) and tell them they must buy the books and check out the really cool forum and then sign up for the school as soon as they can.
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ok, i have to sleep on this, but, i really think that's it.
two years ago when i studied gyroscopic precession, i came to the conclusion that leaning the bike in causes a turning in force at the rear wheel, but, I never thought to turn that around. wow.
i really think we did it. i'm totally stoked.
thanks everybody. thank you thank you thank you.
hehehehehehehehe
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he he he
this is awesome stuff. exactly what i hoped for. thank you everybody for your time and effort ( and pain!
)unfortunately i am totally mentally blown out from yet another 12 hour day on 5-6 hours of sleep (wearing five different hats while learning yet another). i can't remember my last day off... at least 3 weeks ago. so, i am having difficulty using the shift key tonight much less reading through carl's posts. dude, you have to learn to use less words.... lol. (kidding!
)) seriously, i really dig your posts, i just need more time to read them! that said...
i think you/we/us have really nailed down the landscape wrt three basic inter-related variables. to quote lando molari, "I believe we have it surrounded!". really great stuff.
like so many things in analysis, perception depends on the node from which a system is analyzed (up looks like down from over there) and everything is dynamic and in flux hence attempting to nail down a single slice or moment in time with a static freeze frame snapshot can really make things more difficult to grasp, yet, at the same time, looking at all the angles, turning it this way and that, taking it apart and putting it back together from each direction can be really valuable.
considering our progress so far, I can see that I was trying to bite off too much at once. hopefullly, everyone is close to being on the same page now. (eyes bottle of headache pills warily)
ok, enough talking about talking. moving on...
i like the angle of saying that the front wheel must turn outward more to accomodate more velocity for the system to remain in balance. if that is true, then here is my question...
why is the front wheel turning out more at a higher velocity (without a higher rate of acceleration), what is causing that to happen? i don't mean what is the primary mover, i mean the mechanics of it. there is more centrifugal force that needs more centripetal force to balance it, (I believe the centripetal force is being supplied by the pavement and is essentially limited by the amount of available traction) i mean, where is the lever? is it simply more centripetal force applied orthogonally to the angle of the front wheel at the contact patch which is behind behind the steering stem angle due to the rake/trail (like 2big and i discussed way back when)? hence that forces the wheel to turn outward...
yes, that makes sense. that really makes sense. wow. I need to think through the other angles but i'm feeling excited.
so that might explain the front wheel angle... but... i still feel like the "conical steering" at the rear wheel has to dominate the system if the bike is accelerating, ie on the gas. the front must be trailing or it would countersteer the bike. it is like the inverse of countersteering as the the wheel turning outward actually maintains the lean angle... or does it? (or would prevent the bike from coming up from that lean angle). BUT the stabilizing gyro force at the rear is what really keeps that from happening... that keeps the bike from coming up. the front simply must turn outward due to increased centripetal force and the rake/trail. but is it really what causes the bike to run wide or is it a response to the bike running wider?
a gyro stabilized wheel will not come up with increased velocity. hence the rear wheel MUST run wide due to the gyro force.. and and and... here it is... holy ######.... it's the precessional forces that turn the rear outward due to the torque applied to the rear wheel itself!!!
whoa.
is that it? can that be it? it has to be. oh wow. i have to go sleep on this.
warning: stand clear.... epiphany in progress...
and if the front comes off the ground, the rear still runs wide!!!
HA!!! HAAAA!!!
I did it!!!
er... WE did it!!!! (heh heh)
hahahahahhaahhahahhahahahahahahahhhaah
(turns handsprings in his mind)
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PS. I used a very high-tech illustration program called "Paint", which is a modern version of the wellknown "Paintbrush"..
ha ha
MS Paint?
That's what I used to create my "stick figure" type drawing. I guess I just need to spend more time with it then.
Thanks.
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I significantly edited my post above after leftlaner read it. (I saw you pop in and out)
I have not finalized my observations of whether the angle of the wheel changes due to cornering force or weight on the front regardless of wheelbase. I do think that its angle is determined mostly by rake and trail and may change at different lean angles as well. But just one lean angle for now.
2bigalow admitted that the hook turn is caused when the bike turns sharper due to a shorter wheelbase caused by weight compressing the forks.
So, if the wheelbase shortens with the same turn angle on the front wheel, the bike turns sharper. So, the angle of the front wheel seems to determine the arc or line the bike travels.
Carl said, way back (and i agreed), that he thought the amount of weight on the front wheel affects how much effect the front wheel has on the arc.
But, once the wheel is sufficently lightened, or even comes off the ground, does something change?
Of course for that to happen, there is acceleration happening.
OK, my head really hurts now and I am really going to bed this time.
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PS -
leftlaner,
What software program did you use to create your beautiful graph/illustration?
I have had limited success creating that type of illustration and would really appreciate any hints or help.
Thanks,
racer
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OK... one last thing before I go to bed.
When the fork compresses, the wheel base is shortened, hence the wheels are closer together on the arc of the path they are traveling. But does the wheel angle (turned into the corner) change?
If the forks extend under acceleration, the wheelbase lengthens and the wheels are further apart on the arc. Does the turn angle of the wheel change?
Does the rake and trail change?
What happens to the line?
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I have not had time to read through the last few posts entirely or well, but, a couple of things occured to me while skimming. (Leftlaner pretty well spelled out these ideas)
At nominal speeds, gyroscopic force will stabilize a wheel at whatever lean angle it is at. Expermiment with a bicycle wheel hung from a string and watch as it defies gravity and maintains whatever angle or position wrt gravity/earth that it is placed.
So, I believe that, properly, what might be being balanced between gravity and centrifugal force is all the rest of the non-rotating mass attached to the wheel.
So, IMO, while the front wheel is pointed into a corner, without pressure on the bars, just like going in a straight line, it is trailing. And, the angle of the front wheel is an effect of lean angle (due to rake/trail), not a cause.
Like carl alluded, there is a difference between steering in the sense of causing a change in direction (left right like a car) and steering in the sense of determining the direction in a stable state (or conical steering).
In the case of the bike being leaned into the wind, it will be countersteering. The front wheel is not neutral or trailing then. I believe that pressure is being applied to the bars to maintain the line. IN that case, once that pressure is released, the front wheel becomes an effect again. Not a cause.
Forgive me if this was acknowledged above somewhere, and for not responding directly to points made. I really am too tired to read through it all again tonight with any understanding. My head hurts too.
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Hey Chris,
Welcome to the forum and thanks for sharing your story!
I've often thought that data acquisition would be a benefit to the school, both as a learning tool for the students and as a teaching tool for the coaches. So, I think it's great that it is finally happening. Congratulations to you and your company for being the ones to make it happen!
The CSS is one of the most well run, organized, and professional groups of its kind. I was just floored by the entire experience of working with Keith, Will, and the others I got to meet that day.Indeed! Refreshing, innit?
I attended my first CSS class twenty years ago and Keith's crew have always been in a league of their own. In my opinion, CSS flat out defines the state of the art in riding instruction worldwide. And their program always sets the highest standard of professionalism and class by which all other riding schools (or any organization) might hope to be judged by... if they could qualify to compete on the same field. Of course, it's a little difficult to catch up when CSS continues to set and re-set the bar so high, never content to sit back and rest on well-earned laurels. Choosing to add data acquisition to the program just proves it again.
Have you attended the California Superbike School?
Not if you haven't attended this year!
Congratulations again on your success with the school, Chris. I hope I get to see your contribution in action soon!
Best regards to you, sir.
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You're a standup guy, racer. I accept your "pardons" and your explainations
You had me going for a while there, though. I was starting to get the wrong perception of you, the way you "killed" my thoughts on the subject..
Oh well, I respect your quest for knowledge, and now that I've "figured you out", I won't take it personally when you critisize my ideas.
..and I see how the language barrier might have caused some extra mess too.
Thanks for understanding.
Be back soon.
)
What's Your Favorite Track?
in School Questions/General Discussion
Posted
I just downloaded and watched the qualifying from Britain today (British Euro-Sport) and Ben Spies looked freaking phenomenal sliding around like he was at his home track and running as high as 5th at one point! And forget a track he's never seen, this is his first time ever on the bike after like half a day testing on a different bike at Valencia(?) months ago! WOW!