Mathematical definition of Boat planing

I am a student doing some preliminary research about boats, with a special interest into planing. However, I have yet to come across a mathematical description of this behavior. Can anyone help me out?

 

I'm sure you'll get differing opinions on this, as I believe there are more than one definition out there.

For instance, a recent article in Professional Boatbuilder (No. 85 - pg. 78) states "in rough terms, a boat is planing when it's traveling faster than its transverse stern waves, which occurs roughly at a speed in knots of 3.4 times the square root of its transverse beam in feet. Full planing is about twice that speed..."

This seems like a rough estimate, but I can think of exceptions having to do with weight. A very light "skimming" hull with beam X could be on a full plane at the same speed that a heavier vessel, also with beam X, is not planing at all.

I don't think there's a clear definition, but I'd like to hear other ideas...

 

There is no mathmatical definition of planing. There are mathmatical formulae to calculate planiing AFTER you have decided on the definition of planing that you like. There is no clear consensus on exactly what constitutes planing except at higher speeds where everyone agrees that the boat is planing. The transition region from displacement to full planing is where the disagreements occour and this varies a lot with different hull types.

 

One opinion

Often the onset of planing is defined as when the boat's center of gravity moves up (presumably due to dynamic lift), but when "full planing" is acheived is another issue.

 

Your actual question

The Journal of Ship Research (www.sname.org) has numerous papers on planing. Other papers are in Marine Technology (same source). SNAME is also publishing a CD of collected small craft papers, some of which will involve various aspects of planing.

Much current interest is focused on Zarnick entering wedge techniques for planing. One site for this is http://www.shipmotion.com (as well as the SNAME site).

 

There is no exact definition, particularly after you enter the semi-planing stage. There is general agreement that at planing speeds the hull is "over the bow wave". I usually assume it is about three times the hull speed.

 

gonzo says: "I usually assume it is about three times the hull speed."

Which equates roughly to a Froude number of 1. Clever things, Froude numbers....

 

Saildesign: do you agree that the boundaries between displacement, semidisplacement and planing are arbitrary? I think that a twenty foot boat at fifty knots is planing without question. However, how about at ten knots?

 

Gonzo - the boundaries are decidedly vague....
No-one has defined the limits of each mode to my entire satisfaction, and I think it is more a matter of observation of behaviour of the boat that makes the decision.
My 2-cents.
Steve

 

OK, we all know that in practice that the transition point is not clearly defined. However if you take the definition of going faster than the speed of a wave of the same length of the hull ie the point afterwhich the hull will climb over the bow wave (hull speed) it can be defined.

Based on the speed of a wave in deep water of c=sqrt(gL/(2 PI)) g=acceleration due to gravity, L = wavelength and substituting in L for LWL you get the hull speed definition. Watch your units here.

(Don't ask me to derive all the above as it has been several years since uni and I am working from memory of my ocean engineering/oceanography classes)- especiaaly the first eqn. (Note this is a deep water eqn)

As far as a mathematical planing theory, probably best to look at flat plate planing as a starting point for the forces/pressures involved. A number of sources should have something on this including most classical naval architecture texts and some others such as Peter Du Cane's "High speed light craft" or Principles of naval architecture.

Might get you pointed in the right direction anyway.

Brett

 

Entering wedge theory

Entering wedge theory is probbaly the most current technique. Ths is a stripwise approach to developing the forces based on the added mass of a wedge entering the free surface.

See papers by Martin, Payne, Zarnick, and recently by Troesch and his group at U. Mich.

Other researchers have used vortex lattice approaches.

 

A paper question...

From someone that never went to University...
Where do I start searching for various intresting published papers about boat related research?

I guess SNAME and the Uni's themselves could be a startingpoint, but I don't have access to SNAME and dont know where to start looking/searching when it comes to published uni. papers...

--------------------------------------------------------------------------------
So much to learn, so much to know and so much I can't find

 

Brett defines planing but needs to accept a definition before defining it. This is not wholly satisfactory.

There is a non-mathmetical explanation at:

http://www.woodenboatworld.com/boattalk.asp?contentid=135

If you can get access to the "Ideal Series" published by MotorBoating magazine years ago, there is a whole series of articles on the subject.

After reading all of the material available, there is still no universally agreed on definition. So what? No definition is needed to understand the phenomena or to design planing boats. In fact, if any one of the most popular definitions that I have seen is taken as the whole story, then the creative processes will be short-circuited.

Many will start with a definition of "hull speed" and go from there. That is the worst place to start since a full planing hull has little in common with a boat designed to increase hull speed and is usually absolutely awful in the lower transition speed range. That is why (along with heavy, low power engines) all early attempts at high speed resulted in long, narrow boats to raise the hull speed.

I quit worrying about just what defines planing and when it occurs and work on boats to run at whatever speed is desired. Being an amateur in this field, I don't pretend to follow all the papers published by Savitski and other researchers, but that does not keep me or many other amateurs from designing small boat hulls that work.

Tom Lathrop

 

Tom,

Most people can tell the difference between a displacement type hull and a planing type hull by simply looking at them. A planing hull reaches speeds where the weight of the vessel is supported by dynamic rather than static forces.

Hull speed is the generally accepted upper end limit of a displacment craft beyond which the power requirements become excessive. (Not to say it cannot be done without effort) Planing craft exceed this limit going over the hump and into pre planing regeime and then to full planing. Why not start here? Hence I defined this point.

As far as planing mathematics is concerned, a flat plate is the simplest and most basic concept available however far derived it might be from a real world boating application. Hence my suggestion as a starting point to the original poster who is looking for a mathematical description and not a design solution. There are plenty of ways to go from there.

Brett

 

Where do semi-displacement boats fit in?