Ever wonder why triathlon bikes tend to have 650c wheels instead of 700c? The 650c wheel will spin up faster at the beginning - less mass to begin rotation - and therefore have a slight advantage at startup.

But there's no free lunch. Drivetrains being equal, 700c wheels have a higher top end than 650c, so you are ultimately gear-limited at the very top end of the gear range with 650c vs 700c assuming gear ratios are equal on both bikes.

Now extrapolate this argument to 20" wheels vs 700c. Same rules apply. They spin up a little faster, but the difference is more obvious. But then we get another variable to deal with, namely, rolling resistance being greater in a smaller wheel than in a larger one.

So if we compare a 20" wheel to a 700c wheel, the 700c wheel has higher top end and less rolling resistance. The 20" wheel spins up faster but has more rolling resistance.

We didn't even mention aerodynamic turbulence/drag yet. The smaller wheel has less drag than a larger wheel, but that difference is probably so miniscule that in real world conditions (i.e. outside world record setting) it's not a factor.

That's the way I understand the physics involved. As always, YMMV, ask your doctor or physicist, etc.

Wow! True because it's on the Intenet?

Quote:
Originally Posted by makeinu http://www.bikeforums.net/images/buttons/viewpost.gif
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Myth: Since small wheels have less inertia they accelerate faster.
Fact: No. Since a properly designed geartrain will make small wheels spin faster (so you don't have to pedal more) they will not have less inertia and they will not accelerate any faster unless they are lighter. Physically speaking this is really the same myth as the "pedal more" myth, but, paradoxically, proponents of small wheels usually cite the former while opponents usually cite the latter.

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Feel free to post more myths and facts if you have found a convincing scientific proof.




Simple physics: Rotating inertia = 1/2 Iw^2 where w = rotational speed (ie RPM) and I = moment of inertia of the object about its center of rotation; for all practical purposes here, the rim diameter.

I = pi r^4/4. r^4. radius to the fourth power. So, to make things idiotically simple, a rim of half the diameter has (1/2)^4 the inertia of the larger rim. The rotating velocity is twice as high, therefor the rotational component is 2^2 = 4. Do the math. 1/16th of the inertia. 4 times the rotational velocity. Difference of the radius squared. You can make that smaller rim a a lot heavier and it will still be much easier to accelerate.

Real life - look at a 24" wheel vs a 27" wheel. (24/27)^2 = 0.79. The (just slightly) smaller wheel takes just over 3/4s the effort of the larger wheel. Its been known for decades that smaller wheels win criteriums. The practicalities of bike interchangeability and "status" have kept top riders from using them so we don't see them winning.

Now, it has been known just as long (we are talking good research done perhaps 110 years ago - the brightest minds on the planet were researching bikes then, not outer space or video games) that larger wheels had lower rolling resistance. Over one hundred road miles, that could nullify the advantages of smaller wheels. But in a 25 mile 4 corner criterium with many hard accelerations, small wheels rule, but for tradition.

Those same researchers could have told mountain bikers that from day one, they had it wrong going with 26" wheels off0roads and poor surfaces, that they should be much larger. We are beginning to get there. The 29ers.

Oh, my source for the inertia equations? "Engineer-in-Training Reference Manual" for the professional engineer's license. Just the routine stuff to design anything.

(Edited to make my post easier to read and spaced on the rotational velocity difference)

Ben

Might want to check your reference book again. The moment of inertia of an object depends on its mass, its shape, and the axis about which it rotates. For a hoop shape rotating about its center, the moment of inertia
I = m r^2 where m is the mass and r is the radius of the hoop. [No idea where your I = pi r^4/4 came from, but if that's what your Engineer in Training book says you should demand a refund.]

So yes, if you have two rims of the same mass the smaller one will have a smaller moment of inertia. But the energy required to get them spinning also depends on the rotational speed squared and for a given speed, the smaller rim will need to be rotating faster (higher rpm) by the ratio of the radii. If the masses are the same then the two r^2 terms cancel and both rims will need the same energy to be accelerated to the same speed. In practice a smaller rim is likely to be less massive so there will be a slight advantage to the smaller one.

I agree with this. It's also correct IMO that the larger diameter tire (same tires) will have less rolling resistance, and will have greater drag. Say, eight square inches more exposed to the wind which is small but not necessarily trivial. Plus possibly some extra on the back wheel.

Many false physics statements here guys...

203^2 is not the same as 350^2

First of all ---someone said smaller tires have more rolling resistance---you'd best come up with some real world testing to prove that.

Someone else said smaller wheels have less wind drag---show us the real world experiments.

700c tires are standard for racing because UCI requires it. Moultons used to race but were banned.

20" wheels allow groups to ride closer together which probably give significantly less wind resistance to the group (especially a small group like 3 people). I don't have proof.

Great arguments but feelings and theories need to be backed up by proof.

Other "known facts" that have been proven false recently--narrower tires are faster---higher tire pressure is faster---Higher thread count has less resistance---

So if you do not have actual proof---talk is cheap---But fun...

Anybody know why Prius wheels are so small?---less rolling resistance? Less mass to accelerate?

CdA p [v^2/2] is sufficient.

The issue is the bike/rider and wheels need to have less wind resistance.

That's what CdA p [v^2/2] means.

1) Smaller tires have more rolling resistance. Just like thinner tires do. It's a real effect. But it's not overwhelming. (World's fastest bicycle has 406 tires).

2) Smaller tires are going to have less aerodynamic drag than big tires. But effect of that will depend on rims and will likely be dwarfed by rider's aerodynamics.

3) Narrower tires have less aerodynamic drag and more rolling resistance. So it isn't a simple one is faster/slower than the other. These effects are smaller than other aerodynamic effects.

4) In a pelaton, yes, I believe a Bike Friday rider would do better than a rider on 700c wheels because she would be able to get closer to the rider in front of her. The aerodynamic benefit of this will outweigh the (real) deficit caused by rolling resistance increase. Yes, the UCI made this illegal in races.

5) As far as smaller wheels having faster acceleration, yes, there is a real effect. No, it's really a small effect.

6) I'm assuming the Prius has small tires so the car can be made smaller. If you put bigger tires on it, you'd need to make the car bigger and therefore heavier and less aerodynamic.

There has been very little valid testing of bike, tire, wheel rolling resistance.
The recent change to wider tires and complete changing of the tire design from real world testing is why I question many of the assumptions.

The bicycle industry assumptions I have just recently seen proven false--Narrower tires are faster---higher pressure tires are faster----suspension forks are slower---higher thread count gives less rolling resistance---

give me pause to question what many people see as absolute givens like ---smaller wheels have more rolling resistance (I believe this is true but I haven't seen proof).

Your statement number (6) ---- overall size is critical and keeping the vehicle components small but I think smaller wheels take less energy to get to a given speed. The reason this comes into question for me is they are smaller than Corolla wheels. I do know also Toyota was attempting to get the Prius to the lowest possible wind drag so you may be right, I may be wrong.

Sometimes physics does not work in the same relationships that we think it should.

The historical testing of bicycle tires on a smooth drum (which was industry standard as recently as 2011) shows how little testing is really done.

Campagnolo And the Other Italian Companies Got Into The BMX Racing, in the early Years , in the 80's they got out of That

This is the kind of racing that has now been in the last 2 Olympics short, fast and on a track with corners and small hills ..

They made Sew up Rims and Glued on smaller versions of Cyclocross knobby Tires ..

Being small diameter + Light , Those were a rapidly accelerated wheel..




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There has been a fair bit of testing of this. It isn't that the science said thin tires were faster, it's fokelore.


There's been plenty you can find on the internet, you just have to look for it (e.g., Velomobiel Quest en Wim Schermer: Bandentest overzicht en correctie Cr waarden).

The physics here isn't too complicated. 100 lbs on a tire that is pumped up to 100 PSI will have a contact area patch that is 1 inch squared. For a thin tire to get 1" square, you need a longer piece of the tire to deflect; a wider tire needs less length and therefore has less rolling resistance.

This is true for big tire versus small tire (of same width). To get same contact patch, you need a bigger angle of the small tire than the big tire.

Physics works very well here. What isn't obvious is aerodynamic drag and for that you need to measure it either in a wind tunnel or in real world situations using roll down tests or a power meter on a closed course.