# A useless formula (froude displacement formula)

Discussion in 'Boat Design' started by Mik the stick, Jan 17, 2013.

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### Mik the stickSenior Member

The froude displacement formula. Just what does it tell you.

Last edited by a moderator: Jan 23, 2013
2. ### Number4Previous Member

Hi Mik,
You are certainly becoming an expert at useless thread titles,

V/(g*L)^0.5 is Froude Number, Fn, a dimensionless ratio. It was invented by William
Froude, a British naval architect back in the 1870s, who developed the system of
measuring and analyzing ship resistance in towing tanks that we use to this day. His
contribution was that ship resistance was made up primarily of frictional resistance, form
resistance, and wave-making resistance. If you towed a model of the ship that was
geometrically similar (same shape only smaller) to the one you wanted to build, you
could reduce the drag to dimensionless coefficients that would apply either to the model
or to the ship. The coefficient of frictional resistance varied with Reynolds number,
another dimensionless ratio. The coefficient of form resistance was the same for both
model and ship. And the coefficient of wave-making resistance varied with Froude
number.
Through experimentation it was found that when Lwl, the length of the waterline on the
ship, equaled L, the length of a free-running wave, ship resistance went up dramatically.
This made sense—the length of the wave was as long as the ship, and if the ship tried
to go any faster, it would have to create a wave longer than itself, and this requires a
tremendous amount of added energy—i.e. more power. The ship would have to start
climbing up the back of the wave that it was creating.

Thankyou Mr Sponberg,
Best Wishes,

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### Leo LazauskasSenior Member

Yep, that's the Froude number based on length, but it's not what the OP
was interested in.
What about the Froude "Displacement" ratio V/(g*D^1/3)^0.5?

4. ### Number4Previous Member

Hello Leo,
Thankyou for pointing out my ignorance.
I am glad to have learned something interesting today!

I see that it is FnV!
It is not at all a useless number.

Blount's view......
Displacement and planing hulls operate in very different manners, as the planing hull lifts it's waterline length changes, making any coefficient based on it's length meaningless. Naval Architects use the Volume Froude number as a dimensionless coefficient for comparing boats, using speed in relation to at rest displacement.

Equation for Volume Froude Number.
FNV= v/(g x dis^1/3)^1/2

v= velocity in feet per second (knots * 1.6889)
g= acceleration due to gravity (32.2)
dis= volume displacement in cubic feet

DISPLACEMENT HULLS operate at a FNV of 1.3 or less. SEMI-PLANING HULLS operate at a FNV of 1.o to 3.0. PLANING HULLS operate at a FNV of 2.3 or more.

As can be seen in the above table there is some overlap between groups because there is no precise point of differentiation. Where exactly does planing start? There are many different opinions; when water breaks cleanly from the transom, when water breaks cleanly from the chines, or when the boat's CG lifts above its static position.

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."

From Hydrodynamics of High-Speed Marine Vehicles.

Best Wishes,

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### PARYacht Designer/Builder

Mik, the problem with many of these rules, ratios and formulas we use, is they are meaningless without some understanding. Most are for comparative purposes and fruitless unless you have a point of reference (or many). Knowing the inverse of the √ may be directly proportional to something or why ╥² times a particular constant might be helpful, is meaningless gibberish without a reference and understanding of the principles and concepts.

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### Mik the stickSenior Member

Thank you for your replies. What makes the formula useless for me was I did not know how to use it.

I looked at Par's Murphy, my conclusion is, if the wind is strong enough for 4kts the boat will be operating in displacement mode, at 8kts it will operate in semi-displacement mode, and at 11kts it will be planing. Even if Par never intended the boat to go that fast with v bottom and single chine I would expect it to go very well. With a round bilge hull if the wind could force a boat of equal displacement to 11kts it would probably have water coming in over the stern.

I also looked at the Willard 40, (Fn 1.18)and the Neville 39 (Fn 0.99) I know the Willard has a round bilge but should operate fine at 10.5kts if you can afford the fuel bill

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If the boat is in planeing mode, the water will break away from the transom cleanly and has little tendency to climb the stern. True for a round bilged boat as well as a hard chined one.--- or is there something I am missing here?

8. ### FrostyPrevious Member

Meaningless gibberish, how dare you come and ask a question about something you did not understand.

All these complicated math stuff is for us /we boat designers and you would not understand it if I we could be bothered to explain it.

Instead I we/us would rather just point out your ignorance because I/ we /us / are so much cleverer than you.

( PS--when you do find out what it is tell us.)

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### jehardimanSenior Member

FWIW, the volumetric froude number was developed specificly for planing hulls so you could compare geosims between models and full size. Because of the rise of the hull during planing, you couldn't use just LWL for Froude comparisons. See the discussion of DTMB Series 62/63/64/65 high speed hull data (http://www.dtic.mil/dtic/tr/fulltext/u2/743966.pdf) .

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### PARYacht Designer/Builder

A Froude number is useful in calculations of hydraulics and ship design, where gravity and inertial forces are governing. In these cases, geometric similitude and the same value of the Froude number in model and prototype, produce a good approximation to dynamic similitude.

The dimensionless quantity U(gL)-1/2, can be interpreted as the ratio of the inertial to gravity forces in the flow. This ratio may also be interpreted physically as the ratio between the mean flow velocity and the speed of an elementary gravity (surface or disturbance) wave traveling over the surface.

When the Froude number is equal to one, the speed of the surface wave and the flow is the same. Commonly called in "the critical state". When the Froude number is less than one, the flow velocity is smaller than the speed of a disturbance wave, moving on the surface. Flow is considered to be subcritical (tranquil flow). Gravitational forces are dominant. The surface wave will propagate upstream and, therefore, flow profiles are calculated in the upstream direction. When the Froude number is greater than one, the flow is supercritical (rapid flow) and inertial forces are dominant. The surface wave will not propagate upstream, and flow profiles are calculated in the downstream direction.

So, has the definition helped Frosty, which was the point of my previous post. This stuff isn't hard (nothing more than high school math), but (again), you do need a grasp on the concepts.

11. ### FrostyPrevious Member

Could you give me the contact number for your pedestal supplier .

Does it have steps on it as Ive never before seen any one use one that high.

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### PARYacht Designer/Builder

I can't explain it any simpler than that Frosty. If you need a step ladder to get a handle on the concepts, that's not my fault . . . You are familiar with Isaac Newton's second law of motion, right?

What do you need, definitions?
Inertial force: a force (resistance?) opposing the direction of an accelerating force (an outboard?), acting on a body (the boat?) and equal to the product of the accelerating force and the mass of the body. Actually, the addition of the parentheses comments, for your sake, makes it slightly inaccurate. Maybe rubber ducky for boat and hand guiding it through your bath water would help for accelerating force? How's your algebra skills?

13. ### FrostyPrevious Member

It is very interesting to see you really enjoy honoring yourself, Im beginning to feel a little nauseous.

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### Mik the stickSenior Member

To frosty from mik the stick

GET A LIFE.
Naval architects are skilled at their jobs, otherwise they would be forced to do something else for a living. Don't understand you'r attitude, don't like your tone, wonder why you are a member of this site.
Because I want to learn I find your attitude frustrating. My questions may come across as stupid/nieve and Naval architects who bother to respond should be treated with much more respect.

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### PARYacht Designer/Builder

Frosty prefers words with less then 3 syllables and 7 letters. I don't understand his attitude either, much like most here. He seems to think we should break down complex concepts, into things he can relate too or that they (the math) are wholly unnecessary. Mik, you'll get a handle on it, but it'll take some effort. If your brain is built for it (Frosty's isn't), then you'll have a relatively easy time (again it's not hard, unless you refuse to learn). Most folks can get a basic grasp of things, though some are just better equipped or geared, for these "processes" than others. Obviously, Frosty is the latter.

Lastly, Murphy is designed as a rough conditions craft. Compared to others off her general configuration, she's slightly under powered, has proportionally higher freeboard, ample built in buoyancy to float her and a crew of 4, completely swamped, all with the rail still above the water. She can also sail as a Bermudian cat, by striking the jib and moving the mast to the forward step. She'll plane and if lightly loaded, fairly easily in about 8 knots of wind, though at 10, she starts to show her abilities. At 15 knots she'll want her first reef, but will carry on to SCA before needing another. She's very simple to build, has a built in engine well for an outboard and about as easy to setup as they come.

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