On Sep 12, 1:22 am, "

[email protected]" <

[email protected]>

wrote:

> On Sep 10, 3:42 pm, [email protected] wrote:

>

> > Our legs have no natural flywheel action and stop spinning as soon as

> > we stop trying to pedal--it takes constant power to churn those big

> > chunks of meat and bone up and donwn.

>

> But obviously very very little power, as anyone who has ever broken a

> chain or dropped a gear will know. It also takes power to lift a foot

> up higher than ground level only to put it down again when walking.

> Which do you think is a greater waste of power, and why? Have you any

> quantitative estimates of either effect on which to base a comparison?

>

> James
Dear James,

Dear James,

Let's consider a 33.3% grade and a rider whose weight and fitness

reduce him to using 1-to-1 overall gearing.

Obviously, some riders would need more gearing and others could use

higher gearing, but we need a specific example, and most posters would

consider a mile of 33.3% grade steep.

There are two ways to calculate slope as a percentage. In this case,

we mean a 33% grade where you gain 1 foot in height for every 3 feet

that you move forward and upward as measured by an odometer.

The other method of calculating slope as a percentage would gain 1

foot in height for every 3 _level_ feet forward and would call our

slope a 35.3% grade (1 / 2.83) instead of 33% (1 / 3.00). This

wouldn't matter much to the overall calculations, but it's best to

avoid confusion.

With 1-to-1 overall gearing, the foot travels just as far around the

pedal circle as the rear wheel moves forward. For a 2100 mm 700c tire

and a 175 mm crank, this means 20 x 38 gearing and a 350 mm high pedal

circle.

Pi * 350 mm gives an 1100 mm "stride" with each pedal cycle.

In other words, for each 1.1 meters up the 33.3% grade, you turn a

full pedal cycle, raising and lowering your left foot 350 mm relative

to its initial bottom dead center position on the 175 mm crank.

Here's a diagram with numbers:

http://i6.tinypic.com/6crrg3n.jpg
Half-way up the 1100 mm slope, the whole bicycle has risen 183 mm,

which is 33.3% of 550 mm.

Meanwhile, the left pedal has risen another 350 mm, from the bottom to

the top of the pedal cycle, so the pedal is 533 mm above its starting

position (183 + 350 = 533 mm total rise).

Then the left pedal descends back to the bottom of the pedal cycle,

reaching bottom dead center again at 1100 mm up the slope and dropping

166 mm from 533 mm down to 367 mm, which is 33.3% of 1100 mm.

In other words, the left foot rises much more sharply than the slope

for the first part of the pedal cycle.

Then it drops more gently about 6.5 inches from its highest point,

roughly the height of a stair step.

When walking, most people don't lift their feet as high as the step

_above_ the step that they plant their foot on, unless they're doing a

very strange goose-step.

Cheers,

Carl Fogel