Calculating hydrodynamic Lift?

I was wondering if there are any formulae for calculating the lift produced by the motion of a hull through the water. Mainly with respect to planing. I gather beam is more important here than chord the same as with a wing. Given a rough area and Angle of attack with respect to the surface of the water the velocity of the boat and its displacement is it possible to work out how much lift will be produced. I have done some calculations using this formula

L=0.5*p*v^2*A*CL I just guessed the CL as 0.1 and used density of water for p but im not sure if this formula applies to hydrodynamic lift.

I think planning hulls have wider stern to enable the boat to keep on planning as the bow lifts out the water. But to enable the boat to plane easily does it need a large flat area at the front and what is the most efficient hull shape for generating lift early on at low speeds?

This would be for use on a model boat which is 1m long and weighs 4kg my calculation showed i could get about 5N of hydrodynamic lift but that is most likely wrong.

Thanks
Alex

 

Although I am not able to provide mathematical formulas for hydrodynamic lift, I will give you a few general principles gleaned over years of experience and careful observation.
Very high L/B ratio boats are generally poor planers (eg catamaran hulls) but can plane initiated at relatively high Froude no's. Depends a lot on bottom shape. Arguably a Tornado cat never planes even though it can exceed 25 knots. However the "Cigarette" power hulls for offshore racing have very large L/B ratios and are fantastic planers. Bottom shape is critical, as is total power available to be applied.
Very low L/B ratio boats plane very early but ultimate speed reached can often be relatively low due to considerable form resistance and substantial wetted surface. An example here would be the Australian scow Moths of the 70's. Typical dimensions were length 11 ft. beam 4 ft 3 inch. (Hard to design a very beamy boat with low wetted SA).
A wide stern and fine bow sections sounds at first an ideal solution, with an expected ability to cut through rough water effectively, and then lift onto the wide flatter stern sections under more power to commence planing.
Is this true then? Well yes, but the handling could be disastrous in some circumstances. There were a number of wide skiff design Int. Moths designed in this manner in the mid 80's, and many were notorious nosedivers off the wind, so were not good performers around the whole track.
The question is so complex that a book could be written, and not all the variables even considered.

 

It's a lot more complicated than that. Loading, beam/length, trim angle all come into play here. Go Google up Daniel Savitsky's work on planing surfaces. Start with NACA Tech Note 4187 (June 1958) so you get the terms, symbols, and concepts down before moving on to the later papers.

 

Just do a search on BoatDesign.net on Savitsky and you get a lot of hits. The information you want may be already here. Savitsky's formulas have been much discussed on this forum.