[Karsten (OP)]

I want to win this race and I want to milk someone's brain about hydrodynamics for very small scale sail boats.

Here is the situation:
Boat max. Length 35cm
Max width: 12cm
Power: Wind from a window box fan
Length of race track around 4 meters
Max. sail surface: 256 square cm
No min. weight

First question:
Does waterline length matter at this scale? I know it matters with bigger boats in displacement mode. Such small boats too?

Second question:
At this scale, should I worry about water resistance more than about water surface tension?

Third question:
What is the ideal shape at that scale and at such speeds (maybe 0.8m/s)

Can't wait to hear your comments and ideas!

[RD]

If you can get the hull out of the water on hydrofoils it will be quicker ...

[Chemistry4me]

Make it a hovercraft!

[RD]

Make it a hovercraft!

If you are allowed a motor make it a ground effect vechicle. (a.k.a. "sea skimmer")...

[Chemistry4me]

You'll have no problems winning.

[LeeE]

An interesting question, and an interesting competition too.

I see that you've clearly specified that it's to be a sailboat, so most of the suggestions about using motors are nonstarters (unless the rules allow you to use wind-turbines to generate electricity, to drive an electric motor, and even then it would be questionable whether you could generate/capture more energy that way - there's only a finite amount of energy in the wind to be used).

I don't think you'll be able to capture enough energy to get your boat hull out of the water, either by planing or in hydrofoil mode, so I'll just stick to conventional designs.

With a conventional type boat i.e. where its hull stays in the water, its speed is limited by the length of the hull.  This is largely due to the bow-wave created by the hull as it passes through the water; the water displaced by the hull cannot simply be pushed aside because water is not easily compressible, so it has to be displaced upwards with the result that the boat ends up traveling up a 'hill' of water.  The length of the hull becomes significant then, because the length, and therefore the gradient of the bow-wave is proportional to the length of the hull; the longer the hull, the longer the bow-wave.

So the first thing you need to do is maximise the hull-length.

Next you need to reread the rules carefully again.  You've said that the max width (beam) is 12 cm but I strongly suspect that this actually says the min width.  Once you've clarified that point, you then need to establish if that is the minimum waterline beam or just the overall min beam.

Along with the length of the hull, the waterline beam is important regarding speed because this dictates the cross-section of the hull below the waterline, and a lower cross-section will require less power than a greater cross-section.  Because it would be difficult in practice for people to ensure and measure the waterline beam, I'm guessing that the rules only specify the overall beam, and this gives us some scope for a bit of cleverness.  The best below the waterline shape for a hull, for optimum speed, is circular.  This is because it has least surface area for volume, and it's the volume that dictates buoyancy.  However, if you simply design a circular shaped hull where the diameter of the circle is equal to the min beam it will be more buoyant than you need and most of the hull will be out of the water, so what you do is design a narrower hull that is circular below the waterline but with flat sides above the waterline, extending outward to meet the min beam requirement; think in terms of a 'V' shaped hull but with a circular rounded bottom, or point of the 'V', with only the rounded part in the water.  This will take some time and effort on your part to get right because you don't want the flattened sides to be touched by the water - they have a large surface area, and therefore surface friction.

Because you're going for speed, and not maneuverability, you don't want much 'rocker' on the hull; this is the curvature along the length of the hull.  So although the below-waterline hull cross section will be circular at the widest parts of the hull it will need to get progressively narrower and more elliptical towards the bow and stern.  Oh, and don't bother sloping or angling the leading edge of the hull - keep it vertical to maximise hull length.

There's one big problem with circular hulls though; they're unstable if the Center of Gravity (CoG) is below the Center of Buoyancy (CoB) - think in terms of trying to balance when sitting on a floating telegraph pole.  Using out-riggers is one way around this, if allowed, but otherwise you'll have to get the CoG below the hull's CoB.  However, you don't want to add unnecessary ballast because that'll reduce your acceleration and require more buoyancy, which mean more hull in the water, which in turn means more surface friction.

The last thing I can think of are the sails.  If you know that the wind is coming from behind you, you just need a spinnaker type sail, but I doubt that will be the case, so that means you could consider using a 'wing' type sail.  With these you replace the normal low-aspect ratio cloth sails with a rigid glider wing type sail.  These long and narrow wings have a very high aspect ratio and are more efficient, but they are also more critical, so you'd need some sort of active control system to keep them at the optimum angle to the wind.

If you're capable of designing and implementing an active wing sail, then you also ought to consider a wing type keel too.  This would mean that you could use a longer and thinner keel, which would lower the size of the counterweight and reduce the below the waterline cross section.  The boat would then only need to be marginally stable when stationary - it would become more stable as it moved and as the wing became effective.

If there are any real geeks in this competition, I would expect to see micro-processor controlled wing type entries.

(Edited to replace a couple of incorrect references to drag with surface friction)

[Karsten (OP)]

Hovercraft/skimmer: Cannot do. No additional power is available. Only the box fan.

Hydrofoil: Interesting idea. I will have to create underwater "wings" to lift the hull out of the water. Will they create more resistance than the hull itself (which can be VERY light and does not need to sit in the water very deeply at all)? I am afraid that the speeds the boat in the youtube link need to reach to lift out of the water is far above the speed of the air created by the box fan. My race is a downwind drag race. The boats don't even reach planing speed.

Don't get distracted from my issue but here is a cool video of a hydrofoil trimaran that holds the world record for sailboats.  

 
Or this one for the opposite on the size spectrum:

Only windsurfers and kite surfers can go faster.

But don't get distracted! I only have wind available from directly behind the boat.

[Karsten (OP)]

Thanks Lee for the long post.

First of all, the maximum width of the boat can be around 12 cm. It is a basic 7th grade student competition but some teachers are competing as well and I have a reputation to lose. So, the boat hulls have to fit in a box of 35 cm by 12cm.

I am actually thinking multi hull. Trimaran or catamaran. Maximum stability with least amount of hull touching the water. Buoyancy is not much of an issue since you can make the boat as light as possible. I appreciate you suggestion to make the hulls circular in cross section. I worry that with such a design I will deal with a lot of water surface tension issues. My previous thinking was to create almost knife-like hulls (two). Something that is big enough to keep the boat afloat (close to the fans where there is a lot of wind & further down the "lake" when there is much less) but sharp enough to cut though the water surface easily.

What is better: trimaran (one large hull with two shorter outriggers in the front to deat with the almost violent winds at the start) or catamaran (two hull equal in length)? If I go with long waterline I would have to think that the shorter outriggers will slow the boat down more than two longer hulls. Right?

Rocker and bow shape: What you say is just what I thought. Maximum water line length is critical.

Send me some of your thoughts regarding multi hull design and shape in this case.

Keel: Necessary? On down wind courses small sailboats pull the centerboard out of the water. To reduce water resistance I assume. My previous boat has raced even without a rudder. It is only 4 meters straight.

Sail: Way in the back to deal with the violent wind at the start. Don't want to bow to plow under the water. The wind is coming exactly from behind and it does not change. Like I said, basic competition. Will it be best to have a sail that is shaped to capture the wind (like a spinnaker)? What does that do in comparison to a flat sail that has the same cross section? I may have to vacuum form a thin plastic film sail.

Microelectronics: Nah. Not that much of a geek. Or better: Not smart enough to do this. And not enough time to learn how to. I would love to see this though. And I don't think the sails would need adjustment since the wind always comes from behind.

I assume that making the hull as smooth as possible is important as this scale. I wonder if I should shape the hull from foam and vacuum form a thin plastic layer over it.

Thanks so far. Good and helpful info. Send me some thoughts on multihulls and downwind sail design!

[LeeE]

Aha - downwind only, using an artificial wind-source []

In that case you just want a single spinnaker sail.  I don't know anything in particular about their design though, so you'll have to research that yourself.

If multi-hulls are allowed then it's a tossup between tri and catamarans, and as you say, a keel won't be needed with either of these types as they have a Plane of Buoyancy, not just a point, so you don't need to keep the CoG beneath a Point of Buoyancy; as long as the CoG stays within the area of the Plane of Buoyancy it'll be stable even though the CoG is above the Plane of buoyancy.

Because of the bow-wave issues, I'd make each hull full-length, but as to whether you use two or three smaller equal-dimension hulls, or go for one main hull with two less buoyant outrigger hulls is up to you.  Using a single main hull with less buoyant outriggers may give optimum buoyancy for the wetted surface area, but using less buoyant outriggers will reduce stability.

For simplicity and ease of construction, and for maximum stability, I'd go for an equal-length twin-hulled catamaran design.

Using a multi-hulled vessel also means you can forget about complex hull profiles and just use circular hulls, because you just need to work out the hull width needed to supply the required buoyancy and place them as far apart as you can within the max beam limit.

Circular hulls are definitely the way to go.  Water tension isn't the issue here; it's the wetted surface area and the resulting friction from it that's important.  Circular hulls give maximum volume, and therefore maximum buoyancy, for minimum surface area and cross section, so for any given buoyancy requirement, a circular hull will give least friction and cross section.  Knife, or pure 'V' section hulls will result in both greater cross section and surface friction to provide the same buoyancy.  Although boat hulls are sometimes described as 'cutting' through the water, they actually do no such thing; they have to push the water aside.

I'm guessing that there's no requirement for the hulls to be convex only (this is a rule in many types of racing boat design) and this means you have some options regarding your hull planiform i.e. when viewed from the top.

In general, using straight lines is a bad idea in aero/hydro-dynamics because, iirc, they increase turbulence along the straight surfaces and don't give the best gradients in terms of how quickly the medium, in this case water, is moved aside.  As I said earlier, a convex hull is a rule for some vessels, and for larger non-racing vessels introducing concavities in the design requires more strength, and while they should be avoided in the hull cross section, as they'll only increase surface area and cross section, they can be useful along the length of the boat, in its plan shape.

Therefore, consider a planiform where you have a very long and slender bow, which then flares out to the max beam, which in turn should be located aft of the mid-point, and which then converges more steeply at the stern.  The trade-off here is between reducing the bow volume, which in turn reduces the bow-wave gradient that the boat is trying to climb (and with less buoyancy in the bow, the boat should stay more level - ideally, the boat should sit slightly bow-down when stationary) against slightly increasing the drag from the water flowing back into the space left by the boat as it moves forward, as it now has to do this over a shorter distance.

This trade-off is hard to get exactly right though, so don't try anything too drastic; in any case, you want to avoid radical changes of direction in the surface of the hull and smooth flowing lines are the order of the day.

One thing about the sail:  You'll need to experiment for the best place to anchor it.  The sail will tend to push the bow down into the water, so if you're using a slender bow design consider placing the mast a long way back, and not at the mid-point.  In general, iirc, I think the mast should be a little aft of the max beam location.

Hopefully sophiecentaur, being a bit of a sailor, will see this thread and comment on the sails.

[Karsten (OP)]

I just lost my post before I could post it.

Anyhow, much shorter now:

I am not sure I understand the the hull shape details you describe, especially the "flaring out" part. I have seen some concave designs in racing canoes, but maybe you can look at the pictures I linked and tell me what you think comes the closest:
1) http://www.kayakcentre.co.za/images/mustang.jpg
2) http://blog.mlive.com/lcn/2008/07/CANOE3.jpg
3) http://img.nauticexpo.com/images_ne/photo-g/rowing-shell-touring-single-scull-130942.jpg

And what do you think about this rowing catamaran I just found:
4) http://www.fotothing.com/photos/0b4/0b48d42c02c342c69bbbdca51e9919d2_adc.jpg

Lee, I love all this information you post. This will be a great boat!

I will wait for Sophiecentaur to talk about sail design for downwind only.

[wolfekeeper]

If the rules allow it, and it's downwind, you're theoretically better off with a propeller and a windmill- these devices can outrun the wind.

The other thing to think about is reynolds number. If you're moving at 0.8 m/s I think it's about 10^5, so it's fully turbulent flow around the boat; I would think normal boat hulls would work reasonably well at this scale.

[Karsten (OP)]

If the rules allow it, and it's downwind, you're theoretically better off with a propeller and a windmill- these devices can outrun the wind.

The rules do not allow to use an engine on board. If that is what you mean. I do not understand how a propeller would work without an engine.

How about the stern end of this boat?:
http://farm1.static.flickr.com/115/273686080_9ac118f85c.jpg?v=0

Or the bow of this one?:
http://upload.wikimedia.org/wikipedia/commons/c/c4/Seacycle.jpg

 

[wolfekeeper]

You stick a windmill on the boat and use that to turn the propeller. If the gearing is right, it's very, very counterintuitive, but it can in principle outrun the wind.

I must admit though I've never heard of people doing it with a boat, but it definitely has been done with land yachts type things. Normal land yachts don't do that though, they just go at an angle to the wind and can go faster than the wind that way with only a relatively simple sail; but the sail type land yachts can't do that directly downwind, whereas the windmill version can.

[Karsten (OP)]

You stick a windmill on the boat and use that to turn the propeller. If the gearing is right, it's very, very counterintuitive, but it can in principle outrun the wind.

I must admit though I've never heard of people doing it with a boat, but it definitely has been done with land yachts type things. Normal land yachts don't do that though, they just go at an angle to the wind and can outrun the wind that way with only a relatively simple sail; but the sail type land yachts can't do that directly downwind, whereas the windmill version can.

You are saying I am using the wind created by the box fan to run a wind turbine that moves a propeller that pushes forward the boat faster than the wind blows in the same direction?

I must admit I never heard of anyone doing this with anything and would love to see a picture of anything moving faster than the wind blows directly from behind. How can anything moved by the wind move faster than the wind in the same direction the wind blows? Where does the energy gain come from?

This will turn into a completely different discussion. I can already feel it. I want to discuss my problem a bit longer please.

[wolfekeeper]

For example for the land yacht type thing:

Since your race is downwind you could theoretically do the same (normal sailing is rarely directly downwind).

If you can engineer this kind of thing (it should be possible I think), your boat should absolutely slaughter the others  []

[Karsten (OP)]

Post this in a thread. I would love to see a discussion of this. I want a peer review so to say.

[LeeE]

I just lost my post before I could post it.

Anyhow, much shorter now:

I am not sure I understand the the hull shape details you describe, especially the "flaring out" part. I have seen some concave designs in racing canoes, but maybe you can look at the pictures I linked and tell me what you think comes the closest:
1) http://www.kayakcentre.co.za/images/mustang.jpg
2) http://blog.mlive.com/lcn/2008/07/CANOE3.jpg
3) http://img.nauticexpo.com/images_ne/photo-g/rowing-shell-touring-single-scull-130942.jpg

And what do you think about this rowing catamaran I just found:
4) http://www.fotothing.com/photos/0b4/0b48d42c02c342c69bbbdca51e9919d2_adc.jpg

Lee, I love all this information you post. This will be a great boat!

I will wait for Sophiecentaur to talk about sail design for downwind only.

Heh - the kayaks in the first two pics appear to be sprint K1s.  These are the class of boat I used to race (along with a bit of K2), and although the hull may seem to have some concavity in the hull planiform, the actual hull shape is actually entirely convex (or flat).  This type of hull uses the rounded 'V' cross section at the max beam point (in the second pic this is just behind they guy's head) to meet the minimum beam requirement and the reason that it looks as though the hull is concave around that region is because the sides of the 'V' are extended higher than the rest of the hull.  I think this pic of a K2 (nothing to do with me - just something I googled) shows it quite well:



The sides of the 'V' section hull are flat, but that's ok here because they're out of the water; the hull below the waterline will be rounded.  The trade-off in doing this is that being higher up out of the water, the hull can be adversely affected by crosswinds - not what you want in an inherently unstable design.  You can also see how the bow wave has piled up around the front of the boat as the water is pushed aside and up, and how you get a trough at the back of the boat as the opposite happens - the water is being 'sucked' in to fill the gap left by the hull, producing drag and resulting in a 'trough' which accentuates the hill-climbing effect.

Re the hull planiform I was referring to: I couldn't find any good pics, but think of a reversed and very elongated teardrop shape, but pointed at both ends.

The cat rowing boat is weird  []

Incidentally, I believe that a minimum beam has never been a requirement for racing rowing boats, so they don't need 'V' hulls.

...and oh yes, you might want to consider using a bulbous bow.  These are normally only found on quite large vessels but they can also be effective with very long narrow hulls running near their max speed, so they might work.  The convex hull requirement for many racing boats normally precludes their use.

http://en.wikipedia.org/wiki/Bulbous_bow

[LeeE]

If the rules allow it, and it's downwind, you're theoretically better off with a propeller and a windmill- these devices can outrun the wind.

This cannot work.  As the boat starts to move, the wind speed over the boat decreases; wind speed over the boat, and therefore its 'windmill' will be absolute wind speed - boat speed.  If the boat's speed is equal to the wind speed there is zero wind over the boat, meaning there's nothing to drive the windmill.  If the boat travels faster than the wind then the wind speed over the boat will be negative, effectively slowing the boat down.

[Don_1]

If the rules allow it, and it's downwind, you're theoretically better off with a propeller and a windmill- these devices can outrun the wind.

This cannot work.  As the boat starts to move, the wind speed over the boat decreases; wind speed over the boat, and therefore its 'windmill' will be absolute wind speed - boat speed.  If the boat's speed is equal to the wind speed there is zero wind over the boat, meaning there's nothing to drive the windmill.  If the boat travels faster than the wind then the wind speed over the boat will be negative, effectively slowing the boat down.

I see the logic in that!

If your sail surface must not exceed 256 sq cms, and you will have a permanent tail wind, I wonder if your sail should be 13cms high by 20cms wide giving a total of 260 sq cms. then cut 5 x 1cm sq holes in the centre keeping you within the allowed surface area and creating the same effect as a parachute.

[diagram=478_0]

[Bored chemist]

Is it cheating to freeze the water and mount the "boat" on skates?