[hpv] Re: hpv-digest V7 #1047
F.A. Karelse
> roadway at right angles to your wheel's path. Make them X width. Now roll
> two test wheels across these grooves at an arbitrary speed: the first wheel
> is 3X diameter, the second wheel is 5X diameter.
>
> Obviously, both wheels will fall into and climb out of the grooves the same
> number of times in a given interval, so their frequency of fall/rise is the
> same. But the smaller wheel will fall further and have to climb further
> with every groove it passes. Thus the smaller wheel experiences falling &
> rising of greater _amplitude_. Therefore, on a non-smooth surface, a
> smaller wheel will use more energy than a larger wheel, all other factors
> being equal.
>
> Comments, anyone?
>
> Jeff
Hi Jeff,
Of course I have comments! ;-)
You say that the small wheel falls further and has to climb further. I
agree, but this introduces no loss mechanism. It only means the
variation of potential and kinetic energy is larger for the small wheel,
but as long as no loss mechanism is present, the sum of both is
constant.
Further, suppose the wheel sizes go to more reasonable values of 15X and
25X, then your oscillation effect will be reduced drastically.
I'd like to make another comment as well:
Kinetic energy is 1/2m v^2, rotation energy of a hollow cylinder (which
resembles a wheel usually quite well) is also 1/2m v^2. A wheel usually
weights less than 1 kg, so the rotation energy is m/M-th part of the
total energy, where m is the wheel mass and M is the total mass of
bicycle and cyclist. So, this is less than 1%. Now, the difference in
diameter between a 20" and a 28" wheel is 40%. Let the mass ratio be the
same, then the rotation energy varies 0.4% of the total energy when the
wheel size is changed. No way you notice that during acceleration or
decceleration.
People saying a small wheel is very nervous are probably talking about a
small FRONT wheel and probably do not have an optimal steering geometry.
The wheel diameter plays an important role in steering geometry, but so
a couple of other parameters do. I know stories of people cycling hands
free on their 2020 bikes and stories of people who cannot even think
about releasing the steer (like me :-( ).
Frank -M5 Blue Glide 2026- Karelse
Jeff Wills
> >
The loss mechanism is the additional energy required to move the mass in the
vertical direction. The smaller wheel (and associated vehicle) must move
further, so greater energy input is necessary.
> Further, suppose the wheel sizes go to more reasonable values of 15X and
> 25X, then your oscillation effect will be reduced drastically.
>
"Reduced" but not "zero"- aren't you conceding that vertical oscillation
requires energy input? This contradicts your earlier contention that "no
loss mechanism is present".
............................................................................
..
The point of this whole debate has been which wheels are more efficient.
Personally, I'm in the camp that says you need to look at the whole system
before making statements regarding efficiency. If a design requires 10%
smaller wheels (which would have greater rolling resistance) but results in
a 15% reduction in aero drag, I say it's a good trade-off.
Jeff
Scott Talkington
Concerning the "rumble" argument: (Rumbles are those cross-cutting grooves
in the pavement, used in the Midwest to warn drivers that they're
approaching an intersection, if they happen to be taking a nap.) It seems
reasonable to me that the arc of the larger wheel would smooth the vertical
irregularities so that you wouldn't fall and rise so much. I think in that
instance you'd loose energy simply as a result of having to travel farther
on a smaller wheel. If there were irregularities oblique to the line of
travel at less than 45 degrees, however, than the fatter tire would fall and
rise less than a thinner tire on wheels of the same diameter. So the
efficiency of the tire on a randomly irregular surface would be a function
of the diameter and the width/shape of the cross-section. The
irregularities that cross the direction of travel at right angles, however,
would tend to have the greatest effect so you might need an impossibly wide
tire to make up for the lesser arc of the smaller wheel. But this can't
really amount to much in
the real world, can it?
In other words I'm back to the point that there's not much difference
between big and little wheels when it comes to speed. I still think that
smaller wheels would cause you to over and under shoot a target speed more,
but can't convince myself that it makes any difference. In other words, I
don't try to maintain a target speed anyway. I usually maintain cadence and
heartrate, and may not even look at the speed until the end of the ride.
I will note this one caveat. I've never understood why a hillier ride,
that's a closed loop, is always slower than a flat ride of the same distance
and under the same conditions. Somehow you invest energy on the uphill that
you fail to recapture on the downhill. Perhaps it's just a matter of
maintaining a safe speed so that by braking you are deliberately throwing
away energy rather than spending it. Does this mean that if you kept the
downhills shallow enough so that you didn't need to brake you'd achieve the
same average speed as on a flat ride? Gosh, I wish I could store that
braking energy somewhere...
-Scott
Jeff Wills
> I will note this one caveat. I've never understood why a hillier ride,
> that's a closed loop, is always slower than a flat ride of the
> same distance
> and under the same conditions. Somehow you invest energy on the
> uphill that
> you fail to recapture on the downhill. Perhaps it's just a matter of
> maintaining a safe speed so that by braking you are deliberately throwing
> away energy rather than spending it. Does this mean that if you kept the
> downhills shallow enough so that you didn't need to brake you'd
> achieve the
> same average speed as on a flat ride? Gosh, I wish I could store that
> braking energy somewhere...
>
Yeah, me too.
There's probably a dozen different explanations why hillier rides consume
more energy than flat ones (I think that staring at hills makes you tired)
but try this:
Aerodynamics, my boy. As has often been pointed out on this list,
aerodynamic drag increases by the third power of speed. Simply coasting down
the downhill reduces your average speed. If you pedal down the downhill and
maintain the same average speed as the flat ride then you use more energy
overall.
Someone's done these calculations- I know they have!
Jeff