Analysis of the Hydroplane 
by G. F. Crouch
During the past year several photographs and descriptions of hydroplanes, designed to make high speed with small power, have been published in The Motor Boat and the various foreign journals which touch upon the sport of motorboating. From these reports, the success of the gliding craft in smooth water seems to be unquestioned, making such a boat of practical use on the quiet water of a small lake or river. In fact, the effect of moderately rough water is not so much to reduce speed as to cause severe local strains in the hull, due to the impact of the waves on the flat gliding surfaces.
Gliding boats may be divided into two distinct classes; the first class comprising those in which the hull itself forms the planes, the second class those in which the planes are attached to a separate hull, the hull being lifted clear of the water when at speed. Of the first are the Yarrow-Napier series, the Ricochet-Nautilus, the Hydroglisseur, and the new boat now being built for the Monaco meet, mentioned in The Motor Boat of January 10, 1907. The first French gliding boats were of the second class, as the hydroplanes of Count de Lambert.
The first class having the gliding surfaces part of the hull itself, would seem to possess more than a little advantage over the second class, which must have a hull of some sort to support the weight of the boat when at rest, in addition to all the necessary bracing. This undoubtedly allows the first class to be built more strongly and lightly than the other, and, as will be shown, this weight consideration is of the very first importance in the design of any type of gliding boat. Then, too, the combined surface of the hull and planes will exceed that of the hull alone, which will result in the second class form being more difficult to work up to a lifting speed. it may be truly stated, however, that a boat with external submerged planes would be a far more successful type for rough water than either of the others, but would not be as easily driven.
The following elementary investigation of the action of a gliding boat of the first class will perhaps be interesting as it shows an agreement with results which have been obtained experimentally.
Assume that the boat has a form of two or more planes; the weight of the boat when at rest is supported by the displacement of the immersed wedges. When running at speed the boat lifts out on the planes to the running water line. If the boat is running at a uniform rate, the relation of the thrust of the screw, the weight of the boat, the horizontal and vertical components of the lift of the planes, and the frictional resistances of the wetted surfaces becomes a problem in statics.
After calculating static equations regarding angles of planes, total areas of planes, hull weights and hull velocities, and considering Froude's experiments on moving planes, it can be seen that the total resistance to the motion of these types of boats is the sum of frictional resistance of the planes and the horizontal component of the normal pressures on the planes. It can then be stated that these equations are entirely independent of speed, and show that after a boat has reached a speed that the displacement of the wedges is small, the resistance is constant, neglecting the air pressure. It is also well to note that the necessary approximations made in reducing this equation are such that the error would tend to increase the estimated resistance over that actually required at the higher speeds. In practice this would allow somewhat for the air resistance. It may be thought that the formation of eddies behind the wedges would be a serious objection to this type, but by actual trial the water is found to leave very smoothly at speeds of eight knots and above.
Referring again to the equations for total resistance, the weight will be a constant for any given boat, so that the resistance will depend entirely upon the inclination of the planes. The paramount importance of lightness in the design of a hydroplane is now clearly evident, each pound of weight is a direct addition to the resistance. It also shows that the gliding principle is entirely incorrect for ordinary vessels and launches, it explains why former experiments, made when light-weight, high-power motors were unknown, were such hopeless failures.
U.S. torpedo boat Biddle. Data from Trans. Am. Soc. N. A. & M. E. W = 376,320. Actual resistance at 30 knots is 26,700 pounds. If the gliding principle had been employed the resistance would have been about 33,870 lbs., which is 27 per cent in excess of that actually given. This vessel is probably the fastest and most powerful for its weight in the U.S. Navy. Even with this extreme craft the gliding principle is a failure, and it is to be expected that the trials of gliding vessels conducted by Mr. Froude some time ago were unsatisfactory, as the weight for a given power was even greater.
Motorboat Vingt-et-Un II. Data from Trans. Am. Soc. N. A. & M. E. Weight 3,850 lbs. Resistance at 21 knots is 700 lbs. If built on the gliding principle the resistance would have been about 350 lbs., and this speed could have been obtained with 35 horsepower.
(Excerpts transcribed from The Motor Boat, Feb. 10, 1907, pp. 29-30. )
[Thanks to Greg Calkins for help in preparing this page. --LF]