# Froude and planing

Discussion in 'Hydrodynamics and Aerodynamics' started by sandhammaren05, Feb 26, 2017.

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### sandhammaren05Senior Member

This is from an older post:

Faltinsen states.....

"The pressure carrying the vessel can be divided into hydrostatic and hydrodynamic pressure. The hydrostatic pressure gives the buoyancy force, which is proportional to the submerged volume (displacement) of the ship. The hydrodynamic pressure depends on the flow around the hull and is approximately proportional to the square of the ship speed. Roughly speaking, the buoyancy force dominates relative to the hydrodynamic force effect when Fn is less than approximately 0.4. Submerged hull-supported vessels with maximum operating speed in this Froude number range are called displacement vessels. When Fn > 1.0-1.2, the hydrodynamic force mainly carries the weight, and we call this a planing vessel. Vessels operating with maximum speed in the range 0.4-0.5 < Fn < 1.0-1.2 are called semi-displacement vessels."

I disagree in part. For planing I use a Froude nr. based on submerged depth of hull, or on displacement vol.^1.3. It doesn't matter much. With submerged depth, plowing/displacement holds for F≈1 but also up to a higher Froude nr. At F^2≈10 the Kutta condition holds, the flow separates from the sharp trailing edge where the transom meets the bottom (I assume that your trailing edge is squared, not rounded). Up to that point the trailing edge vortex is seen as backflow up the transom. I have verified this scientifically by leaning over the transom to look whilst my son piloted the craft and looked at the GPS. For F^2≈10 the trailing eddy is washed downstream. That is exactly the point where lift sets in, with the running surface as half a hydrofoil. At F^2≈100 the boat plans, buoyancy is negligible, lift carries essentially all the weight (I can write a formula based on Froude nr. if I am forced). F^2≈1000 can be taken as typical of high speed craft.

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### RastapopNaval Architect

What part do you disagree with?

Am I correct in understanding you use the submerged length of the hull, even as it varies with speed?

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### daiquiriEngineering and Design

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### sandhammaren05Senior Member

I estimate submerged depth very roughly.

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### sandhammaren05Senior Member

Thanks for the interesting ref. I was motivated by Prandtl's classic flow visualization of the vortex on the leading edges and trailing edges of the wing in the rest frame of the fluid. Plus Newman's remark in Marine Hydrodynamics that he could see the trailing vortex shed from a flat plate in the kitchen sink. I couldn't, so I looked over the transom. My definition is not going to work for a sailboat with rockered bottom and inadequately squared, sharp transom-bottom edge. It works for motor-powered planing hulls with properly squared trailing edge and straight planing surface.

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### sandhammaren05Senior Member

I use the Froude nr. along with the lift coefficient for any 3D flow, c≈.96alpha
where alpha is that boat's trim angle. I first found this lift coeff. by calculating for outboard race boats. I later found a navy paper with the same lift coeff. It works for the air flow over the deck of a tunnel boat or for the water flow over the bottom of any boat where the flow is not channeled 2 dimensionally. An example where the two dim. lift coeff. c= pi alpha holds is for air flowing between the sponsons under a tunnel boat (half of a lifting surface). An exact def. of planing is impossible, but at F≈10 lift overwhelmingly dominates buoyancy. At F≈3 where lift first develops buoyancy still carries the rig's weight. One might worry about measuring submerged depth accurately but I would not. It's a rough idea, its the important length scale in the problem. Wet bottom area can be roughly the same at low planing speeds as when the boat plows.

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### sandhammaren05Senior Member

I disagree that F<.4 or F<1 has any significance at all, that's all displacement regime, no lift is involved. You cannot understand the onset of lift without taking the Kutta condition at the transom into account. Where lift sets in is a sharp transition (no backflow up the transom), and after that one must use the correct lift coefficient along with the Froude nr. to understand exactly how planing dominates buoyancy. I can write an eqn. for it.

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### sandhammaren05Senior Member

The running surface of a boat on a plan is half of a hydrofoil with the right lift coefficient. The lift coefficient is zero until the backflow up the transom (the starting vortex) is shed so that the flow separates cleanly from the sharp trailing edge where the transom and bottom meet. Prandtl's old flow visualization is worth more than all the wrong guesses about planing. This is why there is no lift when F^2 ≤ 10, roughly speaking.

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### RastapopNaval Architect

You dispute what Faltinsen wrote, while using a different definition Froude number. That argument doesn't hold. You need to pick one definition (that remains constant, i.e. not submerged length of a planing hull), and use it consistently -and as Faltinsen has already chosen one and can't alter it for this debate, you'll need to follow his example if you want to compare with what he's said.

And for your interest, here's an image of flow separating cleanly from the transom at Fr(L)=0.5

And curves for both total lift and dynamic lift for a semi-displacement vessel at Fr(L)=0.96. Even though it's a semi-displacement hull and not a planing hull it still manages to generate 15% of total lift dynamically, below Fr(L)=1.

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### BarrySenior Member

Can your substantiate this comment? That the running surface of a boat is half of a hydrofoil. IF this is correct there must be some calculations in a scientific text somewhere that accommodates this statement.

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### sandhammaren05Senior Member

Any planing surface is half a lifting surface. I think that's called 'hydrofoil' in the trade. I don't restrict the term 'hydrofoil' to the usual useage. A lifting surface is a vortex sheet, a planing surface is clearly that (water below, no water above, flow separates from trailing edge). So it's scientific. Qualitative.

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### Mr EfficiencySenior Member

This is the first thread I've seen where "planing" wasn't called "planning" in the title.

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### sandhammaren05Senior Member

Hello Rastapop, I don't have Faltinsen's tome with me here in Austria. What did he take as the length scale? Clearly, a vertical scale is required since we're talking about gravity and lifting. The important thing is that there's an order of magnitude difference in F^2 for the regimes of lift onset, planing, and high speed. Semi-planing with a rounded aft-portion is a tougher nut than a squared transom, I'm not talking about rockered bottoms and rounded transoms. I agree that it would be good to stick to one scale, but I'll need to see what scale Faltinsen used.

PS I found this definition with B=Beam, F=U/√gB in a paper on the web by Sun and Faltinsen. I recommend a vertical length scale to discuss lift through a height d where displacement V=BdL. One could use V^1/3 instead of d. One can argue that both B and L decrease as d decreases (planing higher at higher at higher speeds) but d is the more direct parameter. Frankly, attempts to discuss planing whilst ignoring the onset of a non-zero lift coefficient miss the main point. Sun and Falt. introduce a 'lifting analogy' in their 3D discussion but lift is the main point, not simply an analogy. In any case, the length scale used must decrease as the boat plans higher with speed. Using B for a flat bottom will fail, using d wil not fail.

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### sandhammaren05Senior Member

PS That picture looks like a simulation result. I would need to see results of real experiments.

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### RastapopNaval Architect

I don't know for certain what he used. I do know for certain that he didn't use the submerged length of a planing hull, because that changes significantly with speed, and is therefore useless.

Length is most commonly used, except when talking about planing hulls. For planing hulls, beam is often used.
There is no point in using any vertical measurement.

It is.
This is good enough for companies and entities that have far, far higher standards, and far, far stricter requirements than you do, and put tens or hundreds of millions of dollars on the line based (partially) on what simulations like this tell them.

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