Textbook: Chapter 11
Ship resistance and the concept of model testing
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Introduction P 214
Froude P 214
The background to model testing P 218
The fundamental principles of model testing of ships P 219
Implications of Froude’s work P 224
Critical speed and the Froude number P 225
Geometrical and dynamic similarity P 226
Endnote P 227
Examples on model testing P 228
Chapter 11 Ship resistance and the concept of model testing
One might argue that ship resistance is not relevant to the activities of a mechanical engineer. This text is about the construction of an empirical science and the work of Froude (1810 – 1879) is woven into that science because it showed that the testing of models is a way of gathering data about the way that flowing fluids interact with solids to produce forces on them. His work opened the way for wind tunnels and prepared the way for the computer modelling that is now used in tandem with model testing to reduce the amount of physical testing that is needed to achieve some result. It was a seminal piece of work. Froude’s papers have been published and figure 11-1 is the flyleaf of the book. I enjoyed reading them.
Froude’s celebrated work, that was continued very ably indeed by his son, was initiated in 1868 with an application to the Chief Constructor of the Navy for funds to construct a towing tank and employ three people in order to carry out a programme of experiments over a period of two years. Froude was then 58 and an intensely practical engineer with great experience including a very extensive knowledge of ships of all sorts. He was a man of independent means who lived in Torquay in England and gave his time without payment to undertake his programme of testing. Very wisely he stipulated that the programme of testing would be free from any outside direction and be entirely in his control. Equally wisely he also stipulated that his son should work with him on a salary. The Navy gave him £2,000 and got a bargain. The work eventually lasted 14 years when the site on which the facilities had been built was restored to its owner again as farmland. In those years the testing of models had been firmly established as an aid to ship design and subsequently led to the use of wind tunnels for the design of aircraft etc..
It always interests me to try to decide why one man produces a piece of work that changes everything when others who were contemporary did not. Froude graduated in 1828 with a first in mathematics and a third in classics from Oriel College Oxford. His principal interest appears to have been sailing but his real strength was as a very practical engineer. He spent most of his life in and around the River Dart and he must have been well aware of, and interested in, all things to do with ships. His degree shows that he had the intellect to think about mechanical things at a quite different level to that of, say, George Stephenson. In order to place Froude in his context we must have some idea of the state of the knowledge of ship design in the mid 19th century.
I think that it is fair to say that ships are the only form of mechanically-powered (sails) transport to have existed for hundreds of years. They had always been designed by various rules of thumb that had grown up over a long time. By the start of the 19th century science was influencing design of mechanical devices but it was emerging in an era when everyone had grown used to thinking in empirical ways and attempted to deduce everything from observation. Inevitably, during the gradual evolution of science, ships attracted the attention of all sorts of people as being a very interesting subject for the application of the emerging science. After all now there was the hull, the engines, the boilers, the propulsion system to be developed and all of them might be improved by the use of science combined with improved manufacturing methods. All sorts of ideas were advanced to try to improve the design of all the elements of ships and my impression of naval architecture is that many of these ideasstill persist long after they should have been discarded. Froude was born into this era with, seemingly, an inbuilt interest in ships.
So what was happening in ship design when Froude was a young man? The ssGreat Britainwas launched in 1843 just 5 years after Froude graduated. It was half as long again as any other ship that had ever been built, it was the first large iron ship and Brunel designed the engines and the newly-invented screw propeller. Brunel knew how to make a very good estimate of the resistance to motion of his ship and how this resistance would vary with speed. His engine worked with a boiler pressure of 5 psi and exhausted to a jet condenser giving a vacuum of 10 psi. Sea water was used in the boilers that were in three sections so that any one section could be blown down to get rid of very saline water that resulted from the evaporation of the water fed to the boiler. The four cylinders were very large because the low-pressure steam in use involved very large volumes and they were of a size (88 diameter by 70 stroke) that came to be used much later as the low-pressure cylinders of compound engines. The “theory” of screw propellers was in existence and Brunel knew about slip and the way the blades should twist. He was able to predict the performance of his ship from engineering principles and he did it very accurately as was proved on the first run of ss Great Britain when it was worked up to its design speed. The ship was launched over 30 years before Froude started his work and many improvements must have taken place in every aspect of ship-building during that time. Froude, who knew Brunel, would have been well aware of the general situation.
I think that Froude tells us much about the state of ship design in the second half of the 19th century in his application for funds to the Chief Constructor of the Navy. This is an extract :-
Moreover while it was found in my experiments that on comparing the performances of a 3 foot and 6 foot similar model, the former exhibited a slight excess of proportionate resistance possibly attributable to the above cause; between the 6 foot and 12 foot models no such difference was observable. Lastly this is worth notice. Calculations based on a large number of indicator diagrams taken from the largest well-proportioned vessels of the wave-line type, at such speeds as not to create notable waves, have satisfied me that we may regard from 23 lb. to 24 lb. per square foot of mid-ship section as the resistance of such vessels at 10 knots, this figure, reduced by the rule of the squares of the velocities, which my experiments shew to be fairly correct below such speeds as create notable waves, would give 0.74 lb. to 0.78 lb. per foot as the resistance due to 1.8 knots. Now, at that speed, the 6 foot wave-line model makes, according to my experiments, a resistance of just 0.75 lb. per square foot. Whereas, if a 6 foot model were considerably affected by the action referred to, its resistance should be markedly greater.
It appears then that so far from the foregoing objections having any real foundation, we are able, in fact, to frame from the results of small scale experiments by a precise and simple method an accurate prediction of the performance of full size ships.
(ii) The existing state of knowledge as to the merits of particular forms in ships is very unsatisfactory.
(a)It is generally held that Vessels of what is called the "wave-line" type offer the least resistance, and there is nothing either in the reasonings or the statements of its advocates to limit its superiority to the condition of comparatively moderate velocity.
Now, if it is allowed as I have contended that the performance of such models as were used in my experiments is precisely similar to that of similar ships, it is clear from those experiments, that at high speeds the wave-line form is markedly inferior to a form totally dissimilar to it in appearance and utterly opposed to it in principle
(b)An opinion is beginning to gain ground and, with good reason, that surface friction forms a large share of the resistance of a ship, yet concerning the nature of this force much misconception plainly exists; for by the best authorities who have treated of the subject it has been held as the basis of calculation that a long plane surface of say one foot in width moving endways through the water encounters the same resistance of friction for each square foot throughout its length. Now it is quite clear that the first square foot in its length in experiencing frictional resistance from the particles passing it, and thus impressing force on them in return must communicate to them some velocity in the direction of its motion. The particles in contact with the second square foot having thus already received forward velocity must exert less frictional resistance upon it, unless the degree of that frictional resistance be independent of the degree of velocity with which the particles traverse the surface; a supposition manifestly erroneous, and quite as subversive of received opinions as the alternative conclusions, I advance that surface friction is not uniform for every part of the surface?
(c) In the existing state of knowledge there is no guide for determining the influence upon a ship's resistance of the ratio of her length to her breadth and to her depth; a question of the most vital importance in the construction of ships of war, where by increasing the length though we no doubt increase the carrying power, we increase also in a greater degree the weightiest and costliest parts of the structure, adding at the same time to the difficulty of handling the ship; whereas by increasing the breadth we can add almost as largely as we please to the carrying power with an increase only to the less weighty and less costly parts of the structure, leaving the handiness unimpaired.
(d) Though there are current very precise rules by which it is said we can determine the limit of speed beyond which a vessel of given length cannot economically be driven, these rules have been fixed by an (as it appears to me) arbitrary and not strictly relevant application of the theory of wave-motion. Moreover, the rule implies that the limit will be at the same speed for all ships of the same length, but this according to my experiments is obviously not the case, for instance in the experiments on the two 6 foot models* the same in length, breadth and displacement, one has the limit at a speed fully 8 per cent, higher than the other, making at that speed 20 per cent the less resistance of the two though at the lower speeds it had made the greater resistance.
I have here enumerated certain deficiencies and inaccuracies in the received views on the subject. These alone are manifestly of very high importance, moreover we may reasonably expect that an extension of the inquiry will discover many other deficiencies and errors equally serious.
We see quite clearly that the science of ship design was attracting rival theories just as yacht design does now. Some of these theories were downright destructive, (see the activity of Lardner on page 11 of “The Iron Ship” by Ewan Corlett.) and others were insidious in leading to the design of ships that were much less safe than they would have been had not the spurious “theories” been accepted. Froude was a far-sighted man.
Froude clearly recognised that if it were to be possible to test scale models of the hulls of ships in some sort of towing facility and to predict, from the outcome of these tests, the behaviour of the full-sized ships many of these ill-founded ideas would be proved to be wrong. I think that we may take it for granted that the design and construction of the towing facility would not be seen by Froude, with his undoubted skill as an engineer, as anything more than an interesting challenge and he was very well suited to such activity. However the scientific basis for the testing was not readily obvious and had been the subject of much debate over the years. As I read his papers I sense that he seems to have been acutely aware of the acrimonious nature of the scientific debate that was going on and knew that the standard of his work would have to be beyond criticism.
A towing tank had first been used in France 100 years earlier. Unhappily the idea seems to have been that there was some underlying relationship between speed, resistance and size that would be more or less the same for all ships. This sounds a bit naïve but ships at the time were all the same shape. The idea was to take measurements of resistance of arbitrarily shaped models when towed and then to think of a way to use these measurements to predict the resistance of any other full-size ship. It could not work even though several celebrated men tried to make it work. A result of this activity and of other attempts at towing was a split in naval thinking between those who favoured testing full-sized ships as a means of improving ship design and those who favoured model testing. The testing of full-sized ships would have been very expensive, exceedingly difficult, as Froude discovered, and very slow to yield results. The testing of models would be, by comparison, cheap and speedy and not subject to the vagaries of weather, wind and tide. Froude found a way to use model testing and, probably more importantly, a way to prove the method cheaply, so that even the most sceptical could not really say that it was not worth the very tiny investment involved. Froude appears to have been either very shrewd or knowledgeable about the ways of men.
All this tells us why Froude needed to be able to follow his own agenda of testing and why he gave his time to the project as distinct from seeking to be paid. Had the Admiralty funded the programme in its entirety it is almost inevitable that a committee would have been formed to oversee it and that members of that committee would have wanted Froude to pursue their ideas and not his own. As it was, £2,000 was a very modest sum to set against the immense rewards that followed from the investment.
The outcome was that Froude built a very large towing tank of 278 feet long 36 feet wide and 10 feet deep and showed that it is possible to predict the behaviour of a full-sized ship from towing tests on a scale model of the hull and then went on to pursue a programme of investigation to create a more coherent body of empirical knowledge about ship design. He was the instigator of a programme of investigation that was pursued by his son R. E. Froude for more than three decades and made them architects of this branch of our empirical science. It was a great achievement.
So what was his idea? It is contained somewhere in his published papers but it is difficult to winkle out and I suspect that every reader of those papers will come to a slightly different view of the work. I shall give mine.
The background to model testing
There can be no doubt that Froude’s first task had to be to show that tank testing of models worked. There was only one way and that was to test a model of an existing ship, predict its resistance to motion, and then go out and measure the resistance of the full-sized ship.
It all seems very simple but one must consider the situation in the mid 19th century. We are accustomed to seeing photographs of vessels of all sorts under way. The photographs are taken from the air and, even if they are not taken with the study of the waves and the wake in mind, the surface effects are there for anyone to study. Froude would have had to look at bow waves and wakes as they were being made and never from a useful observation point. Nevertheless it seems that Froude over the years had recognised that the resistance to motion of a ship was caused partly by friction between the hull and the water that created a wake in which energy was stored and then lost in random eddies and partly by making waves that very obviously carried energy away from the ship.
Figure 11-2 is a photograph taken from an advertisement and shows a racing sculling boat on the move. The use of oars means that, with the exception of the circular waves on the right, the effects that we see on the surface are entirely due to the action of the hull on the water and not confused by the presence of a propeller. We can see the wave pattern coming from the bow and another wave being generated at the stern and we can see the confused wake caused by friction between the hull and the water. In the extract above Froude has commented on all these things. I think that one can have some sympathy with the people who were trying to think about the problem of ship resistance in the 19th century.