This is a paste from rec.motorcycles: I thought this could make for an interesting thread here... So, what might be the differences re physics of braking in a car and a motorcycle? -------------------------------------------------- Maybe you could explain your comment "The stickier tire is offset by a much smaller patch. This is countered by the biker normally being poised over the brakes, except a defensive driver is also off the gas and over the brake in dodgy situations." actually means. In theory, in conditions which are likely to occur in the real world, the contact area isn't supposed to matter. It sort of does, but it's probably safe to assume it's not significant for this. It's the vertical or "normal" force and the friction coefficient which matters. The stickier tires mean a higher coefficient and the similar CG height to a car but shorter wheelbase of the bike provide a higher "normal" force due to more weight transfer. You also have to concider the difference in momentum between a car and a bike and related geometry. It's true the rear brakes do proportionately more in a car, but it might not matter for this. I could be wrong, I'd like to get the real scoop on this, but with some good data and maybe a blurp to go along.
Not so much is the realm of physics. Newton is Newton. The actual physics is the same for cars, trucks and motorbikes, but the tire technology of the motorbike is different, they need soft sticky rubber compounds to get maximum braking and traction out of what little contact patch area meets the road... Newton's Laws of Motion apply more directly to *your* body, though. Let's reel in the years, back to when I was a novice roadracer... At 100 mph, I wasn't going fast enough for the guy on the RZ-350 and neither of us were going as fast as the guy on the 500cc Interceptor thought he could go... We were headed toward Willow Springs' Turn 3, one of the slower turns, a 90 degree bend that I suppose you could take around 55 to 60 mph if you were a better rider than me. You have to brake down smoothly from 100+ mph on the flat to avoid running off into the desert, and then make a smooth left hand turn up a hill so steep that newbie riders shift down into first gear and climb it at 25 to 30 mph. Piece of cake... Anyway, the guy on the Interceptor nailed the brakes too hard, locked up the front, the bike swerved violently as he was still trying to start his turn with the rear wheel of the bike off the ground... So his unicycling attempt didn't work, he and motorcycle parted company, and he begain to demonstrate his gymnastic skills for me, first he somersaulted head over heels for a few revolutions around his pitch axis then he translated his motion though 90 degrees to doing cartwheels down the track around his roll axis and he once again translated his motion through 90 degrees, he was up on his feet spinning around his vertical axis... Just as I was about to hit him, he had the awesome presence of mind to step off the pavement into the desert... Motorcycle tires are loaded about twice as heavily, per unit of contact patch area as a single axle truck tire. Everybody knows how hard vulcanized truck tires are, in order to last for 100,000 miles (I had one original equipment truck tire last 90K miles on my little pickup truck), and yet you see trucks managing to slide to complete stops with their tires smoking... You don't see much smoky drama like that when a motorbike equipped with performance sport or race compound tires. The motorbike's soft compound rubber sacrifices itself more easily and leaves a black streak on the road, instead of going up in smoke, but smoke or smoke-free stops still mean that some of the uppermost layer of rubber has been torn away from the tread... Tire engineers might describe the smoke as coming from "reverted rubber", that rubber which has been heated so much it is no longer vulcanized it returns to its natural soft crumbly state and goes up in smoke... Motorbike tire manufacturers are supplying race tires in the "green" or uncured state. Those tires cure themselves and harden *during* the warm up laps and the actual race. They get hard and lose traction. That's why you hear so much discussion about whether a race team has chosen to use Pirelli's softer "A" or harder "B" compound tire and the compromise made between initial cornering power and still having consistant traction near the end of the race... Then there is tire loading per pound of inflation pressure. Motorbikes carry about twice as much load for every pound of inflation pressure, yet, with the soft sticky tire that has two, two, TWO! modes of traction, the race tire equipped motorbike can decelerate at more than twice the rate that the truck can manage. This lower inflation pressure ratio means that tire contact patches can vary quite a bit on a motorbike, because extreme weight transfer that can place 100% of the motorbike's weight on the front tire and the carcass will distort... Maybe a truck can decelerate at a maximum of 0.75 g's, no se exactamente, none of the magazines I read goes out and does comparo's on Peterbilt vs. Kenworth stopping distance, but they do compare sportbike tires a lot, and every once in a while they leak out some awesome bit of information about GP bikes being able to corner at 1.5 g's... That indicates they could probably *brake* at 1.75 or even 2.0 g's, considering the weight transfer and the soft sticky little bun they run on the front of the bike... Engineers have been very concerned with quick turn-in to start the bike cornering. They started putting little tiny 16-inch wheels on motorbike back in 1983, but 17-inch wheels became more popular. Some GP riders have insisted on a compromise 16.5-inch wheel for their personal taste in steering quickness... So the motorbike does have a really small tire contact patch, and what does this mean in terms of braking physics and how does it relate to the classical "coefficient of friction" discussed in your high school physics text book? Back to what I said about TWO modes of tire traction. When you are riding fairily slowly (or at a low lean angle, the natural rubber of the tire sticks to the road like one of those octopus-looking wall walkers you used to fling at the wall when you were a kid. Natural rubber is sticky... So, if you took a honey bun with a fish scale attached to it and you laid it on a table top with a 10 pound weight on top of the bun and you tried to drag that sticky honey bun across the table like you did in high school physics class, you could get some measurements and calculate the coefficient of friction, comparing the two forces at right angles to each other... But tire manufacturers came up with a combined natural/synthetic rubber compound back in the 1960's. It's called "high hysteresis" rubber. The first time I ever heard of it was when I was looking for big fat tires to put on my little 250cc Yamaha cafe racer... My mindset was still in "coefficient of friction" mode. I thought I needed more contact patch area to get better braking and cornering performance, I wasn't into adhesion and sticky buns and "hysteresis" might have something to do with female troubles and uteruses for all I knew... Anyway, the parts guy behind the counter explained to me that high hysteresis rubber got really *hot* as it rolled down the road and got its traction that way... It took me decades to learn about internal hysteresis of the long polymer chains that made up the rubber of the tire tread. If you push or pull on one of those polymer chains, it pushes or pulls back, and it doesn't return *all* of the energy of the push or the pull, some of it turns into heat. The rest of the energy turns into *traction*. On the Bridgestone Tire Company's Japanese language web page you can find an English language brochure called something like "Introduction to Motorcycle Tires" in .pdf form. It has has a little graph showing a standing wave in the distorted rubber, a wave that's pushing against the road as the road pushes against the rubber... Informed people talking about tire traction don't use the term "coefficient of friction", and they haven't been using that term for about 30 years. Instead, they talk about *grip*, but they will still be claiming that the tire "grips" the road, instead of the opposite true statement... Excepting for the adhesion of natural rubber at low speeds and low lean angles, the *road surface* actually grips the rubber. Small surface irregularities stick up and deform the tire's tread surface. This is the interface where high hysteresis rubber gets pushed and pulled and does its pushing and pulling in return... The tire tread can be described as gripping by interlocking with the pavement surface irregularities. Smmother surfaces are less irregular. This explains why the apparent "coefficient of friction" of a rough concrete surface is so much higher than a surface made of smooth asphalt. When I say "asphalt", I mean tarry, slick, black gooey asphalt, not blacktop, tarmac or macadam paving compounds composed of bituminous material and gravel... Real asphalt has a "coefficient of friction" of 0.3 if rough concrete is considered to be 1.0... So, if you've read all of this screed, let me remind you that my original point is that Newtownian *physics is the same* for cars, trucks and motorbikes, but the *tire technology of the motorbike is different*, they need soft sticky rubber compounds to get maximum braking and traction out of what little contact patch area meets the road....
As Krusty did a very good reply, I'll just highlight two problems in the quoted reeky posting. Tire friction does not follow the "school book" formula. If it did, we could (for a short time) ride sportsbikes on racing pushbike tyres. My favourite explanation of this compares a narrow tyre to a finger that you drag trough a pot of grease, a wide tyre being like sticking all four fingers into the grease. Every ounce of normal force added to the front tyre by weight transfer is taking from the rear tyre. The total normal force availible for creating braking is always determined by total vehicle weight, the only way to increase it is to fill up the tank, add some luggage or a pillion (but then the inertia that the brakes need to overcome increases as well).
OK, but I still have a problem.... ) I think it does depend somewhat on the geometry etc. The sum of the normal forces on the front and rear tire patches would have to add up to the weight of the bike/rider when the bike is not accelerating/decelerating (or parked). But when you brake or boot it, stuff changes. There is a moment created in the framework of the bike in reaction to the braking, brought on by the inertia of the bike acting thru the CG and the tangent forces at the contact point(s) of the tires and road . A FBD would show this. I agree the reaction between tires and road are more complicated than just normal force and friction, but I don't think I agree with the grease theory. Dragging your fingers thru grease is not the same thing. The idea behind the "only normal force and friction coefficient matters" is of coarse that is if you reduce the area, the pressure goes up in response. But I agree that in the real world things are different.For one thing, the rubber tends to conform to the road surface. A sort of reverse example I can think of is where they try get the engine as high as possible in a drag car, this transfers more weight to the back wheels. Actually "weight" may be the wrong word, it is actually increases the reaction back there to the acceleration. Another thought is that if you could somehow get the CG of the bike below the surface of the road, when you hit the brakes, it would tend to wheelie instead of dive!.Stopping would suffer. D.
FBD = free body diagram? Your original question wanted to know if there was some mysterious difference in *physics* between motorcycles and cars, and I said that there was no difference in physics, the difference is in technology. I stand by that statement... There was an unusually *technical* article in one of the silly Brit bike mags a few years ago that explained how a sportbike would transfer all its weight to the front tire and stoppie because of the height of the CG, which is typically around 24 inches above ground level. That article had diagrams with deceleration and normal forces and it showed a line projected from the contact patch that went under the CG of the sportbike. That's the moment you're talking about, I presume... Then the article said that a cruiser, with its longer wheelbase and typically lower CG (around 22 inches AGL)would slide the front tire instead of doing a stoppy. Same diagram. The line projected from the contact patch went above the CG of the cruiser... I imagined those projected lines as levers under the CG, or on top of the CG, picking it up, or pushing it down. The diagrams showed what you described... Turn the diagrams around and relabel the deceleration force as *acceleration* and you've got a wheelie/squat diagram... Famous drag racer, GP driver and Indy car chassis builder Dan Gurney is a big guy. I met him one day at the Mikuni Calendar Show which used to be held at Santa Monica's Museum of Flying. Gurney had ridden in that day on one of his early Alligator prototypes. I took some pictures of it. Gurney never liked the high CG's of the dirt bikes he rode in the desert. Because of his size, he raised the typical CG even higher, and those tall bikes were always trying to throw him over the handlebars... He didn't say that when I met him at the Calendar show. He said that the goal of the project was to build a single cylinder bike that would go 150 mph. He revealed the lowered CG business in later magazine interviews. I saw one of his limited edition $30K Alligators on display in Otis Chandler's vanity museum in Oxnard, CA a few years ago... Gurney said that the lowered CG made the motorcycle far less intimidating to ride. So what if it wouldn't wheelie or stoppie with the extended wheelbase? So what if you couldn't just flick the bike into a corner with a lot of upper body strength and do the Daytona backstraight chicane at 180 per? The Alligator simply accelerates or decelerates without drama, and isn't *that* what streetbike riders want to do? An Alligator is something that an Indy car chassis designer *would* build. Indy cars weigh around 1500 pounds, have 800 horsepower, and a CG about 12 inches AGL. Nobody ever saw and Indy car wheelie or stoppie. They slide, they spin, they roll over, they fly, they flip and tumble, but they don't wheelie or stoppie... I want a V-twin Alligator-clone, not a $30K limited edition collector's bike with Dan Gurney's signature on it. It wouldn't cost the manufacturer's a lot of money to build one either... If you ever heard that 1960's song that goes, "She'll have fun, fun, fun, til her daddy takes the T-bird away" you may also remember that the song speaks of a "hamburger stand"... That was the A&W Root Beer drive-in in Hawthorne, CA. If you'd been a cruiser in 1964, you might have sat in the drive-in restaurant parking lot watching the awesome display of big block pony cars cruising through by, with their race-tuned engines loping and the whole car shaking to the rough idle of the big motor and the cars were being jacked up ever higher and higher to achieve the weight transfer you speak of. Rich kids were showing off cars on the street that normally would have been trailered to the dragstrip. They painted their best ET's on the rear side window and made bets to be won or lost on deserted side streets by the Hawthorne airport... By 1967 or 1968, CG's had been raised so radically, a guy in a Barracuda with a Hemi motor in it was getting completely off the ground with weight transfer. The car was called "Hemi Under Glass"... You're actually talking about a virtual *pitch" center, yannow. Maybe you would like to buy Tony Foale's book and study it to stimulate your mind with thoughts of "what if...?" while the motorbike manufacturer's continue to produce what the slack jawed morons have been conditioned to salivate over... You can build a funny front end with one or two swing arms and get the rest of the chassis to rise up in front, or dive, according to the angles of the swing arms and the positioning of the pivots... Anti-dive FFE's have been built that remained level under braking, but racers accustomed to telescopic forks didn't like them, they were get clues to how hard they were braking from chassis dive. So they couldn't gauge braking feel and they would slide the front tire under hard braking... FFE's are just automotive independant front suspensions turned sideways. An unequal length A-arm is just an IFS turned sideways. The simplest IFS is a long swing arm and early VW Bug's with swing arm independant rear suspensions were known for flipping over when the swing arm would jack up the transaxle. Ford used a pair of really long I-beam swingarms pivoted at opposite ends to reduce swing arm jacking effect in their pickup truck IFS... An unequal length A-arm IFS is like a swing arm of infinite length. The more parallel the arms are, the longer the virtual swing arm gets... But car chassis designers want to keep the front tire's contact patch flat on the road surface and they want to control body roll. They can project their virtual swing arm lengths to place the chassis' roll center anywhere they want, even below ground level... I learned about that stuff from reading "Sportscar Chassis Design" by ? Costin in the mid-1960's. I don't have that book any more, but I think I still have an article written by Jim Hall (of Chapparal Indy and Can-Am Challenge Cup fame). Hall discussed esoteric subjects like "polar moments of inertia" in that article... Buicks and Oldsmobiles were known for a soft mushy ride and a lot of body roll in the 1960's. Buick actually built an IFS with a *long* upper arm and a *shorter* lower arm so the car would bank around corners like an airplane... Again, drivers used to gauging their cornering limits by body roll instead of contact patch feel would be tricked out, the front end would slide away "unpredictably"... When it all comes down to what sportbike riders will purchase, they will stick to the tried and true, the old familiar high CG, telescopic fork front end stoppy/wheely monster. Even if somebody started winning all the races and taking home all the marbles on a high tech resurrected ELF, the race fans would still want the final excitement of the winner's wheelstand show and burnouts. The fans are hooked on drama...
There's a reasonable article on various motorcycle front suspensions located here: http://splashmedia.co.nz/users/britten/art3.html [snip] It's not obvious that this is the case, though certainly the drama has something to do with it. There are real disadvantages to the various front suspension setups (telescopic forks included). Given that, sticking with the disadvantages that you know is rather appealing, particularly when racing rules work to limit the advantages offered by alternative technologies and when racing is a primary means of attracting customers to your machines. However, BMW and Michael Cycz are two examples of current attempts to push front suspension (BMW doing it in manufacture first with their K1200, Cycz going for the race market first with his C-1 prototype) in directions other than refinements of the telescopic fork. It will be interesting to see whether anything of long-term significance comes out of these efforts WRT production motorcycles.
They will always add up. All forces from the contact patches are at right angles to the weight/normal force direction. All the inertia and brake forces do is trying to rotate the bike, you can not lift or press down on something by applying a torque. It is the forces you apply to balance the torque that do the lifting,pushing and shoving. Actually, it is better to forget the imaginary "inertial force" that form the force pair you talk about. In reality there is no force because what we do is decelerate and to do that we need to be out of balance on the longitudinal forces, F=m*A you know. Actually, there is variation in the total normal force but that is due to the bobbing up and down that the sprung weight will do because of suspension action if we consider the dynamics when the braking is initiated or changed. In a perfect world this would not happen on level ground during steady state braking. Please! This is not a theory or any sort of full explanation of rubber tyre/road friction. It just sets your mind in the right direction to digest Krustys somewhat scientific post yesterday. It should start you thinking about irregularities plowing through a material with relatively low strength but with viscosity and hysteresis (not returning immediatly to its original shape). Not only that. If you know anything about how the thinking behind schoolbook friction it is assumed that none of the surfaces are affected at all by the friction force or the normal force and further that they stay unchanged the whole time. Very not true in our case. A perfect analogy if there was no brake on the rear wheel of the bike. Or do you think of 4WD drag cars? On such a beast, weight transfer would probably be your worst enemy. No, but you would need double 300 mm discs with 6 pot calipers on the rear wheel
OK. Thankyou! But, if the the idea of the total normal force on the road doesn't (at least not more than very momentarily) excede the weight of the bike, then wheelies,stoppies, or those stunts you see where trials types jump people lying on a flat road with no ramp, shouldn't be able to happen. Something has to push on it hard enough to cause it the CG to gain height, that which would be greater than its weight. Otherwise I think I got it though ) D.
Sustained wheelie or stoppie - no problem - all the weight on one wheel. Trials rider jumping on flat ground - a combination of the suspension dynamics I mentioned and gymnastics (they jump on flat ground to ;-) ).
One of my old notebooks from the mid-1970's contains some interesting statements concerning weight transfer on braking... 1. Weight Shifted to the front wheel = (braking force X CG height)/wheelbase weight and braking force is in pounds, CG height and wheelbase is in feet... (The weight shift may be reduced by lowering the CG or lengthening the wheelbase, or by having the rider sit further rearward...) When a wheel is braked, 2. The maximum retarding force = coefficient of friction X weight on the tire (But, as I mentioned in an earlier post, racers don't believe in coefficient of friction anymore they talk about "grip" instead. Whereas the older standards of performance under the coefficient of friction theory was that a coefficient of 1.0 would result in a vehicle being able to stop at 1 g, modern race rubber compounds allow motorcycles to stop at 1.6 g's for sure, maybe as high as 2.0 g's [but I have no documentary evidence of that level of braking performance].) 3. At the brake itself, the maximum retarding force = coefficient of friction of the brake material X force applied to the brake pads... 4. Since we are equating torques applied to the wheel, the ratio of distances from the wheel centers must be inserted, ergo disk swept radius from X mu X force applied to pad = wheel radius X CF X weight on the wheel... (When talking about brake material, it typically takes about 3 or more pounds of perpendicular force from the pistons to achieve 1.0 pounds of braking force. Engineers call this ratio "mu" and use that Greek letter in their formulae. I calculated that 1000 psi force from the pistons would give me the 1 g stopping deceleration and 575 pounds of retarding force.) I have a diagram here, showing a Honda 750cc motorbike with a 57.3 inch wheelbase. The center of mass is located 40 inches back from the center of the front axle and 17.3 inches ahead of the center of the rear axle. The center of mass is quite high, it's 27 inches above ground level. The static weight on the front tire is 283 pounds, the static weight on the rear tire is 413 pounds, The total weight of the machine and rider is 696 pounds... If you want to work with those numbers, remember to convert inches to feet... Going back to formula #1, a 1 g stop shifted 329 pounds of weight to the front wheel. In a 1 g stop, the retarding force would equal the normal force. It took a 1.45 g stop to shift 423 pounds of weight to the front tire. The bike in the example was doing an endo. My friends on their little RD-350's with the high CG's had no problems doing endos with the soft rubber Dunlop K-81 tires they favored in those days...
Thanks Krusty, I appreciate the research you did. Something you said is actually just my point. ) You said at one point "1. Weight Shifted to the front wheel = (braking force X CG height)/wheelbase" This is how would I build on that: 1.When you apply the brakes, the road pushes on the bike thru the tire contact patches (braking force you mention, influenced by the F=MA deal), this stopping force being parrallel to the road, and limited by the "grip" and whatever is the normal force on the contact patch(es) . 2.There will be an equal but opposite reaction by the bike acting thru the CG of the bike due to its inertia. As long as the bike is accellerating (either + or -) these forces are sustainable. 3.Because these 2 forces are not colinear (CG height you mention), a moment or torque is created within the bike framework. There must be a reaction to this moment (Newton again) and is ultimately a force perpendicular to the road at a contact point.Another component involved in this reaction, to counter this moment, is the weight acting downward thru the CG. It's not supposed to matter what point you choose as a pivot point, the results are supposed to be the same regardless. 4. The wheelbase and CG height influence the creation/reaction to this moment, because a moment is a force times a perpendicular distance, and changing the location of the CG alters these. If the wheelbase is longer, or the CG is lower, this reaction will be less. Just as in your formula. 5. If this moment induced by the braking is greater than that of the weight of the bike acting thru it CG times its distance to the front contact patch (or actually any point, it's not supposed to matter what reference you pick), the bike will do a stoppie or an "end over" if you don't back off. This is what I meant when I said it was not just a case of simple weight transfer. If it was simple weight transfer, then you could never do a stoppie or an end over as you point out, because you could never create a vertical force greater than the weight of the bike to lift it up.This moment thing can temporarily create vertical forces in excess of the weight of the bike. Granted they can be sustained only as long as some part of the bike is in contact with the ground and it is accelerating in some fashion. OK physics type folks.....there it is.... do your worst! ) My goal is just to wind up with a valid useful image in my mind of these concepts. D.
