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#51
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if you wanted maximum braking, where would you sit?
Omitted assumtion: the tires are at or near the limits of adhesion.
Hence, the equal load on the front and rear tires, since optima traction occurs when both tires are equally loaded - |
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#52
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if you wanted maximum braking, where would you sit?
Nemo wrote: “I believe that a standard road bike can has a maximu
deceleration rate to the tune of about .6g's. That’s in accord with the .57g figure the article I later cite indicated as a strong braking level ”Because quality tires now have coefficients of friction around .9 t 1.5, in almost all situations involving a traditional bike on clean, dr pavement, the deceleration rate is limited by the bike's tendency t roll over the front tire. As previously stated in the thread, this roll over tendency is a function of the angle of the CG relative to the fron contact patch and the ground. I initially though the coefficient of friction might be that high, bu when I calculated rollovers at those levels, I though it might be of since I remember skidding fronts on road bikes on occasion without doin endos. So the presented tabulations were for lower decel rates assumin the adhesion limits were close to the .6G. Apparently, we need plug i higher decel rates into the optimal seat placement formula I derived fo more realistic seat placement on the braking specialized bike Assuming that it is possible to locate the CG anywhere we like, it i possible to use the maximum available traction between the tires and th road. If the coefficient of friction of tires is assumed to be constan regardless of load, weight distribution is a null factor “Unfortunately, real tires have a coefficient of friction that drops a load increases.” Yep, that’s why I calculated seat placement spreadin load over both tires equally under decel “(I believe this has something to do with the thermal properties o rubber.)” Nope, it has to do with the flexibility and distortion of th rubber letting the tire embed itself into small irregular contours i the pavement and then increasing tractions due the tires horizonta abutting of those irregularities “It thus becomes evident that ideal weight distribution minimize weight on both tires, implying that they each carry half of th constant load. The easiest way to do this on paper is to simply cente the CG between the tires and put it at ground level. We all know tha the CG will always be some distance above ground level. In that case it must be located further back to compensate for the forward weigh shift while braking. In fact, the CG location can be determined by th following formula Df= h*CF+WB/ Where, Df is the horizontal distance of the CG from the front contac patch, h is the CG height above the ground, CF is the coefficient o friction between the tires and the road, and WB is the distance betwee the front and rear contact patches Having said all that, it may be true that the drop of the CF for bicycle with unequally loaded tires is so small that it is not wort considering. In that case, the weight must only be shifted back to distance of Df=h*C to achieve maximum braking. I made bike and rider cg independent variables Since the OP was interested in the maximum braking position, calculated optimal seat position premised upon the even weigh distribution under decel, independent of whether deviations from tha position might be small or large. The non-linear coefficient of frictio not trivial with automobile, although I’m not sure whether the round to profile of the bike tire reduces or enhances this effect relative th flat top profile of a car tire or if the lighter weight of the bike tir would place the function of coefficient of friction as a function o weight in a flatter curve Obviously, positioning a seat for maximum braking means ignoring idea handling positioning, so this is a braking purpose only solutio equation, and except for the low cg recumbents, is so poorly weigh distributed outside of decel as to be a very poor handling bike. A roa bike optimized for a coefficient of friction of 1, will be doomed t wheelies when seated and not braking Changing the decel rate to 1G, gives the following seat positions fo the previously posted bikes Road bike 77.11 inches behind patch Second lowracer (9” seat height 35.38 behind patch (that puts us in the rear tire). LWB recumbent 53.2 “behind patch (that also puts us in the rear tire). MWB recumbent 56.14” behind patch (above the rear, 2” back of axle, so no wheelies.) Carbon Prone 61.11” behind patch. -- |
#53
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if you wanted maximum braking, where would you sit?
meb wrote:
... Changing the decel rate to 1G, gives the following seat positions for the previously posted bikes: Road bike 77.11 inches behind patch Second lowracer (9?seat height) 35.38 behind patch (that puts us in the rear tire).... On my recumbent lowracer, the (estimated) combined CG is about 24" behind the front tire contact patch. Tom Sherman - Quad Cities |
#54
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if you wanted maximum braking, where would you sit?
On Sun, 11 Jan 2004 22:55:58 GMT, meb
wrote: clipped In fact, the CG location can be determined by the following formula: Df= h*CF+WB/2 Where, Df is the horizontal distance of the CG from the front contact patch, h is the CG height above the ground, CF is the coefficient of friction between the tires and the road, and WB is the distance between the front and rear contact patches. Having said all that, it may be true that the drop of the CF for a bicycle with unequally loaded tires is so small that it is not worth considering. In that case, the weight must only be shifted back to a distance of: Df=h*CF to achieve maximum braking. “ I made bike and rider cg independent variables. Since the OP was interested in the maximum braking position, I calculated optimal seat position premised upon the even weight distribution under decel, independent of whether deviations from that position might be small or large. The non-linear coefficient of friction not trivial with automobile, although I’m not sure whether the round top profile of the bike tire reduces or enhances this effect relative the flat top profile of a car tire or if the lighter weight of the bike tire would place the function of coefficient of friction as a function of weight in a flatter curve. Obviously, positioning a seat for maximum braking means ignoring ideal handling positioning, so this is a braking purpose only solution equation, and except for the low cg recumbents, is so poorly weight distributed outside of decel as to be a very poor handling bike. A road bike optimized for a coefficient of friction of 1, will be doomed to wheelies when seated and not braking. Changing the decel rate to 1G, gives the following seat positions for the previously posted bikes: Road bike 77.11 inches behind patch Second lowracer (9” seat height) 35.38 behind patch (that puts us in the rear tire). LWB recumbent 53.28 “behind patch (that also puts us in the rear tire). MWB recumbent 56.14” behind patch (above the rear, 2” back of axle, so no wheelies.) Carbon Prone 61.11” behind patch. CG is approximately at the navel I've read, so the lowracer with 9 inch would have a CG at 16 to 18 inches high or 16-18 inches behind the contact patch for 1 G braking. Practically, the front wheel can do 100% of the braking without changing the CF much, using automobiles (front or rear engine) as an example. Tom Schneider |
#55
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if you wanted maximum braking, where would you sit?
Tom Sherman wrote:
meb wrote: ... Changing the decel rate to 1G, gives the following seat positions for the previously posted bikes: Road bike 77.11 inches behind patch Second lowracer (9?seat height) 35.38 behind patch (that puts us in the rear tire).... On my recumbent lowracer, the (estimated) combined CG is about 24" behind the front tire contact patch. Tom Sherman - Quad Cities The equation I derived had seperate bike and rider cg premised upon th rider location being adjustable If the 24" coincides with the bike cg position, the optimal braking sea position would shift rearwards Obviously, the designer of your lowracer was not focussing on bes braking as the ultimate design objective to sacrifice all othe attributes in hopes of achieving the optimal braking bike. : - |
#56
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if you wanted maximum braking, where would you sit?
ZeeExSixAre wrote:
"David Damerell" wrote in message ZeeExSixAre wrote: True, but braking on a road bike isn't usually as nearly effective as on an MTB because you can't really pull big leverage while on the hoods. Bunk. I can lift the rear wheel from the hoods. How much more braking can I have? I can too, but I have to lean way forward. I was thinking more of the insta-endo that most people can do with flat bars. Er, if I can lift the rear wheel from the hoods in a controlled fashion, but getting a free flying lesson is easier from flat bars, I think I would describe the road bicycle's braking as more effective. -- David Damerell flcl? |
#57
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if you wanted maximum braking, where would you sit?
David Damerell wrote:
ZeeExSixAre wrote: "David Damerell" wrote in message ZeeExSixAre wrote: True, but braking on a road bike isn't usually as nearly effective as on an MTB because you can't really pull big leverage while on the hoods. Bunk. I can lift the rear wheel from the hoods. How much more braking can I have? I can too, but I have to lean way forward. I was thinking more of the insta-endo that most people can do with flat bars. Er, if I can lift the rear wheel from the hoods in a controlled fashion, but getting a free flying lesson is easier from flat bars, I think I would describe the road bicycle's braking as more effective. That's just because you've defined effective as "easily able to stop as quickly as possible" rather than "easily able to brake so hard I can kill myself." What on earth are you thinking? -- Benjamin Lewis Everything that can be invented has been invented. -- Charles Duell, Director of U.S. Patent Office, 1899 |
#59
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if you wanted maximum braking, where would you sit?
Sheldon Brown wrote in message
I think you are correct because the OP misstated the problem. In reality however Tim M is correct. In practice, when we go over the bars it is not [usually] because the front wheel stops and the bike and rider pivot around the contact patch. More often we go over the bars because the frame and fork and rider and rear wheel pivot around the front axle. 'Fraid not. For that to happen, the front wheel would have to stop moving forward, while the frame and fork did the endo. I don't think the wheel has to stop - so every nose wheelie is preceeded by a wheel locking? A relative slowing would suffice, presuming the necessary rotation got it's start somehow... ...Such a scenario would actually involve the front hub bearing reversing direction, so the wheel would be rolling backward with respect to the frame. Where is there a force that would cause the front wheel to rotate backwards? From rider movement. The same way that riders do nose wheelies, or "stoppies" -- by throwing ones weight forward into the bars, or by picking up the rear wheel by lifting one's feet -- except unintentionally -- an accident of rapid deceleration. Surface irregularities in the road could do it as well. In a case where the front wheel is forcibly stopped by falling into a deep pothole or hitting a high curb, it _is_ possible for the bike to pivot around the front axle, but there's no way this can happen under the influence of the brake alone. Agreed. There has to be something else there to get it started. Doug |
#60
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if you wanted maximum braking, where would you sit?
On Fri, 09 Jan 2004 19:33:12 -0600, Tom Sherman
wrote: The following website will be instructive to mechanically inclined people interested in trike construction details. That is so cool, it makes me want to go and build one right now. Unfortunately, there are any number of limiting factors, such as my lack of equipment, supplies, knowledge, ability, money, and time. I've got the enthusiasm, although with my short attention span I don't know if it would last long enough to finish the project. In http://www.ihpva.org/com/PracticalInnovations/weld.html under the section titled "Trike steering geometry", sub-title "Ackerman steering compensation", steering is treated as if there was a live axle with no differential for the front wheels. I think such trikes are nearly all rear wheel drive, leaving no need for a live axle; why would there be front wheel scrubbing? Does your trike use Ackerman steering compensation? Tom Sherman - Quad Cities -- Rick Onanian |
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