# Length and Beam for Froude Number

Discussion in 'Boat Design' started by Adis, Mar 13, 2010.

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Hi Guys,

I would like to ask you about the calculation of the Froude number.

The Length that we take into account to perform the calculation, I have seen that it is either the overall length of the boat, or the waterline length.

This is ok if the boat is a displacement hull or semi-displacement hull, since the length (either the overall or the water line one) do not change or do not change significantly.

However, as long as we are having a full planning hull, like an offshore powerboat, the wetted length can change significantly with the speed as we know.

I know that in this occasion, we use the beam of the boat instead of the length.

However I would like to ask a couple of questions :

1. Is it accepted to take into account for a specific speed (already well "inside" the planning region) the representative water line length at that speed in order to calculate the Froude number? Or for any given speed, the length parameter is "constant", i.e. either the boat's overall length, or the water line length when boat at rest.

2. If we are using the beam to perform the calculation of the Froude number, I suppose that the beam we are using is the one while the vessel is at rest and not in the planning region (similarly the the water line length at rest and not the one at planning at specific speed).

Any clarification on the above, will be highly appreciated.

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### jehardimanSenior Member

1) When looking at planning vessels it is normal to use the volumemetric Froude number = U/sqrt(g*volume^0.333..) to remove the whole LWL problem. You can then develop curves of resistance normalized against weight (i.e. displaced volume) for various Lp/Bpx ratios.

2) When using a Froude number based on b, b is defined as "the maximum beam over the chines or spray strips".

See Hadlers paper in the 1966 volume of SNAME Transactions or the data from the Series 62 and 65 tests.

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Thank you very much for the reply.

Can you please clarify if the volume taken into account at any given speed is the correspondent volume at that speed, or the initial volume of the boat at rest?

As the speed increases in a planning V-Bottom (take this as an example), all the parameters are changing, i.e. the water line length, the wetted beam as well as the submerged volume. Those parameters are speed dependent (mainly).

Therefore my understanding is that we will have to "stick" with initial value, i.e. the value that we measure at rest, irrelevant if we are going to use the water line length, or beam (in the chine as you correctly mentioned) or the submerged volume.

If you can confirm the above please.

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### jehardimanSenior Member

The volume is the at rest volume. It is important to remember that this also represents the weight of the vessel that must be supported by the combination of displacement and speed. The resistance of a planning hull is usually non-dimensionalized by R/W, the intial weight of the vessel being the design point of interest.

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First of all let me thank you for taking the time and reply!!! I assume that the ratio of Total Resistance to Total Weight of the vessel (at rest) is used as a kind of measurement for the performance of the boat?

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### jehardimanSenior Member

Yes, the R/W is constant across the weight of the vessels for geosims. For example, a Series 62 hull shape with a Lp/Bp of 3.06 at a volumemetric Fn of 2.5 will have a R/W = .121. So considering geosims, a 1000 lb boat will have a resistance of 121 lbs at 22.3 ft/sec, a 10,000 lb boat will have a resistance of 1210 lbs at 32.8 ft/sec, and a 100,000 lb boat will have a resistance of 12100 lbs at a speed of 48.1 ft/sec. The 10,000 lb boat will be 2.15 times the length of the 1000 lb boat, likewise the 100,000 lb boat will be 2.15 times the length of the 10,000 lb one.

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Although I am a naval architect, I have not deal with the designing aspect the last 14 years I left the university, since I am working in another field of shipping industry.

However I always wanted to be a designer, thus I would like to refresh my memory and improve my understanding.

It took me a while to understand how you came to the results you wrote above, but I think got it.

Based on the constant volumetric Froude number of 2.5 we can find the relevant speed for each volume (or weight) of the vessel (i.e. 1000 lbs, 10000 lbs and 100000 lbs)

S= FnV * sqr(g*V^0.333)

FnV= 2.5
g= 9,81
W=.454T (for 1000lbs), 4.536T (for 10000lbs) and 45.36T (for 100000lbs)
V= W*1.025

Therefore S is 22.6 ft/sec, 33.2 ft/sec, and 48.7 ft/sec respectively.

I had some problem to understand how you derive the constant ratio of length to be as 2.15, but I think I figured out.

Using again the normal Froude number as a constant, we can see that the length difference is the ratio of speeds squared.

So the length ratio is (32.2^2) / (22.6^2) = 2.15
and (48.7^2) / (32.2^2) = 2.15

Am I correct or I did something wrong?

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### jehardimanSenior Member

Actually, I calculated the 2.15 from the fact that the hulls are geosims, each 10 times the volume of the previous. Therefor the scale factor is the cube root of 10, i.e. 2.154434688.....

Since the Froude number is related to the square root "length" of the hull it follows that the ratio would also hold for the square of the speeds. I hadn't really considered that, but it is a nice check.

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Ooooopsss, yeah, you are right!!!   Glad to be of some "help" here.

In any case, thanks for all the time and patience my friend!!! I do appreciate your help!!!  10. Joined: Feb 2002
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### tspeerSenior Member

There is not one Froude number, but many. Boats typically use the static LWL to define the Froude number, but there is also a volumetric Froude number in which the reference length is the cube root of the volume. This takes into account the beam and depth as well as the length. Hydrofoils may use the chord in their calculation of Froude number, so if you have a leeboard, the board may have a chord Froude number quite different from the Froude number based on hull length, when the two are part of the same boat and going the speed!

The main thing to realize is we're talking about fluid dynamics - the science of the non-constant constant. If you define Froude number (and reference area) using the static waterline, then variation in waterline length with speed and loading are implicitly included in the variation of the force coefficients with speed/Froude number. If you base the coefficients on the dynamic waterline length and wetted area, they may show less variation with Froude number, but it will be more difficult to determine what the appropriate length and area are to convert the non-dimensional coefficients into actual forces and moments.

Fundamentally, Froude number is a book-keeping device, used to separate out gravity related forces, such as wave drag, from forces that do not depend on gravity, such as skin friction. What matters is the thrust-drag accounting system be clearly defined and used consistently. The static waterline length is the convention used most often, but it is only a convention. You can use whatever you want for Froude number if that makes it more convenient to get at the values you need - just pick a unique symbol to distinguish it from the convention!

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However, I really wanted to clarify the Froude number and the principle behind it, in order to have a better understanding and therefore to "know" what I am talking about. I assume that the volumetric Froude number is a more "consistent" way to have a first kind of "evaluation" regarding the behaviour of a hull until it goes to the planning region. After that first "feeling" you can proceed with more detailed analysis. Am I correct?  