Phil Holman wrote:
> "Peter" <
[email protected]> wrote in message
news:[email protected]...
>
>>Phil Holman wrote:
>>
>>>"Peter" <
[email protected]> wrote in message
news:[email protected]...
>>>
>>>
>>>>bfd wrote:
>>>>
>>>>
>>>>>The following are some rolling resistance test of 700c and 26" mt
>>>>
>>>bike tires
>>>
>>>
>>>>>that may help:
http://www.terrymorse.com/bike/rolres.html
>>>>
>>>>While these rolling resistance measurements are very valuable, some
>>>
>>>care
>>>
>>>
>>>>must be used when comparing tires of different diameters. Many rolling resistance measurement
>>>>stands use a cylindrical drum rolling against the tire under test with a fixed load. Unless the
>>>
>>>drum
>>>
>>>
>>>>is very large in diameter, this measurement procedure can mask the effects due to changes in
>>>>wheel size.
>>>
>>>
>>>On the contrary, it isolates the effect of wheel size. The
>>
> difference in
>
>>>contact patch is only a small effect.
>>
>>It makes the test only valid if you spend your day riding over small diameter drums instead of
>>roads. The contact patch is where the vast majority of rolling resistance occurs (some also
>>occurs in the
>
> bearings
>
>>but this is tiny for properly maintained wheels).
>
>
> When talking about rolling resistance of bicycle wheels, the discussion should only be about the
> losses at the contact patch.
>
>
>>>>Note that when comparing two tires of identical pressure and width
>>>
> but
>
>>>>of different diameters there will be a change in the shape of the contact patch on the road. The
>>>>wheel with a smaller diameter will
>>>
>>>have
>>>
>>>
>>>>a shorter but wider patch compared with the larger diameter wheel.
>>>
>>>This
>>>
>>>
>>>>also means the sidewall of the tire on the smaller wheel will be deformed more at the point of
>>>>contact. But if the test is performed with a small diameter drum pressed against the tires on
>>>>the two
>>>
> wheels
>
>>>>then the two contact patches will have almost the same shape (essentially identical if the drum
>>>>size is much smaller than either wheel size). Therefore a major factor affecting the rolling
>>>
>>>resistance
>>>
>>>
>>>>of different wheel sizes on the road (with a flat surface) cannot be measured with a test setup
>>>>that involves a small-diameter curved
>>>
> drum
>
>>>>pressed against the tire tread.
>>>
>>>
>>>This is not the major determining factor with differences in wheel diameter. What you have shown
>>>above would probably demonstrate a
>>
> lower
>
>>>rolling resistance for smaller wheels which empirically is not the
>>
> case.
>
>>Only if you argue that greater deformation will somehow lead to less energy loss - clearly
>>nonsense. The smaller diameter tire will have greater deformation in the contact patch area
>>leading to greater
>
> rolling
>
>>resistance.
>
>
> The amount of deformation is only part of the equation. Shorter but wider contact patches generate
> less rolling resistance than longer but narrower patches given identical amounts of tire
> deflection. This is observed in cases where the same tires but different widths are compared. The
> wider tire has identical or even less rolling resistance at the same pressure.
But we're not talking about an inherently wider tire in this case - we're talking about two tires
that are identical in pressure and width but one is smaller in diameter. The area of the contact
patch is therefore the same in both cases (since the pressures are equal), but the smaller diameter
wheel has to be pushed down more in the area of the contact patch to create that area. Therefore it
suffers from greater deformation and has a wider but shorter contact patch - and also has more
rolling resistance as a direct result of this. More deformation implies more flexing implies more
heat generation implies greater energy losses.
That's completely different from the case you're imagining of two tires with the same diameter but
where one is wider than the other. In that case if the pressures are the same the wider tire will
have less deformation. But with two otherwise identical tires but of different diameters we can't
satisfy your assumption above of 'identical tire deflection'. False assumptions lead to bad
conclusions.
>
>>>The effect is small and overshadowed by the increased force required
>>
> to
>
>>>overcome the slightly less or identical resistance torque of a
>>
> smaller
>
>>>diameter wheel. I.e. a 5 inch-lb resistance torque will result in a
>>
> 5/R
>
>>>force to over come it. Obviously this reduces with a larger R (a larger wheel).
>>
>>On the contrary, think about where energy is wasted - that is the
>
> cause
>
>>of rolling resistance. The main energy waste comes about directly as
>
> a
>
>>result of the deformation of the tire and tube materials in the
>
> vicinity
>
>>of the contact patch. If the tire deformation is greater (as it is
>
> with
>
>>a smaller diameter tire and shorter/wider contact patch), then there
>
> is
>
>>more energy going into making the tire squirm and deform. This
>
> process
>
>>transforms some of the kinetic energy into heat in the tire and slows you down.
>
>
> Yes, but this is converted into a resisting torque which the rider has to overcome.
No need for any conversion. It's already in the form of a force from the ground pushing back against
the leading edge of the contact patch of the tire. This force is slightly greater than the rebound
force of the trailing edge of the contact patch as that part of the tire leaves the ground (the
forces are unequal due to energy losses in the tire/tube material as they flex and heat up in the
area of the contact). The net difference of these two forces is the rolling resistance drag force
pushing back on the bike. Why insist on converting anything?
>
>
>>The resistance you're talking about above is in the bearings which is very small in comparison to
>>the tire losses for a properly lubricated ball bearing hub.
>
>
> No I'm not referring to this at all. Converting tire deflection into a resisting torque is the key
> to understanding how contact shape and wheel radius effect the energy required to overcome the
> rolling resistance. You originally brought up ..... "Bicycling Science, Whitt & Wilson, MIT Press
> has some data and indicates that resistance should increase in inverse proportion to the wheel
> radius (half the radius would double the rolling resistance)"
Which I stated initially and fully agree with. And my posts since then have just established the
physical reason why that statement is true and pointed out that doing the testing with small
diameter drums will generally not be valid for comparing tires of different diameters.
> For identical amounts of tire deflection (lets increase the smaller wheel's tire pressure to
> achieve this) the larger diameter wheel will have less rolling resistance.
Now you're introducing another variable which was not done in the Bicycling Science book when they
concluded that there is an inverse relationship. Their conclusion was reached under the assumption
that the tires were otherwise identical - same width, same construction, same pressure - and that
the only variable was the wheel diameter. With such an increase in pressure I expect that we would
not see anywhere near a doubling of the rolling resistance for a halving of the diameter.
I saw a published paper a while back that claimed to prove that 406 size Tioga tires have less
rolling resistance than 622 size tires of similar construction. The error in the paper was that they
used a test rig with small diameter drums to measure the rolling resistance and as a result they
erroniously reached conclusions that were opposite to the part of Bicycling Science you just quoted.
>
> Both effects lead to increased rolling
>
>>resistance with smaller diameter wheels, but the tire/tube contact
>
> patch
>
>>area is the main source of internal energy loss for typical bicycle wheels. Rail bikes with steel
>>wheels on rails can have far less
>
> rolling
>
>>resistance than typical pneumatic-tire wheels although the losses in
>
> the
>
>>hub bearings will be the same in both cases. Unfortunately when the measurements are done using a
>>small-diameter drum the effects of changing the contact patch shape are largely lost.
>
>
> Rolling resistance is a result of the compression of the tire/wheel. When a wheel rolls on a
> surface it compresses at an area directly below the center of the wheel.
Actually the compression occurs just forward of the center of the wheel
(i.e. in the front half of the contact patch) and this is quite important since it means that the
force from the ground on this part of the tire has a component backward in the horizontal
direction in addition to an upward component.
> This sets up a compression force and a rebound force. At the area where the wheel compresses, the
> forces are higher than in the rebound stage due to the internal friction of the materials. This
> internal friction is known as hysteresis. This sets up a resisting torque which we call rolling
> resistance.
The portion of the resistance due to tire contact patch effects exerts a direct retarding force. I
agree with everything you state just above paragraph except when you call it a "resisting torque".
It is a direct force backwards on the bicycle of some number of pounds of force. Note that this is
also in the correct units to use for rolling resistance: it will be some number of pounds (or
Newtons) of drag. But torque is measured in lb-ft, not lbs., so no, we cannot call a torque rolling
resistance - the two are not the same type of quantity. You correclty point out that your "rebound
force" is less than your "compression force". The difference of the horizontal components of these
two forces directly give you the rolling resistance drag force. Why complicate things by imagining
that they have to be converted into torques and then converted back into rolling resistance? You
already have the answer in the form you want.
On the other hand, the small resistance due to bearing friction is manifested as a torque since it
acts to retard the turning of the hub and this in turn slows the rim rotation through the tension in
the spokes. The resisting force of the bearings at the hub is therefore reduced by the ratio of the
radius of the bearing race divided by the radius of the wheel resulting in a very small retarding
force on the bike since the torques (force x eff. lever distance) have to balance. That's why I
thought you were talking about bearing friction when you brought up the issue of torque - it's a
useful concept for the bearing friction but is not necessary when talking about resistive forces due
to the deformation losses in the tire/tube at the contact patch. But I see now that this was not
your intention and we are in agreement that bearing friction can be neglected.
> The actual resisting force calculated from the resisting torque is an inverse function of the
> wheel radius.
Which you should note is exactly the conclusion I gave in the very first response provided by anyone
in this thread (although I didn't use the word torque and still object to it here as stated above).
Unfortunately I've seen improperly done tests used to try to deny that relationship between
resistance and wheel radius and the flaw in the tests was that they used a small drum pressed
against the tires under test. Such tests are fine for comparing tires of a fixed size against each
other but give misleading results favoring the smaller tires when they are used to compare tires of
substantially different diameters. That's why I objected when someone presented just such tests and
suggested that they should be used in studying the effects of wheel diameter on rolling resistance.
The specific charts shown also had other discrepancies that would make reaching clear conclusions
impossible - the loads were different and the tires were of very different types. Far too many
uncontrolled variables to separate out the effect of wheel size by itself.