The original and fundamental idea in the establishment of experimental basins, or, as they are otherwise called, "model tanks," was to assist in the determination of the resistance of ship-shaped forms at various speeds of propulsion, and thence the deduction of the power required to drive a given form at a given speed, and also the most desirable form for any given speed.
Their functions have been extended to include experiments with propellers, tending toward the solution of the problem of the best form, dimensions, and locations of propellers, and to include other experiments of kindred nature in connection with problems of ship construction and propulsion.
Originally, the underwater forms of vessels were determined by experience with full-sized ships, or by considering, by looks and touch, the shape of a small wooden model.
Some experiments on the resistances of various surfaces were made in the eighteenth century by several naval architects and others interested in the subject; notable among these was Colonel Beaufoy, the results of whose experiments were published in 1834
In 1874, in a paper presented to the British Institution of Naval Architects, Mr. William Froude propounded what is now known as "Froude's Law," or the "Law of Comparison," which is a special application of the law of similitude, first propounded by Newton.
The whole usefulness of model-basin experiments is due to the truth of this law, which permits accurate and exhaustive experiments at reasonable cost, and the accurate determination of characteristics of a given model prior to building, which in turn permits ready determination of the horsepower necessary to give any required speed in the full-sized ship.
The law, which was deduced by Mr. Froude, with the aid of the British admiralty, from consideration of results of experiments with the British ship Greyhound and with models towed in the basin at Torquay, may be expressed in the following words:
Eliminating the resistance due to skin friction, if a ship be D times the dimensions of a model of similar form, and if at the speeds V1, V2, V3, the measured resistances of the model are R1, R2, R3, then for speeds √DV1, √DV2, √DV3, of the ship, the resistance will be D3R1, D3R2, D3R3.
The speeds V1, V2, V3 for the model and √DV1, √DV2, √DV3, for the ship are termed corresponding speeds.
It was early found that the skin friction did not follow this law.
The three elements of ship's resistance have been determined to be, (1) skin friction, (2) eddy resistance, (3) wave making resistance.
The total resistance, minus the skin friction, is termed the residuary resistance.
The skin friction of a ship has been found by many experiments to be practically the same as that of a plane surface of the same nature, area, and length in the direction of motion as the
curved wetted surface of the ship.
The skin resistance of a ship may then be expressed as a
formula:
R8= fSVn.
where R8=skin resistance.
S = wetted surface in sq. ft.
V = the speed in knots.
f,n= semi-constants changing somewhat with the nature and dimensions of the surface and determined by experiment only.
Tables of these constants, as separately determined by Mr. R. E. Froude and Dr. Tideman, are given in Taylor's "Resistance and Propulsion of Ships."
The original experimental basin, as stated, was developed by Mr. Froude and was located at Torquay, being established in the seventies. (The British experimental station has since been removed to Haslar. See be ow). Since that time a number of experimental stations have been established, both by private firms and by governments. A partial list of such stations follows:
EXPERIMENTAL MODEL STATIONS.
Date. | Location. | Length. | Breadth. | Draught. |
1884 | Leven Shipyard, Dumbarton | 300 | 20 | 8.8 |
1886 | Haslar | 400 | 20 | 9.2 |
1889 | Spezia | 479 | 19.7 | 9.8 |
1900 | North German Lloyd S.S. Co., Bremerhaven | 538 | 19.7 | 10.0 |
1903 | Charlottenburg | 528 | 34.5 | 11.5 |
1904 | John Brown & Co., Clydebank | 490 | 32.0 | 10.0 |
1899 | U.S. Government, Washington, D.C. | 470 | 42.8 | 14.8 |
1905 | University of Michigan, Ann Arbor | 300 | 22 | 10 |
1907 | French Government | (Just completed.) |
All these vary in matters of constructional detail, but all aim at the same results, and the variations are due in most part to differences of local conditions or considerations of expense.
Probably one of the most complete is the U. S. Government basin located at the U. S. Navy Yard, Washington, D. C., and operated under the Bureau of Construction and Repair of the - Navy. The design and installation of this basin was under the direction of that able officer, Naval Constructor D. W. Taylor, U.S.N., who has also been in charge of the experimental work since the opening of the basin in 1900.
The basin holds about a million gallons of water. It is filled from the city supply for Washington.
Before reaching the basin the water is treated with a small quantity of alum, which removes any mud present, and is then clarified by passing through a sand filter.
A small stream is kept constantly running through the filter to freshen the water after filling, and to make up for leakage and waste.
The basin can be pumped dry in about four hours by an electrically-driven centrifugal pump. Two other electrically-driven pumps are fitted, a four-inch centrifugal pump connected with troughs on each side of the basin just at the surface, by which the water can be "scummed," and a small plunger pump used for drainage and piped to take the water from inside or outside the basin as desired.
The building is heated by hot air. The temperature is generally kept slightly higher than is usual for an ordinary living or working room. Otherwise the operators of the traveling carriage are liable to discomfort from their constant motion to and fro through the damp air.
Steel troughs about 12 inches square in sections are located on each side and just below the usual working level of the water. They act as absorbers of wave disturbances and cause them to die away rapidly. In addition there is at one end of the basin a "wave-breaker," consisting of a large number of square strips of wood set vertically at varying distances apart. These, with the side troughs, result in reducing any wave motion set up by a run of a model into minute ripples by the time eddies and currents due to the passage of the model, have been dissipated. Without wave-breaking appliances, running trials at high speeds would be a long operation as long waits between runs would be necessary to allow the waves to subside.
The apparatus for measuring the resistance of models is carried on the traveling carriage which spans the basin as shown in Plate I. This carriage weighs about 70,000 pounds, and hence has sufficient inertia to resist sudden variations of speed.
The carriage is driven by four motors, one on each corner. The speed is controlled on the Ward-Leonard system. Current from an "exciter" generator at 100 volts keeps constant excitation in the field coils of the motors and current from the same exciter passes through the controlling rheostats on the carriage and also around the field coils of the main generator.
The main generator runs at constant speed controlled by a governor which limits variation of speed within 1 1/2 per cent from no load to full load. The generator armature is in series with the motor armature, so that all the current developed at the generator passes through the motors, the voltage at the generators varying according to the amount of excitation of the generator fields which is controlled from the carriage.
The four motors are so arranged that they may be connected all in series, or two and two in series, the pairs being parallel.
The maximum generator voltage is 250, and as there are two generators which can be arranged in series, the maximum available voltage is 500. The motors are geared together, two and two across the carriage, and also geared down to the main driving wheels. In addition, the forward pair of motors has back gearing for low speeds. For many experiments one generator only is required, the motors being arranged all four in series for speeds ranging from 1/2 knot to about 6 1/2 knots, and two and two in series parallel for speeds from 6 1/2 knots to about 12 1/2 knots.
The maximum speed at which the carriage can run is about 20 knots, developed in a run of about 200 feet.
With such a heavy mass moving at this speed in a confined space, very careful provision is required for stopping.
With the Ward-Leonard system a powerful electrical braking effect is obtained from the driving motors, through the back current generated when the exciter current around the generator fields is shut of for reversed. This enables the carriage to be stopped more rapidly than it is started. This method of stopping is not relied upon solely, since it fails if the circuit is broken either accidentally or by the automatic circuit breakers in case of an overload. This method also necessitates proper manipulation on the part of the person operating the carriage. At least one method of braking to stop the carriage in the minimum possible distance was desirable, independent of the electric current, and not requiring manipulation by the operator. Wheel brakes could not be used, as they would cause objectionable wear on the wheels of the springless carriage, and would stop it no more rapidly than the electric brake supplied by the Ward- Leonard system. (it may be noted that from time to time the wheels require truing up to insure accurate measurements). Friction brakes closed by hydraulic pressure were therefore fitted. These are fitted at the north end of the basin in the form of a pair of iron strips on each side, securely anchored at one end to the main walls of the building, and pressed together by hydraulic cylinders. They are 15/16 inch apart when the pressure is on and 1-1/16 inches apart when it is off, being pulled apart by springs when the pressure is released. A strip of iron about 1 inch thick and 12 feet long is securely bolted to each forward corner of the carriage, and is adjusted to enter without shock the space between the stationary strips, and by friction against them bring the carriage to rest. Hydraulic pressure is obtained from a small electric pressure pump, and an accumulator is fitted, through which the pressure can be varied from 100 pounds to 600 pounds per square inch. Two gauges at the south end of the basin indicate the pressure in the hydraulic cylinders, so that the operators may know before starting a run that the friction brake has pressure on. The strips are kept lubricated in order to avoid seizing or violent shock.
In addition to these, there is an emergency brake, which takes hold of the carriage if it should get through the friction brake without being arrested. This consists of a taper piston rod passing through a round hole in the cylinder head, which it gradually closes as it moves; the principle is the same as the hydraulic recoil brakes for heavy guns. The hydraulic cylinder is below the water level when the basin is full, and when this is the case the emergency brake is always ready. The parts of this brake are bolted in place by fastenings which will be broken in case the brake comes into action, but up to the present time this has never happened.
MODELS.
Paraffine, which is largely used for models in experimental basins abroad, has many advantages, but cannot be used in Washington as it will not stand the summer temperature without too much softening.
As compared with paraffine as a material for the construction of models, white pine has the following advantages and disadvantage:
ADVANTAGES.
1. Wood retains its shape better during changes in weather.
2. Wood is many times stronger.
DISADVANTAGES.
1. Wood is harder and more expensive to fashion.
2. Wooden models are harder to keep tight.
3. Wooden models are harder to give a uniform surface.
The first and second objections have been overcome by the adoption of special machinery designed by Naval Constructor Taylor, and the third by using a special varnish to finish the models, which gives a surface practically uniform.
Owing to the greater strength of wood it is feasible to make models 20 feet long, and the sectional area of the basin is such that these models may be run with no greater interference from the size of the basin than 12-foot models in the smaller foreign basins.
The advantages of this size, as compared with the 12-foot size, in determining resistance, are great. It is found that for the 20-foot models of many U. S. naval vessels, the resistance at the speeds corresponding to the actual maximum speeds of the vessels, is below 40 pounds. With 12-foot models the resistances would have been below 9 pounds. A 20-foot model is 1/1728 the displacement of a 240-foot vessel, and 1/13,824 that of a 480-foot ship.
For a 12-foot model these figures are 1/8000 and 1/64,000, respectively.
With the large model, resistance is measured more easily to a given percentage of accuracy, and the gap between models and ships to be bridged by the Law of Comparison is not so great.
It is the usual practice at the U.S. model basin in the case of models of men-of-war to determine five resistance curves, each extending somewhat beyond the speed corresponding to the maximum speed of the vessel. These curves are as follows:
No. 1. With the model at a displacement corresponding to the designed normal displacement of the ship and at the designed trim of the ship.
No. 2. With the model as in No.1, except the trim is changed four inches by the head.
No. 3. With the model as in No. 1, except the trim is changed four inches by the stern.
No. 4. With the model as in No. 1, except that it is 10 per cent lighter.
No. 5. With the model as in No. 1, except that it is 10 per cent heavier.
Plate II shows these five curves for a model representing the Yorktown. The displacement of this vessel corresponding is 1680 tons and the designed trim 2 feet 1 1/2 inches by the stern. The maximum speed of the Yorktown, when tried at 1680 tons, was 16.7 knots. The corresponding speed of the model is 493 knots. The curves of Plate II are carried higher in proportion to the designed speed of the vessel than is necessary.
The speeds of 20-foot models corresponding to the maximum speeds of some of our battleships are given below:
Battleship. | Length. | Maximum. | Corresponding speed of 20-foot model. |
Oregon class | 348 | 16.8 trial | 4.03 |
Iowa class | 360 | 17.1 “ | 4.03 |
Kentucky and Alabama classes | 368 | 17.1 “ | 3.99 |
Maine class | 388 | 18 | 4.09 |
Georgia class | 435 | 19 | 4.07 |
Plate I shows the carriage in operation, towing a model of the battleships of the Georgia class.
PREPARATION OF MODELS.
Models are as far as practicable made of the standard mean immersed length of 20 feet. The length over all is usually somewhat greater, The model-making apparatus is designed with the idea of working from a body plan. Having a correct body plan upon a certain scale, sections of a 20-foot model corresponding to the sections in the body plan are first determined, using an eidograph, and with the usual scales for drawings and sizes of vessels, it nearly always involves enlargement. The eidograph works upon a table covered with a sheet of glass.
Having properly adjusted the length of arms by means of the scales provided, the pointer on the short arm is run around the sections of the body plan, the pencil on the long arm describing the sections desired upon pieces of paper. These paper sections are used as patterns for use in cutting out the wooden sections for the former model. These are clamped in their proper relative positions upon an iron table and a skin of round strips of wood nailed securely to them. Plate III shows this skin partly in place. This completes the "former model," as it is called, except that plaster is later applied as described below. Its ends are not made to accurately represent the vessel, as it has been found more desirable to rough finish only from the former the ends of the final model and finally finish them by hand.
While the former model is building, a wooden block is built up of white pine planks about 2 inches thick, sawed hollow and glued together hot under heavy hydraulic pressure. This block is so proportioned that when the finished model is cut from it, the wood will be left amply thick, generally not less than about 2 inches. Additional thickness is not especially avoided, as the models require ballast in every case. The former model and its corresponding block are now secured in the model-cutting machine, the former model being below. As may be seen from Plate IV, the roller below rolls over the former model, and the saw above, driven at high speed, is constrained by the balanced link work to move exactly above and at a uniform distance from it. The sizes are so arranged that the saw does not cut within one-eighth of an inch of the intended finished surface of the model. There are two traversing cutter heads, one on each side.
Each is traversed (by an electric motor) three-quarters of an inch or so at a time and then a saw cut made. Then the superfluous wood is knocked off, the interstices between the battens of the former model plastered with plaster of Paris to give a smooth surface, and a rotary cutter substituted for the saw, with a corresponding roller. This cutter rough-finishes the model to very near its exact size. The model is then removed from the machine and finished by hand, the ends, which are left quite rough, being also shaped by hand from paper patterns or light wooden templates obtained from the lines. Sandeddisks, driven at high speed by an electric motor, are used to finish. The models are carefully painted, inside and out, and a standard varnish finally applied to the outside to get a uniform surface. Before being taken to the basin, the models are carefully measured.
From the results of measurement, a body plan is drawn and compared with the original lines to insure that the model accurately represents the ship. All calculations at the model basin are made from actual lines of the models.
The tops of the completed models are parallel to their designed water lines, and with the level straight-edges fitted in the south end of the basin, it is easy to determine the exact trim of the model when afloat.
All trials are run by weight and draught is used only as a rough check. Before beginning a trial a model is suspended to one of the cranes on the carriage, and weighed. It is then ballasted until its weight in fresh water corresponds to the desired displacement of the ship which it represents. After a trial the model is weighed again for checking after the ballast has been removed. Models are handled by electric cranes, one on the forward side, the other on the after side of the carriage. The models are stowed on the galleries on each side of the basin.
The dynamometer is shown in Plate V. Its object is to record the resistance of the model, being towed through the water of the basin. The dynamometer is attached to the carriage which runs to and from rails above the water. The model has vertical plates attached to it in the center line at each end which play With very little freedom between the pointers rigidly attached to the carriage, so that with practically no friction the model is constrained to move in the same direction as the carriage and Without deviation, and at the same time is free to rise and fall, or change trim. The towing rod (10) takes the resistance of the model, and the fore and aft motion of the model, relative to the carriage, is very little.
The recording drum (44) is arranged to have sheets of paper about 16 inches by 22 inches secured to it somewhat as paper is secured to an ordinary indicator drum. The drum (44) is mounted upon a shaft which ordinarily can be turned by hand by means of the little hand wheel (49). Mounted loosely upon an extension of this shaft is a worm wheel (43) driven by a worm (42) which is connected by the parts numbered (41) to the main driving shaft (40), revolving with the wheels of the carriage. An electric clutch (50) seizes the worm wheel to the shaft or releases it, so that when desired the drum can be thrown into gear and driven at a speed proportional to the speed of the advance of the carriage.
Pencils (48), in connection with the magnets (47), record upon the drum "time" and "distance." The "time" pencil is connected with a break circuit chronometer (38), and records every second upon the drum. The “distance" pencil records contacts with pins spaced along the track 30.4 feet apart. This distance of 30.4 feet is 1/200 of a knot, a knot being taken as
6080 feet. From the record of time and distance the speed could be readily calculated, but in practice it is found that the working of the drum is so accurate that the speed can be read off directly by an arbitrary scale and the distance pencil is not ordinarily used. The length of record corresponding to 10 seconds of time is measured on a special scale which gives at once the speed in knots. This scale requires calibration and changing from time to time due to wear of wheels, etc. The distance record is used from time to time to check these direct readings in order to make sure that no wear of parts or lack of adjustment has vitiated accuracy.
Paper with metallic surface is used upon the drum, and the so-called pencils are really pieces of brass wire.
Considering the dynamometer proper, the spring (5) is connected at its rear end to the swinging cross-head (31), which is suspended by rod (19), about 4 feet long, and so arranged as to swing very freely. A pin runs through this cross-head over which the towing rod jaws fit loosely. Out board of the towing rod on this pin are vertical and horizontal flat surfaces upon which knife edges (34) in the saddle (9) bear. The cross-head moves in the guide (35) rigidly bolted to the fixed bracket (2). Its travel is about 3/4 of an inch between positive stops (32). At the extreme end of the rod, just below the cross-head, are electric contacts (33), adjustable and usually set so that the contact is made on either side just before the cross-head reaches the positive stop, which is also adjustable.
The forward end of the spring is attached to a screw (6), which is secured to the lower end of the traveling bracket (1). Attached to this traveling bracket is the arm (20), carrying the record pencil (21), which then marks upon the drum the exact position of the traveling bracket and thus determines the position of the forward end of the spring. The rear end of the saddle (9) is fitted with horizontal and vertical knife edges (34), engaging vertical and horizontal surfaces on a pin attached to the lower arm of a bell crank lever. This bell crank is balanced upon knife edges (8) and carries by means of the scale beam (7) a scale pan (13). It also has attached to it the auxiliary beam (14) which is connected by double pivots to the pointer (15) which records upon the drum the position of the rear end of the spring. The distance up from the knife edge center (8) to the line of action of the pointer (15) being 5 feet 6 inches, while the distance down to the line of action of the spring is 2 feet, it will be seen that the motion of the rear end of the spring is increased at the pointer in the ratio of 2.75 to 1.
The dash pot (16) is filled with glycerine and has a hollow floating piston with detachable connection rod (17), the rear end of which engages, as shown, a pin in the bracket upon (14). The rear end is so suspended by the chain (18) that no weight is taken on the pin, and the latter has a play in the jaws of the connecting rod (17) of 1/ 16" or so.
The traveling bracket (1) is actuated by a screw (4) being rigidly held by guides as shown. The screw (4) is driven by the worm wheel (3), which in turn is driven by the worm (28). This worm is upon a shaft which carries the gear wheels (24) and (24a), which mesh with the pinion (23a) and the idler (25); the idler (25) being driven in turn by the pinion (23). These pinions (23 and 23a) are loose upon the shaft of a motor (22), which is running all the time. At the ends of this shaft are magnetic clutches (26 and 27) which grip the pinions (23 and 23a). It will be seen that when clutch (26) is in gear so as to grip the pillion (23a), the traveling bracket (1) and recording pencil (21) must move in one direction, and when the clutch (27) has hold of pinion (23), the pencil (21) moves in the other direction. When both clutches are out, the pencil does not move, and the apparatus is so arranged that but one clutch can be in at one time.
There is a magnetic brake (29) upon the idler (25), so arranged that when neither clutch is in, a spring throws the brake in and thus promptly checks the motion of the pen when the clutch releases. When either clutch is in, the spring is held back by a magnet, and the whole gear moves freely. The clutches can then be thrown in by hand as desired, and in addition are connected through a magnetic relay (51) to the contacts (33) at the lower end of the dynamometer cross-heads, the connections being such that when the cross-head swings against the rear contact (33) the bracket with the recording pencil (21) is screwed forward, and when contact is made forward the bracket is screwed back. This is done automatically when the switch with the magnetic relay is in.
The various electric contacts for operating the device described are all controlled by the handle of the controller (37). When the pointer is brought opposite" tension" the traveling bracket is screwed forward so as to give the spring tension. When it is brought opposite "release" it is screwed back. When it is brought opposite "automatic" the contact arrangements just described (33) automatically traverse the traveling bracket (1). Then as the pointer reaches "drum" the drum is set in operation, and as it reaches "time" the time pencil begins to record, and as it reaches "distance" the distance pencil begins to record. In practice, in making a run, when it is desired to begin the record, the pointer is thrown at once to the right until it reaches “distance," when all the operations above described are in.
The following process of adjusting the apparatus and calibrating the spring is used:
Before putting in the spring, the cross-head is brought to its central position by means of the balance weights (12) upon the bell crank, and care is taken that the cross-head swings in this position whether the pin securing the scale pan (13) rigidly to the scale beam (7) is in or out. The position of the auxiliary pointer (15) is then noted. There are fitted, so as to mark upon the drum when desired, a number of fixed pencils, such as which can be set to record at any position. One of these, called the auxiliary zero pencil, is now, set so as to indicate always the position of the auxiliary pointer (15) when the cross-head is central and everything balanced.
Next the spring (5) is slipped into place and a corresponding back weight (11). The record pencil (21) is then brought to a convenient position for zero of the main scale, and a scale pencil set to mark always this zero. By adjusting the screw (6) forward or back, as may be required, the auxiliary pointer is brought back to its zero. When this is the case the back weight (11) gives the spring a certain initial tension by means of the saddle (9) and cross-head (31), while at the same time the cross-head is swinging freely in exactly its natural or zero position. Supposing the spring in use is a forty-pound spring, or a spring which, at its maximum extension of 9 or 10 inches will record 40 pounds. It will be noted that the extension of the spring is not from its natural position of equilibrium or from zero tension, but from its arbitrary zero position, the amount of tension at the arbitrary zero depending upon the amount of back weight used. It has been found that the springs are more reliable if given an initial tension by the use of such a back weight. The scale pan (13) is next allowed to swing freely, and a weight of ten pounds placed upon it. This extends the spring until the cross-head brings up against the positive stop. The bracket (1) is then screwed forward by throwing the motor in gear until the auxiliary pointer again comes to zero. A scale pencil (45) is now set to mark the position of the recording pencil (21). Twenty pounds is now placed upon the scale pan and equilibrium again restored by screwing the traveling bracket forward. Similarly thirty and forty pounds are used. The scale pencils, such as (45), now record upon the card lines which correspond to extensions of the spring, measuring 10, 20, 30, and 40 pounds. The weights are removed, the recording pencil (20 returned to about its zero position, the scale pan (13) clamped in its zero position, and the work of adjustment and calibration is complete.
The model is then attached by the towing rod (10), which it will be seen (although it may be at an inclination) transmits to the spring wily the horizontal pull upon it, the resistance of the model being all in a horizontal plane. It is customary to start a series of runs with the lower speeds and work up by degrees to the highest speeds, plotting roughly the results as they are obtained after each run. In this way, knowing the speed of a run about to be made, the approximate corresponding resistance can be guessed at very closely, and it is the practice to set the record pencil (20 approximately at this position before making the run, so that the automatic appliance may be called upon to traverse it as short a distance as possible. It is evident that if, during the run, the auxiliary pointer swings from its zero position, the indication of the record pencil (20 must be corrected according as the auxiliary pointer is above or below its zero position. The correction is evidently 1/2.75 of the deviation of the auxiliary pointer, supposing the extension of the spring to be such that its stress diagram is a straight line.
It is found in practice that the stress strain diagrams for the springs used are practically straight lines. The operator can, however, after experience and practice, by means of a touch of "tension" or "release," bring the auxiliary pointer very close to zero during the majority of runs, so that the automatic devices do not come into play at all, although thrown into gear.
Plotting.—Supposing the difficulties to have been overcome, we can plot the results of towing experiments upon a model in the shape of a curve, such as AAA, in the figure below, showing the resistance in pounds of the model plotted upon speeds as abscissae. This curve represents the total resistance, made up, as we know, of skin resistance, eddy resistance, and wave
resistance. We also know that the latter two alone (eddy resistance and wave resistance), constituting the residuary resistance, follow the Law of Comparison.
The first step, then, is to deduct from the total resistance the skin friction, which is calculated from the wetted surface and the results of experiments on planes of various character. Setting down the skin friction from the curves AAA in the figure, we obtain the curve BBB, representing the residuary resistance of the model. Now we know from the Law of Comparison that this curve also represents the residuary resistance of the ship, provided the scales of speed and resistance are suitably changed.
In the case shown by figure, the model was 1/16 the size of the ship; hence, corresponding speeds of the ship and model are in the ratio √16:1 or 4:1, and residuary resistances at corresponding speeds are in the ratio 163:1, or 4096:1.
Drawing in the scales for the ship as shown, the curve BBB represents the residuary resistance of the ship in either fresh or salt water, according to the scale used.
Salt water resistance = 1.026 (fresh water resistance).
It is now necessary to calculate the skin resistance of the ship, and set it up above BBB, to obtain the curve CCC, which represents the total resistance of the ship.
From the above it is evident that the relative resistances of different forms of models may be obtained and plotted in such form as to be readily comparable.
To obtain an estimate of the horsepower required to drive a given form of ship at certain speeds these resistances and speeds may be readily converted into horsepower by the formula:
H.P.=ft. lbs. per minute ÷ 33000.
The figures so obtained permit plotting a curve of effective horsepower or E.H. P. required.
The tabulation and careful consideration of results of many experiments and trial trips permits the determination of a factor giving the ratio between indicated horsepower and effective horsepower, and assuming, after due consideration of the conditions obtaining, a value for this factor, a curve of probable indicated horsepower or I.H.P. may be obtained.
I.H.P. is an expression too well known to require defining.
In the case of turbines, the measure of power obtainable from the completed installation is taken from the shaft and therefore becomes brake horsepower, or B.H.P., and the factor giving the ratio between B. H. P. and E. H. P. will differ considerably from that giving the ratio between I.H.P. and E.H.P.
The foregoing deals only with a small portion of the functions of the experimental tank, which is of value for a wide range of experiments in connection with ship resistance and ship propulsion.