Re: On low gears

On Sat, 7 Feb 2009 20:21:35 -0800 (PST), Frank Krygowski
<frkrygow@xxxxxxxxx> wrote:

On Feb 7, 11:12 pm, carlfo...@xxxxxxxxxxx wrote:


As for the bobbing, it's hard to ignore the much greater and therefore
faster movement of the legs as the rider's feet follow the 350 mm
pedal circle.

Carl, I'm sure you agree that cycling is more efficient than walking
on flat ground. That's despite far greater aerodynamic losses.

Why, specifically, do you think cycling is more efficient for the flat
ground case?

Which of cycling's advantages do you think would go away on an uphill?

- Frank Krygowski

Dear Frank,

On hills, bicycles lose the advantages that they enjoy on the flats,
namely friction reduction and gearing.

***

Let's start with friction reduction.

Stand on one pedal on a level road and give a single push with one
leg. You and your bicycle should roll thirty feet or so.

The same one-legged push moves a pedestrian only a foot or two.

Those friction-reducing wheels and bearings are darned useful.

Wheels with bearing roll beautifully on the flats. Shoes don't.

That's true even on the moon, where there's no wind drag.

***

With gearing, the same gentle pushing lets practically any bicyclists
use friction-reducing wheels and bearings to beat the world's fastest
13 mph marathon runners on a flat course.

In 53x12 with a 2124 mm rear tire and a 175 mm crank, the short 1100
mm pedestrian "stride" around the pedal circle moves my rear wheel
over nine times as far. My foot moves the pedal only about three and a
half feet, while my bicycle moves over 33 feet on the flats.

That leverage also converts my foot speed, moving the bicycle over
nine times as fast. At 20 mph in 53x11, my feet move at a lesisurely
2.15 mph around the pedal circle at a stately 52 RPM.

Because I'm not fighting friction, gearing turns my short stride into
33-foot "strides" on the flats.

It's worth noting that even the tiny increase in stride for a double
amputee with longer-than-normal artifial legs raised hell in the
sprinting world. He was slow at 100 meters, but by 200 meters was
reaching Olympic levels with his improved "gearing", just as a bicycle
with its fixed gearing loses at first to a sprinter, but then
overtakes him further down the track.

***

But the bicycle's advantages dwindle when we pedal uphill.

We start fighting gravity, which didn't matter on the flats.

Even I can easily beat the world's best marathon runners on the flats,
where I'm not fighting gravity. But good runners would pass me on even
a gentle hill because most of our effort would be going into raising
our weight and I'm not much of an athlete.

It's easy to see how gravity kills the bicycle's advantage.

The winning Tour de France riders average about 26 mph lately, almost
exactly twice the speed of 13 mph marathon runners. who cover just
over 26 miles in just over two hours.

Bicyclists on a flat 26 mile marathon course would be even faster. I
don't know of any specific 26-mile flattish TT times, but I think that
33 mph would be a reasonable low estimate.

But bicycles go over twice as fast as runners only on flat courses.

When riders and runners race up Mt. Washington, the riders no longer
double or triple the speed of the runners. As Peter Cole pointed out,
the bicycle advantage drops drastically on that ~11.5% grade.

Rising a just one foot every eight or nine feet has a dramatic effect
on bicycles because the wheels and bearings of bicycles don't offer
the same advantage. The hill shifts the fight from friction to
gravity.

Because bicycle speed drops on hills, the gearing advantage drops,
too. The rider can't trade as much force for distance.

For Mt. Washington, the bicycle record now stands at 49:24, versus
56:41 for runners, 2964 seconds versus 3401 seconds. As Peter Cole
pointed out, the runners take about 15% longer, not 100% longer.

That's 9.23 mph versus 8.04 mph on the 7.6 mile course.

Here's a crude graph, to scale:

34 *-33 mph TT
32
30
28
26 *-26 mph TDF
24
22
20
18
16
14
12 *-13 mph marathon
10 *-9.23 mph bicycles
8 *-8.04 mph runners
6
4
2
0 mph
-------- ------
flatter courses Mt. Washington 11.5% climb

Bicycle speed (and presumably efficiency) nose-dives with even gentle
climbs, dropping _much faster than pedestrian speed.

***

What about a bicycle on a much steeper hill than Mt. Washington, a
slope steep enough to reduce the rider to using 1-to-1 overall
gearing?

I predict that when a hill is so steep that the pedal travels as far
as the tire, the bicyclist will be more efficient if he gets off and
pushes.

For some riders, this means Fargo Street at 32% grade. For more
powerful riders, a steeper hill is needed, while riders like me would
dismount with profit on gentler slopes.

***

What goes wrong on such steep climbs?

To start with, the gearing advantage is lost when it drops to 1-to-1
overall and the tire moves just as fast as the foot on the pedal.
Choosing a little higher or lower gear isn't much help at that level,
since our feet provide infinitely variable gearing at walking speeds,
far superior to any fixed chain and sprocket ratio.

Dropping to walking speed reveals the complexity of the bicycle.
Tranmitting the same power between the leg muscles and the ground
through a shoe, pedal bearing, crank bearing, front sprocket, chain,
rear sprocket, and rubber tire is not likely to be as mechanically
efficient as running it through the much simpler path of the shoe and
the ground.

Getting off and pushing makes another aspect of the drag literally
visible: the crank and chain stop moving.

Minor drags like these be easily ignored at higher speeds, where the
bicycle's advantages far outweigh them.

Frankly, the minor drags can also be ignored at ulta-low speeds, where
only RBT posters care about the tiny differences. No one is trying to
get up Fargo Street in the most efficient fashion, and most riders
prefer to ride as long as they possibly can

***

On walking-speed hills, the bicycle also loses its tremendous
friction-reducing advantage.

On the flats, as mentioned earlier, a single gentle push with one foot
can propel the bike and rider thirty feet from a standstill.

But friction isn't the problem on a hill steep enough to knock a rider
down to 1-to-1 overall gearing.

A single gentle push from a standstill straight up Fargo Street won't
propel a bicycle at all--it takes a considerable push to move an inch
up the hill.

On hills, gravity becomes the 800-pound gorilla, replacing the
friction that rules on the flats.

Most riders have no hope of "coasting" up hills like Fargo Street,
which reduce them to 1-to-1 gearing.

Of course, there are powerful riders who can "coast" up Fargo Street
in much higher than 1-to-1 gearing:
http://www.youtube.com/watch?v=W6ZuVteNvrQ

He just needs a steeper hill to knock him down to 1-to-1 gearing,
curse him.

In theory, a rider could be powerful enough to pedal straight up an
elevator-style rig at 20 mph, using the bicycle's friction-reduction
and gearing advantages. But such nuclear-powered riders are only
theoretical. Real riders are reduced to 1-to-1 overall gearing by
slopes much gentler than ordinary stairs.

***

Ultra-steep hills and their low speeds reveal other drawbacks that are
normally hidden by the bicycle's advantages on the flats.

A common claim is that the rider is supported by the bicycle and
doesn't jiggle and bob as much as a pedestrian, so the bicycle must
still be more efficient.

That claim doesn't seem to be supported by this video:
http://www.youtube.com/watch?v=FgIL6eHHgZU

At ~4:50, a yellow-shirted pedestrian starts walking up Fargo Street
at ~48 RPM, next to a rider using ultra-low gearing at ~85 RPM.

At ~6:00, they reach the camera and can be seen from the side.

Even at a glance, the pedestrian looks smooth and relaxed compared to
the rider.

The rider's legs bend and straighten far more, knees rising much
higher, high-stepping. The pedestrian would have to goose-step or run
in place to match that inefficient motion, which again doesn't matter
at speeds on gentler slopes, where the bicycle's other advantages far
outweigh the losses.

The rider's high RPM also hides to some degree the dead spots and
straining that would be noticeable if his gearing were raised and his
cadence dropped to match the pedestrian.

But even with ~85 RPM smoothing things out, you can see the front
wheel wavering and hunting erratically for balance from side to side.
At higher speeds, the effort to balance a bicycle is next to nothing,
probably even easier than standing upright. But at such low speeds,
the rider is obviously working harder to maintain his balance than the
pedestrian and following a much shakier route.

The smoothness of the pedestrian's gait reminds us that the pedestrian
is using infinitiely variable gearing. There's no dead-spot jerkiness,
no teetering, no side-to-side wobbling and recovery--he's just walking
naturally up the hill.

In fact, the whole thing is being filmed by _another_ pedestrian,
who's walking smoothly up the hill while turning sideways to film the
bicycle and yellow-shirted pedestrian. That's how natural and
efficient it is to walk uphill at that speed.

Almost anyone can walk up Fargo Street, hands behind his back,
stopping and starting whenever he pleases, and even turning around and
then heading back up again.

But a bicycle requires balancing and has rigidly fixed gearing with
dead spots, so I doubt that we'll see anyone riding no-hands up Fargo
Street, stopping, rolling back, and heading up again. They work much
better at higher speeds.

Again, look at that video and see who appears to be moving smoothly
and efficiently up the hill:
http://www.youtube.com/watch?v=FgIL6eHHgZU

Other videos will show the rider straining against the bars and pedals
to balance and to overcome the dead spots eliminated by the infinitely
variable "gearing" of walking. The pedestrian's arms swing in the
efficent pendulum manner, while the rider heaves this way and that to
stay upright.

***

Rolling resistance is complicated, but I think that it will be easier
to push the bike up a steep slope at walking speeds like the ~2 mph in
that video.

When riding, power is lost to the endless bulges rolled into each
heavily laden tire--and to the shoes of the rider as they press and
release on the pedals.

This applies even to the seat and crotch of the rider, as pedal
pressure raises and lowers the seat pressure. Again, at higher speeds
this minor drag doesn't matter and can't be avoided, so we forget it.

But comfort is so important that no one rides a metal seat in hopes of
reducing power losses.

The rider squashes and releases two heavily-laden tires, his shoes on
the pedals with enough power to move him and the bike up the hill, and
his seat.

The pedestrian squashes and releases two very lightly laden tires, his
shoes on the ground with enough force to move him and the bike up the
hill, and the same shoes with the weight that squashed the rider's
saddle.

The pedestrian's shoes hit the ground, but the rider's shoes may see
more peak force because of the dead spot in the unnatural round pedal
cycle.

The tires may or may not be more or less efficient at rolling over the
same distance than two widely separated footprints.

But the rider either spreads the squashing out through the extra
interface of the saddle, or else rides standing, with greatly
increased pedal pressure and shoe-squashing, not to mention the
heaving and relaxing on the handlebar for balance.

So I expect more rolling resistance (for lack of a better term)
because more areas are being squashed. A counter-argument would be
that a smaller part of the shoe squashes under the pedal, but then
there's the whole seat that seems to be overlooked by many posters.

***

To sum up, bicycles work primarily through reducing friction, so they
work wonderfully on flat ground where friction is the problem. Their
advantage drops dramatically as gravity replaces friction as the
problem on hills. At low enough speeds, the demands of balancing rise
sharply, the exaggerated leg motion's inefficiency seems obvious, and
putting the power pulses through the complicated interface of a
bicycle seat, pedals, and tires seems likely to make riding the
bicycle less efficient than pushing it.

If a picture is worth a thousand words, then this video, starting at
about 4:50, is easily worth all that I've written:
http://www.youtube.com/watch?v=FgIL6eHHgZU

A heart rate check for the same rider, pushing and riding up a slope
that reduces him to walking speed, would probably show whether there's
any significant advantage, one way or the other.

Cheers,

Carl Fogel
.

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