November 1, 2012

Sizing up is complicated

LIKE MOST OF US, Old Wotsisname sometimes wishes his boat was just a bit longer. And, like others of us, he sometimes finds plans in yachting magazines that would be just perfect if they were stretched out a few feet fore and aft. This is what drives yacht designers berserk, of course. People just don’t realize that you can’t just magically stretch a set of sailboat plans out to some arbitrary length and expect to end up with your dream boat.

Apart from anything else, interesting things start to happen when you vary the size of a boat. The Law of Mechanical Similitude works like this for boats that are similar in basic shape:

If you double the size of a vessel evenly all around:

Length increases by 2 times

Beam increases by 2 times

Draft increases by 2 times

Wetted surface area increases by 4 times

Volume increases by 8 times

Weight increases by 8 times

Stability increases by 16 times

The new boat, rather than just double the size of the old one, would actually be 41 percent faster, able to carry four times as much sail,  be eight times heavier, eight times roomier below, and 16 times more stable.

No right-minded person would build a boat to the new dimensions, of course, but it helps explain why large sailing yachts are so much stiffer than small ones, even if they carry proportionately less beam and draft.

This law also explains why you can’t just take a set of plans for a 25-footer and blow them up 200 percent to build a 50-footer. As a boat gains length, she needs proportionately less beam and less draft because she gains stability so rapidly. The rule of thumb is that large boats are skinnier than small boats, which is why the smallest type of boat, the coracle, is as wide as it’s long — round, in other words.

Today’s Thought
Some people will never learn anything, for this reason, because they understand everything too soon.
— Pope, Thoughts on Various Subjects.

Tailpiece
“Did you find a good math tutor for Johnny?”
“Yeah, he’s great. Even his teeth have square roots.”

(Drop by every Monday, Wednesday, Friday for a new Mainly about Boats column.)

1 comment:

NeonTetra said...

Sounds like you have just given a very convincing argument for scaling up boats!