Critical speed and the Froude number

The Froude number is just a device that we choose to use when it suits our purpose. It has no counterpart in reality like a depth. It is dimensionless because it is the ratio of two velocities one of which, the numerator, is normally an actual velocity. The denominator is usually derived from a length and is a notional velocity that is used as a reference value and possibly called a critical value because it might be the line of demarcation between two regimes of flow.

 

For displacement hulls a critical speed is worked out for the speed of a wave that has a wavelength equal to twice the length of the waterline when stationary. The idea behind this is shown in figure 10-14 where the model yacht is on a wave with crests at bow and stern. There is an expression for the speed of this wave and it is :-

                                   speed of the wave =  in some consistent units. It is often called the critical speed but it can be exceeded by a small amount without the need to plane but progress at speeds in excess of this critical speed involve a pronounced bow up attitude and very high resistance. The critical speed concept is a good guide to the maximum practical speed that can be attained by a displacement hull.[1] Obviously a dimensionless group can be constructed from the ratio of actual speed in knots over hull speed in knots but ordinary ships do not operate at speeds anywhere near to their critical speeds (Or any other consistent units.) and, at the critical speed, the number will be 1. This group has been called the Froude number in recognition of Froude’s contribution to ship science.

 

But Froude, as we have seen, did not use this idea. He needed only to claim that if two hulls of exactly the same shape but of different sizes move at speeds that are proportional to the square roots of their lengths their bow waves would be exactly proportional to their lengths. There is the common element here that speed and length are related by a square root relationship. This is hardly surprising when one considers Bernoulli with his interchangeability of kinetic energy and potential energy. We have a ratio

         wave height on the model/wave height on the prototype = Ölength model/length prototype.

 

Froude used speeds up to 12 knots but now we routinely think of speeds of twice this for tankers and higher for passenger ships. These higher speeds are the result of using much larger ships and driving them with high-powered, efficient engines running on cheap oil.[2] Typically a tanker will be up to 350 metres long and it will run at 25 knots.

 

Now we need some idea of the variation of critical speed with length. It is shown in graph 11-5. Immediately it is evident that the tanker is operating at about ½ the critical speed as indeed was ss Great Britain.

 

As I showed in graph 11-1 the power to propel ss Great Britain

is increasing very rapidly at speed of 12 knots and there is quite clearly a speed that gives the best return on the money that has been invested in the operation of the ship. Presumably this applies to all ships and the most important item in that financial compromise is probably the cost of fuel and, if it is not now, it soon will be.

 

It seems that comparison of ship performance is made easier if one thinks of the operating speed as a Froude number rather than a real speed because it tells us where the ship is operating on the graphs of resistance and power versus speed. The range of Froude number within a group of ships designed for the same purpose is really quite small. Oil tankers run at about 0.5 and cruise liners at about 0.7. Size-for-size the power installed in a tanker is about 70 % of that installed in a cruise liner and this reflects the different economics and the difference in the way in which they are used.