Scaling Factors

Hello All,

I'm trying to make sure I understand scaling factors and need a little help.

If I scale a displacement hull down to 1/2 size, from length X, displacement D, power P:

Length = X/2
Displacement = D * (1/2)^3 = D/8
Power = P * (1/2)^3.5 = P/11.3 (is this correct?)

So if the original hull goes 8 kts at 100 hp power input, how fast should the half-sized hull go (approximately) with 100/11.3, or 8.8 hp?

Many thanks.

 

Unfortunately for powering it far more complicated. The wavemaking resistance is a function of Froude Number, the skin friction drag is a function of Reynolds Number as well as surface area. The displacement will be reduced to 1/8 th of the original.

 

Thanks John, and understood.

I would agree that skin friction drag would be a big variable if I was scaling down to a 1/10th size or a similarly extreme scale. But since I'm only cutting the scale in half, keeping all dimensions/shapes constant, I wouldn't expect skin friction to have such a disproportionate effect.

If I get accuracy inside of 20% that'll suit my needs.

 

1/2 scale is extreme. The laws of mechanical similitude apply regardless of scaling factor employed and yes, it does seem disproportionate, because it is, none the less the law still applies.

 

Look at Larsson's 'Principles of Yacht Design', they discuss scaling factors from Barkla for sailing boats.

If we are talking about powerboats, scaling factors are in my paper:
'On the Application of a Parametric Method for Design of Planing Craft'
http://www.powerboatsymposium.com/allcpbspapers.html

But yes, scaling with length factor of 0.5 is extreme, I would not recommend that!

 

Sorry guys, but I would have to disagree about the 'extreme' aspect of this plan. The scaling is only to model hull performance and contemplated modifications to the full-sized boat. It won't be a functional boat itself - just a rough model for testing.

I think the equations in my first post indicate that I have a rudimentary understanding of the laws of mechanical similitude, but thanks for pointing them out anyway.

As I understand it, a half-sized model should reasonably accurately reflect the full-sized hull. If I was to try to extrapolate a 1/10 sized model to the full-sized, the other factors such a Reynolds Number and surface tension would become difficult to model and introduce considerable error.

Further research suggests the Froude's calculations would predict that the full size hull speed would be equal to the scale model's hull speed multiplied by the square root of the scale factor. Therefore, if a half-size scale model runs 6 kts, the full-size model should run about 6 x sqr rt of 2 = 6 x 1.41 = 8.48 kts.

The boat is a power catamaran intended to run in displacement mode.

 

OK, now I understand what was the purpose of scaling.

Speed - not really, because of many factors related to propulsion system, etc. What You can do is to identify resistance curve from results of sea trials for 1/2 scale test boat, and then re-calculate the resistance into full size craft using same method as for model testing.