Most riders know about Crr, the coefficient of rolling resistance, and most are aware of charts showing which tires are the fastest. And everyone knows that a smaller Crr number means a tire is faster. But few understand how to apply that number to get wattage numbers, the numbers that we really care about as riders. I’ve Googled the topic and couldn’t find a page that pulled it all together, so here’s my attempt at explaining Crr as it relates to bike racing.Â
How does Crr relate to drag force?
Crr is a number assigned to a tire at a certain psi that allows you to compute horizontal drag force as a percentage of down (‘normal’) force. This means a better tire will create less drag, and a heavier rider’s tires will have bigger contact patches and create more drag. The formula is simply:
F = Crr * Nf
F is the drag and Nf is the normal force. The normal force is your mass times gravitational acceleration, or:
x kg * 9.81 m/s^2
So, for example, for a rider and bike weighing 82 kg with tires with a Crr of .005, the rolling drag force would be:
.005 * 82kg * 9.81m/s^2 = 4.02 Newtons.
A Newton is the force of gravity on 102 grams, or roughly the weight of an apple. So this rider’s tires are pushing against him with the weight of 4 apples.
Is the drag force independent of speed?
Yes, your tires push you back with the same force no matter how fast you ride. Aero drag, on the other hand, increases exponentially as you go faster. It is this discrepancy that allows uber geeks to separate aero resistance from rolling resistance in testing.
Is that for one tire or two?
It’s for both, since the two tires split the burden of your weight, or normal force. So the front tire might be contributing 40% of the drag and the rear 60%, but it still adds up to the same drag.
If the drag force is the same does that mean the watts required to overcome rolling resistance is always the same?
No. The faster you go the more watts you need to overcome rolling resistance. To get the power needed multiply the drag force by velocity. For the same 82kg rider/bike combo going 25 mph, the power required is:
4.02 Newtons * 11.17m/s = 45 watts
At 12.5 mph, it’s 22.5 watts. Why the difference? When you go twice as fast you’re fighting that resistance for twice the distance, so you’ll need to do twice the work in the same time.
Will I go faster on the flat if I lose weight?
Yes, sort of. If our 82 kg rider + bike were to drop 2 kilos, he’d only save 1.2 watts at 25 mph. However, the 66 kg bike + rider next to him (on the same tires) would be putting out 9 less watts, and probably enjoying much more of a draft as well. So smaller riders get an edge on the flats as well as the climbs.
How much power can I save with tire choice?
Let’s have that same rider ride Tufo’s and Veloflex’s, with Crr’s of .008 and .005 at 108 psi. The Tufo’s would cost him an extra 27 watts! If that rider were to do a flat 40k TT at 350 watts with a CdA of .24, Tufo’s would cost him 72 seconds.
Thanks Andy, so if heavy riders press tires more to the ground (greater down force), making horizontal force higher, wouldn’t inflating to hire psi make contact patch smaller and therefore reduce Crr?
Which tires do you recommend on this basis?
Beats me. Check those charts. You still have to consider grip, flat resistance, cost, clincher vs tubular, does it match the color of my frame…
Yes, Crr decreases with higher tire pressure, but you have to balance it with handling and traction.
The more supple the tire the less rolling resistance high or low pressure.
pro2 might be fastest at 116psi but Evo CX can have less rolling resistance at 125 psi(be faster)
I think the reason suppleness of the tire decreased the rolling resistance is because you end up with a more perfect circle at points tire makes contact with the ground, which does usually mean smaller contact patch. But I also agree with Andy that there are diminishing returns. For example why do race motorcycles not have super skinny tires? The forward force needs a certain size patch to brace the ground depending on weight of object it’s trying to move.
supple tires flex easier= less force required to create contact patch+higher psi= less rolling resistance
roundness of the tire affects its aerodamics
if by roundness you mean shape of tire’s cross-section then yes, but I meant roundness of the tire looking at it from the side at contact points, ergo contact patch, so we’re saying the same thing more or less…
Andy, doesn’t slipping factor into speed attributes? Mainly that a bigger or more supple contact patch will keep the tire in contact with ground more and therefore exert more constant forward force?
The shape of a contact patch will save less wattage, then supple tire.
Compare supple tire like (evo) Crr .0039 to (Continental
GP 3000).0067.
.0039 * 75 kg * 9.81m/s^2 = 2.86 Newtons.
.0067 * 75 kg * 9.81m/s^2 = 4.92 Newtons.
Wattage needed to overcome rolling resistance will increase with speed:
2.86 Newtons * 11.17m/s = 31.9 watts
4.92 Newtons * 11.17m/s = 54.9 watts
that’s 23 watts
I’ve always been a fan of the landing strip patch over the little triangle
Too much friction, I prefer a bald patch.
“I think the reason suppleness of the tire decreased the rolling resistance is because you end up with a more perfect circle at points tire makes contact with the ground”
incorrect,
shape of contact patch is in correlation with its size not suppleness
“I think the reason suppleness of the tire decreased the rolling resistance is because you end up with a more perfect circle at points tire makes contact with the ground”
think pressure
The Corsa Evo CS will be perfect for that wheel, and I would recommend 100-125 psi (6.9-8.6 bar) depending on your weight. You will want to run 0.2-0.5bar more in the rear than the front to account for weight bias. I personally weigh 155lbs (70kg) and run my tires at 105 psi front (7.2 bar) and 110 psi (7.6 bar) in the rear. When I was racing and lighter I ran them at 100/105, but now that I’m heavier it is safer to run a few extra psi and I may go even higher on bad roads, which has worse rolling resistance, but better protects the wheels from damage in the event of hitting a pothole or something else which could damage a rim or tire. The better option is to run a wider tire at lower pressure on rough roads, but that is just not always feasible, so I would rather have higher rolling resistance and protect the wheels than lower rolling resistance and increased risk of damage to the wheel.
Higher pressure is definitely slower on anything other than perfect surfaces. Think of it in terms of a bunch of 1mm tall bumps in the road. If you have a lower tire pressure, the casing of the tire will deflect over each bump (we’ll assume the casing deflects the entire 1mm) converting a small amount of energy into heat as the casing deflects, but the amount of energy necessary to compress the air is almost non-existent. Now at a higher pressure, we will assume that the tire deflects half as much. Now the bike and rider are lifted by 0.5mm and the casing deflects by .5mm, the energy necessary to deflect the casing by .5mm is less than it takes to deflect it by 1mm, but is nothing compared to the amount of energy necessary to lift the bike and rider by 0.5mm, so the end result is that the total energy requirement for the high tire pressure condition is much greater.
The other thing that happens is that on smoother roads, high tire pressures keep the casing from deforming over and into small cracks and crevices and over pebbles, which means that some of the deflection is transferred into the tire tread, which is not as elastic as the casing. Excessive tire wear comes about as the tire rubber begins to fail in shear as it is deformed by the road surface, and this generates heat as well as breaks down the cross-linking within the tread material…. overall, you are using more energy to go slower and you’re wearing your tires out faster. The problem is that high tire pressures feel fast as your body perceives all the high frequency vibrations from the road surface as being faster than a smooth ride.
Lennard Zinn had a great analogy when he said that 100kph in a Jeep will scare the crap out of you but 200kph in an S class Mercedes feels effortless…the same is true of bike tire pressures, but it’s just hard to convince ourselves of that. As athletes we tend to buy into the ‘if some is good, more must be better’ philosophy, but this is rarely true. Of course the tire manufacturers have given up on this and continue to try and make higher pressure tires as that’s what the consumers demand, as I think that they’ve decided that it is easier to just give people what they think they want than to try to educate and argue with them 🙂
Will Schneider
vo2mxout.com
Jobst Brandt has published data for tire rolling resistance. His data forms the basis for this analysis. He has also provided an explanation along with the data.
We expressed this data as families of curves and identified them by a generic description of a tire. We calculate rolling resistance as the nominal Crr for the surface multiplied by the ratio of one tire to another. We picked the tire with the lowest rolling resistance (Premium Clincher) as a standard to which the other tires are compared. Hence the Crr used in the formulas becomes
Crr = NominalCrr x RollingResistanceTire1/RollingResistanceComparisonTire
As Brandt explains, the glue line in tubulars glued with road glue gives a flexible contact between the tire casing and the rim. This causes rolling resistance losses. Track glue dries stiff and prevents these losses. Track glue requires a perfectly clean rim. Once glued, the tire cannot be removed for repair. If removed, the rim will have to be throughly cleaned to base metal before mounting another tubular. The data show that if one does this, one has a tire with rolling resistance that is equivalent to a Premium Clincher.
Figure 1—Plot of families of tires (Premium, Utility, & Touring) for Clinchers (black) and for tubulars mounted with road glue (red) and track glue (blue).
Tire Descriptions
Premium Thin tread, thin high-thread count casing, thin tube
Utility Thicker tread, more layers of casing under tread, typical tube
Touring Thick tread, thick sidewalls, typical tube
Anecdote:
A rider asked how much time it was worth to ride clinchers in a 3k pursuit. Our analysis said it would be about a 2.5 second advantage to ride clinchers over tubulars glued with road glue. After some research the rider concluded that tubulars were the only choice since the the rider’s federation was providing the tubular disc wheels.
The rider’s mechanic tried mounting tubulars with shellac, an alternative to track glue (he could not find track glue). Shellac would not stick to rims previously glued with road glue; he could not get the rims clean enough. He tried other adhesives, but could not find one that would be stiff and not dissolve the base tape.
The moral of the story is that, although track glue is a theoretical possibility, don’t take for granted that you can make it work.
Will,
vo2maxout.com
E=mC^2 means: The energy in matter is equal to (the mass of the matter times the speed of light) times itself.
Dec 21 05, 8:00 AM
my_baby_love
Energy = Mass X (Speed of Light)Squared
Dec 21 05, 8:01 AM
superdupersue
Energy = mass x (speed of light in a vacuum) x (speed of light in a vacuum)
Dec 22 05, 5:25 AM
kevinom
while all this is good it just means matter can be transformed into energy and vice versa.
http://www.analyticcycling.com/DiffEqWindCourse_Page.html
how much wood would a woodchuck chuck if, a woodchuck could chuck wood???
lets see you work that out in a wind tunnel.
I don’t think ’roundness’ of the contact patch has an effect. Better to be shorter and wider, which is why 23mm tires roll faster than 20mm tires. Longer contact patches have more leverage against the axle of the wheel to push you back.
I don’t know if suppleness saves more watts than contact patch shape. It would be cool if someone would test the same clincher tire on a regular rim vs Hed’s wide Ardennes rim. Then you could actually quantify that. (Hed’s wider rim is supposed to make the same tire wider, so you get a shorter contact patch).
Roundness doesn’t dictate the size of the contact patch. Size of contact patch explained here:
https://nyvelocity.com/content/equipment/2008/contact-patch
As for friction and slippage, I have no idea. The formula for friction is just coefficient of friction * normal force, so it seems to indicate that size of contact patch is irrelevant. But, a bigger patch might deal with road irregularities better.
I am to care about CRR because…I need an excuse to not win?
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there is not sort of. you will. CRR is mimial when it comes to hauling your fat ass up an incline. just pump your tires to the recommended psi and shut up.
I sense more douche. Is that you again, Baby C?
Can a lower Crr help my 401(k)?
((Crr * (401k) / (mass * velocity)) / (Cervelo net income / # of bento boxes in 10013 zip code) ^ # of 16th place finishes in Cat 5 crits = it’s basically futile & time to try another sport.
With all those calculations I need to lose weight, get a lighter bike, buy fancier tires to get faster and more efficient. Why didn’t the bike shop or the stinking coach mention this? I’m feeling ripped off! Time to buy a calculator and dump the coach.
Thanks for the heads up, you guys are the best! My financial advisor is sending me a shrink for using those equations in my 401k, what a loser.
To the dumb rider below me you need to get a brain man!
I knew something else was missing! Now I’m gonna dump the financial Advisor as well.
Thanks! You’re the best!
Sounds like something Ken would ride up?
“but is nothing compared to the amount of energy necessary to lift the bike and rider by 0.5mm”
This is oversimplistic, although still basically correct. In an ideal system, a bounce causes a conversion of kinetic to potential energy. However, gravity has its way eventually, and the potential energy is traded for kinetic energy as the bike returns to the road. The issue is the initial kinetic energy was parallel to the road (in the direction of motion) while the returned kinetic energy is perpendicular to the road. In theory, the bike could continue to bounce forever. In actuality, every bounce has some loss, so the kinetic energy eventually converts to heat. The result is that even “elastic scattering” off the road surface results in a loss of forward momentum, ie an increase in drag. But it’s not always true that raising the bike’s center of mass does so. For example, riding over short rollers, the work done to raise the bike up the roller is returned as propulsive force when the bike descends the opposite side. The key is that the slope is sufficiently consistent to translate the direction of motion without loss of kinetic energy, a condition not meant by a rough road surface.
i ride my own handmade super pinky rubber ball tread tubulars.
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I rocked the Hed Ardennes for the first time over the weekend with 90psi in Vittoria Open Corsa Pave 23c tires. They ARE faster and more comfortable than 105 psi in a 19mm rim, making me want to ride longer, which will make me faster in the long run. less rolling resistance and greater rider comfort is a winning combination.
$1000 for box section clinchers is a tough sell for most folks, unfortunately. great idea, bad price.
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