SPI-4,F4,1) BOAT 1Di-4:SIGN
R. R. POOLE, B.Sc.,
IN any kind of boat hull, three main considerations govern the design. First, resistance to motion, which determines the speed obtainable with a given propeller thrust ; second, stability and control, both when running straight, and when, cornering ; and third, mechanical strength. It is proposed in the following article to deal with the first of these problems, and to indicate the various sources of resistance and methods of minimizing them.
There are in general two types of boat ; firstly the displacement hull, in, which a considerable volume is immersed and in which water is displaced sideways and downwards, flowing in behind as the boat moves forward ; and secondly the hydroplane or skimmer, in which advantage is taken of the lift on inclined planes or hydrofoils to cause the boat to skim on the surface, only accelerating sufficient water to obtain the necessary lift and propulsion. All modern speed boats fall in, the latter category, as do many heavier craft such as coastal patrol boats, on account of their enormously greater efficiency at high speeds.
A general discussion of the sources of resistance applies equally to both types of boat, but the relative magnitudes of the power losses incurred differ widely in the two cases.
When, a body is propelled on the water, the power necessary to drive it is equal to the product of the velocity and the total resistance, the latter quantity depending on the former in a very complex manner. It is practically impossible to obtain a complete quantitative analysis of this resistance, but its qualitative treatment enables a practical design to be evolved, in which the performance can be predicted fairly well with the aid of certain empirical rules.
The total resistance is made up of five distinct terms, most of which are to a certain extent interdependent. These terms are :
(1) Skin-friction on the sliding surface.
(2) Eddy formation round the hull and appendages.
(3) The wake, or following turbulence.
(4) Wave formation.
(5) Air resistance.
And we may proceed to consider them separately.
(1) SKIN FRICTION.
A perfect fluid is defined as one which is totally unable to transmit shearing forces ; from which it follows that a thin plate drawn edgewise through a perfect fluid can impart to it zio motion. In other words the surface of the plate would be sliding past a stationary wall of fluid, a thin, layer of which, say one particle thick, separates the surfaces and acts as a perfect lubricant. Water being by no means a perfect fluid it follows that the layer in contact with the plate will be carried along, and a shearing force will exist between this layer and the next, and so on, to an extent depending on the speed and size of the surface, so that an appreciable body of water is involved in. a forward movement. From layer to, layer, then, there exists a force and a relative displacement, and hence useless work will be done on the water. In addition to the direct loss of power occasioned by this frictional action, the volume of water participating in the forward motion may be sufficient to alter the effective shape of the body, and appreciably to disturb the streamline motion of flow round it, so giving rise to eddying movements. This occurs particularly in displacement hulls, where the immersed volume is large, and also in the case of the projecting parts on hydroplanes, such as struts and rudders. The empirical formula : P = fAV2 is generally used to determine the resistance
‘P’ in pounds on a short area ‘A’ square feet travelling at a velocity ‘V’ feet per second. The constant ‘f’ depends on the nature of the surface, and is taken as about 0.003 for varnish or bright metal.
This coefficient may be reduced a little by lubricating the surface with some solid lubricant such as soft graphite, though this is not very lasting in its effects. Also if air is introduced in the form of bubbles between the bottom and the water, very considerable reduction in the friction may be obtained. Boats have been constructed with numbers of small holes in rows across the bottom, out of which air was forced, and were found to have a low frictional loss, though the additional weight and power required for the air pump practically nullified the advantage. In a skimmer a fair amount of air is carried underneath both in, the forward section and behind the step. An interesting effect was noticed in the case of the Schneider Cup seaplanes, which could not attain full water speed on glassy smooth water while the least ruffling of the surface enabled air to be carried underneath the floats, aiding the ” unsticking ” process both by increasing the speed and consequent lift, and by reducing the direct adhesion. On the basis of the above formula, a varnished surface offers a frictional resistance at 30 m.p.h. of a little less than 6 lbs. per square foot, which represents about
H.P. at the propeller, or say I B.H.P. at the engine. for every square foot of surface in contact with the water.
2. EDDY FORMATION.
As water flows round an immersed body, the velocity of the streamlines decreases as they expand in behind it, resulting in a rise in. pressure head, according to Bernouillis Theorem. If the particles are for any reason unable to give up sufficient kinetic energy to produce this increase of pressure, the surplus energy will dissipate itself in a vortex or spiral motion instead of producing a useful thrust on, the after part of the body. For instance, if a submerged object is too abruptly curved in at the stern, the radial acceleration required for a particle to follow round the curve may produce centrifugal forces greater than the pressure head, in which case a partial vacuum will form behind the object. A blunt, square stern will produce this effect if moved fast enough while immersed, and. less extreme cases give rise simply to trains of eddies or vortices. It would appear from experiment that if the tangent to the surface is inclined at more than about 16° away from the driection of motion for a speed of 30 m.p.h., eddizs are certain to form, and in practice th,after fairing of projecting parts is designed so as to present less than this angle, the apex angle (at the trailing edge) being generally under 24′ so that the tangent angle does not exceed 12′.
The energy put into a system of eddies or vortices, is proportional to the product of velocity of rotation x size x rate of generation of eddies, but there are no available data relating any of these quantities at the spec d and shape of the disturbing body. As with friction the direct loss is not the only trouble arising from extensive eddying. Turbulence in the vicinity of the screw lowers its efficiency considerably,
and the rudder often behaves erratically if placed in a region, where irregular eddying occurs, owing to the liability for strings, of eddies suddenly to change their direction or intensity with small changes in the balance or trim of the boat.
Step bottomed boats have to attain a fair speed before they can rise or commence “planing.” During the preliminary run violent eddies form behind the square ends of the step and stern, and often the engine has not sufficient power reserve to overcome this initial resistance, so that the boat can never attain the planing speed.
3. Tim WAKE.
This term relates to the turbulent water following immediately behind the boat, which is due mainly to a combination of local eddying and the body of water to which a forward motion has been imparted by skin friction. The displaced streamlines, expanding in behind the boat, tend to confine the zone of disturbance into the familiar tapering wake, the presence of which interferes with the return of energy in the form of following thrust. Generally the wake proper is broken up by the spiral slipstream from the screw, and the foaming spout of water often to be seen following at a distance of a couple of feet from the stern is principally due to the screw, the large rotational eddies from which break through the surface.
It has already been mentioned that it is undesirable to operate the screw in turbulent water. Some advantage, however, can be gained by placing it in water that already has a forward motion, though it is generally difficult to find a part of the following zone which is not in a state of turbulence. The position usually adopted as most efficient is a few inches forward of the square edge of the stern, and as near the bottom of the hull as is consistent with avoiding hydrau:ic interference, i.e., about 3 inches clearance. In outboard drives the first consideration is to place the disc of the screw well below the bottom, in order to avoid the reg:on of powerful eddies behind the stern edge. Too low a centre of thrust, however, affects the trim, tending to lift the bows, and the stability in rough water is redtced. A fair ‘position is to have the top of the blade circle some three inches below the bottom, as with shaft driven screws.
(4) WAVE MAKING .
When the boat is at rest, the pressure on its sides in every direction in a horizontal plane is the same. When it moves forward water is displaced so as to flow round the immersed parts ; in other words particles are accelerated outward from the bow, and kinetic energy is put into the water. From Bernouillis Theorem it follows that this increase of kinetic head must be accompanied by a decrease of potential head or pressure, and since the pressure on the water surface is constant (atmospheric), a fall of level will occur, and the level will be lowest where the velocity of the streamlines is greatest. Evidently this region of low pressure must move with the
boat, and in doing so it will give rise to a system of waves whose origin is at a point a little behind the cutwater, and which diverge at a definite angle to the direction of motion. This angle is known as the obliquity and is designated #.
A corresponding area of high pressure resulting from the deceleration of the streamlines round the stern of the boat will give rise to another independent group of waves, generally, smaller, and originating a little forward of the stern.
It is clear that all the energy put into the water to maintain these groups of diverging waves is entirely lost, since the waves move clear of the boat, carrying their energy with them.
A third system of transverse waves is produced, mainly by the expenditure of energy in accelerating water downwards to obtain the. lift. Under certain conditions, dependent to some extent on the depth of the water, this system moves at the same speed as the boat. It can be shown that the energy in any wave per foot length along its crest is proportional to Lli2 foot pounds, where L is the wavelength in feet, and h the height or double amplitude. In the transverse or following group, the rate of generating waves is clearly proportional to and the rate of dissipation V
of energy is therefore proportional to Lh2 x or Vh2.
Now h the pressure head and this varies with the square of V, so that we find that the power expended varies as the fifth power of the velocity, other things being equal.
In the case of the diverging waves, it is generally found that the stern group are unimportant compared with those originating at the bow. The power loss due to the latter can be shown to be proportional to : . h2V3 sin 2# cos f3, where # is the obliquity of
the system. As before h depends on V2 and hence the power is proportional to the seventh power of the speed, under the same conditions.
However, in both cases it is possible to reduce h inthpendently by careful design of the hull lines, and owing to the increased lift at high speeds its reduction is partly automatic. In general, the accelerations and displacements of the water should be kept as small as is practicable, this necessitating small angles of incidence in both vertical and horizontal planes, and very gradual curvatures in either direction. Further, # may be reduced by making the entrance angle very fine and avoiding deep immersion of the
vertical sides near the steps. In general decreases slightly as the speed increases, though in small boats it does not vary greatly either side of 20.
A small percentage of the energy given to the transverse wave system may be recovered by suitably proportioning the step and the after body, as part of the water sweeping up from behind the step may be arranged to impinge on the bottom of the after body and increase the lift. However, unless the boat is very long not much energy can be saved by this means. The lift is given approximately by :
F.-.016 AV2 pounds, where A is the total area of the lifting surface in square feet, and V in feet per second, assuming a mean angle of incidence of 50, an angle found by experiment to be the most efficient. To summarize then, at high speeds less volume is immersed, and the wavemaking loss when planing is relatively small due to independent reduction of the wave height h to a very small value, particularly in the diverging groups.
5. Am RESISTANCE.
Most of the foregoing losses are reproduced to some extent in the air as well as in the water, and their analysis is considerably more difficult in the case of the elastic fluid. It is generally assumed that the resistance due to the air is negligible at the relatively low speeds attained in small speed-boats, and the acceptance of this erroneous view has led to little progress being made in reducing this resistance. Recent development has yielded such improvement in hydrodynamic design that the air resistance now represents a considerable proportion of the total, and may be regarded as a source of power loss as serious as any of the others.
It has been established that reduction of the wind resistance by as much as 50% at 25 m.p.h., can be accomplished by quite simple fairing over the top of the hull, including the pilot, who must not be left protruding in the air. Now since the air resistance depends, like water friction, on the square of the speed, it follows that in a head wind of only 10 m.p.h., with a water speed of 25 m.p.h., the head resistance will be double the stillair value, and the power loss nearly three times as great. It is perhaps worthy of note that the only completely faired boat in the 1500 c.c. class of the last Duke of York’s Trophy race, was undoubtedly the fastest on the straight co uise
The shape offering least resistance is the well known ” raindrop ” form, having its greatest width about one third of the length from the front. It is of course generally impossible to fit this exact shape to the hull proper, the plan of which is fixed by other considerations, and so a compromise must be made, depending on the actual shape available. The modification having more or less parallel sides, and the side elevation of ” raindrop ” form, swept down to a horizontal edge at the stern somewhat of the shape of a garden slug, is perhaps the simplest. In addition a smooth fairing, running down the centre from behind the pilot’s head, might be extended to mask the outboard engine if this type is used.
Much can be learnt from modern aircraft and racing car practice, and though boat speeds are at present very much lower than those of their counterparts on land or in the air the same principles apply, even though the effects are much smaller.
(Further articles by Mr. Poole will appear in later issues, so that anyone wishing to build their own craft during the winter will have plenty of useful data to work with).