MEGO: Prismatic Co-Effiecient

I was reading some specs on canoes and they mentioned Prismatic co-effiecent. Sounded interesting so I made the mistake of looking it up. My Eyes Glazed Over as I stared at these equations that I could not understand even if I took off my shoes so I could count to 20. Most I could figure out is that you need a tank of water to get the displacement of the hull, then you need a tape measure and an internal rule…

Is it really that involved or is it just that my Arithmatic is that poor?

Prismatic Co-Effiecient
Yes it is that complicated. If I had to describe Prismatic Co-Effiecient in a sentence, I would say: The Prismatic Co-Effiecient is a term to describe how fast a boat gets wider or remains narrow.

I too have read a lot about that stuff and know very little. The bottom line is every move you make in boat design has several trade offs in another direction. Make a boat narrower for example and it also sinks deeper. Paddling is more fun.

Prismatic co-efficient is complicated to compute but the concept is easy to apply. The widest part of the hull, below waterline shapes the prism, the waterline length determines the prism’s length. Basically, the less of that geometric shape a hull fills, the more efficient it is, except that if the stems get to fine they cut down through the transverse wave at the bow and limit speed.

not that complicated
It depends on how math adverse you are. All that is required is a little multiplication and division.

If you want a relatively quick way to figure out the prismatic coefficient of a boat, first paddle in some scummy fresh water so you get a good line of crud at the waterline.

Bend a piece of heavy solder over the widest point of the bottom of the boat, mark the waterline on the solder. Without bending the solder lay it on a piece of metric graph paper. Mark a straight line between the waterline marks, trace the solder. Count the squares contained by the lines. This is your cross-sectional area. Now measure the length of your waterline in centimeters. Multiply the two. Convert this using one cubic centimeter = one gram.

Weigh yourself holding your boat. Divide this weight by the weight above. That is your prismatic coefficient.

For a more complete explanation of what you just did:

Take your boat and imagine another that has the same shape as the widest point of your boat, but does not taper at all at the ends. It is just a long rectangle with a cross-sectional shape as the widest point of your boat.

This is the “prism” in “prismatic”. You want to know the the displacement of this prism. This is the area of the cross-section at the widest point times the length of the waterline. A cubic centimeter of water weights about 1 gram (for freshwater this is exactly 1, saltwater is a bit different)

The prismatic coefficient is the displacement of your boat divided by displacement of this prism. The displacement of your boat is the weight of your boat, plus you, plus all the gear.

If you have a barge that is not pointed at the front, it will be very close in shape to the prism so the ratio you get when you do the above division it will be nearly equal to 1.

As the shape gets pointier of “finer” at the ends the ratio gets smaller.

It has been found that for any given speed for a boat there is an “ideal” prismatic coefficient which will be the most efficient - usually something around 0.5 to 0.6.

In other words the displacement of a boat should be just over 1/2 the displacement of its “prism”.

The next question is how does the average boater use this information. If you have a boat you like, there is probably not much point in trying to figure out its prismatic coefficient. Unless you want to design a new boat or start making comparisons with boats you have not tried. For example Sea Kayaker Magazine uses the prismatic coefficient and other parameters in their kayak reviews to perform drag predictions.

You can go to Matt Brozes’ spreadsheet to use this information to get speed comparisons with other boats:

I thought I might design a canoe
There’s a boat I want that AFAIK does not exist.

How hard could it be?

There’s plenty of software available. Much of it free.

But it comes with all sorts of terms like Primatic coefficient, center of buoyancy, center of lateral area, etc. What’s all that?

So I got ahold of John Winters “The Shape of the Canoe”. And I read everything else I could find including a bit of history.

After a while I realized that the more I understood the less confident I was that I could design a boat that would make me happy. Indeed it seems many designers keep tweeking their designs for years.

I had visions of stacks of unloved prototypes rotting in my back yard.

Nope I’m not going to design a canoe. Too many boats that I want to paddle as it is.

I will raise my glass and toast Mr. Winters, Yost, Scarboro, Henry, Jensen, both Krugers and many others for their efforts.

It ain’t easy what they do.


Nicely put - that actually makes sense to me physically - thanks.

I am less confused now and think I will join TommyC1 in not designing any boats now!


A link

Bald, sterile, bipolar
Those are the least of the symptoms that will afflict anyone who tries to understand this stuff.

Just remember, all the people who claim to understand this jabberwocky nevertheless design, recommend, paddle and/or try to sell to you wildly differing canoe and kayak hulls.

It is more important to like a canoe with your eyes, skin and muscles than with your mind.

Hey I resemble that remark NM