Thank you racer for your detailed respond, and for the time you took to relate to my post. For the record, I don't find this post of yours offending in any way so I think we can put this issue behind now. Your vast experience and that of other users of this forum is exactly the reason I'm here: to learn, And learned I have.
As you, I also like a good discussion. In contrast to you though, my experience is very limited (probably not more than 5 track days overall, some in a limited form) so I try to combine my little experience with logical analysis of situations, and theoretical (for me) knowledge from TOTW books and other sources. Therefore, when I say IMO, it means just that, and its definitely open for criticism and discussion as far as I'm concerned. The same goes for this entire post.
I also apologize for my typos and possibly for my syntax errors. I'm not a native English speaker, nor do I speak it daily. I believe negligible is the "passive" form (?) of neglect but my spell checker couldn't fix "neglictible" properly so I left it as is. You interpreted it correctly as I've expected. As for "breaking", oops anyway, thx for your corrections, keep them coming.
Before I respond to your comments, let me clarify myself about some terms I've used, just to make the discussion clearer. Please correct me if I'm not precise.
- Weight balance of the bike is not body position. Weight balance as I referred to it is the ratio of the vertical force-interaction between front-wheel-to-ground and rear-wheel-to-ground. If the front wheel is off the ground then I refer to it as 0/100 weight ratio (100% of the weight is on the rear wheel). If the rear is off the ground, then I refer to it as 100/0. When I refer to balance in the form of X/Y, I put the front tire 1st (X) as in 40/60. Weight balance can be affected by BP, acceleration and the engineering of the bike itself.
I've read your entire post carefully and it did make me reconsider and organize my thoughts, and made me change my understanding of things. I agree with most of your corrections of my post: the inconsistencies you mentioned, the duration we stay at max lean angle (I agree it's not short at all), cause and effect of weight balance and acceleration/braking. I also Agree with your weight transfer comments, although for the sake of keeping this discussion and post focused (as much as it can be), I won't relate to them and will explain why. For the same reason I will also not relate here to the steering action itself. I do not agree with your claim that the turning radius keeps constant through the duration of max lean angle. This will be one of the conclusions towards the end of this post.
I will 1st describe my understanding of straight line physics (acceleration/braking limits how they're effected from BP) to set basis for the cornering section of this post.
My general understanding of things is that you cannot go much (if at all) beyond 100% weight on either wheel, either in braking or in acceleration. That's where BP can takes part. If your max theoretical acceleration is X(m/s^2) with a certain fixed BP (0/100 weight ratio), then its less than X if you sit more backwards, and more than X if you sit more forward (in each case, after we're at 0/100 weight balance). This is due to the angle formed at the rear contact patch between the combined CoG and earth (While braking: front contact patch). If you move your body forward while accelerating, you can accelerate at a larger rate than X before we reach this maximum 0/100 weight ratio. Same goes for braking. Moving backwards on the seat allows greater braking force to be applied before we reach the maximum 100/0 weight ratio, after which the rear comes off the ground and we cannot brake harder.
It's obvious that the weight shifts backwards due to acceleration and forward due to braking. However, the amount of acceleration/brake-force that can be applied at any certain time is related to overall weight balance and maximum vertical force at each wheel.
IMO, 3 factors can limit the rate of acceleration that we can apply:
1. Spinning of the rear wheel before we're at maximum possible weight on the rear (before 0/100 balance on a straight line)
2. Spinning of the rear wheel after we're at maximum possible weight on the rear
3. Front wheel coming up
(In braking: locking the front before we're at max front weight, locking the front after we're at max front weight, and the rear coming up).
- The 1st is related to the speed/balance/efficiency of the weight transfer process (combination of amount of acceleration and BP)
- The 2nd is related to the maximum theoretical traction force from the rear (rubber/asphalt type, weight of the bike+rider) and rate of acceleration
- The 3rd is related to BP and rate of acceleration. we need as much forward BP as we can to make that X as large as we can before the front comes off the ground.
Although I think the 1st reason (weight transfer process) is both very important and frequent enough in practice, it can occupy an entire discussion by itself on one hand, and OTOH it can be discarded for the sake of this discussion of absolute limits by making all actions more progressively. It is greatly affected/improved by experience IMO. I'll disregard it for the rest of this post as it puts more variables into an already complex discussion, and it can be neutralized by changing the amount of acceleration/braking in a much slower rate. It will obviously harm lap times, but it's also unrelated to the maximum forces that can be applied at any given "fixed" state of the bike. So for the rest of this discussion I'll assume optimal weight transfers, and concentrate on the limits after we've reached "steady" states of weight balance.
So that leaves us with the 2nd and 3rd points.
I believe the 2nd and 3rd points are 2 implications of the same cause: we're at 0/100 balance (if on a straight line) and we try to accelerate more than the theoretical maximum. If we increase the rate of acceleration beyond the theoretical maximum too fast, the rear will spin. If we increase it slower beyond the maximum, the front will come up. The exact rate of speed of acceleration needed to differentiate between 2 and 3 is a direct function of the available traction (only forward on a straight line), and combined mass and CoG of the bike+rider: the smaller the mass or higher the "grip factor", the easier it will be to wheelie, the lower and forward (in braking: backwards) the CoG , the easier it will be to spin (in braking: lock) and vice versa.
IMO BP can affect the 1st point and the 3rd point, but not so much the 2nd point.
I think I didn't explicitly relate to "overloading" either tire although I probably related to this effect implicitly. Speaking of which, could you define "overloading" as you refer to it? I can interpret it as either closing the forks due to excessive braking force, not allowing enough weight transfer before we apply more braking/acceleration, apply more brake power than possible with current grip factor (regardless of forks state), excessive angular velocity which causes either wheel to run wide, etc. I think I'll be able to better relate to your post if we're clear on the terms we use.
This was a straight line discussion (well.. at least my current understanding of things). I believe it is essential to try and understand straight line physics before we can discuss the extra complexity that cornering adds. At least for me, it makes it easier for me to "combine" and add the effects of cornering into this existing understanding.
While leaning, on top of the vertical force (fixed overall but balanced differently on the front/rear depending on BP and acceleration/braking) and acceleration/braking forces, we also have a centrifugal force. The angular velocity of the bike and the bike's+rider weight define the amount of absolute force in that direction (perpendicular to the direction of the bike's progression). The angular velocity by itself is the only factor affecting the the amount of leaning needed to balance this force.
Because this centrifugal force needs some traction resources to balance, that leaves less absolute traction resources to accelerate/brake. The larger the angular velocity (and directly related: lean angle) is, the larger the amount of traction needed to be devoted to keeping us on track and from sliding sideways, and the less freedom is available for acceleration/braking needs.
In contrast to acceleration/braking on a straight line though, where we can shift 100% of the weight to one wheel for maximum effect, leaning requires a different "tactic". Now we're no longer interested in maximum acceleration/braking force, but we're interested in maximum centrifugal traction. If we want to achieve maximum cornering rate (= max angular velocity), we need maximum combined traction from BOTH wheels to achieve maximum absolute centrifugal traction. And this is where the 40/60 rule comes in handy. I agree that 40/60 (or a similar figure) is the balance that would give us most centrifugal traction (derived from the size of the contact patches). So how do we achieve this balance? Combination of BP and acceleration.
To achieve maximum angular velocity/traction, we need the weight to be balanced 40/60. BP would affect it to some degree (I'm guessing not more than 5%), but acceleration is probably the most important "tool" in this regard. It has to be mild and steady such that the weight moves backwards from the natural 50/50 of a still bike+rider, to 40/60 of an accelerating bike (let's call it "40/60 acceleration"). As long as we're at our max lean angle, the same acceleration should be kept, to keep us at 40/60 balance.
The closer we are to the maximum possible absolute angular velocity (and lean angle), the less reserves of "forward traction" we have, and therefore the less freedom we have to change that balance and our 40-60 acceleration, or else, one of the wheels will break loose.
To cause one of the wheels to break loose, it's again one of the 3 reasons I've stated earlier in this post, with two differences:
1. There's much less traction that can be devoted to acceleration/braking, due to the resources devoted to centrifugal traction, and we're therefore mostly limited to spinning the rear (/"locking" the front) and we don't have to worry about the front coming up because there isn't enough driving traction left to make it happen (It may happen later though, when we're more straight on the last phase of corner exit, again, depending on grip factor of the tires/asphalt).
2. There's now a new 4th possible reason: We can also lose traction sideways (due to centrifugal force) on either wheel.
Since the 3rd reason is irrelevant here, and we're neutralizing the 1st one, we're left with the 2nd and 4th reasons.
To get to the 2nd reason (spinning the rear due to more than max possible forward traction or locking the front for the same reason): accelerating at a too fast rate will spin the rear, braking with the front at a too fast rate will make the front lock. "Too fast" is very small here since we're at very little "forward traction" reserves now. That's why we need the throttle control: to keep the acceleration as fixed as possible.
To 4th reason (sliding sideways) comes into play when we have more angular velocity than either tire can hold. This can happen if we're at 40-60 acceleration but we lean (make the angular velocity higher) more than the maximum possible: both tires slide (I guess this one is quite rare?) or if we get closer to maximum lean angle but we're accelerating at less than 40-60 or closing the throttle to get the same result (more weight on the front, it will break lose sideways 1st) or if we're getting close to max lean angle at a higher acceleration than 40-60 (more weight on the rear, it will break loose sideways 1st).
So to maximize angular velocity, we need that 40/60 fixed acceleration as long as we want to keep max lean angle. This brings an interesting issue of what "cornering speed" is. Derived from this analysis, we can see that this is a problematic term, since the cornering speed is not constant through the entire "max-lean" duration. To have a constant lean angle and angular velocity, we need constant acceleration. But cornering speed is not constant, and neither is the turning radius. Corner speed gets progressively faster and the turning radius gets progressively bigger WHILE we're at max lean angle.
This brings me to your claim about widening the arc/radius. As it turns out both from my analysis and from TOTW books (acceleration is required throughout the entire "max lean" duration), this 40/60 forward acceleration is required for max lean angle. If lean angle (and angular velocity) is kept at max constant for this entire phase, but the bike is going faster and faster (40/60 acceleration), the arc MUST widen since the bike cannot keep the same radius and lean angle while going faster and faster.
As we exit the corner towards the straight and straighten the bike up, the angular velocity decreases, more traction is available for acceleration, the arc widens at an even faster rate (infinite arc on the straight) and reason 3 comes back into consideration.
Phew.. this was probably my longest post ever on any forum. Please excuse me that I haven't directly related to all of your points (at least I agree with most). As it turned out, I was sorting my thoughts and understandings of cornering while writing, relating directly to your points less that I've intended. However, I did enjoy writing this post very much, and I think it presents the issues of cornering limits (excluding issues of the process of weight transfer itself and steering action) both in a manner that complies with the facts/tips/instructions of Keith's books, and in a manner I can relate to with reasoning.
Again, my theory and understanding are open for discussion by anyone.