[Yak] Re: Yak Digest, Vol 22, Issue 17

[John S. Allen]

At 19:18 4/12/2006, David Duncan wrote:
>>An interesting question which sent me googling.  Here's one theory 
>>I found at Santana's website:  the footprint on a smaller tire 
>>(assuming identical tire pressure, casing, tread, etc.) is shorter 
>>and wider, causing increased rolling resistance::  700c vs. 26" 
>>wheels. <http://www.gtgtandems.com/tech/700-26.html> I don't have a 
>>clue whether it's true or not, but maybe the physicists and 
>>engineers among us do.

That should be true in theory, all other things being equal, but to 
summarize the discussion from a few weeks ago, they aren't equal. 
Smaller wheels have less air resistance and nimbler handling, 
compensating to some degree for the slightly higher rolling 
resistance. Tire construction and air pressure differ. And the 
difference big and small wheels in rolling resistance is in any case 
slight, because tire rolling resistance itself is slight and requires 
only a small fraction of the bicyclist's effort under any condition 
where the effort is large -- that is, when traveling fast on level 
ground, so the main resistance is air drag, when accelerating, or 
when climbing.

Man oh man, there's a lot of crap in the Santana article. Lots of 
estimates, subjective impressions and speculation, no actual 
controlled comparisons (coast-down tests, dynamometer tests  with 
actual *measurements*).

One incorrect attribution, with a misspelling:

>Fred de Long, Technical Editor of Bicycling, disproved the "gyro" 
>theory in the late '60s when he assembled a unique bike with side by 
>side front wheels --- a normal front wheel plus an identical 
>counter-rotating wheel slightly above and to one side. The second 
>wheel (which rotated at the same speed but never touched the ground) 
>offset the gyro effect of the first.

This was David E. H. Jones's experiment, one of several described in 
an article in the December, 1970 issue of Physics Today, see 
http://ist-socrates.berkeley.edu/~fajans/Teaching/bicycles.html -- 
which contains a link to the original article. This was not Fred 
DeLong's [correct spelling] experiment unless we are talking of Great 
minds Think Alike -- but I've never before heard of it in connection 
with DeLong. Probably, DeLong reported on Jones's work, and someone 
at Santana just gave the attribution without bothering to check the source.

Here's the real corker from the Santana article, though:

>when you want to stop, because braking power is a squared function 
>of effective brake radius, a rim brake on a 26" tandem is 19% less 
>effective than the same brake on a 700c tandem.

That's complete, total, bizarre nonsense, dressed to impress in the 
language of algebra and physics! The power of a rim brake is a direct 
(not squared) function of the speed of travel of the rim between the 
brake shoes. This speed hardly varies at all depending on bicycle rim 
diameter because the rim is so nearly at the same diameter as the 
outside of the tire. If the Santana statement were true, rim brakes 
on a Friday or any bike with 20-inch wheel would be wimpy (mine sure 
aren't!) and the old Sa'R'Day with 16 inch wheels would be a disaster.

As to hub brakes (disk, drum, coaster), they work *better* the 
smaller the wheel, because the wheel turns faster for the same travel 
speed of the bicycle.

There's another article online about rolling resistance, from Greenspeed:

http://www.discoveryride.com/human/rolling.html

It's interesting, and offers direct comparisons that reveal 
considerable differences among tires, but I don't regard it as 
translatable to actual riding conditions, because the rolling 
resistance was tested by driving the tires with a 4.5 inch diameter 
roller rather than rolling them on a large roller or flat surface. 
The roller diameter is so small relative to the diameter of the tire 
that the diameter of the tire hardly matters.

The article also describes results of an interesting experiment that 
Dr. Alex Moulton had conducted decades earlier. It showed lower 
rolling resistance for some smaller tires than for larger ones! Wow. 
I'd like to see Moulton's original article.

See also the article on rolling resistance of small wheels in Human 
Power #33, http://www.ihpva.org/HParchive/PDF/33-v10n2-1992.pdf . on 
pages 15 and 16. This nicely-controlled experiment shows that drag 
does vary widely from one tire to another and that some 20" tires had 
nearly as low drag as 27" tires.

There's a major source article by Dr. Chester Kyle as well, cited in 
some of the other articles, but it apparently is not online.

Dr. David Gordon Wilson's book Bicycling Science has a good treatment 
of the topic, 
http://mitpress.mit.edu/catalog/item/default.asp?ttype=2&tid=10062

John S. Allen

jsallen *at* bikexprt.com (replace " *at* " with "@")

http://www.bikexprt.com/