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Punting vs. Paddling


leong

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3 hours ago, Ken said:

You are making the assumption that force is limited and speed is not.  Perhaps the punter can produce unlimited force but it is his motion that is limited to a certain number of strokes of a certain distance per minute regardless of available force.  So he could push a gondola at five knots or a supertanker at 5 knots but no matter the load, his speed maxes out at five knots because that's how fast his arms can move regardless of load.  Consider how fast can you throw a baseball.  Now throw a BB.  The BB weighs 1/1000th that of the baseball but does the BB leave your hand at 1000 times the speed of the baseball?  

>>You are making the assumption that force is limited and speed is not. 

No, I'm not. I'm assuming that power is limited.

>>So he could push a gondola at five knots or a supertanker at 5 knots but no matter the load, his speed maxes out at five knots because that's how fast his arms can move regardless of load. 

No. The water's drag on a supertanker is much greater than it is on a kayak or gondola. For example, say the drag on a gondola is 6 pounds at a speed of 5 knots. That means the punter's maximum power is 30 pound-knots. Now assume, for example, the water drag on supertanker is 5000 pounds at 5 knots. So the power to move the supertanker at 5 knots is 25,000 pound-knots. But the punter can only generate 30 pound-knots. So, let's calculate X, how fast the punter can move the supertanker. We have,

30 pound-knots = 5000 * X pound-knots. Solving for X,

X = 0.006 knots. That is, at steady state, the punter can push the supertanker at only 0.006 knots.

I pulled the numbers out of a hat so the exact answer is probably different.

You are correct that the punter's speed of pushing is also limited. But that's not needed to solve the problem. It just introduces an unnecessary constraint that is trivial at the low speeds we're discussing. For example, if the current is 1000 knots, the punter will not be able to push off the ground that is moving away from him at 1000 knots.

>>... does the BB leave your hand at 1000 times the speed of the baseball?  

That's a completely different kind of problem regarding Newton's Second Law of Motion (F = mass * acceleration). We're assuming constant speed in the brain teaser I posted, so acceleration = 0. I can solve that kind of problem, but I'll leave it as an exercise.

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Still missing the point the punter can generate 15 gazillion knot pounds of force.  But no matter how much force it generátes, it can only move its arms to go five knots.  Think of it as an engine that has reached redline and can't  spin any faster.  Now change the gear ratio on the read end Andy it could.  Give the punter a 200 foot pole and it would be planning at 85 knot s but he only has a ten foot pole.

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3 minutes ago, Ken said:

Still missing the point the punter can generate 15 gazillion knot pounds of force.  But no matter how much force it generátes, it can only move its arms to go five knots.  Think of it as an engine that has reached redline and can't  spin any faster.  Now change the gear ratio on the read end Andy it could.  Give the punter a 200 foot pole and it would be planning at 85 knot s but he only has a ten foot pole.

>> Still missing the point the punter can generate 15 gazillion knot pounds of force.  

Knot-pounds are not force, Ken. Knot-pounds represent the units of power (force times speed).

Here's a thought experiment for you. Say at your maximum effort you can push a heavy block of wood on a wood surface at a speed of 1 knot with a pushing force of 100 pounds of force. Do you think you can speed up and push it at a speed of 10 knots with the same force? Don't you realize it would require 10 times the effort (power). The amount of work you can do per unit time is limited by the power you can exert. The force would be the same. However, you couldn't do it unless you were able to increase you power by a factor of 10..

Note:  For "dry friction", such as a box on a floor, the sliding friction is independent of speed.

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21 hours ago, Ken said:

Still missing the point the punter can generate 15 gazillion knot pounds of force.  But no matter how much force it generátes, it can only move its arms to go five knots.  Think of it as an engine that has reached redline and can't  spin any faster.  Now change the gear ratio on the read end Andy it could.  Give the punter a 200 foot pole and it would be planning at 85 knot s but he only has a ten foot pole.

>>Give the punter a 200 foot pole and it would be planning at 85 knot s but he only has a ten foot pole.

Okay, let's consider this with more familiar units (horsepower). Give the punter what ever "gear ratio" he wants, say a long pole that he can handle. Say the punt boat (note: a gondola is not pushed with a pole) is drifting down stream at 80 knots and that the punter can move the boat at 5 knots in still water. Further, assume the water drag at 5 knots relative to the water is 6 pounds. So pushing off the fixed bottom to reach a ground speed of 85 knots (80 knots from the river current plus another 5 knots) requires a power of 510 pound-knots (85 * 6).

1 pound-knot is equivalent to approximately 11 horsepower. So, in HP units, the required power is 5, 610 HP (510 * 11). Obviously, this power is impossible for any punter but superman.

 

Edited by leong
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