Paddling and Sailing Questions

[leong]

The Kayak Brainteaser:
A river runs straight from West to East at 5 knots. Yesterday, 5-mile time trials were held paddling downstream, from West to East. The first time trial was held in the morning, when there was no wind. The second time trial was held in the afternoon, when there was a 5-knot wind from the West. (For simplicity assume a kayaker paddles at a top speed of 5 knots in still air and no current.)

Question: Not neglecting air resistance, which kayak time trial was faster?

The Sailing Brainteaser:
Similar to above, a river runs straight from West to East at 10 knots. A 10-mile sailboat race is held: the boats sail downstream, from West to East. The first heat is held in the morning, when there is no wind. The second heat is held in the afternoon, when there is a 10-knot wind from the West.

Question: In which heat are the faster times recorded? Hint: A sailboat can tack downwind (note: they do that in the America’s Cup match races)

[billvoss]

All the factors fall out of the equation except the tailwind. Baring something really weird, all other factors being equal, moving with a moderate tailwind is always faster than still air or a headwind.

Of course for the sailing brainteaster the first heat held in the morning was called off because there was no wind! So the second heat has the only times. If they didn't call off the morning heat, a kid in an inner tube could kick occasionally and beat the sailboats as they both drifted with the current.

P.S.

I'm no sailing expert, but I believe sailboats normally tack upwind. I've never heard of a sailboat needing to tack when they are traveling directly downwind, except to avoid an obstacle.

[leong]

All the factors fall out of the equation except the tailwind. Baring something really weird, all other factors being equal, moving with a moderate tailwind is always faster than still air or a headwind.

Yes for the kayaks.

Of course for the sailing brainteaster the first heat held in the morning was called off because there was no wind! So the second heat has the only times. If they didn't call off the morning heat, a kid in an inner tube could kick occasionally and beat the sailboats as they both drifted with the current.

But suppose the first heat wasn't called off. If the skippers did nothing they'd be moving downstream at 10 knots. But if they did some clever sailing is it possible that they could move even faster than 10 knots? That's the heart of the question.

P.S.

I'm no sailing expert, but I believe sailboats normally tack upwind. I've never heard of a sailboat needing to tack when they are traveling directly downwind, except to avoid an obstacle.

Normally yes, but not always. For instance from here

The Extreme 40 catamaran can sail at 35 knots (65 km/h; 40 mph) in 20–25-knot (37–46 km/h; 23–29 mph) winds.^[8] The high-performance International C-Class Catamaran can sail at twice the speed of the wind.^[9] Iceboats can typically sail at five times the speed of the wind.^[10] By sailing downwind at 135 degrees off the wind, a sand yacht can sail much faster than the wind.^[11]The velocity made good downwind is often over twice as fast compared to the same land yacht sailing directly downwind.^[11] The catamarans used for the 2013 America's Cup were expected to sail upwind at 1.2 times the speed of the true wind, and downwind at 1.6 times the speed of the true wind.^[12][13][14] They proved to be faster, averaging about 1.8 times the speed of the wind with peaks slightly over 2.0.^[15]

Today I sailed my Sunfish downwind at a downwind tacking angle about 30 degrees off of straight downwind, both starboard and port tacks. According to my GPS and some simple trigonometry later, my velocity made good downwind was faster than just pointing directly downwind.

Another hint for the sailing brainteaser:

When the wind and the water both move W to E at 10 knots, the boats drift down the river at 10 knots, with their sails hanging limp. In the heat with no wind (as measured on the land), a drifting boat has a headwind of 10 kt. You can take advantage of that headwind by tacking.

Edited April 22, 2014 by leong

[EEL]

Paul S. is the person with sailing knowledge/experience, but I believe tack and tacking refer to changing the sail from port to starboard or vice versa as opposed to simply setting a course or an angle of attack. I believe most refer to tacking when the change is done by rotating the boat into the wind and jibe is when it is done by rotating downwind. You can have either a port or starboad tack when running dead downwind and the boom 90 degrees to keel of boat. If you brought boat from dead downwind to closer hauled you would not necessarily change your tack.

Ed Lawson

Who cannot believe he posted on one of these threads

Edited April 22, 2014 by EEL

[leong]

Paul S. is the person with sailing knowledge/experience, but I believe tack and tacking refer to changing the sail from port to starboard or vice versa as opposed to simply setting a course or an angle of attack. I believe most refer to tacking when the change is done by rotating the boat into the wind and jibe is when it is done by rotating downwind. You can have either a port or starboad tack when running dead downwind and the boom 90 degrees to keel of boat. If you brought boat from dead downwind to closer hauled you would not necessarily change your tack.

Ed Lawson

Who cannot believe he posted on one of these threads

When a current is pulling you downstream at x-knots and the wind (with respect to the earth) has the same velocity as the current there is no apparent (relative wind) for the sailboat. So you can’t really sail. You just float downstream in the apparent still air.

When a current is pulling you downstream at x-knots and the wind (with respect to the earth) has zero velocity there is an x-knot apparent (relative headwind wind) for the sailboat. So, you can tack to either side of this apparent headwind. You wouldn’t be jibing in this case.

Tacking downwind is a term currently being used, especially for high-speed catamarans. I do it myself several times a week. Take a look at this “Advanced Racing Tactics” book.

Leon

Who’s been sailing small and large sailboats since 1962 and who cannot believe he had to answer this downwind tacking question after all of the publicity about the last few America’s Cup races.

PS

In strong winds if I jibe with my Sunfish there’s about a 10% chance of a capsize. So, in windy conditions, instead of jibing, I just turn towards the wind, tack around, and then head down to my new course with the boom on the other side of the boat.

Edited April 22, 2014 by leong

[EEL]

"Tacking downwind is a term currently being used,"

Yes. Tacking is not the same as tack and now some people describe jibing as tacking downwind.

I do not recall talking about downwind tacking. I said it would not necessarily change the tack to go from downwind to closer hauled.

Whatever.

Ed Lawson

Edited April 22, 2014 by EEL

[leong]

Enough with this fine tuning of nomenclature. I think we agree. My only point is that when I want to head straight downwind I usually head about 30 degrees off of the wind’s direction vector. This increases my speed made good downwind (obviously, I have to jibe or do an almost 360 turn to get to the other side of the direction vector). I call that tacking downwind, whether I jibe or do the upwind turn to get to the “opposite” downwind tack.

So now, with all said in this thread, can you answer the second brainteaser?

Peace,

-Leon

PS
Heading to the kayak right now ... it’s not windy enough to enjoy sailing.

[billvoss]

So now, with all said in this thread, can you answer the second brainteaser?

The 10 knot current provides an initial apparent 10 knot headwind in the "no wind relative to the shore" morning, and an initial apparent 0 knot headwind in the afternoon when the "10 knot relative to the shore" wind becalms the sailboats relative to the water.

Assuming a wide river and modern racing style sailboats, the racers will be able to go faster down the river into the headwind by following a zig-zag course than they can drift while becalmed. So the morning sailors are faster.

Assuming a narrow river and/or an old fashioned square rig, the sailors will not be able to follow a zig-zag course and will drift faster while apparently becalmed than while fighting an apparent headwind. So the afternoon sailors are faster.

[leong]

Bill,

Yes, of course, you’re right.

Here’s a way (perhaps in theory at least) that you could increase a kayak’s speed while floating downstream on a windless day.

Mount a wind generator on the kayak that powers an electric motor that drives the boat directly into the apparent wind. Of course the apparent wind’s force on the wind generator’s blades would slow the kayak below the speed of the current. But (perhaps?) you’d get a net gain in down-river boat speed due to the electric propulsion. Or does this violate some principle(s) of physics?

-Leon

[JohnHuth]

Attached is a file showing wind performance of a replica Poynesian Voyaging Canoe/sailboat as a function of degrees into the wind. You can see it goes faster on a reach than running downwind.

Edited April 23, 2014 by JohnHuth

[leong]

John,

Thanks, I like that kind of speed-ratio diagram. Wish I had one for the Sunfish.

I wonder if your posted diagram was derived from measurements or determined analytically?

Here’s my interest. Say you want to sail to a point that’s in the no-go zone (~ +/- 60 degrees in your diagram). So you have to sail a sequence of tacks to get there. The general question becomes, “Given the speed-ratio versus angle diagram, what’s the optimal set of tacks to maximize your speed made good to that point?” I assume bigger racing sailboats have programs to solve such continuous optimization problems.

The simplest example is when you want to sail to a point that is directly upwind from your starting point. Perhaps the answer is trivial for this case. I just sail about as close hauled as possible for half the distance and then sail the opposite close-hauled tack. I don’t know if this is optimal. If I had a speed-ratio diagram for my Sunfish I could find out.

Any ideas?

-Leon

PS
On the Sunfish my speed (not speed made good) seems to maximize at about 90 degrees off the wind. Actually, a little more downwind than that but, in really strong winds, the bow digs in (pearls) and it slows down.

PPS
The foiled catamarans (like the America’s Cup boats) now have speed rations over 2!

[JohnHuth]

That plot was empirically derived.

I don't know the answer offhand how to optimize the angle to the wind, but I think that being too close hauled is not optimal. For that vessel, I'm guessing that 70 degrees would be the best you could do. Modern yachts can do maybe 35 degrees - mainly because the keel is so deep.

There *must* be a polar diagram for a sunfish somewhere, but I couldn't find one with a cursory inspection.

Yes, the AC-72 (Oracle America's cup entry) is a beast!! Check it out on some YouTube videos.