As someone who is trying to educate themselves here I need some clarification: in referencing different driving surfaces; ice, wet and dry, is the coefficient of friction a shared value between the surfaces or does each surface have its own coefficient of friction referenced to something else?
I feel it might be a little foolish but I have to assume you would want to be able to reference the coefficient against a hypothetical surface for times when you have an object in isolation. A predictive value if you will
So we would need to be looking at each portion of the tire tread that is touching at any given moment against whatever road surface at that same moment and it would by necessity be ever changing. Or roughly speaking, it’s a lot more complicated than you guys have been letting on, and maybe more complicated than that still
I am also assuming cutting into the surface such as a metal rasp/file would do is not permissible in this measurement? Though the fact I change my tire or rather have to change them tells me some level of cut or transfer is permitted.
Very much a shared value. But more to the point, the so-called coefficient of friction is a construct that was introduced to help non-physicists conceptualize the idea of friction (generous view) and/or a construct that provides easy-to-solve numerical problems for introductory physics courses (cynical view).
Consider “drag” for example. This “coefficient” relates the shape of a car of given frontal area to its friction whilst moving through air. You can measure it by seeing how much power it takes to move the car (subtracting out the friction of the tyres on the road). It clearly depends on velocity and air density. And the shape of the car, obviously. So it’s not a constant, and you can’t predict it–you can only measure it for a given car driven in given atmospheric conditions. You can rank different cars by measuring each one of them, but you can’t extrapolate results to predict how a new design might work.
Roadholding friction between tyre and pavement is just as complicated. “Rolling” friction is the relevant friction that is added to aerodynamic drag to get a total drag for the car. It varies with the “normal” force (weight plus added downforce if any). You can calculate a “coefficient of rolling friction” but it’s relation to normal force isn’t linear–it’s not a constant. It depends also on the tyre material, size, air pressure/contact patch, tread design, etc. and also on myriad properties of the pavement. Static friction (tyre not rolling) limits stopping and accelerating, and also depends on all of these factors. Static friction when the car is accelerating laterally (changing direction but not speed, as in a corner) is similar, and this defines the limit of lateral acceleration (usually expressed as a fraction of the acceleration of gravity). This gives you the calculated coefficient of friction, mu, BTW…0.8g means mu is O.8 while 1.3g means mu is 1.3.
So most of this isn’t physics at all but empirical observation. There seem to be empirical rules as to what is possible, though, which haven’t been broken since the beginning of racing, and despite advances in tyre technology.
One rule is that less weight on a tyre increases its measured friction coefficient mu (after optimizing tyre pressure). Another is that mu in corners seems to hit a limit around 1.1g or so unless downforce is added to corner weight. Then it can go up to around 1.5 in practical race cars. Perhaps the most well-known rule is that the most grip comes with tyres that are not only the most expensive but also the ones that wear out the fastest. The rubber compound of those tyres digs tenaciously into crevices in the pavement and has to be sheared off (left in the pavement) to get the tyre to skid. IMHO.
It’s funny back back in the late 50’s the mathematicians had figured out that the fastest speed that a dragster could obtain in a quarter mile was something like 150MPH!
Bob
Yep: the source of the infamous “marbles,” and not only are they slick, they whack you in the helmet, as you watch them peel off the tires, in corners.
Robert
Interesting that CoF for a tyre increases with decreasing load…but is somehow contradicted by the increase in CoF witH load in a corner.
I suspect there is a mixing of static and dynamic CoF’s in these observations. As I noted earlier…once there is slip the CoF increases with increasing slip…to a maximum at 15-20 % wheel spin… and returning to the same value as the static level at 100% slip. Drag racers are aware of this fact…and it may be this phenomenon that explains the apparent contradiction…??
Matt
Kirbert
(Author of the Book, former owner of an '83 XJ-S H.E.)
54
Mixing apples and oranges. Adding load increases friction but decreases CoF. The simplistic theory is that CoF is relatively constant, so friction (load x CoF) increases linearly with increasing load. The contention that the CoF increases with decreasing load merely indicates that the friction doesn’t increase linearly with load. It’s saying that increasing the load increases friction, but not as fast as the load is increasing.
Not a contradiction, Matt, but poor semantics on my part. What you call “load” above is what I mean by weight, W = mg. Grip increases with decreasing corner weight, and that is the basis of chassis tuning. When I said “downforce added to corner weight” I didn’t mean more weight, but rather additional force that comes from something other than weight. This applies mainly to race cars. Wings add downforce. So does pumping the air out from under the car (“ground effects”, which adds the weight of the atmosphere to that of the car–up to 15 lbs for every square inch if you do a perfect job. These techniques greatly benefit lateral acceleration because they increase grip but they don’t add to the inertial mass of the car (because the car isn’t dragging the atmosphere with it). In contrast, the only known way to increase weight is to increase mass.
BTW, the reported motion of UFOs (very rapid change in direction) suggests to me that aliens have mastered gravity–possibly separating inertial and gravitational mass, or making negative mass.
I left out another empirical “rule.” That one says that grip is max when the tyre is flat on the ground. This rule explains why roll bars, which transfer weight, can help cornering. They trade off loss of total grip due to weight transfer to a gain in grip by limiting body roll and helping keep the tyres flat. The better your suspension is in keeping tyres flat as the body rolls (camber gain, etc), the less roll stiffness you need. IMHO.
Yes…the downforce courtesy of an aero aid is better than adding weight because the downforce can be removed by altering angle of attack of a wing or cleverness in the chassis…but i thought we were talking about the CoF…or mu…if, as you say…“mu is limited to 1.1 unless downforce is added…then it can go up to 1.5 in practical race cars” …then I’m assuming the mu is increasing from 1.1 to. 1.5 in a heavily loaded corner situation. I wondered if this is due to the increase in coefficient of friction with slip between the tyre and the road.
I have a curiosity about gyroscopes and the empirical method of explaining reaction forces. The methods explained the forces but left intuition behind!!! Maybe the physicists bashing sub atomic particles into each other in Switzerland will figure out how to manipulate gravity so we can have anti gravity belts and float off to the neighbours place if the winds are favourable!!!
wing idea , 1966, car in museum Midland TX ,plus other intersting cars , the famous sucker car showing twin vacuum fans, BANNED after just a test on a real track!
like i said all talk no action here, OOPs a reaction!
Matt, the downforce courtesy of an aero aid is fundamentally different than downforce due to weight. Adding weight increases the frictional force available for reaction to the car’s inertia (the property that resists change in velocity). So does adding downforce from wings, etc. But the car’s weight and its inertia are proportional–both depend on mass. In contrast, adding downforce from a wing doesn’t increase mass. So available frictional force increases, but inertia does not.
If the coefficient of friction were a constant, then adding/subtracting weight would be of no consequence–the ratio of friction force to weight (coF or lateral acceleration in g’s) would stay the same. But the coF goes down slightly with increasing normal (downward) force, so the lighter car wins out (slightly). On the road, Loti and SUVs both do well, whereas on the track the Lotus advantage would be significant.
Assuming again that the coF is constant, adding downforce by means other than adding weight would be of great consequence. Friction increases but mass does not. The ratio of friction force to weight (lateral acceleration in g’s) could increase without limit. [A “road test” of a race car in the current R&T measured 2.0g in a skidpad.] But as always, the coF does decrease slightly with increasing normal (downward) force, regardless of whether that force is due to weight or due to weight plus other tricks. So you don’t get as much added friction as you might like, but all you do get adds to grip because it is without penalty of added inertial mass.
I apologize for misleading you with my previous post, which was in error. I didn’t mean to say that CoF (mu) increases when you add non-weight downforce. Lateral acceleration does–and that number (expressed in g’s) is the coF for road cars without added downforce. But the actual physical property of the tyre/road interface–the coF or ratio of available reactive frictional force to total normal (downward) force–always (AFAIK) decreases monotonically as downforce increases. That’s regardless of the source of the downforce–weight, fans, wings, someone running alongside with their finger pushing down on the bonnet.
