Is the ratio of energy required to propell a boat: the hull area linear

I know this is a tricky question, so let me try to make the parameters really simple.

Assume you have two hulls which are completely rectangular, are both solid foam, of the same density, with no fiberglass, the same height, shape, width, and the only variance is length.

Assume that hull A is 20 ft LOA, 4 ft beam, weighs 100 pounds, and displaces 40cubic feet of water.

Assume that hull B is 40 ft LOA, 4 ft beam, weighs 200 pounds, and displaces 80 cubic feet of water.

Would hull B need twice as much energy to get it moving at the same speed as hull A?

Is the amount of energy required to accelerate the hull to a given speed linear to either the displacement, surface drag or length of the hull?

Thanks!

 

It depends on all of them.

 

In the example provided:
surface drag and displacement are linear.

Does that mean, that the energy required to propel the boat will also be linear?

 

40 cubic feet weights (displaces) about 2500lb. Surface drag depends on shape and not only on the measurements of beam and length. A longer hull of square ends will have less wave making resistance in proportion to its displacement. You can't reduce everything to a couple of parameters. Also, power is not linear to velocity.

 

/sigh

I just want to know if it is more or less energy efficient to go with a big boat vs a small boat.

I want to do a solar powered RC boat project. The amount of energy I can generate goes up linearly with the size of the boat. The question is... does energy consumption go up linearly with the size of the boat. Knowing this will help me determine the size boat I should build.

 

I want to build an RC solar powered catamaran.
The amount of electricity the solar panels generate goes up linearly with the length of the boat.
A boat which is 2ft X 1ft can generate 30W of energy.
A boat which is 4ft x 2ft can generate 120W of energy.

Will a 120w electric motor, propel the larger boat, faster than the smaller boat using a 30w electric motor assuming the hull shapes, and all dimensions are exactly 2:1?

Basically, should I build a 10 ft boat, or a 1ft boat, or does it not matter?

 

It absolutely matters. Physical systems do not scale up linearly.

 

Find and download Freeship. It's free. You can design a hull shape and double the length and see what the expected results could be. The load can be adjusted by adjusting the draft.

You can move a tanker with your little finger if there are no other forces, ie wind opposing. It's just the rate at which you make it happen.

You can also float the same tanker in 1mm of water... think about that one

Longer hulls usually are faster than short hulls because of the hull speed.

Play around with it first before you assume things, it's not that simple and it can be very disappointing and expensive and and and...

"Boat" is a four letter word if you screw it up

 

Don't miss the boat on this one. You may be excited to get the prop turning and the solar panels up and so on, but the success for this project is going to be how efficient your hull(s) will be.

If you build a drogue and call it a boat, no amount of power is going to get it moving well, if you have a decent shape hull then you need a lot less power to get it sailing quite well.

Mind you, with a big enough outboard you can get a dustbin to plane...