# Design Ratios, British And Metric Units

Discussion in 'Boat Design' started by BASIL J WALL, Nov 10, 2011.

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### BASIL J WALLdesigner

Hi...
I Am Setting Up Tables To Determine The Preliminary Data For New Design Concepts...the Data For S/l And D/l Ratios Are Readily Available In British/imperial Units But In Metric/si Units Things Become Confusing...
I Just Want To Know If These Ratios In British Units Are The Same Number In Metric Or Are They Converted To A New Number In The Metric System With Appropriate Units?
I Suppose Someone From Europe Or Asia, Who Uses Si/metric Units In Preliminary Design Concepts, Would Be The Best Source For This But I Have Not Been Able To Locate Anyone...
Thanks
Bjw

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### Olavnaval architect

It depends on the "type" of ratio. If it's a dimensionless ratio (like L/B, B/T, cB, cP, cWP or Fn, Rn etc.) then it's the same, regardless of the unit system that is used.

Things like S/L or D/L do have dimensions (for example knots/ft and lb/ft in Imperial units or (m/s)/m = 1/s = Hz and kg/m respectively, when using the metric system) and therefor need to be converted.

Just on a side note: I can't recall any publication in metric units that uses other than dimensionless ratios (but maybe someone else does). S/L, D/L etc. is something I only come across frequently in literature by authors from the U.S. who utilise the Imperial system.

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### BASIL J WALLdesigner

Hi...
Thanks For This ...the Question Is, Do Designers Who Use Metric Use The S/l, D/l Ratios That The Us Uses AND IN WHAT UNITS?
Bjw

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### Olavnaval architect

Well, I personally use them very rarely, only when I need to compare some of my own numbers with those from publications from the U.S. When I go sailing I use non-metric units such as nautical miles, cable lengths and knots and a coordinate system with a clock-wise sense of rotation, but all my calculations within the ship or boat design process are exclusively metric (being a European I'm much more comfortable with them) with dimensionless ratios, i.e. Froude number instead of S/L, L/Displ.^(1/3) instead of D/L and so on.

Actually I don't know any naval architect or engineer from my part of the world who would do it differently to what I do.

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### DCockeySenior Member

I assume the "Disp." is the volumetric displacement, not the weight/mass displacment. Otherwise it will be dimensional.

"D/L" as used in the the US is not Displacement (mass/weight) divided by Length. It's more complicated and is:
Displacement/(LWL/100)^3
where displacement is in long tons (2240 lbs) and LWL is in feet.

If I did the math correctly:
LWL/[Disp(volume)]^.333333 = 1/"D/L"^.33333 * 30.57
where "D/L" is as defined above.

"Speed/Length" is Speed(knot) / [LWL(ft)]^0.5

Froude Number from Speed/Length ratio is simplier.

Fn = "Speed/Length" * .297

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### Olavnaval architect

DCockey,

of course you are right. I stand corrected.

I guess I shouldn't write about not-so-familiar things (for me) without having another look at some reference books before. Let's take it as a sign of my rare use of these ratios.

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### BASIL J WALLdesigner

Hi...
Based on Olav's comments, the metric community does not use the british system...They (metric ) use non-dimensional ratios, which to my Physics mind is much more useful...it eliminates much confusion...However the US and Canada designers have become so accustomed to the D/L ratio with units of long tons/cu ft and the associated mind set or recognition of these numbers that it will be very hard to change tack now ...
So I will assume that, when using metric values to communicate with metric using yards, the dimensional ratios are not very useful and it is not worthwhile converting the units..
What do you think?
BJW

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### DCockeySenior Member

I assume that you understand that most ratios are non-dimensional and have the same value whether calculated using metric, "british" or any other system of units. Examples include:
Length/Beam
Prismatic Coefficient
Block Coefficent
Midships Area Coefficient
Sail Area to Wetted Surface Area
Center of Buoyancy

"D/L" as commonly used in north america is not dimensionless but it's easy to calculate the non-dimensional equivalent and vice-versa. See my post above. Also note that the non-dimensional form can be calculated directly using "british" or any other consistent set of units.

"Speed/Length" is not dimensional but very easy to convert to Froude number. Just multiply by 0.3, or 0.297 if you want to be more precise. Froude number can also be calculated directly using the appropriate value for g.

Other than the "D/L" and "Speed/Length" I don't see any issues with design ratios and units. And those two are simple enough to convert.

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### rxcompositeSenior Member

Ratios and Coefficients are non dimensional except for the displacement to length ratio which is often seen in the design lane. It is expressed in British/English units. Expressing in other units would give you a meaningless value.

I use them all the time in preliminary design stage.

Also as mentioned by DCockey, Speed to length is dimensional, but I use froude number, which is non dimensional.

10. ### Submarine TomPrevious Member

Don't be confusing a ratio with a formula.

A ratio cares not on units, providing they are the same units within the ratio.

A formula relies on a certain type of unit, again being consistent with it's use through-out.

-Tom

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### DCockeySenior Member

Not all formulas are dimensional with units.

A ratio can be either dimensionless or dimensional. Example of a dimensional ratio is cost/mass. It is inherently dimensional.

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### gonzoSenior Member

Basil: The British and American Standard systems are not equal.

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### rxcompositeSenior Member

Now I am confused. When we say English System, are we referring to the U.S. system of measurement? And when we use the term Imperial System, are we referring to the British system of measurement such as the Imperial or U.K. gallon?

Lastly, is the Long Ton (2240 lbs.) strictly British, and the Short Ton (2000 lbs.) strictly U.S. system?

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### marshmatSenior Member

I, and most engineers I know, consider these terms to refer to the United States customary system, as it is the only such system still in common use in the engineering community. It is, of course, defined in terms of conversion factors from SI units, and I don't think I know a single engineer who doesn't immediately convert the given data to SI before doing any calculations.

There are several units called "gallon". 1 USgal = 3.785412 L, 1 UKgal = 4.546092 L, 1 US dry gal = 4.40488377086 L. Only the 3.785 L version is likely to be seen anymore, although a very small handful of folks in Canada and Britain still insist on using the 4.54 L version, in which case "imperial gallon" will be explicitly stated.

As for the ton, it should always be stated as "short ton" or "long ton". If neither is stated, Brits usually prefer 2240 lb and Yanks usually prefer 2000, but that's not always true.

If in doubt, simply check your units of choice in the formula. Usually, you'll be left with no units / dimensionless, i.e. any consistent system of units would give the same number. If you do have units left at the end, you must convert your input values to the same units used in the historical literature on the subject.

The main ones to watch for are:

-DLR (long tons per cubic foot) - the modern version is LDR = length / cube root of displacement, which is dimensionless and works in either system.

-Bruce number (feet per cube-root-of-pounds) - it's just a very weird way to twist SA/D = sail area / displacement^2/3, which is dimensionless and works in either system.

-Speed/length ratio (knots per square-root-of-feet) - it's a colloquial rule of thumb, the serious scientific literature mostly uses Froude number, which is dimensionless and works in either system.

-S-number, which takes the old-style DLR as one of its inputs.

A useful and relatively trivial exercise in understanding these ratios is to do a few lines of algebra to find the conversion between the old ratios and the modern dimensionless ones, then apply this conversion to your old reference tables and note the new values in the margin. It only takes a few minutes and is a good way to improve your understanding of what the ratios mean and how they compare.

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