# Rolling resistance of solid tires versus pneumatic

Hi everyone - quick question on something that's been bugging me. So, train wheels, which are solid steel, have incredibly low rolling resistance, an order of magnitude less than average car tires. This is because they don't bend significantly, so you're not wasting energy to heat as in the bending rubber of car pneumatic tires. Indeed, to minimize losses in pneumatic tires, one technique that's used is reinforcement to stiffen the sidewalls to minimize their flexure.

Okay, got it. So then why is it that everything I've read about solid tires versus pneumatic tires in wheelchairs says just the opposite? Everything I've read, including a paper doing rolldown tests on a dynamometer, say that the pneumatic tires have lower rolling losses.

Why is this? What is the factor here that's causing the difference? Is it possible to have a solid tire that gets low rolling resistance like a train wheel but has a weight like a bicycle/wheelchair tire, or is it somehow inherent that in order to get super-low rolling resistance you have to significantly increase the weight, and thus negate your benefits?

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jbriggs444
Homework Helper
Hard vulcanized rubber as is found in tires does not bounce well. Its coefficient of restitution is not high. It will absorb energy when stressed and then not give that energy back when de-stressed.

A container of air has a near-perfect coefficient of restitution. The energy used to compress a bladder of air is readily given back when you stop squeezing.

So what you gain by using a material that flexes less, you lose by using a material that has a poorer coefficient of restitution. A "win-win" solution would be to increase air pressure instead.

Actually, I have two problems with this response. First, your statement about a container of air. If you compress and then decompress air, part of the energy of compression is lost as heat while pressure is higher; whatever is lost is subtracted from the return energy when it springs back (hence the reason that pneumatic energy storage is so inefficient)

And secondly, it's not speculation that train wheels (which have no air in them) have extremely low rolling coefficients. They do - better than even off-the-wall extreme pneumatic tires like the 110psi ones used for solar cars or 120psi bicycle racing tires. Train wheels are, however, extremely heavy.

(There are other potential issues with using solid tires on cars, namely the reasons they stopped in the first place - ride comfort and handling - but we'll ignore that for the purpose of this question)

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Some cited numbers that have references on Wikipedia:

0.0003 to 0.0004: "Pure rolling resistance" Railroad steel wheel on steel rail
0.0010 to 0.0024: Railroad steel wheel on steel rail. Passenger rail car about 0.0020
0.001 to 0.0015: Hardened steel ball bearings on steel
0.0019 to 0.0065: Mine car cast iron wheels on steel rail
0.0022 to 0.005: Production bicycle tires at 120 psi (8.3 bar) and 50 km/h (31 mph), measured on rollers
0.0025: Special Michelin solar car/eco-marathon tires
0.0045 to 0.008: Large truck (Semi) tires
0.0055: Typical BMX bicycle tires used for solar cars
0.0062 to 0.015: Car tire measurements
0.010 to 0.015: Ordinary car tires on concrete
0.0385 to 0.073: Stage coach (19th century) on dirt road. Soft snow on road for worst case.
0.3: Ordinary car tires on sand

So yeah... why do all of the solid steel, non-pneumatic tires do incredibly well - including at the small scale (ball bearing example) - but then solid wheelchair tires do worse than pneumatic?

I do have a guess.... and it's that the energy loss in the wheelchair tires is from slight bending of the polyurethane wheels, and that if they were made out of something light but stiff - for example, foam-backed parallel-grain carbon fiber - one could get both low rolling resistance and low weight in a solid tire. Does this sound plausible?

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256bits
Gold Member
Actually, I have two problems with this response. First, your statement about a container of air. If you compress and then decompress air, part of the energy of compression is lost as heat while pressure is higher; whatever is lost is subtracted from the return energy when it springs back (hence the reason that pneumatic energy storage is so inefficient)

Hysteris, as jbriggs was describing, does bring about a heat build up in a flexing material.

I guess if the change in pressure is rapid enough, maybe. Either way, the fact remains that solid wheels get *extremely* low rolling resistance in some cases (for example, train wheels and ball bearings), an order of magnitude better than regular car tires, but solid wheels have poorer rolling resistance in the case of wheelchair wheels and the like. So I'm curious as to the reason. And my guess is that in the latter case they're not making the wheels stiff enough so the wheels themselves are flexing and losing energy, not just the rubber. But I really don't know.

jbriggs444
Homework Helper
And my guess is that in the latter case they're not making the wheels stiff enough so the wheels themselves are flexing and losing energy, not just the rubber. But I really don't know.

I think you meant to distinguish between wheels and tires there.

If you make the tires stiff enough that they don't flex at all, then you are likely to run into problems with noise and vibration. Any tiny shock from the pavement will be delivered to the wheel, to the bearings and to the body of the wheelchair. Nuts and bolts will vibrate loose, bearings will wear, welds will tear loose. If you are running the tires over concrete, you are going to be crushing sand grains on top of the pavement, making noise and leaving marks. There are good reasons to make tires that are slightly flexible.

You can get away with steel wheels on railroad cars because they ride on smooth rails.

Two weeks ago I actually did a somewhat relevant experiment. Out on my morning walk, I waited until a long freight train had passed and felt the steel rails. They was no detectable warming.

I think you meant to distinguish between wheels and tires there.

Really, it's the whole assembly together that I care about, wheel + tire. You can't compare them otherwise, because train wheels and ball bearings don't have "tires".

If you make the tires stiff enough that they don't flex at all, then you are likely to run into problems with noise and vibration.

As stated previously:

(There are other potential issues with using solid tires on cars, namely the reasons they stopped in the first place - ride comfort and handling - but we'll ignore that for the purpose of this question)

I could elaborate more on what line of thought led me to this inquiry if you want, but it might take a bit ;)

Two weeks ago I actually did a somewhat relevant experiment. Out on my morning walk, I waited until a long freight train had passed and felt the steel rails. They was no detectable warming.

A real testament to the low rolling loss data above, given the mass they bear. And so we return to the intial question: why are solid wheels/tires so much more efficient than pneumatic in the case of trains, but in the case of wheelchair tires, why is the opposite true?

Meh, I'll go ahead and elaborate :) The speculation was that one could design a vehicle specifically for special solid wheels, wherein the vehicle has adjustable camber, based on a double wishbone suspension with a linear actuator. The centerline of the wheels would have a tread of only thin, hard, low-tread rubber, while to the edges (the part that would come into contact when the wheels are cambered) would be thick, sticky, high tread rubber. The vehicle would drive on the centers in normal conditions but automatically increase camber for cornering, acceleration, deceleration, or when there's an unexpected differential in wheel rotation rates (slip), or from explicit instruction from the driver. Instead of relying on an air cushion in the tires for reducing vibration, the main body of the vehicle would be entirely isolated from the wheel assembly by means of long rope isolators, which should offer little flexure losses (picture bending a rope versus bending a tire tread).

Just a speculation at this point. Rolling drag is, after all, the majority of drag in city driving and about 30-40% of drag on the highway, and that percent only increases with efficient vehicles since it's easier to reduce Cd*A than m*Crr (especially in EVs, which can be heavy). Having a Cdd around 0,002, combined with an Aptera-like sub-0,2m²CdA, could yield an insanely efficient EV, esp. at low speeds (ballpark of 20N at 35kph/22mph, or about 5.6 W/km or 8.9 W/mi (plus perhaps 15-20% for powertrain losses and some extra for parasitic losses) at a power usage rate maybe 20% that of a typical hair drier), which likewise would mean extraordinarily long range). But of course it's all based around the premise that solid wheels offer an order of magnitude lower rolling resistance than wheels with pneumatic tires, as in the case between train wheels and car tires, but which seems contradicted by the contrast between solid and pneumatic wheelchair wheels.

My hypothesis is that wheelchair wheels simply aren't stiff enough and that the wheels themselves are bending and losing energy (after all, are bearing losses not proportional to bearing hardness? Steel is vastly harder than polyurethane!) But I really don't know, so if any of you have any other ideas, I'm curious.

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jbriggs444
Homework Helper
And so we return to the intial question: why are solid wheels/tires so much more efficient than pneumatic in the case of trains, but in the case of wheelchair tires, why is the opposite true?

And we return to the initial answer: because "solid" does not equal "rigid" and isn't supposed to.

And we return to the initial answer: because "solid" does not equal "rigid" and isn't supposed to.

And so is your answer then the same as my speculation, that the polyurethane wheels on wheelchair tires are bending and losing energy? Because I only see you talking about air and rubber - I've been the only one bringing up rigidness here.

Or maybe they have more rubber than pneumatics, to act as a shock absorber in lieu of air... hmm, I guess that's a possibility I didn't consider. Perhaps I need to compare some up close.

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jbriggs444
Homework Helper
And so is your answer then the same as my speculation, that the polyurethane wheels on wheelchair tires are bending and losing energy? Because I only see you talking about air and rubber - I've been the only one bringing up rigidness here.

I've seen you talking about "solid". I've not seen you talking about "rigid". In context, I took "solid" as referring to the fact that the rubber tire has no void -- that you were discussing solid rubber tires as opposed to hollow semi-pneumatic rubber tires.

It is certainly plausible that with a rigid tire there is energy loss due to hysteresis in the wheel rather than in the tire. I have been trying to suggest that "solid" rubber tires are non-rigid and have been avoiding considerations of the wheel.

One might also consider the possibility that with a perfectly rigid tire/wheel on a rough surface, some energy would be lost to vibration that is ultimately damped in the frame or between chair and rider. A less rigid tire would be more compliant and could potentially absorb and then release the energy from small bumps without transferring it into vibrational motion in the frame. By contrast, a railway wheel runs on smooth rails. The vibrational problem is avoided in that application.

OmCheeto
Gold Member
...
My hypothesis is that wheelchair wheels simply aren't stiff enough and that the wheels themselves are bending and losing energy ...

I believe this hypothesis is correct.

You could create a model of your flexible tires using shock absorbers and springs.
Kind of like this:

The stiffer the springs, the less energy is wasted in the shock absorbers:

Shock absorbers, more properly called dampers
...
Technically speaking, it does this by taking some of the energy that is being used to compress the spring and turning it into heat.

So why don't they use highly rigid tires, shock absorbers, and springs, in wheelchairs?

Cost. They've simply designed a tire that replaces all three.

Why do they use solid tires instead of pressurized tires?

The person is in a wheelchair.

Would you want a flat tire in such a situation?

No.

Why do they use such soft tires?

Because the person in the wheelchair doesn't want their teeth rattled out.

By contrast, a railway wheel runs on smooth rails. The vibrational problem is avoided in that application.

Hmm, interesting concept. It can't be a full explanation - for example, harder ball bearings have less loss than softer bearings, without any variance in the smoothness - but it certainly could be a factor. Wheelchairs have no suspension system that could return the energy from vibrations, as in a train or car; anything not absorbed in the wheels is likely being damped near 100% in the occupant's body.

So all in all, it sounds like the sizeable difference is probably some combination of thicker rubber on the solid tires than the pneumatics, more bend in the wheels, and the lack of a suspension system to return energy.

Thanks jbriggs444 (and OmCheeto! :) )

OmCheeto
Gold Member
By contrast, a railway wheel runs on smooth rails. The vibrational problem is avoided in that application.

Hmm, interesting concept. It can't be a full explanation

Why not? It's the closest thing to a bearing that I can think of.

- for example, harder ball bearings have less loss than softer bearings, without any variance in the smoothness - but it certainly could be a factor. Wheelchairs have no suspension system that could return the energy from vibrations, as in a train or car; anything not absorbed in the wheels is likely being damped near 100% in the occupant's body.

So all in all, it sounds like the sizeable difference is probably some combination of thicker rubber on the solid tires than the pneumatics, more bend in the wheels, and the lack of a suspension system to return energy.

Thanks jbriggs444 (and OmCheeto! :) )

You're welcome.

ps. On a pre-PF science forum, someone asked why we didn't use magnetic bearings. I told him the idea was ludicrous. Then I googled it, and found that the idea was over half a century old.

Live and learn.

Baluncore