Mathematical Q. about theoretical max boatspeed...

Hi I have a question about the maximum theoretical boatspeed for a displacement sailboat.

According to Larsson & Eliasson's Principles of yacht design there are two ways to find it.

The simple one is called speed to length ratio, defined as:
Speed in knots divided by the square root of the waterline length in feet.

I cant get this around my head. (my math skills are way old).
As an example: A 40 foot yacht would have a max boatspeed of 8.7 knots

What would the formula look like when you don't know the speed?

Any ideas or suggestios are appreciated!

pop

[Polarity]

For a displacement hull I know it as 1.3 x Square root of lwl in ft gives max theoretical in knots. I have also seen this from 1.2 to 1.34 instead of 1.3!

Ted Brewer has a good explanation of many of the ratios and numbers: http://www.tedbrewer.com/yachtdesign.html

Also interesting "what it is and is not " - here: http://www.hydrocompinc.com/news/news25.htm

General speed/ trim stuff:
http://www.sailnet.com/collections/a...eid=carrmi0024

However the reality depends on quiet a few other factors which I will leave to the naval architects on the board...

Cheers

Paul

[Stephen Ditmore]

1.34 x wavelength^0.5 is the speed the waves of your wake travel. If your boat cannot climb over or drive through its own bow wave it's speed will be limited by the wavelength that its shape will support, and the primary, but not sole, determinant of that is waterline length, so "hull speed" is generally calculated as 1.34 x waterline length^0.5

The scientific/metric version of this is Froude Number, and the conversion factor is about 0.3 (I think it's 0.298 if you want to be exact). "Hull speed" occurs at FR=0.4

[Stephen Ditmore]

Actually, I have a question related to this. In the article at http://www.sciam.com/1097issue/1097giles.html David Giles sites a speed-length ratio of .87 (FR=0.26) as being viewed as a maximum for conventional cargo ships. At the other extreme I have seen Dick Newick and others quote a maximum speed for displacement multihulls in the vacinity of FR=1.0 (though I suspect parameters other that length may be involved). Does anyone know where these numbers come from? Better yet, is there a single formula that would account for all cases?

[Steve Hollister]

I don't want to be a nit picker, but:

1. There is no such thing as maximum theoretical boatspeed. If you can put on a big enough engine, almost anything will go faster!

2. The value of 1.34 * LWL^0.5 as a maximum speed is only useful as a rule of thumb - actually, a crude rule of thumb. You really need a different estimate for each type of vessel. I haven't heard of anyone trying to come up with one formula for each type of vessel. For planing powerboats, however, many use Crouch's formula for a simple speed-power estimation. See Dave Gerr's "Propeller Handbook" for details.

3. Most designers know about this formula, but it really isn't that useful.

4. As mentioned in a previous post, see the HydroComp site for the best technical details on resistance and propulsion of all types of vessels. www.hydrocompinc.com

Dear Mr Hollister and nitpicker :-P~~

Well it does say Sailingboat! What speed you can get the hull to perform at with an engine is not what I was after.
This ought to have been quite obvious. This is the sailboat forum afterall.

These are my first trembling steps into understanding theoretically what I've been intrested in for some time.

My next step will be to take up math studies since I didnt do to well in math in school since i didnt find it that useful.

Now I do! Boatdesign is so fascinating that I'm determined to learn about it.
To know boatdesign I ned to get better at math!
When i did get the first answer from Glen i realised I had the answer all along, I just didn't realise it.
I just had to remember how to apply it in an equation (not hard at all, but I haven't done one in over 15 yrs).

Sincerely

Pop

[Steve Hollister]

Well, sailboat, powerboat, barge; paddle, engine, sails; it doesn't make any difference. There is no such thing as a theoretical maximum boatspeed. Speed length ratio is a VERY simplified way to estimate some point where the resistance curve gets really steep and the vessel doesn't go much faster without a lot more driving force. The 1.34 factor is interesting, but misleading, since it tends to lend an exact or theoretical air to the equation. It really does not apply that accurately many types of vessels.

What most designers use for sailboat performance prediction (before getting into the more complicated CFD analyses) is an empirical/theoretical model called the LPP/VPP (Lines Processing Program/Velocity Prediction Program). Larsson & Eliasson do the best job of explaining how this theory works. (Be careful, since there are some corrections in the formulas in the second edition.) It is based on towing tank tests at Delft University of a number of series of sailboat hulls and also based on a number of airfoil lift and drag curves for the sails. It also takes into account the true 3D shape of the hull for calculating the righting moment at any heel angle. In a number of ways the LPP/VPP is rather crude, but designers have used it successfully for many years.

Sailboat performance prediction is very complicated due to the hydrodynamic, aerodynamic, free surface, and unsteady aspects of the problem, but that is what makes it so fascinating.

[Stephen Ditmore]

Steve, I take your point about its being a less exact affair than 1.34xL^0.5 might suggest, but I think you're overstating the case when you refer to this as meaningless. For one thing, it describes a relationship between wavelength and wave velocity that is exact, or very nearly so, and important. As you well know, speed/length (or its metric cousin) are used for scaling wave drag by naval architects every bit as steeped in theory as you, and a hull optimised for the displacement regime with a Displ/L ratio over 200, a low Cp and no immersed transom is not well suited for speeds above 1.34xL^0.5 . America's Cup boats, which have enough horsepower to get going in all but the lightest winds, spend most of their time in the narrow band of speeds around this value. Do you not agree that wave drag starts to increase dramatically at a speed length ratio at about 1.0, and that there are clear differences between boats with target speeds above and below 1.34xL^0.5?

I'm arguing the point because Pop's reaction didn't surprise me; I, too, was irked by your answer. 1.34xL^0.5 may not be the whole answer, but it is far from being meaningless. As far as my question is concerned, we can speak in terms of target speeds rather than maximums if you prefer. I'd be interested in a formula that would relate design parameters to target speed across types. The answer does not need to be exact, but it should be generalizable.

[Stephen Ditmore]

On reexamination I see you didn't say it was meaningless, just crude. I still disagree, but I apologize for having misquoted you.
Happy New Year.
-SD

[Steve Hollister]

Boy, I had to check to see if I really used the word "meaningless". I didn't.

What I said was:

"3. Most designers know about this formula, but it really isn't that useful. "

Well, I didn't take a survey on this, but I can't recall ever discussing this formula with any of my fellow naval architects over the last 25+ years. You may disagree with me on its usefullness, but I'm entitled to my own opinion.

As I mentioned before, you might be able come up with a displacement speed/length ratio formula (like Crouch's formula for planing hulls) that has different factors for different types of vessels. However, it is my opinion that this type of formula will still be practical only for the most conceptual stages of design. That doesn't mean that it would be useless!

However, you really need to be able to move on to more advanced techniques, like the VPP for sailboats and Savitsky's technique for planing powerboats. For displacement boats, there are numerous techniques that try to come up with a formula for resistance based on the principal dimensions of the vessel. These are based on regression analyses of existing boats and are much more sophisticated than trying to convert 1.34*speed/length ratio into something useful. For example, see the polynomial used by the VPP that is based on towing tank test results. This is a formula that could easily be implemented in any spreadsheet. See Larsson & Eliasson, Figs. 5.18 and 5.19, on pages 75 and 76 in the first edition of the book.

[colinp]

Hi Pop

This "hull speed" business is easier to understand if you think about the physics behind it.

The resistance any object moving through an incompressible fluid experinces comes from only 2 sources: shear and pressure.
If we consider arbitrary tiny piece of the object's skin the shear on the element is the force acting tangent to its surface and the pressure is the force acting normal to it's surface.

If you "sum up" the forces acting on all these tiny pieces of the objects skin you end up with 1 force vector acting through a point in space.

For example, when a boat is floating in still water the sum of pressure acting on the skin is a vector acting vertically up through the center of buoyancy. All the pressures sum to zero in the horizontal plane. The shear forces are zero because the water is not moving relative the skin.

Once the boat moves through the water the sum of the pressure and shear acting on the skin is a vector inclined backward. Not all of the pressures sum to 0 in the horizontal plane. This is called pressure drag. The shear force on the skin is experienced as viscous drag.

When a boat hull is moving through the water its pressure field makes waves. Some of these waves propagate in the same direction and at the same speed the boat is traveling. The waves increase the area the pressure is acting on on wherever there is a crest because more of the hull is immersed. Where there is a hollow the water pressure acts on less area. (*this is not the only source of pressure on the hull skin, and yes the waves lag the dynamic pressure)

If there is a crest at the bow and a crest at the stern most of the pressures cancel out in the horizontal plane. When there is a crest at the bow but a hollow at the stern less of the pressures cancel out in the horizontal plane. The result is more pressure drag.

So there is nothing magic about it. Hull speed is not a physical limit. The boat does not tow along or otherwise own the waves somehow. All there is is pressure and shear on the skin.

This helps explain why hulls with a very light displacement for their length have a less prominent resistance hump at hull speed. They make lower waves and the pressure is acting on less area normal to the direction the boat is traveling. These type of hulls often exceed hull speed. (destroyers, catamarans, ULDBs..)

This also explains how heavy displacement keel boats can sail faster than hull speed without planing when sailing in swells longer than their waterline. A swell adding pressure to the skin near the stern can cancel out some of the pressure acting on the bow (in a trough). No planing or surfing required.


Talk to you later
-colin

[Polarity]

Now that's interesting - I never thought of it like that.

I thought it was because the (heavy) boat was going down hill!

But what you say makes complete sense.

thanks

Paul

PS how does changing the aft shape of the hull to detach the stern wave work ?

[Steve Hollister]

As a background note:

William Froude observed that ... "the speed at which wave resistance is accumulating most rapidly, is the speed of an ocean wave the length of which, from crest to crest, is about that of the ship from end to end"

From Froude, W. 1955, "The Papers of William Froude", edited by A.D. Duckworth, London: Institution of Naval Architects, page 280

This is a pretty good comment on the "practical" limiting speed for heavy, displacement surface vessels. Some people think that this formula is more accurate or theoretical than it really is. I think the misconceptions about the speed length "hull speed" formula come from how this speed is derived. This formula comes from the formula for the "phase velocity" (celerity) of small amplitude gravity waves in deep water.

Cwave = sqrt(g*Lw/(2*pi)) = 2.26 * sqrt(Lw)

Where

g is gravity in ft/sec^2 (32.174)

pi is 3.14159...

Cwave is the celerity or phase velocity of the wave in ft/sec.

Lw is the length of the transverse wave in feet.

If the vessel is riding in the trough of this wave with the bow at one crest and the stern at the other, then you can substitute the velocity of the ship for the phase velocity and the length of the vessel with the length of the wave, to get (after some rearrangement and conversion from ft/sec to knots):

Vs / sqrt(Lship) = 1.34

This equation may be derived from an accurate formula for waves, but its use for ships is far from exact or theoretical. Also note that this formula is for deep water and that it tells you nothing about the amount of resistance it takes to get the boat to that speed-length ratio.

As you get away from heavy displacement vessels, this formula has less and less meaning. For narrow, light, high speed boats (like catamarans), the resistance curve might show only a small hump at that speed/length ratio.

[colinp]

Hi Polarity,

Actually, no waves are attached to the hull.

The hull disturbs the waters surface. The pressure field of the hull moving through the water accelerates the water. Since moving water has momentum it overshoots its new equalibrium position and then falls back down past it (again and again...) . The 1 dimensional equivalent is a weight on a spring. Waves seem to travel across the the surface of the water but most of the water particals in a wave are just moving in little circles around their equalibrium position. The waves that seem to be attached to a boat's hull are really just moving with a celerity equal to the boats velocity. The hull only directly effects the pressure and shear in the thinnest layer of water touching the skin- and vice versa.

Most boats that travel at higher speed to length ratio have a transom stern. This allows the hull forward of the transom to have less curvature. The water does not need to accelerate toward the hull as much to follow this lesser curvature. The result is higher pressure acting on the skin in this area. Higher pressure is good here. A higher pressure on an arbitrary little area of skin near the stern creates a force angled in the same direction the boat is traveling. A negative pressure on the skin in the stern would slow the boat down (and cause a bigger stern wave too by the way)

If there was more curvature near the stern the pressure would be lower at high speed. So there is an optimum shape for the afterbody of a boat. The faster the boat goes the less curvature it should have aft.

When a hull is designed with an immersed transom stern it will be less efficient at lower speeds. The higher pressure in the stern will be acting on areas inclined less forward- which means a smaller forward component to the pressure (recovery of pressure). The pressure on the immersed transom itself is quite low even at slower speeds.

Talk to you later
-colin

Actually, there IS a maximum theoretical boat speed. It is right around 25,000 mph. A boat at this speed will develop an LWL of 0 and depart the planet. Semantically, you could argue it is still a boat, but technically, the math changes. Tongue in cheek here.