On Sun, 5 Sep 2004 20:09:09 +0100, "Trevor"
<
[email protected]> wrote:
>
>[email protected] wrote in message ...
>>Wind drag increases markedly for an object moving up and
>>down or side to side relative to the airstream or for an
>>object changing back and forth between two shapes.
>>
>>If you think a moment about a situation in which drag is
>>more noticeable, such as an object moving underwater, this
>>should be obvious.
>>
>>Uphill or on the flat, bicyclists have no choice but to
>>pedal. The steeper the downhill, the quicker they discover
>>that rapid leg movement is slower than a motionless tuck.
>>
>
>How have you determined this?
>How have you determined this?
>How have you determined this?
>
>It is simple to show that two riders side by side at 60mph, that the one who
>pedals (presumably correctly trained) will accelerate past his companion.
>This is self evident that useful force is being applied via the pedals.
>
>Trevor
>
Dear Trevor,
Further down, we'll use a calculator, but let's start out by
going through the theory.
To simplify matters, consider just a crank on a riderless
bicycle with no chain.
Now add a convenient and steady magical force to cause the
bicycle to move 60 mph against the wind drag when the crank
is in its most aerodynamic postiion--horizontal and
presenting the smallest wind profile.
Remember, you have balanced the forces. Whatever magic force
is propelling our riderless bicycle, it is perfectly matched
by the rolling resistance and wind drag.
Now we add a happy gremlin inside the bottom bracket and put
him to work, busily spinning the crank at 175 rpm, which is
how fast it would have to spin to engage a 700c 2124 mm rear
wheel at 60 mph--if we hadn't removed the chain to clarify
matters.
Damn! That's hard work, spinning a crank so that each arm
rapidly changes from its best to its worst aerodynamic
profile 350 times per minute (think of one full spin and the
arm straight forward, straight down, straight backward, and
straight up).
Spinning an exposed crank produces significant wind drag at
higher speeds. Attach a pair of long, poorly designed,
leg-shaped flails to this crank and things get even worse.
Assuming feet on the pedals, the most aerodynamic position
is level, which improves the shape of both legs by bending
them back at the knee and reduces crank frontal profile to
its minimum with a nice long trailing run relative to the
windstream.
Spin the crank at 175 rpm and you're whipping up a huge
plume of invisible turbulence--which slows things down.
This is why a pilot feathers the prop if one engine dies in
flight. The blades of the prop are turned to knife into the
wind (like a level crank on a bicycle) to avoid the
tremendous drag of windmilling the unpowered prop.
Another example is an electric egg beater in the kitchen.
Unplugged, its blades do not move and it doesn't stir things
up much when moved around in wide circles. Spinning,
however, the blades produce obvious turbulence--and drag.
Some speed calculators specifically include the drag of
pedal motion, figured from rpm:
http://www.kreuzotter.de/english/espeed.htm
Let's choose the triathalon bike configuration and use its
defaults, but roll it down a -10 slope (10% grade) at 0 rpm
and 0 watts, coasting.
Result: 53.3 mph coasting
Now let's do the same thing, but spin the cranks at 154 rpm
(just a hair less than the cadence for a 700c 2124 mm tire
going 53 mph with a 54 x 12) and apply a silly 0.1 watts of
power just to make the calculator work (it doesn't like a
cadence that produces no power at all).
Result: 48.8 mph spinning without applying any power
The prediction is that we lose 4.5 mph just to the increased
wind drag. Obviously, we have to put out a fair amount of
effort ot spin a crank at 154 rpm, but we haven't yet put
any force into the rear wheel. We're just demonstrating that
thrashing our legs provides aerodynamic braking.
How much power do we have to put into the rear wheel to get
back to where we started? (Ignoring the effort just to wave
our legs rapidly--that's just wasted effort.)
Let's try 345 watts at 154 rpm for the same triathalon bike
rolling down the same 10% grade.
Result: 53.3 mph spinning at 154 rpm with 345 watts
In short, this calculator predicts that a rider rolling down
a 10% grade on a triathalon bike can either coast or put out
a steady 345 watts at 154 rpm, but either way he'll be going
53.3 mph.
It gets worse at higher speeds. Here's a table for the same
bike on a 17% grade, where it reaches 70.1 mph and needs 204
rpm to engage a 2124 mm 700c tire with 54 x 12 gearing:
mph rpm watts
70.1 0 0 coasting, not pedalling
62.6 204 0.1 coasting, but pedalling w/no power
70.1 204 1046 pedalling 52 x 12 gear
If the rider enjoys pedalling on such a steep grade, the
calculator predictst hat he can either give up 7.5 mph (more
than 10% of his speed) or go just as fast as he was coasting
by producing a steady 1045 watts.
Does the calculator adjust for rpm? Let's try a huge 104 x
12 gear that requires only 102 rpm on a 17% grade:
mph rpm watts
70.1 0 0 coasting, not pedalling
66.1 102 0.1 coasting, but pedalling w/no power
70.1 102 665 pedalling 104 x 12 gear
Yes, a slower fan action produces less drag, so the bike
doesn't brake as much absolutely and doesn't require as much
power to return to its original coasting speed. (This, of
course, just shows that the algorithm does indeed adjust.)
So that's one way that I know that pedalling motion
increases wind drag. The other way is that, like any rider,
I can tuck in, coast down a long slope, and notice how my
speedometer drops when I lower my landing gear to start
pedalling again, even at speeds much lower than the examples
above.
Increasing motion means increasing turbulence. Increasing
turbulence means increasing wind drag. We can't wave big,
badly designed fans around rapidly in a 60 mph gale for
free.
Carl Fogel
