# Rolling resistance – theory and practice

In theory, the rolling resistance of wheels decreases as the diameter of the wheel increases. This is on the assumption that all other factors are equal: the tyres are of identical cross-section and carcase construction, with equal internal air pressures and equal external applied loads, rolling at low speeds in still air where no significant aerodynamic effects apply, on smooth hard road surfaces, with the wheels on hubs with insignificant bearing friction.

Yet it is clear from observation and testing that, under some circumstances, some smaller diameter bicycle wheels can roll as easily, or even more easily, some larger diameter wheels. This does not mean that the theory is wrong – merely that one or more of the “other factors” is not equal. The easiest factor for the average rider to control is tyre pressure. It’s a fair assumption, confirmed by everyday observation, that most cyclists ride on tyres that are at sub-optimal pressures. So, pumping up the tyres of a small-wheeler to the maximum recommended by the tyre manufacturer may well be enough to allow it to roll more easily than many other cycles with larger wheels. Choosing a small diameter tyre with a supple carcase will also help. At racing speeds, wheel aerodynamics and unsprung mass of the whole bicycle and rider ensemble can also enter into the equation and may, for example, favour a well-designed small-wheeler with suspension.

Between 1998 and 2002, British engineer John Lafford carried out rolling resistance tests on various tyres, ranging in tyre bead seat diameter from 305 mm to 622 mm (i.e. nominal wheel diameters of 16-inch to 28-inch). The manufacturers and product types, cross-sections, tread patterns, state of wear and tyre pressures all varied quite considerably. His full data may be found here: http://www.legslarry.beerdrinkers.co.uk/tech/JL.htm

Below is a chart generated directly from John Lafford’s data using Microsoft Excel. The vertical axis shows the various tyres tested, ranked by bead seat diameter – biggest at the top and smallest at the bottom. The horizontal axis shows rolling resistance – the less the better. The straight, backward-sloping, black line is a computer-generated trend line which reflects the general truth of the theory that rolling resistance decreases with tyre diameter. But it is immediately apparent that the rolling resistance of any particular tyre diameter may vary considerably, confirming the variance due to those “other factors” that may not be equal in reality. Hence we find some of the smaller tyres under certain conditions have actual rolling resistances lower than some of the larger tyres.

To cope with rolling resistance is to reduce amount of radial movement. It’s linear dependence. Less (radial) movement = less rolling resistance. Look at the wheel’s hub bearing – smaller wheel will produce more rpm of the bearing. Smaller wheel will generate more fricton of the bearing (aka MORE rolling resistance). It is very easy to understand.

However … there is also something completely apart from rolling resistance and it is … rotational inertia. Each object has got some inertia which is felt as resistance to accelerate. Increasing diameter of the wheel acts opposite to rolling resistance. Increasing wheel’s size will raise – to square (!!!) – the amount (!!!) of rotational inertia. With inertia we are not dealing will linear growth but with the square! This means some troubles: bigger wheel will be always percepted as more sluggish compared to small ones. Bigger wheels will require more power to GET UP TO SPEED. Only when the wheels start to rotate at fairly constant speed then inertia “settles up” and is acting as capacitor of the energy. This also means … that bigger wheels require much more energy to stop them than small ones. Bigger wheels require stronger brakes as they accumulate more energy.

For short rides with much accelerating/ decelerating moments (ride in town, traffic lights) smaller wheels are better choice, because small wheels will accelerate fast and are very easy to slow down/ to put complete stop. For cruising speeds and longer distances (no traffic, constant speed) bigger wheels are better choice since rolling resistance is reduced.

There is a smart guy from Netherlands who tests rolling resistance of different tires and luckily enough He has tested few same type of tires with small/ larger diameters. Based upon His test we can conclude that bigger wheel have less rolling resistance:

http://wimschermer.blogspot.com/2012/12/bandentest-overzicht-en-correctie-cr.html

I believe the big advantage of small wheels to be quite simply that they are smaller. This makes them lighter, but more importantly reduces the frontal area. A 559 for instance has a frontal area roughly 10% smaller than a 622. Stands to reason that that means 10% less aerodynamic drag.

From the figure above I estimate the increase in rolling resistance to be around 5% when you switch from 622 to 559. That alone would make the 559 faster, but if you assume that at 25mph or 40km/h 80% of the total resistance is due to aerodynamics and 20% due to rolling resistance it becomes clear that you can make a real saving from going with the 559 wheels. Lets say you have a total of 100N resistance on your 622 wheels, 80N due to aero, 20N due to rolling. When you switch to 559s you would now have 72N due to areo (10% win) and 21N due to rolling. A win of 7N or 7%! I once read somewhere that the sweet spot between rolling resistance and aerodynamic drag is around 17 inch (!) quite close to Moulton’s bikes I would say, and I wonder in how far he was limited by tyre availability etc. Because of the theoretical advantages (and because I like the feel better) I ride only 559s. I work in a bike shop where nobody gets this unfortunately, but I don’t care about that. What annoys me is that we could have much faster bikes were it not for the incredibly conservative cycling world (UCI and manufacturers) and that I can’t find a time trial bike with 559s. We need more original thinkers like mr Moulton I’d say!

I just realised that the above ignores that wheels alone don’t cause all the aerodynamic drag.. it would be interesting to find out how much of the aerodynamic drag is due to the wheels and how much due to frame and rider. If the above assumption of 80% of the total drag being due to aerodynamics at 40km/h is correct then the tipping point would be around 12.5% of the total aerodynamic drag to the wheels and the rest due to rider and frame.. It’s an interesting problem!

Many thanks for your thoughts on this, Tom.

Tony,

This topic is one that like other Moulton owners fascinates me, but it also often infuriates me, because people comment on it with little reliable empirical data. And testers often compare apples with oranges. Recently in the Moulton Bicycle Facebook page someone shared an article about rolling resistance and wheel diameter and the find was, big wheel have lower rolling resistance. But they compared apples and oranges. They don’t compare a Continental GP 28-406 with a 28-622 GP, no they choose a different Continental tyre in the larger size. The same was true with the Schwalbe tyres.

Consulting Chapter 9 of your book on the Classic Moultons we see Dr Moulton’s through testing, and yet people disputed it without valid empirical data of their own. I think your point here Tony is well made, there are a myriad of factors that determine how well a bicycle rolls and tyre size is just a part of the puzzle.

Regards,

Paul

Hi Paul,

Thanks for your comment. Yes, as the trend line shows on the graph I produced, as a general rule and if all factors are equal, rolling resistance reduces as diameter increases. But all factors rarely are equal. It can also be quite easy to influence some of the variables – not least by ensuring your tyre pressures are appropriate for the kind of riding you are doing. And, of course, one needs to be sensible when selecting what wheel/tyre combination to use for which purpose. Using 16-inch narrow section wheels on muddy bridleways would be insane but so too would be time-trialling on knobbly wide-section 29ers. So for my modest but quite varied cycling I use a range of bikes with tyres ranging from 16 to 27-inches in actual diameter and widths from 32 to 57mm. They all have a place.

Tony

This is a subject which has fascinated me for a long time. The bike I use for triathlons is a Litespeed Tachyon with Vredestein Fortenza tires, which have a psi limit of 160. I’ve done several races with the pressure at 160 and others at 120. Tests have shown that lower pressure is better because the tire doesn’t “bounce” on tiny bumps in the road. I’ve done roll down tests on a hill near my home and I always seem to hit the same speed when I reach the mailbox on the bottom (31.4 mph) regardless of the tire pressure. Is tire pressure levels pretty meaningless?

Hi Jack,

Generally speaking, road bike tyre pressures above about 100 psi are unlikely to reduce rolling resistance in real world situations. As you have found, increasing the pressure further just gives a harder ride and you are likely to get more energy loss due to the inability of the tyre to absorb irregularities in the road surface. (The bike behaves as if it has solid tyres and some energy that should be driving you forward is lost in vertical motion of the whole unsprung mass of bike and rider.) But below about 100 psi, tire pressure can be more critical, and especially so with smaller wheel diameters. On a smooth road, assuming good tyre design, at 100 psi there may be little difference in rolling resistance between good 20-inch and a 26-inch tyres. But drop the pressure in both tyres to 50 psi and the fall-off in performance of the smaller diameter tyre will be much worse.

By the way, coast-down tests should not exceed about 9 to 12 mph, otherwise aerodynamic variations will mask the effects.

For more on rolling resistance, see the third edition of David Gordon Wilson’s classic book “Bicycling Science” (not in any way to be confused with Max Glaskin’s new book “Cycling Science”).

And it’s always worth bearing in mind that, because of constructional differences between brands/models of tyre, rolling resistance can vary considerably for the same diameter even when all other factors (load, pressure, road surface, etc) are equal.

TonyDo you have a version of this graph which lists the make, model and construction of each tire (OK, tyre — you’re British). And the pressure? These would make for much more useful information. Also, I note the work done at Bicycle Quarterly magaine, with the surprising result that wider tires roll better and increasing pressure above an optimum value is of little advantage — see http://janheine.wordpress.com/2012/06/13/bicycle-quarterly-performance-of-tires/

Hi John,

Thanks for your comments. The precise data is all in the Excel table to which a link is provided in my article. To cram that onto the chart would be beyond my skills but maybe you’d like to have a go. The main point of the graph is to show that, whilst the general theory may be correct, the variations between tyres of the same size can be considerable.

The points about contact patch and ultimate pressure highlighted by Jan’s recent work have been made in the past. Wide section tyres with supple walls were advocated by Vélocio a century or so ago, for example, and I remember reading Frank Whitt on the subject a third of a century ago.

By the way, Mike Burrows tells me that, in his recent tests, he’s finding the “Wellington boot” Schwalbe Marathon, officially their heaviest, highest drag tyre, actually rolls better than their supposedly faster tyres.

Tony