# Flat bottom planing hull Sailing boat theory sought

Discussion in 'Boat Design' started by PeteK, Oct 7, 2020.

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1. Joined: Oct 2020
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### PeteKJunior Member

Hello Pete here from SW Western Australia,
I could really use some pointers to the mathematics and theory of planing hulls, windsurf and water skis.
I'm endeavoring to design and build a sailboat with an outrigger to replace the heavy keel.
What I'm looking to understand is:
1. Given that something like a water ski cannot support a person when not moving, what is the maths that dictates its capacity to support weight at speed/surface area?
2. Then knowing that, how much weight/pressure/side force is generated by sail per m2/kts wind?
3. I think you can see where I'm going with this - remove say 350kg keel (20ft/6m yacht) what size planing outrigger will be needed to keep the yacht upright and replace the righting effect of the keel?
4. Ref pt. 2 Obviously side pressure on sail will increase with wind speed, as will yacht's speed, but so will lift on "ski" outrigger with yacht's speed to resist the side force
5. C of G will be raised but balance achieved by "proa" or "catamaran" effect of distance from C of G to length of outrigger

Quite happy to study math formulas of above (don't need/want to be spoon-fed) and would much appreciate pointers from knowledgeable designers.

Many thanks,
Pete

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### bajansailorMarine Surveyor

Welcome to the Forum Pete.

Have you seen the Harry Proa site?
HARRYPROA http://harryproa.com/

Rael Dobkins has quite a few proa videos on YouTube -

Are you planning on designing and building a main hull as well as the outrigger, or could you use an existing hull?
Will the main hull be approx 20' long?
Do you want your outrigger to be on the leeward side or the windward side of the proa?

Last edited: Oct 7, 2020
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### fredrosseUSACE Steam

As you probably know, the overturning moment caused by the wind force on the sail (sail force x effective height of force) is counterbalanced by the boat keel weight, (keel weight x effective horizontal distance from keel weight to center of buoyancy when heeled over). Add to that the dynamic forces contributed by rudder action while underway. Also relevant, as the boat takes on list from the wind/sail, more and more spilling of the wind force occurs, reducing the tendency to capsize.

With an outrigger serving this stabilizing function, the upward buoyancy of the outrigger x the moment arm of the outrigger (to the boat hull center of buoyancy) the moment arm here is generally long (compared to the moment arm of typical lead keels). In this case the hull will act more "stiff", and will not list as much as it would with a conventional keel, hence the spilling of sail effort will be less pronounced. Design should consider this.

The outrigger will not only have buoyancy, but will have dynamic lift (and could plane) at higher sailboat speeds. As I understand, this is the main part of your inquiry. However I think that the conditions where the boat is essentially static, with a wind gust perpendicular to the boat centerline axis, will dictate that the outrigger have sufficient buoyancy to maintain stability under this condition.

As far as dynamic lift for a planing hull, the crude fundamental in one dimensional flow is that the dynamic pressure of the hull/water interaction is equal to 1/ 2 x Fluid Density x Velocity Squared (this equation is dimensionally consistent, and works in any units system) . Multiply that by the submergence (area submerged perpendicular to the outrigger hull axis) of the planing hull, and you have the dynamic uplift force. Add to that the buoyancy due to displacement of the outrigger in the dynamic condition.

There is some loss of this lift in multi dimensional flow around the outrigger, applying an efficiency factor "K", similar to the coefficient of lift for wings, having a value less than unity. A wide outrigger would have a "K" approaching unity, a skinny outrigger has a lower "K". While this information is the fundamental beginnings of equations for your study, there are many additional considerations. The long skinny outrigger will be less efficient at lifting force, but far better at another important consideration, which is the drag associated with the outrigger hull form. Compromise is required here, and at this point one needs to get further background in Naval Architecture, Good luck going forward (pun intended).

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### fallguySenior Member

I can spell it out for you easier than answering...which is outside my credentials.

proa

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Fredrosse showed the equation for force when exerted on a surface perpendicular to the motion of the fluid.. Rho times velocity square product divided by two is the impact force. Planing hulls do not meet the water pressure head on. The hull will need to have an angle of incidence in order to generate any force at all. Say that the boat has its nose up at ...perhaps six degrees. The upward force is far less than the head on force. The upward or Y component of force appears to be described as tangent of the angle. At 6 degrees tan= 0.1051 insert the Tan into the equation to get a wild idea of the upward force.

Just for giggles lets say that the boat is moving at 1o MPH. That is about 14.7 feet per second. The weight of fresh water is about 62.4 pounds per square foot and the mass is then about 1.9 slugs. Plug all that into the original equation including tangent figure and you get something like 21 pounds per square foot. If your boat weighs 1000 pounds you need about 47...48 square feet of surface...........but wait it does not work quite as neatly as that. The maximum pressure on the bottom of the boat in planing mode is at the stagnation point....right where the water first hits the bottom. There is progressively diminishing pressure behind the stagnation point. so maybe we'd need more lift surface. How much more is the mystery that borders on mind boggling.

Alas that is not the whole story either. If your boat is a sailboat, you will not be planing all the time. Chances are that you will spend more time at displacement speeds instead of planing speeds. In that case your design needs to account for that reality and the transom of the boat needs to be at or above the waterline to avoid unwanted drag. so that means that the bottom aft of the deepest part will angle upward or curve upward from it's deepest point to the surface of the water. well that just messes up the whole deal. In order to plane you have to have some angle of attack (incidence angle) for the bottom if it is to develop some dynamic lift forces. That is why you will see planing dinghys that have a bottom with deepest point, well forward of midships. The idea is to diminish the angle of the aft buttocks. I wish that I knew enough about these things to manage a capsule answer. I fear that there are no simple answers.

We do have several very competent members who may weigh in on this subject with better authority than I cold hope for. If there is a bottom line here, it is that you need to do some serious research about the subject, keep an open mind, and don't pay much attention to amateurish opinions.

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### PeteKJunior Member

Hull will be about 20ft/6m, using an existing TS
Outrigger on leeward, or maybe both (yes I know it will become a trimaran!) or with add/lose water ballast when on windward tack
My idea is to re-purpose old GRP yachts which have lived longer than original builders/owners expected, with something fun and go-faster.
Although I don't expect to become the next Roger MacGregor, this may have saleable commercial application, so before putting a lot of detail up on this public site, I'm hoping to refine the design to a point where it may be able to be patented/licenced.
Cheers,
Pete

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### PeteKJunior Member

Wow! Thank you for your detailed response fredrosse. Exactly what I'm looking for. See my reply above to bajansailor, detailing a little of what I'm intending. If I can successfully put your formulae into action (without spending 3 or 4 years studying for a Naval Architect degree at university) my plan is to use a bit of good old Aussie ingenuity and give-it-a-go, using some recycled and repurposed marine parts, and basically test the theory. If I'm totally wrong about it, then probably the worst thing that will happen is that I'll tear up a couple of grand or so, and get very wet!
Cheers,
Pete

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### PeteKJunior Member

Yes, thank you messabout. I am certainly aware that the maths behind this are complicated - particularly for those of us (me) not trained and or competent in this specialised area. As I said in my response to fredrosse above, I'm really just hoping to get enough basic theory right to build a low cost prototype to test the idea. If and when I get past this stage, I'll probably seek professional assistance.
Cheers,
Pete

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### PeteKJunior Member

With yours and Fredrosse's help, I have got to this (not very scientific or mathematical) point: If the 300-odd kg/700lb keel is removed from a 20ft yacht and replaced with a proa/ourigger with a moment or leverage arm of approximately 3x that of the keel, a 45sq ft/4m2 float will support about a tonne@10mph/8.5kts. So for mine to work, I probably only need to resist about 1-200kg/220-440lbs at 7-8knots (weight is not static and will increase with wind and boat speed) which will probably be acheivable with a buoyant proa of around 1 - 2m2/11-22ft2 on a 2.5 - 3m/8-10ft arm.
This is very helpful, as the next stage is to test this theory using low-cost 2nd hand parts. As I said before it will probably be over engineered and can be controlled by the direction relative to the wind, and the amount of tension put on the sail/s through the helmsman's choices, or he will get very wet!
Thank you kindly for your valuable assistance.
My next question , which I'll put up on another thread, is: Given that this isn't a new hull design, nor is it going to exhibit a lot of design aesthetics, where should I look to patent/register my design concepts. (I've seen the Designer's Copyright threat by DCockey2011) maybe nothing's changed since then. If there is no such protection practically available, I'll just build the prototype, see how it goes, and put it out there to seek eoi from interested designers/builders??
All the best,
Pete

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### bajansailorMarine Surveyor

With all due respect Pete (I am trying to be polite here), I don't think that you need to worry about trying to patent your design / invention, as I think that the odds are that very few , if any, people would be interested in blatantly copying it anyway.

Although if you do build a new proa designed by yourself, and it proves to be a runaway success in every way imaginable, then yes, folk will want to copy your idea - but if they found a slightly bigger hull somewhere and re-built it in a similar fashion to what you did, then it would still be different to yours, and hence even if you had a patent I doubt that any legal action taken by you would stand up, as it is obviously very 'different'?
Be aware also that the cost of patenting anything is reputed to be eye-wateringly expensive - patent lawyers do not come cheap.

Do like Dog Cavalry on this Forum - he is building an improved version of a Hickman Sea Sled to his own design, and he would be very chuffed indeed if others want to buy copies of his plans from him when he proves all his skeptics wrong.
But if others simply try to copy him, well, isn't there a saying that goes something like 'imitation is the most sincere form of flattery'?
If they do try to copy him, they will have do a lot of work themselves, to get where he has gotten.
If you can subsequently sell your idea / methodology for the price of a few beers, then I think you would be doing very well.

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### fredrosseUSACE Steam

"Fredrosse showed the equation for force when exerted on a surface perpendicular to the motion of the fluid.."

A clarification here; I am referring to a projected surface, " the area submerged perpendicular to the hull axis". That does not intend to imply that the surface is perpendicular to the relative motion of the fluid.

As an example, say the hull exposed to water (wetted surface) motion is 1 unit dimension wide x 1 unit dimension long, and tilted 6 degrees from the horizontal. This results in a projected area (perpendicular to the flow direction) of about 0.1 units of area. The surface however is not perpendicular to the flow, it is tilted about 6 degrees from horizontal in this case.

My apologies for not being more clear in my statement.

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### gonzoSenior Member

What is your background on math and physics? The theory behind that is really complicated. Would you be satisfied with the basic concepts or really want the math? It is the equivalent to an engineering degree.

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### PeteKJunior Member

Yes Gonzo, I think you're right. And what I've got now from replies in this forum, is enough basic theoretical information to warrant going ahead with trying out the concept, and that I'm near enough in my ideas to have a go.
I do appreciate the valuable input I've received

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### PeteKJunior Member

Thanks Bajansailor, you've confirmed what I thought, and what was posted here about 9 years ago. Sorry if I sound up myself, just being a bit cautious about putting the idea out in the public domain, without some consideration of the possible outcome.
When I've moved forward with the build and sea trials, I'll publish the results on this site.
Kind regards, Pete

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