Help for High School Self-Propelled Boat Design

I would appreciate some help for a high school project for my son. He has to build a boat out of limited number of 8' pieces wood overlaid with waterproof paper that he can paddle with his hands across a pool. Faster is better.

He is supposed to present some physics problems that he considered when designed his boat. Aside from basic buoyancy, we are having trouble tracking down some basic concepts to present related to bow design for a slow-moving boat on still water.

For purposes of this project, assume a flat-boated boat with somewhere around a 2' - 2.5' width and 5' - 6' length, displacing only about 3" of water.

Would it be better to have a pointed bow (aka v-shaped when viewed from above) or an slanted bow (aka angled upward when viewed from the side)? Some general principles would be greatly appreciated.

Thank you!

 

Interesting and different from other similar projects. He has to paddle with his hands so it needs directional stability and low drag. I assume he can have a rudder but keeping the thing straight is an issue. I have judged a lot of quick and dirty boatbuilding contests and keeping straight is usually the thing that gives the most trouble in the rowing part of the contest. A long and narrow boat is best for these issues. I would keep the bow sharp and in the water. Draft will be what it has to be to get the required buoyancy, whether that is more than 3" or not. Have him sit on the bottom for best stability and keep the midships sides low as practical for giving him adequate reach into the water. Deeper reach is better. If you can make a bit of tumblehome in the mid sides, all the better for easier paddling. Not a fan of pointed sterns but in this case that may be best.

 

This is a complex field of study that has many (too many) ramifications. Let's see if we can boil some of it down to the bare essentials.

1. Buoyancy; Decide whether the boat, Case A; is to be capable of fully supporting itself and the paddler. Or case B; will it only be required to afford partial flotation for the paddler, such as small beach boards?. Let us assume case A. You will need to estimate the total weight of the boat and that of the paddler. For a first stab at it, let the boat weigh 30 pounds. The paddler might weigh ......Wild guess....165 pounds...... for a total weight of 195.

Hello Mr. Archimedes. A cubic foot of fresh water weighs 62.4 pounds plus or minus a wee bit depending on temperature and mineral content. A cubic foot of anything amounts to 1728 cubic inches. Divide 62.4 pounds by 1728 cubic inches and we get 0.03611 pounds per cubic inch. There are several ways of doing this but this one is quick and easy. We need to displace 195 pounds so we can simply divide 195 by 0.03611 to get 5,400 cubic inches. That is how many cubic inches of water we will need to displace. If the teacher prefers the metric system, then one liter of water weighs one kilogram. For now, let's use our homely Imperial system.

Let's see what happens when we build our boat 30 inches wide and 72 inches long. It is hoped that it will be immersed only three inches. We could start by assuming the shape of a box, not a boat. Multiply.....30 x 72 x 3 = 6480 cubic inches which is more than enough to do the job. But wait, we are to build a boat not box. The boat will not be simply a slab sided square ended floating object. It might be pointed on both ends so that we lose the displacement of the wedge shaped parts that are not to be part of our boat. Hang on we'll get to that complication in a minute.

Here are some more questions that will play into the design of our boat. How far is the boat to be paddled? We need to factor in the endurance and strength of the paddler. How far can he he sustain maximum effort? What will the water conditions be. If the race is to be be done with several contestants in the water at the same time, then there will be waves, and turbulence. We need to account for that in our design. Flat water may favor one configuration while rough water may need another. Will the paddler be permitted to use his feet for a kick stroke? If so we'd need to think of the shape of the back end of the boat.

The width of the boat at or near the paddlers shoulders will be a determinant. The paddler has to reach the water with an unencumbered arm swing. The boat is getting narrow and longer when this is considered. Let's try 18 inches wide and 92 inches long with 3 inch draft. ....18 x 92 x 3 = 4968 cubic inches. We need 5400 cu. in. If we let the boat sink a little deeper we can get up to the 5400 that we need. Sorry, we have not yet factored in the next important design proposition, which is that the boat may be pointed at one end or maybe both. It's a boat not a box. Obviously the displacement of a cats eye shape is not as big as a rectangular shape. .

That brings us to something called prismatic coefficient usually written, Cp. Divide the actual displacement of the boat by the displacement of the box with the same dimensions and we get a number smaller than one. A canoe like boat will have a Cp that falls somewhere between 0.50 and 0.60. The canoe with fatter ends will have the larger Cp number. You can think of this as a percentage if you like. So now we must consider how to account for that problem. If our boat has, for example, a Cp of 0.55 then we need to increase the size of our design box so that we actually end up with 5400 cubic inches of immersed volume. ....5400/0.55 = 9418 We can experiment with a combination of three numbers that will have a product of 9418.

The boat can not be too wide on account of the paddlers shoulder width. Try 20 inches wide by 92 inches long.......= 1840 so how much draft do we need.....9418/1840 = 5.12 inches. That would be good if the Cp is actually 0.55. How can we be reasonably sure of that? ...Do a scale drawing and divide the length into a number of equal spaces. Let the front of the boat be station number zero and the back of the boat be station eleven. That gives you an odd number of interior stations to measure. You will measure the width and height of all nine interior sections to get the area of each of those. This is getting too long winded. Do this. Have you son Go to Wikipedia or other source and find Simpsons Rule. It is pretty simple and your son will be able to deal with it. It will give you a fairly accurate total displacement number.

With all that, I might consider a scow planform where the sides of the boat are parallel. The math is a lot easier and so is the build. But that is pending the answers of some of those question above.

Who knew that boat design had so many twists and turns? If your son will take this stuff seriously he will surely be able to impress his teacher with Cp, Simpsons Rule, and all that other arithmetic manipulation. In addition to that, it might be fun.

 

Interesting. so far displacement is pretty well covered. But what about resistance. For a small boat like this, that is paddled by hand, speed and resistance is all about wetted surface. Length is also important but here you have a limit on length so we can ignore that. But you can't ignore wetted surface. Wetted surface is directly related to the shape underwater and how much it displaces. A flat bottom boat will draw less water (how far it extends down into the water) and reduce wetted surface. But to further reduce wetted surface, make it pointy on the bow, rather than a box and give the bottom some rocker (curves up at the bow and stern).

 

The most efficient shape, while being fairly stable, will be something like a surfboard.

 

Great, elegant, simple, low cost answer gonzo!

Is the answer to a thinking question sometimes not thinking? Or was it a thinking question in the first place?

Porta

 

Porta; Sure enough Gonzo has offered a best solution as he usually does.

I too am a great fan of simplicity despite my sometimes long winded dissertations. The OP is looking for two things, the design of the boat and some of the physics that the student will be required to present along with his build. The physics presentation and its chain of reason was the intended purpose of all that text in my first post.

 

I don't want to rain on friend Gonzo's parade but a surfboard is not optimized for a use anything like the OP wants. Surfing down a wave powered by gravity is not at all like paddling across a flat pond. That honor goes to the racing canoe. Those who actively race canoes have analyzed and tested all characteristics that optimize performance for a human powered craft to the nth degree.

 

Before you can come up with the best design for the boat you would need to know what the rules for the build are. For instance how much and what material is allowed are there any restrictions on length and width. Is it a competition of speed or endurance or both. How far will the boat need to travel, just across a swimming pool or will it be a pond or lake. Are there weight restrictions? If not then the lightest strongest contestant will have an advantage if there design is efficient that is. Most all boat designs are usually a compromise between what the builder wants and what can be built governed by cost, available materials, coast guard or DNR rules, conditions where the boat will be operated and the skill of the designer and builder. If you could tell the experts what the rules are I'm sure it would be much easier for them to help you.

 

Most likely a winning design would be about 7 ft 8 inches long, about 20 inches wide, float about 6 inches deep and would have 15 inch high sides. It would be pointed at both ends and would be a ***** to get into. It might have to boarded while swamped, then bailed out, or held up right by an assistant, when boarded.

But ridding 6 inches deep, it would provide good tracking and have slightly less whetted area than a wider, shallower model.

A board boat (a boat resembling a surf board) might work, but will need some kind of water tight deck plus a way of transferring the weight on deck to the bottom. But if the skipper is allowed to lay down on the deck, it would be even easier to paddle.

 

Hi, Tom.

Agree that racing canoe designs are the fastest, but wonder how much they were they calculated or did they evolve?

Also I thought that a surf board had to be HAND paddled fast to "catch" a wave, and against oncoming waves to get position. Caveats, as what I know about surfboards is only from observation....

This is an interesting project, but wondering if it's a good idea to be helping only one person on a graded project, unless he will be sharing with everyone involved before building it?

Porta

 

Of course there are many ways to get at the problem of the "best" boat for this problem and a surfboard might well be one of them. The serious canoe racers I've known are very involved in the technology of their craft. Probably more than we who follow other boating ventures because the physical limits are even more fixed by natural forces. In such an arena, evolution can be very powerful.

I think getting advice is part of any such exercise and the internet has become a mainstay in this. The decision of what advice to accept or reject is probably made even more difficult by all this help. I'd hope its all about learning, not what is already known.

 

In the spirit of follow up, we went with a scow design with angled bow and stern. Based on buoyancy calculations, we ended up with 8" total height and 4" at the waterline when loaded (6' total length of boat and 2' width). My son (who is a national level swimmer) was the driver, and we designed the boat to be narrow enough for him to use a double overhand (ie butterfly) arm stroke. In a kneeling position he beat every other boat by 20 seconds on a 25 yard course, and broke the high school record by 4 seconds

I would say this was a good design - one 2" x 4" x 8' board and construction paper (with the help of epoxy paint). It was extremely stable. The only problem he had was that when he got going fast enough he had to be careful to keep his weight back so that he didn't dig the bow into the water.

I wanted to thank everyone for their responses!!

 

He went with the scow design for ease of build or physics showed it was better?

 

We only had a week, and we were getting conflicting information about the design. We ended up assuming that a pointed bow would be more efficient (and better over the long run) but the angled (scow) design would be much more stable and less likely to capsize. Because it was only a 25 yard course, and my son is a powerful swimmer, we decided to go stability over efficiency. Mind you - I was impressed with how this boat "swam". It was almost eerie seeing how little wake and turbulence it generated. I wouldn't want to take it out in any waves, but for a swimming pool and flat water it was awesome.