Stephen,
Initially I agreed with you. But, after thinking more about it I couldn't resolve the fact that you can make headway against a 5mph headwind.
If you can do that on water that isn't moving, why can't you do it on water that is?
Yes, you will have all sorts of forces pushing you upstream, such as your windage and any leeway you may have. But, they all exist in the calm water / headwind scenario too.
The only difference is the water is moving.
sailing puzzle
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Catigale
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IF the argument is you can hold the boat at (say) 45 degree tack angle to the apparent wind and go down stream at 5 knots with current, plus velocity from the apparent wind, then the no wind boat wins. Agreed.
I think you cant do this, the minute you set your sails closehauled, you get a force that now takes your boat away from the downstream 'direct course' and you have to sail a longer path - and it is quite a bit longer based on my tacking every 10 boat lengths calculation above. So, is the extra force you get from this enough to compensate for the longer path - IIRC you have to sail at near perfect efficiency to get there, or I screwed the calculation up.
We are neglecting windage, leeway and all the real things in this puzzle, but thats ok - the real problem I have is I think Dr Bugs oversimplified it to:
You have another force (sails from apparent wind), therefore you can win.
I disagree with that.
I think you cant do this, the minute you set your sails closehauled, you get a force that now takes your boat away from the downstream 'direct course' and you have to sail a longer path - and it is quite a bit longer based on my tacking every 10 boat lengths calculation above. So, is the extra force you get from this enough to compensate for the longer path - IIRC you have to sail at near perfect efficiency to get there, or I screwed the calculation up.
We are neglecting windage, leeway and all the real things in this puzzle, but thats ok - the real problem I have is I think Dr Bugs oversimplified it to:
You have another force (sails from apparent wind), therefore you can win.
I disagree with that.
If your boat is static, with respect to the moving water, then does it matter which direction it faces (upstream, downstream, at 45deg)? Yeah, it might if there is an apparent headwind, and you're not sailing, aka windage. It might also impact acceleration. But, after acceleration - steady-state - it shouldn't matter, should it (other than windage)? Doesn't the comparision with 5mph headwind on calm water address the windage issue?
So, it looks the big issue is increased distance of travel. But, what if the boat with no apparent wind turned directly perpendicular to the river and motored back and forth? Not trying to hit a point on the river bank, but just travelling perpendicular to the river. Yes, he would be travelling a much longer course, but wouldn't he still be making 5mph down river, flowing with the current?
For the boat with the 5mph apparent headwind, yes, he is converting some of that wind into cross-river motion. But, what does that do? The "correct" answer assumes that this cross-river motion does nothing to his down river progress. That should be correct, if motoring back and forth would do nothing...
The bottom line is that the boat with apparent wind has to be converting some of the wind into down river motion, along with that healthy dose of cross-river motion. If you can 'delete' the cross-river motion, then he has to win...
So, the issue is does that cross-river motion reduce the impact of the current? Well, maybe there are fluid dynamics issues, but flight school suggests otherwise.
Again, though, I can't get away from ones ability to make progess upwind. If you can do that in 5mph wind on calm water, then you have to be able to overcome the downwind (upriver) components of the wind, don't you?
We are assuming here that water flow is uniform accross the river, so it doesn't matter where in the river you are, you are always experiencing a 5mph current.
I just don't see how the extra distance you are actually travelling would impact your downstream progress.
The only things I can see that might be problematic are the possible fluid dynamics issues, such as how efficiently would the down river energy of the water be absorbed by a boat moving with respect thereto? But, like I said, in flight school, we were taught to assume perfect efficiency with respect to a moving air mass and a plane moving with respect thereto.
So, it looks the big issue is increased distance of travel. But, what if the boat with no apparent wind turned directly perpendicular to the river and motored back and forth? Not trying to hit a point on the river bank, but just travelling perpendicular to the river. Yes, he would be travelling a much longer course, but wouldn't he still be making 5mph down river, flowing with the current?
For the boat with the 5mph apparent headwind, yes, he is converting some of that wind into cross-river motion. But, what does that do? The "correct" answer assumes that this cross-river motion does nothing to his down river progress. That should be correct, if motoring back and forth would do nothing...
The bottom line is that the boat with apparent wind has to be converting some of the wind into down river motion, along with that healthy dose of cross-river motion. If you can 'delete' the cross-river motion, then he has to win...
So, the issue is does that cross-river motion reduce the impact of the current? Well, maybe there are fluid dynamics issues, but flight school suggests otherwise.
Again, though, I can't get away from ones ability to make progess upwind. If you can do that in 5mph wind on calm water, then you have to be able to overcome the downwind (upriver) components of the wind, don't you?
We are assuming here that water flow is uniform accross the river, so it doesn't matter where in the river you are, you are always experiencing a 5mph current.
I just don't see how the extra distance you are actually travelling would impact your downstream progress.
The only things I can see that might be problematic are the possible fluid dynamics issues, such as how efficiently would the down river energy of the water be absorbed by a boat moving with respect thereto? But, like I said, in flight school, we were taught to assume perfect efficiency with respect to a moving air mass and a plane moving with respect thereto.
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Chip Hindes
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With all the logic exercises concerning tacking angles, leeway, fluid dynamics, etcetera, you are all making the problem more complicated than it is.
The facts are these:
1) On a calm lake with a 5mph actual wind. Do nothing, and the actual wind acting on the boat's windage (exposed freeboard, mast, sails etcetera) will force move you to windward by a small amount. Set the sails and make progress against the wind by tacking. In this frame of reference, you are moving "faster" to windward than the water.
2) On a river moving 5mph on a calm day, you have a new frame of reference, created by the current. The moving current creates a 5mph apparent wind. In this new frame of reference, as far as the boat is concerned, the conditions cited in 2) above are the same as those in 1). Exactly the same, no difference.
Do nothing, and the boat will move with the current, slightly retarded by the 5mph apparent wind. Set the sails, and you can tack into the apparent wind, moving faster than the water.
I don't know how else to say it. You have to ignore all the confounding factors, ignore the scenery passing by at 5mph, and wrap your mind around the fact that as far as the boat is concerned, these two conditions are identical.
From the boat, a 5mph actual wind in still water is exactly the same as a 5mph apparent wind created by a 5mph current.
You don't have to be able to maintain a 45 degree or any tacking angle. You don't need to have a particularly good boat or be a particularly good sailor. You don't have to be able to go faster than 5mph to windward, you only need to be able to go faster than 0mph to windward. As long as you can achieve a relative tacking angle, in relative still water, of 90 degrees or better, you can make progress to relative windward through the relative water, move faster than the relative water, and win the race.
The facts are these:
1) On a calm lake with a 5mph actual wind. Do nothing, and the actual wind acting on the boat's windage (exposed freeboard, mast, sails etcetera) will force move you to windward by a small amount. Set the sails and make progress against the wind by tacking. In this frame of reference, you are moving "faster" to windward than the water.
2) On a river moving 5mph on a calm day, you have a new frame of reference, created by the current. The moving current creates a 5mph apparent wind. In this new frame of reference, as far as the boat is concerned, the conditions cited in 2) above are the same as those in 1). Exactly the same, no difference.
Do nothing, and the boat will move with the current, slightly retarded by the 5mph apparent wind. Set the sails, and you can tack into the apparent wind, moving faster than the water.
I don't know how else to say it. You have to ignore all the confounding factors, ignore the scenery passing by at 5mph, and wrap your mind around the fact that as far as the boat is concerned, these two conditions are identical.
From the boat, a 5mph actual wind in still water is exactly the same as a 5mph apparent wind created by a 5mph current.
You don't have to be able to maintain a 45 degree or any tacking angle. You don't need to have a particularly good boat or be a particularly good sailor. You don't have to be able to go faster than 5mph to windward, you only need to be able to go faster than 0mph to windward. As long as you can achieve a relative tacking angle, in relative still water, of 90 degrees or better, you can make progress to relative windward through the relative water, move faster than the relative water, and win the race.
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Chip Hindes
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Okay, so here's another take on this subject. This will totally blow some minds, so I separated it from the previous discussion to protect the innocent.
There are some boats, mostly high speed catamarans, which under some wind conditions can reach faster than the actual wind. On a calm day, under the right current conditions these boats would be able to make progress upriver, against the current.
There are some boats, mostly high speed catamarans, which under some wind conditions can reach faster than the actual wind. On a calm day, under the right current conditions these boats would be able to make progress upriver, against the current.
Start with following situation: Both sailors have independently ONLY aft wind blowing toward finish line - Sailor A: 5 mph and sailor B: 10 mph respectively and each have no current. Who can make better progress towards the finish?
Now INCREASE current by 1 mph for both and DECREASE wind by 1 mph for both. Do it five times making the same change for both sailor as in step one. Each time answer the following questions: Who has winning advantage and who has more available energy. When in doubt consult polar diagram of any sailboat. You will see emerging patterns.
Bonus question: Is approach of figuring out available energy more general in comparison to diddling with particulars or not.
Now INCREASE current by 1 mph for both and DECREASE wind by 1 mph for both. Do it five times making the same change for both sailor as in step one. Each time answer the following questions: Who has winning advantage and who has more available energy. When in doubt consult polar diagram of any sailboat. You will see emerging patterns.
Bonus question: Is approach of figuring out available energy more general in comparison to diddling with particulars or not.
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Chip Hindes
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Sure you can. You don't need a sailing angle of 45 degrees to the wind to make upwind progress against a 5mph wind in zero current. You only need something infinitesimally better than a "perfect" 90 degree beam reach.You obviously cant get a downstream force component from your sails at an angle of less than 45 degrees from the wind
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MAC26X
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Chip has it right. Stop changing all the variables. The boat with the 5mph apparent wind only has to make some tiny forward headway relative to the current. It doesn't require steerage by rudder (we assume that doesn't work). As soon as you set the boom slightly off the wind the sail will fill, initially causing resistance. Then the airfoil effect takes over. The air travels further on the outside of the sail creating a low pressure area, drawing the boat forward. No matter what the course made good is, there will be a forward component to the pressure difference in the sail.
No one disputes ability to sail in apparent wind. Problem is that the boat movement will change speed and direction of this wind. When boat starts moving its total headway component over the ground toward finish will be less then current. boat will move over the water but it will always lag behind the current movement. It seems like it can do better but this is the trick of this puzzle that according to physics it it not possible. You can not always rely on gut feeling. Unless there are some condition I overlook I stick to my answer. I am open to discussion based on physics, vectors and math and more then welcome to be proven wrong - but according to science - not opinion polls or belief.
Changing variables was meant to visualize the pattern and independence of parameters. Sorry ifcreated confusion.
Changing variables was meant to visualize the pattern and independence of parameters. Sorry ifcreated confusion.
adm,
Unless I'm missing something, your argument boils down to an inability to overcome forces pushing you downwind. But then, how do you explain any boat's ability to sail into the wind (not directly of course)?
When you are sitting on a calm lake and have a 5mph headwind coming from the direction you want to travel, you have essentially the same physics problem, right? As you travel across the wind, isn't the direction of the apparent wind changing? Isn't that the whole idea behind apparent wind?
Unless I'm missing something, your argument boils down to an inability to overcome forces pushing you downwind. But then, how do you explain any boat's ability to sail into the wind (not directly of course)?
When you are sitting on a calm lake and have a 5mph headwind coming from the direction you want to travel, you have essentially the same physics problem, right? As you travel across the wind, isn't the direction of the apparent wind changing? Isn't that the whole idea behind apparent wind?
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Frank C
This puzzle confuses us with immaterial incidentals. As Chip writes, we must ignore the scenery. Using different words, consider speed only relative to the water and to the other boat. (This assumes we have a split-screen movie of what happens in the two different wind conditions).
Both boats are effectively dead in the water. They are side-by-side (on screen) and their only motion is dictated by the current. Regardless that freeboard & rigging makes their speed slightly less than speed of current, these identical boats are making identical progress versus the water and each other - actually ZERO relative progress! In reality, the boat in "still wind" should "suffer" a bit of drag from his apparent headwind, but the author "conditioned" that out of the puzzle.
Now, given that these idential boats that are both dead in the water, setting sail into that apparent headwind permits one of them to make infinitesimal progress beyond the status quo. It matters not that tacking lengthens his path over ground. Both boats already have identical paths over ground, so it is removed from consideration. Examining only incremental progress, the boat under sail is doing better than his dead-in-the-water partner.
Apologies if this description just duplicates others ... Chip's in fact, just using different words. I get so dizzy reading these long descriptions that it's easy to miss the points being made. No offense intended if I simply parrotted something already written.
Both boats are effectively dead in the water. They are side-by-side (on screen) and their only motion is dictated by the current. Regardless that freeboard & rigging makes their speed slightly less than speed of current, these identical boats are making identical progress versus the water and each other - actually ZERO relative progress! In reality, the boat in "still wind" should "suffer" a bit of drag from his apparent headwind, but the author "conditioned" that out of the puzzle.
Now, given that these idential boats that are both dead in the water, setting sail into that apparent headwind permits one of them to make infinitesimal progress beyond the status quo. It matters not that tacking lengthens his path over ground. Both boats already have identical paths over ground, so it is removed from consideration. Examining only incremental progress, the boat under sail is doing better than his dead-in-the-water partner.
Apologies if this description just duplicates others ... Chip's in fact, just using different words. I get so dizzy reading these long descriptions that it's easy to miss the points being made. No offense intended if I simply parrotted something already written.
I am not questioning the ability of boat to make the progress in head wind. I am pointing out that it is important to count amount of the energy available for propeling the boat.
Situation of still water and wind only is exactly the same as current and no wind. In both situations boat will have apparent wind and make exact the same progress over the reference of ground. There always be some inefficiency in energy transfer. Some can not be used for propultion and will go to counteract drag and can be see as "lost" from perspective of moving and it will cause slower progress.
But the situation differs where there is additional energy available in the form of extra wind for other boat. This boat can use this additional source for its advantage - in puzzle case - to eliminate drag and slowdown affecting the first boat.
Therefore the second boat will be faster over the ground to reach finish.
Am I missing something?
Situation of still water and wind only is exactly the same as current and no wind. In both situations boat will have apparent wind and make exact the same progress over the reference of ground. There always be some inefficiency in energy transfer. Some can not be used for propultion and will go to counteract drag and can be see as "lost" from perspective of moving and it will cause slower progress.
But the situation differs where there is additional energy available in the form of extra wind for other boat. This boat can use this additional source for its advantage - in puzzle case - to eliminate drag and slowdown affecting the first boat.
Therefore the second boat will be faster over the ground to reach finish.
Am I missing something?
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Chip Hindes
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No. That's the key to the problem The boats will make exactly the same progress in reference to the current.In both situations boat will have apparent wind and make exact the same progress over the reference of ground.
In reference to water at zero speed, it's zero plus K knots in the direction upwind. You must tack into the wind to make progress directly upwind, but let's further simplfy and say you can just select a direction to beat and continue without tacking.
In reference to the current at 5 knots, the speed is five plus K knots in the direction upwind. We've simplified the problem to the point we're on a river of infinite width, so tacking is not necessary.
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RandyMoon
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1) How long did the Hundred Years War last?
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1) How long did the Hundred Years War last?
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3) From which animal do we get cat gut?
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4) In which month do Russians celebrate the October Revolution?
Answer: In November
5) What is a camel's hair brush made of?
Answer: Squirrel fur
6) The Canary Islands are named after what animal?
Answer: Dogs
7) What was King George VI's first name?
Answer: Albert
8 What color is a purple finch?
Answer: Crimson
9) What country do Chinese gooseberries come from?
Answer: New Zealand
10) What is the color of the black box in a commercial airplane?
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Passing requires ONLY 4 correct answers
1) How long did the Hundred Years War last?
2) Which country makes Panama hats?
3) From which animal do we get cat gut?
4) In which month do Russians celebrate the October Revolution?
5) What is a camel's hair brush made of?
6) The Canary Islands in the Pacific are named after what animal?
7) What was King George VI's first name?
8 What color is a purple finch?
9) What country do Chinese gooseberries come from?
10) What is the color of the black box in a commercial airplane?
All done?
Check your answers below!
ANSWERS TO THE QUIZ:
1) How long did the Hundred Years War last?
Answer: 116 years
2) Which country makes Panama hats?
Answer: Ecuador
3) From which animal do we get cat gut?
Answer: Sheep and Horses
4) In which month do Russians celebrate the October Revolution?
Answer: In November
5) What is a camel's hair brush made of?
Answer: Squirrel fur
6) The Canary Islands are named after what animal?
Answer: Dogs
7) What was King George VI's first name?
Answer: Albert
8 What color is a purple finch?
Answer: Crimson
9) What country do Chinese gooseberries come from?
Answer: New Zealand
10) What is the color of the black box in a commercial airplane?
Answer: Orange, of course.