rick,

thanks for those charts. very interesting.

i'm a little confused though. consider the case of a 1.5 ton displacement in the 8-10 knot speed range. the optimal length decreases from 16.5 m to 14.5 m as the speed *increases*, while the beam and draft both increase to compensate.

my understanding is that to optimize for low speeds one minimizes wetted surface area, while for high speeds one minimizes wave drag, and that one generally has to trade one for the other.

a shorter, beamier, and draftier hull for the same displacement is going to have less wetted surface area. i would think then it would have more wave drag. the "hull speed" is lower, the maximal cross-sectional area is bigger. yet your charts say it has less overall drag.

could you please explain in what other ways the hull shape has changed to make it have less drag at a faster speed?

thanks again,

ben

> That design I posted was a study for someone else and is still in
> development. The comments made about it so far have already provided
> some progression that would improve it. I was still playing around
> with the overall beam. As shown it was 3.5m centreline separation.
>
> There has to be a starting point for the first iteration. I have
> produced some charts that I previously posted without much
> explanation. Here is a link to one for a proa:
> http://www.rickwill.bigpondhosting.com/Proa_Chart.jpg
> These charts provide the principle hull dimensions for the minimum
> resistance displacement hulls for various speeds and displacement.
>
> The particular rectangles drawn over the charts show the limit of
> operating regime for proa hulls for a 2t displacement with a 25/75
> share of displacement under static trim. The overlaid ellipse is
> intended to show the most frequent region of operation for the two
> hulls.
>
> My aim with these charts is to give an idea of how the hull would
> ideally morph to always be close to the minimum resistance. For this
> particular case you can see that a 16m LWL would suit the lw hull
> through quite a lot of the range. If the target was for higher speed
> then the length is going to come down. On the other hand the LWL of
> the ww hull should be reducing as speed increases; implying there is
> advantage in having rocker on the hull. If you decided you would
> like it to be really in the groove with 25% of the displacement on
> the ww hull then that hull could be less than 10m LWL.
>
> The sensitivity of drag to dimensions may not be as significant as
> you expect and the hull coefficients also change considerably. They
> are based on round sections but not much different for rectangular
> sections.
>
> Lighter hulls that can go fast planing will become a factor and these
> charts do not apply to that condition. The speeds to get a 2.5t
> slender hull planing are going to be in excess of 20kts but the
> unloaded ww hull with a flat bottom would have substantial planing at
> lower speed.
>
> The charts are aimed to getting basic dimensions into the ballpark.
> There are other factors like method of construction, longitudinal
> trim, sea-keeping, useful space and so on that might be more
> significant in getting the best outcome than achieving minimum
> resistance hulls.
>
> It does not take long to generate the shape of the minimum resistance
> hull for a single set of constraints like displacement and maximum
> length. It gets harder to develop a shape that might morph the right
> way. Producing polars of the final shape takes longer still and
> those polars only include the things that I consider significant. I
> can check if longitudinal trim is going to be an issue but so far the
> model does not automatically correct for it.
>
> A reason I posted the original image was to make a point that the ww
> hull did not need to be always shorter. One of the sites that Todd
> referred to has a proa with identical hull shapes. This could be
> desirable for simplicity.