Power to push a Hull

[Spuds]

I’ve been writing a program that will approximate the speed of a model boat based on a given engine, prop and hull. The hulls involved are monoplanes, Hydroplanes and Catamarans and generally obtain speeds in the 25-45 range. These model boats are typically 2-3 feet in length and up to a foot in beam.

Anyway I have been able to calculate the prop shaft RPM, given a specific engine and propeller, based on propeller power absorption vs engine output. What I would like to do is get the speed this will produce. I know the rpm, pitch, diameter, weight, wetted area, etc of the boat but am looking for suggestions on good formulas to use. I’ve been trying one that says Power = Rho * V^3 *Cd * S where

Rho is the density of water
V is the velocity
S is the wetted surface area
Cd is the drag coefficient

But have not been able to determine a range of Cd of the various hull styles. Once a hull planes what are the major resistance factors, water resistance, air, wake and how do you determine the power that is lost to those.

Thanks for the help and suggestions.

[Brian]

Check out the tunnel hull software in the software section of www.boatdesign.net.
You can check Dave Gerr's book on Propellers and his book Nature of Boats.
Generally you have two types of water resistance which are fricitional and form. Form includes wavemaking, edies, etc.
These two are added together with a correlation allowance to get water resistance.
Air resistance can be added on top of this but is usually neglected, but for your case may have some significance. Principles of Naval Architecture has a formula for air resistance.
Lots of software are available for calculating hull resistance but your operating in such a high speed length ratio that you will probably be out of thier range of applicability.
You can check out the work of Daniel Savitsky, that may be helpful to you. His work is regarding planing craft. Hullform calculates with Savitsky's method.
Hopefully someone with hydroplane experience can help you with more specific information.

[Jimboat]

Brian is right regarding the complexity of interactions of hydrodynamic lift & drag, and aerodynamic lift & drag of tunnel hulls. The Tunnel Boat Design Software simplifies the analysis with some quite detailed modeling of the interactions at all velocities in your speed range. The software is accurate for all sizes of hulls. Check it out. Call me if you have any questions.

[Spuds]

Thanks for the input, its helped me look into a few areas. The tunnel hull book looks interesting, what formulas are included with the book and are they applicable to RC boats and Mono, Cat, Hydro varieties?

Back on my original post I put in an equation, does anyone know where this comes from and is it proper for planning hulls? I can determine Cp from testing but wanted to understand more about the equation.

I’m also considering balancing the know power at the prop against the energy used to move X pounds at Y velocity plus the energy to push against the hull resistance at Y velocity (iterate to find the balance point) based on Savitsky equations. Would this be a proper approach?

I’ve looked into the Crouch formulas but they did not appear (at least the constants) to be applicable in this application.

Thanks

[Jimboat]

The Secrets of Tunnel Boat Design book has all the formulae for calculating Lift and Drag for all tunnel hull components, both aerodynamic and hydrodynamic forces. Also shows how to do dynmamic force balances. This is important, since the forces of lift and drag from hydrodynamic and aerodynamic sources change as the hull changes velocity - it's not a constant or linear relationship. Also shows Cd's and Cl's to use for all parts and designs of hull configurations. Because the algorithms are developed from first principles and specifically for powercats, they are valid for all velocities and all sizes of hulls, from R/C's to heavy offshore cats and everything in between.

The Tunnel Boat Design software uses the same formulae and analysis techniques, but considers many more influencing factors -and of course, does it all allot faster.

Check out the input data that the Tunnel Boat Design software uses at the design controls web page. You can also check out some of the Performance Analysis output and graphic performance outputs at the webpages.

These pages should help you some