Planing Hull Hydrodynamics Question

[Big Red]

I know I am going to ask a question that will be a pain in the arse to answer. But, if there is someone out there who would like to share, it would be greatly appreciated smile.gif

How do you, mathematically, express the relationship between a planing hulls speed, its surface area, angle of attack and the horsepower required to make it all happen? Well, they are the factors involved as I see them. Might be off course there, let me know ok smile.gif

I guess thats a question for one of the forums resident designers/NA's. I have looked around the internet, but I haven't found anything that in depth. I would read up on it if I new where to look. Recommendations for literature please?

Cheers, Red.

[Tom Brady]

A while back I posted a question that sort of hit on the same information that you are looking for. Your question ask it better. My question was: If two planning boats of the same design and construction were built. Flat bottom for simplicity. Both boats weighing the same. One 5' wide and one 6' wide and a little shorter to keep the weights the same.. Which one would plane with less power. Which one would get better gas mileage? The question was triggered when I was studing Bolger's Dakota design. The Dakota is a fairly narrow boat and that was what triggered the question. :confused:

[Tom Lathrop]

Red,

You are part way there. I am no expert on this stuff, but have learned enough to get me in trouble. If you have the speed, wetted surface area and trim angle, you can get a coefficient of lift. The lift will then be equal to the coefficent C x area A x speed V squared.

To get the HP needed to make this thing plane at speed V, you will need to know the bottom loading in lbs per sq ft. If the load goes up, so must the trim angle go up to generate the extra lift required by the greater load. Obviously the greater load and trim angle will need more power to generate the extra lift at the same speed.

Other things are also important, like the aspect ratio (beam/length) and angle of V in the bottom. Higher V angles need more power and higher spect ratios are more efficient.

That last one answers the other question about the longer or wider boat. In planing boats wider is faster. This is the reason for the fast speeds of stepped hulls. They use multiple "hulls" of very high aspect ratio, often much greater than 1.

There are formulas from Crouch, Hacker, Keith, Burgess and others that give an approximate answer for "normal" hulls. The best known is Crouch's which is: V = Crouch constant C divided by the square root of Weight over shaft power. The constant varies with the type of hull from about 180 for small runabouts to 250 for three point hydroplanes.

There is a lot to learn.

[mmd]

Red; you ask a question that can be posed in one sentence, yet to do the answer justice, you require several textbooks and a few technical papers. A basic equation describing the forces acting on a planing surface is too simplistic to be useful, and the multiple parameters to answer the “what if’s” such as deadrise angles, warped bottoms, steps, plate venting, etc. would take a long time to reference and type out. To be quite honest, and I hope not too mean, I don’t have the time right now to do this. I’ll leave you with two suggestions, though:

One:
Consider evaluating a planing hull design in discrete segments, then apply the data found by these processes into a cohesive whole. Forces acting on a planing hull can be broken into:

Hydro- and aerodynamic forces of skin friction, wave-making drag, appendage drag, and wind friction.

Lift and drag associated with a planar form moving through a fluid.

Dynamic stability of a planing hull underway.

Static & dynamic loading on the hull.

Two:
Buy Peter DuCane’s book “High Speed Small Craft” (Temple Press, London, Third edition, 1964.) It is a very thorough text on the subject. Bring your math skills. It will answer Tom’s questions, too.

If I get some free time in the near future, I will try to give a bit more specific answer to your questions, but right now I have to work for the guy who is paying me to do this stuff.

[Tom Lathrop]

MMD,

I have Peter DuCane's book, along with some others, and, bit by bit, am learning more about the complex subject of planing. Nevertheless, it is quite possible to gain an intuitive inkling of the phenomena without the necessity or ability to digest the whole thing. If that were not so, the early pioneers like Hand, Farmer and Lord would never have gotten as far as they did, which was well along indeed.

For instance, the relationship between trim angle, weight, power and speed is fairly intuitive and pretty obvious just from observing the behavior of different boats in the transition speed between dispacement and full planing. Likewise, the effect of deadrise angle is also clear from observational evidence.

I don't discount the importance of the full scientific approach but, for most of us a more limited view is adequate to design a pretty good boat. Heck, the design of many, if not most, of the planing boats being sold would have greatly benifited from even this simple approach. Certainly, the boat buying public could avoid much disappointment with their boats if they understood even the most basic facts about planing hulls.

[mmd]

Tom, possibly I have presumed that the correspondent wants the detailed answer. Sorry if I overshot the mark. I remember being very frustrated when I started out doing design work and wanted to know where and how such "fudge factors" as the constant "C" in Crouch's formula was derived. As I have wandered down the paths my profession leads me to, I find that the simple questions get more and more complex when they are looked at closely.

Do "Rule of Thumb" equations belong in planing hull design? Certainly. I just thought that Red wanted something deeper than Crouch's Formula.

For those interested in small speedboat design without having to go the thick text route, I again reccommend Frank Bailey's Small Boat Design for Beginners (A.H. & A.W. Reed Pty Ltd, Sydney, Astralia ISBN 0 589 50203 4). It is clear, concise, and easily followed with only high school math.

[Tom Lathrop]

MMD,

I, for one, really appreciate your posts on the forums, even if I have to study them a while. I do doubt that the forum is a proper place to gain intimate knowlege on any difficult subject. The internet forum format seems to foster confusion even on simple problems since the question poser often has no way to sort wheat from chaff.

This case is one where we have assumed the kind of answer Red wanted and formulated our answers accordingly. Since he has not come back, which is too often the case, we may never know.

[Chris Krumm]

Try this link to the design forum at Boatdesign.net, and look for post #31 by Dingo:

http://www.boatdesign.net/forums/showthread.php?t=2187&page=3&highlight=planing+hulls

He has a nice Excel spreadsheet for calculating planing hull power requirements based on Savitsky's methods. You'd have to dig into the spreadsheet to understand the formulas.

Go to the second version of Larsson and Eliasson's "Principles of Yacht Design" to find a good explanation and a bit simpler procedure that also looks to be based on the Savitsky method (if you know how to use Excel and understand algebra and trig, you could write your own spreadsheet based on the Larsson and Eliasson material.)

Have fun.

Chris Krumm

[Big Red]

Thanks for the replies guys smile.gif MMD, your right, but I am stuffing as much of the cake in my mouth as possible. I'll worry about chewin' later on smile.gif

What got me thinking about this was a hull I was looking at. I started thinking how modern variable-deadrise hulls differed from this slightly round bottomed, hard-chined 50's style runabout.

I tried doing the maths myself one night. I knew the estimated weight of the boat, I knew the recommended horsepower. I got stuck cause I couldn't figure out the wetted surface at top speed. I knew there was a relationship between those factors, as well as the way they interact with the water.

I think you would apply a vector calculation, ie velocity and angle to work out lift? But the way I see it the water has "give". Is that the Crouch's number? I also am not sure how the applied power affects hull pressure.

I do want the in-depth answer, but what Tom said is just about my understanding. I know it works, I've seen it.

Quote from Tom:

"This case is one where we have assumed the kind of answer Red wanted and formulated our answers accordingly. Since he has not come back, which is too often the case, we may never know".

Sorry guys, I live on the other side of the pond to you smile.gif I generally post in the arvo or at night, so I have to wait till the world turns for you guys to see it. Generally that will be 24hrs later.

In regards to how you guys percieve the question, well that ought to be based on your experince and knowledge. I am prepared to not get the answer I want, but to get the answer I need to hear. Sometimes when you want to learn something, you really aren't sure what it is your asking. So if you tell me something and I don't respond, probably its cause I'm trying to understand smile.gif And its good to hear the same thing said differently by different people, the perspective can help.

Sorting the wheat from the chaffe ain't that hard Tom. I just disbelieve everything until I can prove it myself or corroborate it elswhere. But I have found the advice posted here on WB forum to be sound and solid. Check out Mr. Smalsers threads smile.gif

Anyway, I qualified my original question cause I knew it wasn't a quick answer. If you can post on this at a later date MMD, then that would be good. But I can understand if its too in depth a subject to go into smile.gif

Popeye, not really sure how that relates, care to elaborate?

Chris I will check that link later on. Friday night is pizza night and I'm starving :D

Cheers.

[Stiletto]

Would a planing boat that weighed say 1000 pounds be exerting that 1000lb over the whole bottom at rest? If so, when planing, say (for arguments sake) half of the hull is immersed, would the amount in the water now have double the pressure on it in direct proportion to decreased area, and so on? or would there be a graduated increase over different parts of the immersed bottom?

Anybody know?

[mmd]

Big Red, I'll try to formulate a proper answer later in the week; tight now I have to design a paravane system for a client's boat.

Stiletto, the pressure varies over the immersed hull, with maximum pressure located about 25% abaft of the leading edge of the planing surface. There was a good article on this in editions 67 & 68 of Professional Boatbuilder magazine, I believe.

[Big Red]

Popeye, nothing top secret smile.gif Just interested is all. I do have some frames my Grandfather made tucked under the house, the 50's style runabout.

Cheers MMD smile.gif

[SkipHeck]

This has alot of calculation pertaining to small craft, hope something in it is usefull

http://www.uscg.mil/d8/mso/louisville/WebStuff/comdtpubp16761_3b.pdf

[Big Red]

Ahem :rolleyes: :D