Lean Angle == Turn Radius?

[tweek]

Sense taking the first two levels of CSS I’ve done 2 track days. I can tell I’m improving, but I think I’m missing something. Specifically, during the last track day I wasn’t being passed much in my group but the guys who could get by me went around the corner faster with less lean angle. What gives? I’m trying to follow the widest arc plan (I’ve been reading!), but still these guys went around w/ less lean angle.

 

Can I make the bike turn tighter without leaning it more? I’m really proud that I can lean the bike over enough to bang the peg on the ground but that doesn’t seem to have anything to do with going fast.

 

Perhaps I’m overstating it. Say we have a corner that I can do now at 80mph while dragging a peg, the guy going around me is doing the corner 5mph with less lean angle. How? I want to do that! I’ll accept that my 600e is a tank and he’s on a shiny new ZX10, but I don’t think that explains all of it. If that is all it is I just gotta open my check book a viola – passapoolza. Sign me up for the next AMA superbike grid. Not.

 

So what am I doing wrong? More input on the bars? Get my body further off the bike (I don’t hang off much – no knee down yet)? CSS level 3?

[jrock7896]

Sense taking the first two levels of CSS I’ve done 2 track days. I can tell I’m improving, but I think I’m missing something. Specifically, during the last track day I wasn’t being passed much in my group but the guys who could get by me went around the corner faster with less lean angle. What gives? I’m trying to follow the widest arc plan (I’ve been reading!), but still these guys went around w/ less lean angle.

 

Can I make the bike turn tighter without leaning it more? I’m really proud that I can lean the bike over enough to bang the peg on the ground but that doesn’t seem to have anything to do with going fast.

 

Perhaps I’m overstating it. Say we have a corner that I can do now at 80mph while dragging a peg, the guy going around me is doing the corner 5mph with less lean angle. How? I want to do that! I’ll accept that my 600e is a tank and he’s on a shiny new ZX10, but I don’t think that explains all of it. If that is all it is I just gotta open my check book a viola – passapoolza. Sign me up for the next AMA superbike grid. Not.

 

So what am I doing wrong? More input on the bars? Get my body further off the bike (I don’t hang off much – no knee down yet)? CSS level 3?

 

You answered you own question.... Get more weight to the inside of the turn by shifting off the bike. The reason for getting off the bike and putting your weight as far to the inside of the turn as possible is that is allows one not have to lean the bike over as far at the same speed. The more you get off the bike and get your weight to the inside the less lean angle required at the same speed. Since you are at less lean angle your corner speed will increase because this means more contact patch which means more traction which means you can go faster.

[tweek]

I'm not so sure, but I think I'm closer to figuring out what is going on. Friday was another track day at an incredibly tight track (Oak Hill Raceway in Henderson TX). This go around I worked on hanging off more. I definately went faster, but that isn't the whole answer.

 

The issue is something Keith pointed out on the first day: I'm buying off turns by going in too soon. Looking at the control riders who are able to go around me at will shows the difference. They stay out longer and quick turn better than I do. The result is that they don't stay leaned over as long as I do and as such are on the throttle sooner and longer. Frankly, up to a certain point, I could just hug the tank if I would flick the bike in to the turn faster and pick a TP a little deeper in the turn. I'm not talking about a late braking drill, just staying further outside of the turn and going in just a few feet more.

 

If you watch my videos you can see me going in too soon. I did the same thing a few turns at Mid-Ohio and end up riding along the inside of the turn too long.

 

Anyway - it isn't like I'm Ben Spies or anything and won't get a paycheck if I don't go fast. Still, it's fun trying.

[briang467]

I'm not so sure, but I think I'm closer to figuring out what is going on. Friday was another track day at an incredibly tight track (Oak Hill Raceway in Henderson TX). This go around I worked on hanging off more. I definately went faster, but that isn't the whole answer.

 

The issue is something Keith pointed out on the first day: I'm buying off turns by going in too soon. Looking at the control riders who are able to go around me at will shows the difference. They stay out longer and quick turn better than I do. The result is that they don't stay leaned over as long as I do and as such are on the throttle sooner and longer. Frankly, up to a certain point, I could just hug the tank if I would flick the bike in to the turn faster and pick a TP a little deeper in the turn. I'm not talking about a late braking drill, just staying further outside of the turn and going in just a few feet more.

 

If you watch my videos you can see me going in too soon. I did the same thing a few turns at Mid-Ohio and end up riding along the inside of the turn too long.

 

Anyway - it isn't like I'm Ben Spies or anything and won't get a paycheck if I don't go fast. Still, it's fun trying.

 

 

You seem to be doing a good job of answering your own questions.

 

Yes, if you work on your quick turn drill from CSS level 1, you can have a later turn point and use less lean angle. If you have ToTW2, study the diagrams on pages 68-69 to see how steer rate works with TPs, lean angle and corner speed.

 

You already mention that late braking is not the answer, and you're correct there too. Keith talks about how late braking is not the answer to faster lap times if you're already off the pace (ToTW1 pg 63). Use the brakes to accurately set entry speed. However, quick turning, and being able to carry more corner speed with less lean angle, or being able to pick the bike up sooner and apply maximum throttle will improve the lap times.

[tweek]

You seem to be doing a good job of answering your own questions.

Sometimes OCD has its uses.

 

Yes, if you work on your quick turn drill from CSS level 1, you can have a later turn point and use less lean angle. If you have ToTW2, study the diagrams on pages 68-69 to see how steer rate works with TPs, lean angle and corner speed.

 

You already mention that late braking is not the answer, and you're correct there too. Keith talks about how late braking is not the answer to faster lap times if you're already off the pace (ToTW1 pg 63). Use the brakes to accurately set entry speed. However, quick turning, and being able to carry more corner speed with less lean angle, or being able to pick the bike up sooner and apply maximum throttle will improve the lap times.

Thanks for the pointers. Right now I'm rereading Soft Science. What is funny to me is how this stuff mixes so well with my NLP training. I have been facinated for a long time how a person's beliefs control their lives. Trying to go fast on a motorcycle is a great place to see people's beliefs drug out in to the light of day. Fears just come bubbling up to the surface.

 

anyway, can't wait for April when the CSS crew goes to Barber again (based on the AMA race schedule) - I want to do level 3 & 4 and get to run on that track for a day or two.

[2bigalow]

Hey Tweek,

 

You are on the right track as far as quick turing the bike and turning in a bit later. Those two items are part of less lean angle, but throttle control and geometry also come into play. Level three touches on moving around on the bike without upsetting the chassis , while manipulating the geometery of the bike to change your line. IE turn tighter. I think you'll really enjoy level 3 and will have several ahha! moments since you are already thinking about this.

[prand]

Fears just come bubbling up to the surface.

Bikes have a way of doing that.

[tweek]

It is amazing how a few more days on the track and a new bike can change perspective. Still don't quite have the answer in hand though.

 

Yesterday (Monday) was my first time to take my Ducati 848 to the track. Usually I ride a 99 ZX6e. All I care to say it WOW! The brakes on the 848 certainly gave me the confidence to push it a little harder down the straights. The 848 is also a lot easier to move around on. Handing off I'm easily able to get my chest parallel to the tank where the tank's ridge is against my ribs. Even better was that I was able to get my knee down 3 times on my right side and once on my left. I've only gotten my left knee down on the ZX6e. I just don't trust it as much as I do the 848. Guess which bike is going on craigslist?

 

So while I'm able to get myself off the bike and lean the bike enough to occasionally touch my knee down - I can't do it accurately or consistently. I'm not even sure what I did differently the times that I did touch. My goal is to be able to accurately and consistently get my knee down once I know where the track is going (ie I'm not looking to do this on a mountain pass). I'd like it to be as controlled as a NASA launch - 5-4-3-2-1- touch down! and then 3-2-1 lift off! (Without NASA's fondness for mixing up standard and metric and blowing things up).

 

Anyway, what is it that I'm missing? At this point I'm easily in the middle of the intermediate pack. Maybe even moving up toward the front of them. But I know that I'm not anywhere close to using up all of the ZX6's potential. Won't even think about the 848's capabilities.

 

So what are you guys thinking about, doing, looking at, (perhaps hearing & feeling too) as you go in to a turn that you absolutely know you are going to lean over far enough to drag bits? Does the speed matter?

 

And before anybody says it - I'm signed up for CSS level 3 & 4 in May. So I'll get to bug Keith and crew all weekend about this stuff. But I plan to read ahead so I can get as much out of those two days as I can.

[Cobie Fair]

Tweek,

 

One thing is, did you get on the lean bike in level 2? If not, we should get you on that.

 

One of the main uses for that bike is to get an excellent body position, so the rider doesn't fight the bike, and is looked on in the right places (legs holding on, not arms).

 

C

[racer]

Hi Tweek,

 

All I can do is repeat what others have said.

 

The quicker you flick it, the sooner you get it leaned over, the faster you change direction, the less lean angle you will need to complete the turn. The longer you take to change direction, the later you get to max lean, the tighter you have to turn to complete the corner and the more lean angle you will need to do that.

 

Look at the diagrams for the "hook turn" in TOTW II. This is key to less lean angle for a given corner.

 

How and where you "lock on" combined with getting your upper body hung off can move your center of gravity forward to alter the geometry and make the bike turn sharper, and... since there is more mass in your upper torso than your butt and one leg, the more you get your upper body hung off the bike, the more mass you get toward the inside of the turn to offset the COG and the less lean angle you will need to balance the cornering force for a given speed. Or, to say it another way, the more speed you can carry at a given lean angle. All of these techniques will help reduce your lean angle in a given corner.

 

Finally, being on the gas raises the suspension which increases ground clearance and will help keep footpegs and such off the ground while also balancing the front to rear weight distribution (60% rear/40% front) for max traction which, again, means more speed is possible. Getting back on the gas sooner not only means you are increasing speed sooner, it also means you can carry more speed outright because you have more available traction when you are on the gas.

 

Hope that helps.

 

racer

[tweek]

racer - yeah. and I'm repeating myself b/c I'm trying to grok this and it aint easy for me. The thing that blew me away though was how much easier my new bike is when compared to my crufty old Tank. I love the ZX6e and its a great bike, but the 848 just crapped in its punch bowl as far as track days are concerned.

 

I realize that the points you and others have made are correct, but for some reason I'm not quite getting it. I also know that touching your knee down is not necassary to going 'fast', in fact up to a certain point it is probably somewhat slower. However, I think what I'm trying to gain is the physical control and confidence over the bike such that I am freely able to choose when my knee touches. Having the confidence to lean the bike over that far (actually, as long as my legs are it isnt that far) should make developing the other skills easier. Or at least that is my working theory.

 

Coby - the lean bike was broken last year when you guys visited Mid-Ohio in August so I didn't get to ride it.

I arrive Friday morning sometime (don't have the plane ticket in front of me). I plan to go straight to the museum and then come over and watch my friend do his two day camp stuff. Sense I'll have all my gear in the back of the car maybe I can weasel my way on to the lean bike so we can have that out of the way.

 

finally, maybe we can work out exactly what it is I need to do in Level 4 so that I can ride fast enough to give my new bike a good bit of excercise.

[racer]

Hey tweek,

 

Best advice anyone ever gave me for riding/racing: "Relax. And remember to breathe."

 

Sometimes when attempting to "grok" something, I find I am trying so hard that I make things harder by trying to bite off more than a mouthful, trying to take everything at once.

 

So, I try to pick just one thing and try to be very specific. Nobody knows what to say to, "I'm just not getting it". I can't answer that, neither can you. My advice is to be specific. Write it down. Make a list. Then make a plan for that one thing.

 

Don't worry about touching your knee down. Or how fast you are progressing. Or how fast you think you "should" be progressing. It takes as long as it takes for everyone. There are no "shoulds". I try to forget all of that and slow down inside my brain a little bit and think about just one thing at a time. And focus on just that. For instance... quick turn. This is the most important to me. How many parts are there to just that one thing? Reference points. Turn point. Off the brakes. Use your whole body to pivot turn. Body position and "hook turn". Two step. Smooth throttle. Apex.

 

Then narrow it down to a simple plan for just one thing... like choosing my turn point.

 

 

So... what exactly is it that you feel you are not quite getting about what we have been talking about?

[tweek]

Racer - you're right. I think I mentioned that I tend to over think things. Part of the problem in my case is that why I intellectually 'get it' translating that in to the kinestic confidence to do the actions is a stumbling block.

 

to save some time (and writing) - we are talking about something that needs to be done and experienced. We can post (and will) on message boards all day about this stuff, but at the end of the day it has to be done. You have to actually experience this stuff. But talking about it is fun.

 

Happily I'll get to bug Coby about this stuff in person in just a few weeks and get all my answers questioned.

[tweek]

Have some free time so I'll bug you guys some more! Not sure where all this will go, I've not quite planned it.

 

First, what should be a straight forward math/physics problem/simulation:

Say you have a 200lbs rider with a 400lbs sport bike. The rider and the bike are on a giant flat cement skid pad. The rider is holding the bike in a constant radius turn that makes a circle with a 50' ft radius. How fast does the bike have to be moving in order for the rider to keep it at a 50degree lean angle?

(I really would like to know the equation for this)

 

The above problem I think is at the heart of all this. what will happen if the rider is going too slow? My gut feeling is that the bike will fall over just like a top that has lost its speed. However, now I have doubts about even that. If the rider is too slow and holding the bike at 50degrees of lean angle will that just cause the circle's radius to shrink? What is the relationship between speed, lean angle, and circle radius?

 

I am simplifying things because we are not considering things like tire grip and surface friction. So for instance, if the rider, while holding the 50degree lean angle, tries to go too fast and force the bike to stay on the 50' radius then the tires will have to slip. Which tire slips first or will both let go together?

 

what does this have to do with the 'real world'? Confidence. At least intellectually. If you KNOW that the bike can be leaned over to 50degrees and not fall over on you then you know how far you can lean the bike. knowing that then you can quick turn the bike that far and know that the bike won't fall down.

 

Some people are blessed with the ability to just hop on the bike and feel their way to this knowledge. My youngest daughter is like that. I on the other hand have to eat the apple first and then practice, practice, practice and ask tons of questions.

 

So there you have it. Anybody up for some physics calculating?

[racer]

Racer - you're right. I think I mentioned that I tend to over think things.

 

Really? I can't imagine what that is like...

 

Part of the problem in my case is that why I intellectually 'get it' translating that in to the kinestic confidence to do the actions is a stumbling block.

 

to save some time (and writing) - we are talking about something that needs to be done and experienced. We can post (and will) on message boards all day about this stuff, but at the end of the day it has to be done. You have to actually experience this stuff. But talking about it is fun.

 

Ah, indeed. "Naming is not knowing" as my Zen-Buddhist guru used to tell me during my years as a callow youth at the monastery.

 

One may open a technical manual and memorize all the words and study all the pictures and talk all about re-building an engine, but, until one actually picks up a torque wrench, one does not know. And, even then, since everything is always changing, how can anyone really ever know anything when there is no such thing as a fact because everything is always changing, er... but that is a philosophical discussion for another time.... like in the evening after school at Mid-Ohio perhaps?

 

Happily I'll get to bug Coby about this stuff in person in just a few weeks and get all my answers questioned.

 

Bug Cobie?! Now yer talkin' turkey brother man!! Count me in!! Can we tie him up and shave his eyebrows first?

 

 

Anway... whether talking or doing... or doing not... the song remains the same. One step at a time. Small steps.

 

So, which technique(s) were you unable to kinesthetically grok?

 

 

r

[GregGorman]

No physics is really needed, just observation. Can a bike be leaned over to 50 degrees? From data acquisition, the answer is yes. I think I've seen 64 degrees from the on-board camera shots on the MotoGP bikes. Then you have the question of, at what speed can a bike be leaned over to 50 degrees and not crash. That really depends on the rider. Physics can only answer the theoretical regarding this. Just guessing, 40mph. But if you really want the physics, just go up to Amazon and look up some motorcycle physics books. You might even try books about game programming physics since they'll have the specific vehicle related physics in them.

[racer]

The physics is simple: lean angle is dictated by speed and radius.

 

Whether it is 50 or 64 or 42 degrees, lean angle will always be the point where the centrifugal or cornering forces are balanced by gravity around a 'moment arm' or common lever defined by using a point between the contact patches as a 'fulcrum' and the center of combined bike/rider mass as the point where gravity (vertical) and lateral g is applied.

 

Centrifugal or cornering forces are determined by speed combined with "radius" or how tight a corner is. So, the faster you go in a given corner, the higher the cornering forces and the more you have to lean to balance. And/or the tighter the corner for a given speed, the higher the cornering forces and the more you have to lean to balance. There is no single lean angle for a particular speed or vice versa. It will always be speed in conjunction with the radius of a given corner. Whether or not you can carry enough speed in a specific corner to be leaned at 50 degrees will depend on the available traction of your tires and your ability as a rider.

 

 

Wiki has a reasonably easy to understand entry on the subject:

 

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

 

 

I find this physics education website very approachable for the layman:

 

http://www.glenbrook.k12.il.us/gbssci/Phys/Class/BBoard.html

 

Have fun!

 

racer

[racer]

You might find this post from another thread helpful: http://forums.superbikeschool.com/index.ph...post&p=5193

[racer]

Have some free time so I'll bug you guys some more! Not sure where all this will go, I've not quite planned it.

 

First, what should be a straight forward math/physics problem/simulation:

Say you have a 200lbs rider with a 400lbs sport bike. The rider and the bike are on a giant flat cement skid pad. The rider is holding the bike in a constant radius turn that makes a circle with a 50' ft radius. How fast does the bike have to be moving in order for the rider to keep it at a 50degree lean angle?

(I really would like to know the equation for this)

 

So there you have it. Anybody up for some physics calculating?

 

If we assume infinite traction, define a moment arm between the combined CoG and an arbitrary point at right angles between the contact patches (regardless of f/r balance) at a constant speed to simplify things, I believe the speed at which the component force vectors applied to our moment arm equal each other (and the acceleration of gravity) will be your answer. (Or close enough to it... I think.) I'll have to work on this when I have more time (and sleep).

 

 

Edit to add:

 

Actually, if you study these links, I'll bet anyone who has had high school algebra and trigonometry can solve it for themselves:

 

1. http://www.glenbrook.k12.il.us/GBSSCI/PHYS...cles/u6l1e.html

 

2. http://www.glenbrook.k12.il.us/GBSSCI/PHYS...tors/u3l3b.html

 

3. http://www.glenbrook.k12.il.us/GBSSCI/PHYS...cles/u6l2c.html

 

 

racer

[racer]

Hey tweek,

 

 

Have you had a chance to study the links I posted above?

 

 

Using the ice skater formula from link #3, substituting 50° for θ (angle of lean) and solving for velocity (v), I tentaively came up with ~ 42 kph or ~ 26 mph.

 

I haven't gone back through to double check my formulas or math; but, did any other "physics students" get anything different?

 

 

racer

[racer]

So, what... no other students of physics out there? Nobody going to check my math for me?

[racer]

OK, let's just try it in reverse. Substitute my result for v, solve for theta and see how close to 50° we get.

 

 

Given Info:

 

m = 600 lb = 272.72 kg

 

v = 42000 m/h = 11.6 m/s

 

r = 50 ft = 15.38 m

 

Find:

 

a = ???

 

Angle of lean = ???

 

 

F_grav = F_vert = m • g = 272.72 * 9.8 m/s = 2672 N

 

a = v²/r = (11.6 m/s)² / 15.38 m = 8.749 m/s²

 

F_horiz = F_net = m • a = 272.72 kg * 8.749 m/s² = 2386 N

 

θ = invtan (F_vert/F_horiz) = invtan (2672/2386) = 48.236°

 

 

Not too far off considering how many significant digits I rounded off.

 

Maybe not quite as simple or straightforward as you thought it might be, Tweek, but... whadya think?

 

Anybody? Thoughts? Questions?

 

[littlefield]

Numbers are right but I think the convension should be higher horizontal force/higher velocity/tighter radius gives a higher lean angle. So it should be Fhoriz/Fvert.

[racer]

Numbers are right but I think the convension should be higher horizontal force/higher velocity/tighter radius gives a higher lean angle. So it should be Fhoriz/Fvert.

 

Hi David,

 

Ah... I think I see what you mean.

 

Higher velocity and tighter radius requires further lean from vertical. If I follow your point, the issue is that (following the example on the physics site) I applied Tweek's given lean angle (theta) to the horizontal rather than vertical as is typical when describing motorcycle lean angles.

 

D'oh! My bad.

 

Thanks for pointing that out, David. I'll re-work it with theta measured from vertical when I get home tonight.

 

Cheers,

 

racer

[racer]

Hey David, et al,

 

I apologize I don't have time to create a diagram to upload, so, for now, please refer to the diagram near the middle of the page at link #3:

 

http://www.glenbrook.k12.il.us/GBSSCI/PHYS...cles/u6l2c.html

 

Forgive me I must be brief...

 

In a nutshell, the diagram of component force vectors forms a right triangle allowing us to utilize right triangle trigonometry to find the angle or vice versa to find the component vectors from which we can substitute and solve for velocity using the circular acceleration formula. In this case, the vertical vector over the horizontal vector equals the "opposite" over the "adjacent" sides of an included angle of a right triangle. Those of us who remember our high school trig will recall that opposite over adjacent gives us the tangent, hence, the "inverse tangent" (INVTAN on your calculator) gave us our angle in this example. I originally reversed this formula to solve for the velocity. Unfortunately, because Tweek probably meant 50 degrees from vertical, not horizontal, my answer of ~ 42 kph was, in fact, incorrect.

 

 

Now, to correct the situation, we could subtract 50 from 90 and solve the same equation(s) for 40 degrees to find the correct speed... OR we can move theta over the hypotenuse so it refers to the vertical. At that point, David's suggestion of horizontal over vertical becomes the "opposite" over the "adjacent" and the INVTAN function on the calculator will give us the angle, or, allow us to reverse the process to find the velocity according to what Tweek most likely meant.

 

(We could continue to use the vertical over the horizontal BUT then the function would be adjacent over opposite (co-tangent)... which is more of a pain on my calculator.)

 

I will try to plug in the numbers before I go to bed tonight. Otherwise, I'll try to get to it in the morning before I leave for work.

 

Cheers,

 

racer