Punting vs. Paddling

[leong]

Time for a brain teaser:

 

Puck the punter and Paddy the paddler can both propel their respective small craft at 5 knots in still water. They decide to race in a river flowing at 4 knots.

Who will win the upriver race? Why?

Who will win the downriver race? Why

 

Punting

Edited August 13, 2018 by leong

[Jim Snyder]

Ok I'll bite. The current shouldn't matter in either direction but this would be a stupid brain teaser if I weren't missing something. It reminds me of the stupid argument that it's possible to plant a paddle in one place in the water and propel a boat without any backwards paddle motion with respect to water.

[leong]

2 hours ago, Jim Snyder said:

Ok I'll bite. The current shouldn't matter in either direction but this would be a stupid brain teaser if I weren't missing something. It reminds me of the stupid argument that it's possible to plant a paddle in one place in the water and propel a boat without any backwards paddle motion with respect to water.

Okay, first let's get the "lock the blade" out of the way. See this video.

With regard to the race, I'm not sure if your saying that it will be a tie between the punter and the paddler in either direction or that the same boat will win in either direction? Hint: Think about this: Suppose the river current is 100 knots. Going down-river the paddler will travel at 105 knots ground speed (100 knots free from the river plus the 5 knot paddling speed). Do you think this applies to the punter too?

End of hints.

[Jim Snyder]

Sorry, I still don't buy the "locked paddle". I'm willing to call it an "apparently locked paddle" but physics would argue otherwise. The only way to avoid the equal and opposite  reaction is paddling in a medium that offers total resistance in a boat that is capable of zero friction.

The punter would find his "punt rod" or whatever he calls it useless in your 100 knot current, wouldn't he? When they turn upstream, the hundred knot current would capsize both of them.

I'm thinking of taking up punting now.

[leong]

28 minutes ago, Jim Snyder said:

Sorry, I still don't buy the "locked paddle". I'm willing to call it an "apparently locked paddle" but physics would argue otherwise. The only way to avoid the equal and opposite  reaction is paddling in a medium that offers total resistance in a boat that is capable of zero friction.

The punter would find his "punt rod" or whatever he calls it useless in your 100 knot current, wouldn't he? When they turn upstream, the hundred knot current would capsize both of them.

I'm thinking of taking up punting now.

Yes, the locked paddle is only an approximate lock. The bigger the paddle the closest to a lock if you have a good stroke.

Yes, the punter couldn't push the pole fast enough to push off the bottom going downstream in a 100 knot current.

>>the hundred knot current would capsize both of them.

This is a hypothetical situation for the purpose of a hint. So forget capsizing.

Anyway, I think your answer is that the paddler would win the downriver race, right?

Now use physics to answer the upriver race. Hint: think of the power exerted to move the boats.

[Inverseyourself]

Is the punter using one of those wide boats in the Cambridge video and the paddler a surfski-like rocket? Yes? OK, the paddler wins.

[leong]

1 hour ago, Inverseyourself said:

Is the punter using one of those wide boats in the Cambridge video and the paddler a surfski-like rocket? Yes? OK, the paddler wins.

Andy,

On the contrary, the punter is using a long skinny racing punter and the paddler is using this kayak. But, remember, both athletes are able reach 5 knots at maximum effort (racing speed).

-Leon

Edited August 14, 2018 by leong

[Jim Snyder]

The difference here in theory is that the paddler is at the mercy or benefit of the current, no matter what. If he had no visual point of reference in perfectly flat water, he would be mercifully unaware of it's effect. How many things in life may be analogous? The punter on the other hand has the ground as his point of reference. Is he limited to five knots in still water because of his strength or the hull speed of his boat? While the paddler is  moving forward with respect to the water at five knots while moving backwards with respect to the ground at 95, it's not clear what effect the current would have on the punter. If he was unable to resist the force of the current, his means of propulsion would totally fail.

Edited August 14, 2018 by Jim Snyder

[leong]

4 minutes ago, Jim Snyder said:

The difference here in theory is that the paddler is at the mercy or benefit of the current, no matter what. If he had no visual point of reference in perfectly flat water, he would be mercifully unaware of it's effect. How many things in life may be analogous? The punter on the other hand has the ground as his point of reference. Is he limited to five knots in still water because of his strength or the hull speed of his boat? While the paddler is  moving forward with respect to the water at five knots while moving backwards with respect to the ground at 95, it's not clear what effect the current would have on the punter. If he was unable to resist the force of the current, his means of propulsion would totally fail.

Both the paddler and the punter are limited by the maximum power they can produce. To keep it simple, assume that both small craft have exactly the same drag force versus speed curves. But this isn't necessary to solve the problem.

[Jim Snyder]

We know in the original example the paddler would achieve 9 knots down current while only 1 knot up current. Since the punter is dependent on the ground, which in either case is now moving with respect to his position in the water, I maintain he would be helped less by the following current and hurt more by the opposing one. Kayaker wins!

[Inverseyourself]

In order to reach his maximum speed, the punter needs to get that pole off the bottom by pulling it up feeding it through his hands. The interval from force-exertion to force exertion with the pole is much wider than the paddler's. The punter drifts downstream between punt-strokes (????) more than the paddler between paddle-strokes and thus loses ground against the paddler.

 

BTW, if you look like the guy in the kayak you referenced, you're gonna win any race!

Edited August 14, 2018 by Inverseyourself

[Inverseyourself]

I know they can achieve 5 kn on flat water, but this is against the current.

[leong]

No time today. I'll post the way to do it soon. It has nothing to do with paddling or punting, although that is a minor contribution. It has to do with whether you propel off the moving water or from the fixed earth. That's a good hint.

[leong]

Everyone is trying to solve the brain teaser by considering the different mechanics of a paddle vs. a pole, the water and boat hydrodynamics, etc. Obviously, these differences count; however, the solution to the brain teaser comes from the fundamental physics of propelling a “craft” from a fixed point vs. a moving point. So, for simplicity, we’ll demonstrate this by replacing the two boats with two blocks of wood and a rope for the transmission of power.

 

Try this thought experiment: Assume two guys, Puck and Paddy, can both generate the same maximum power.

First, pretend the still river is a stationary wooden horizontal platform. The force required to slide a particular block by pulling it with a rope at any velocity with respect to the platform is constant, denote it by F (look up sliding friction). Note that power is the product of force and speed. Therefore, to slide the block to the left at a speed of 5 knots, Paddy, on the platform, uses 5F of power. Say that’s his maximum power.  But this is also true for Puck on the ground who also uses his maximum 5F of power. Therefore, everything else being the same, for the stationary platform, the same power is required if you pull the block from the platform or pull it from the ground. That should be obvious.

 

 Now pretend the platform is the moving river, say moving to the left at a speed of 4 knots. For Paddy on the platform, if he pulls the block to the left with his maximum power of 5F, it will move the block at 5 knots relative to the platform. However, for Puck on the ground, if he pulls the block to the left with his maximum power of 5F, it will move the block at 1 knot relative to the platform (that’s because he has to move to the left at 4 knots faster to keep up with the moving platform). Therefore, for the same power, Paddy’s block wins the race.

 

If you reverse the example so that both Paddy and Puck are pulling in the direction of the moving platform, Puck’s block will win the race. See for yourself why that is true.

 

Also note if you use actual drag forces for the boats (perhaps drag being approximately proportional to the square of speed) you get the same results for who wins the upriver and downriver races.

 

[Dan Foster]

How many of us believe that a punter poling off the bottom against a 4-knot current is best modeled as a constant force propelling a mass forward at a constant velocity. Not me. What happens to your thought experiment if both paddler and punter deliver all of the power of their "stroke" in 1% of the time, and glide forward for the remaining 99% of the stroke time? What happens as the impulse time approaches zero? Isn't that just as valid a simplification of the problem as your "constant force over 100% of the duty cycle" solution?

[leong]

8 minutes ago, Dan Foster said:

How many of us believe that a punter poling off the bottom against a 4-knot current is best modeled as a constant force propelling a mass forward at a constant velocity. Not me. What happens to your thought experiment if both paddler and punter deliver all of the power of their "stroke" in 1% of the time, and glide forward for the remaining 99% of the stroke time? What happens as the impulse time approaches zero? Isn't that just as valid a simplification of the problem as your "constant force over 100% of the duty cycle" solution?

Okay, say the average power to keep the boat going at 5 knots relative to the water is, say, 100 watts. Aren't you implying that you could put out 100 times that power (10 thousand watts) for1% of a stroke cycle and rest for the remaining 99% of the cycle?

I'm not sure how you would model your impulse approach; i.e. Impulse = F delta t = change of momentum.It's hard to believe you could generate a large enough force in a negligible time to keep the boat going against water drag.

Anyway, do you think my answers are wrong? Surely you don't think a punter could punt down stream in a 50  knot current. But the paddler would have no trouble.

Perhaps I'm missing your points.

 

[Dan Foster]

My point was that your proof basically starts by saying "for simplicity, assume the kayak is actually a stern paddlewheeler, and the punt is actually a tank driving through shallow water" (both vehicles where the drive mechanism maintains contact 100% of the time and exerts constant force 100% of the time on the water and ground respectively) and then goes on to show the physics behind a race between those vehicles. I find that simplification difficult to accept, since (among other things) there's a non-trivial amount of time when the kayak blades are out of the water, and the pole is not pushing against the river bottom. I don't disagree with your solution, but I feel you're answering a different question than the one you originally posed to us.

[leong]

Okay. My model is a simplification of reality, and as such, certain details are excluded from it. The question is always what to include and what to exclude for a given application. For the kayak and punt boat I could model the drag force with the simple function; i.e. drag ~ speed squared. I could apply different duty cycles to the punt pole and the paddle.   Or I could go high fidelity and use John Winter's curves of kayak drag vs. speed. But, for the purpose of this exercise, I'm almost certain the results would be the same. I think anymore fidelity would be guilding the lily. The brain teaser doesn't ask by how much will the punter (paddler) will beat the paddler (punter). It just asks which one will win.

Think of this. Going up current in a very strong current the paddled boat will go backwards. But the punt boat can lock to the bottom and not lose way.

Take a look here. It shows the punter using a smooth and continuous motion.

[Jim Snyder]

That's assuming his power is sufficient to overcome the current. He hasn't demonstrated that in still water.

[leong]

17 minutes ago, Jim Snyder said:

That's assuming his power is sufficient to overcome the current. He hasn't demonstrated that in still water.

Who is he and under what situation?

[josko]

I've decided to punt on this thread.

[leong]

10 hours ago, josko said:

I've decided to punt on this thread.

Yes, in Irish, the punt was the official currency of the Republic of Ireland prior to the coming of the Euro. Ireland has great sea paddling and punting on their canals. However, when I was there the local newspapers were complaining that the bars in Dublin had broken the pound; i.e. they charged more than a pound sterling for a pint.

[Ken]

Entirely depends on whether the 5 knot limit in still water is due to the maximum rate of motion of the punter/paddler or the maximum force the punter/paddler can apply.

If the force available is unlimited but the pace of paddling/punting is 5 knots then--

• Paddler makes 1knot over ground upstream.
• Paddler makes 9knots over ground downstream.
• Punter makes 5 nots over ground in both directions.

However if the force available is constant but the pace of paddling is unlimited--

• Paddler and punter both make 1 knot over ground upstream.
• Paddler and punter both make 9 knots over ground downstream.

The reality will most likely be somewhere in between these two extremes in which case the punter wins upstream and the paddler wins downstream.

 

-Ken

 

[leong]

44 minutes ago, Ken said:

Entirely depends on whether the 5 knot limit in still water is due to the maximum rate of motion of the punter/paddler or the maximum force the punter/paddler can apply. 

 

It's the rate of doing work that has to be limited; i.e. the power (force * speed). Consider the punter. In still water say his power to go 5 knots is 5*F, where F is the force to punt at 5 knots (5*F is his maximum power). For the punter to go 9 knots down stream he would have to generate a power of 9*F. But he can't do that because his maximum power is 5*F. Of course he could punt at more than 5 knots going downstream, but his force would be less than F. However, the paddler would go at 9 knots down stream in a 5 knot current if he exerted the same power as his still water power.

Edited September 17, 2018 by leong

[Ken]

1 hour ago, leong said:

It's the rate of doing work that has to be limited; i.e. the power (force * speed). Consider the punter. In still water say his power to go 5 knots is 5*F, where F is the force to punt at 5 knots (5*F is his maximum power). For the punter to go 9 knots down stream he would have to generate a power of 9*F. But he can't do that because his maximum power is 5*F. Of course he could punt at more than 5 knots going downstream, but his force would be less than F. However, the paddler would go at 9 knots down stream in a 5 knot current if he exerted the same power as his still water power.

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?