scaling models

[EDM]

I have built a half scale (12')version of a power boat I would like to build
(24'). It handles nice but I have some concerns about how things will scale up. Are there any "rules of thumb"?

1) If the half size version is traveling at 25mph is that the same as 50mph
on the full size? Will planing speeds be the same?

2) If 2" by 2" strakes are put on the smaller should they be 4" x4" to have
the same effect on the larger version?

3) Have I learned anything by building this smaller version?

4) Is there any good reference material on this subject?

I do know that when I double all dimensions that the boat will actually be four times larger and that the weight is not to scale. This boat was designed as a 24'.

I would appreciate any help anyone can offer. Thanks in advance!

[Raggi_Thor]

1) If the half size version is traveling at 25mph is that the same as 50mph
on the full size? Will planing speeds be the same?

"Hull speed" increases with the square root of length, so if it's 5 knots now it will be 8. Planing speed is different. You will need the same power per weight, basicly.

2) If 2" by 2" strakes are put on the smaller should they be 4" x4" to have
the same effect on the larger version?
Stiffnes increases with the square of the skin thickness.

3) Have I learned anything by building this smaller version?
Yes you hva learned how it handles in a sea, does it plane easily, and so on.

4) Is there any good reference material on this subject?
Many books on boat design will cover this.

I do know that when I double all dimensions that the boat will actually be four times larger and that the weight is not to scale. This boat was designed as a 24'.

If you double all dimensions the boat will be eight times as heavy, and the displacement also. Then you need eight times the power...
I think you can nicrease scantlings with a smaller factor than 2, but the the boat will floathigher.

[RANCHI OTTO]

Scaling metric units where

Lamda = scale

1) Volume = VolumeModel x lamda ^3 Displ. = Volume x Gamma
2) Speed = SpeedModel x lamda^0.5
3) Power = PowerModel x lamda^3.5

[EDM]

Thanks Raggi Thor and RANCHI OTTO for your replys.

What I am most concerned with is, as I see it, there are two problems with my model. First, even though I sized the scantlings at half scale, I could not do the same with the thickness of all material. ie: hull thickness and bulkheads. So I am too heavy to begin with. Also, since my body weight is a larger percentage of the overall weight and I sit twice as tall in the halfscale version, the center of gravity is way off. However, that works in my favor when I scale up.
The strakes I referred to are lifting strakes, should they double as well? I have been playing around with the bottom shape. Should the larger version plane at roughly the same speed as the model?

RANCHI OTTO, in your equations what is ^.....(pardon my ignorance)

[Raggi_Thor]

"^" means "the power of" if thats correct English.
x^2 = x*x
x^3 = x*x*x
x^0.5 = x to the power of 0.5 or the square root of x.

If your half scale model is stable enough for you, then the full scale boat will be much more stable.

[RANCHI OTTO]

thank you Raggi Thor for the "^" explanation.

[FranklinRatliff]

I'll use 1/10th to keep the math simple.

A 1/10th scale model has 1/1000th the volume (1/10th width x 1/10th length x 1/10th height) of the full scale boat and so to be dynamically similar must have 1/1000 the weight.

[RANCHI OTTO]

Not exactly if the weight is referred to displacement in salt water.
The model volume*scale^3 and the displacement in salt water = volume*1.026 (metric units)