Re: Fast pedalling, why? Re: How many gears are enough?

On Jul 9, 8:17 pm, carlfo...@xxxxxxxxxxx wrote:
On Thu, 09 Jul 2009 16:36:14 -0500, Ben C <spams...@xxxxxxxxx> wrote:

[snip]

The heavy thigh does accelerate back and forth, but muscle force is not
required to cause those accelerations (apart from to overcome losses).

[snip]

Dear Ben,

Where does the force come from to accelerate the heavy thighs (plural)
back and forth? If the force doesn't come from the muscles, what
causes them to start moving again.

Partly from the muscles, and partly from the shins and feet that are
moving backwards/forwards at maximum speed. But the energy used to
accelerate the thighs is not wasted as you will see in the next
paragraph.

Both thighs decelerate to 0 velocity at the same moment when you
pedal--twice for each cycle of the pedal.

Where does the kinetic energy of the thighs go when they decelerate to
zero? Conservation of energy tells you it doesn't just disappear. The
only place for it to go is where it goes: into the drivetrain. You put
energy into the thighs accelerating them, and when they decelerate,
that energy they were carrying doesn't just disappear. It goes into
the drivetrain and pushes the bike forwards.

Possibly people are imagining a flywheel effect that's practically
absent?

Reverse the power and consider the consequences.

Imagine a mechanical linkage on a trainer that mimics the mass of the
thighs with metal bars and wonderful bearings (plus the more
complicated knee-lower-leg-foot connection from the end of the thigh
to the pedal).

Make the trainer a fixie and apply power from a motor to spin the rear
wheel, which then spins the unpowered fake legs.

Apply power to the trainer rollers to spin the training wheel for a
distance of one mile at 20 mph (three minutes), moving the fake legs
(which will not be providing power).

Do it with gearing for a cadence of 100 rpm.

What you will find if you are observant enough is that the wheels spin
a little faster at the top and bottom of the stroke, and a little
slower when the crank is level. Or if your motor runs at *exactly* 20
mph, not deviating an iota, you will ind the motor draws less power as
the legs decelerate, and more power as the legs accelerate.

Now change the gearing to lower the cadence of the fake legs to 50,
with the same 20 mph speed and one mile of trainer wheel travel
(again, three minutes).

What you will find is that the rollers spin a little faster at the top
and bottom of the stroke, and a little slower when the crank is level,
and the variation in speed is more frequent and a bit greater in
amplitude than with higher gearing. But the average power required to
run the motor is the same.

How far must the mass of the "thighs" wave back and forth for the same
amount of rear-wheel work (1 mile, 20 mph, 3 minutes) at the two
different cadences?

Why do you insist on conflating distance with force and work?

At the 100 cadence, the thighs must wave back and forth twice as many
times (and therefore twice as far in total distance in the same time)
for the same work from the motor powering the trainer.

Which parts of this setup do you expect to heat up as the purported
energy is wasted? Put a couple hundred watts into it and it should
become burning to the touch. Or does the energy get radiated away in
invisible, heatless Fogel rays?

-pm
.

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