The term “tactical horsepower” is defined as the horsepower available for propulsion. On submarines with direct connected engines it is less than the rated horsepower, except for very short intervals when the bottom is clean. This arises from the two limitations which must be observed in Diesel-engine operation. The first is that the maximum designed piston speed must not be exceeded. The second is really a heat transfer limitation, but is invariably expressed as a limitation placed on the mean effective pressure. Both of these limitations are factors of design and cannot be altered with safety after the engine is built.
With the maximum allowed mean effective pressure fixed, an examination of the familiar horsepower formula shows why the horsepower falls off as the bottom fouls. If in the formula,
Hp = Plan / (k x 33,000)
maximum P is regarded as fixed by design, the available horsepower varies directly with Ji. Submarine propellers are usually so designed that, with a clean bottom in smooth water, maximum allowed mean effective pressure is developed in the cylinders at a speed corresponding to the maximum allowed piston speed. When the bottom fouls, to make the same r.p.m. would require greater than maximum mean effective pressure. A reduction must therefore be made in the maximum allowed revolutions which entails a corresponding reduction in available horsepower.
Figure 1 shows on the conventional diagram how the horsepower for various propeller speeds varies with time out of dock. On this diagram shaft horsepower is plotted against r.p.m., both to logarithmic coordinates. Such a diagram is in current use in submarines, but it should be remembered that two inaccurate assumptions have been made in order to simplify the diagram. The first assumption is that s.h.p.=k(r.p.m.)n. This assumption is probably sufficiently correct for all practical purposes although n does not remain constant throughout the whole range. The second assumption is that_ n equals three, not only for the clean bottom but also for foul bottom condition. This assumption affects the accuracy of the conclusion more seriously because, as the bottom fouls, n probably has a lower value. The value of n for foul bottom conditions is a subject about which little is known. The resistance of a ship to passage through the water may be roughly divided into the frictional resistance and the wave-making resistance, the latter varying nearly as the fifth power of the speed. As the wave-making resistance is the less affected by fouling, it follows that fouling has a relatively greater effect at slower speeds. The slope of the s.h.p.-r.p.m. curves for foul bottom conditions should therefore be less than three. Information on the subject is vague and incomplete. The Bureau of Fisheries pamphlet on the effect of fouling states that a badly fouled bottom may cause increase in power as much as 100 per cent at slow speeds and 60 per cent at high speeds.
The error introduced by making all s.hp.- r.p.m. curves parallel varies with the positions of the points for which data were taken to establish the curves. On this subject no data are at hand and, as the whole question is one on which little is known, the writer has persisted in making all curves parallel. As conclusions are drawn on comparative results, the error introduced will be slight.
All data are taken from a certain division of submarines operating continuously from the same port in tropical waters. Under these conditions fouling is undoubtedly greater than for similar vessels operating in colder water or over a wider geographical range. The writer’s own experience indicates that the conditions shown are by no means extreme, and worse conditions of fouling are frequently encountered. Data on these particular submarines were selected because they were the most complete and represented the accumulation of years of experience, tending to eliminate abnormal conditions.
In Fig. 1 the full lines marked with the plain figures are s.h.p.-r.p.m. curves with propeller of present pitch. The figures represent the months out of dock. The dotted lines marked with encircled figures represent conditions that would obtain if the propeller pitch were reduced. All curves have a slope of three. The intersection of these curves with the line labeled maximum mean effective pressure determines the r.p.m. at which maximum allowed mean effective pressure will be developed in the cylinders. As the hp. with fixed mean effective pressure varies directly as r.p.m. the slope of mean effective pressure line is one. Data for all other curves are taken from Fig. 1, except that additional data on effect of fouling on the r.p.m.-—speed relation were used for curves of Fig. 4.
In this discussion comparison is made between existing conditions and estimated conditions that would be encountered if the propeller pitch were so reduced that maximum allowed mean effective pressure would be developed in the cylinder with maximum piston speed after the bottom has fouled by two months’ operation. Such a reduction in pitch results in an increase in the mean tactical horsepower between docking. No attempt has been made to establish the pitch at which the mean tactical horsepower would be a maximum because the fouling varies so much with different operating conditions that an exact mathematical determination is not warranted, and also because too radical a change in propeller pitch would probably adversely affect the propeller efficiency. Discussion is therefore limited to the two pitches selected mainly to show the falsity of pitching the propeller to get maximum trial speed without regard to foul bottom conditions.
It will be noticed that the effect of reducing the propeller pitch is to reduce the tactical horsepower for the first month out of dock. For the second month the tactical horsepower with reduced pitch is greater by an increasing amount, reaching a maximum at the end of the second month. During these two months the engine is limited by the maximum piston speed and the horsepower increases as the mean effective pressure to attain this piston speed increases with fouling. After the second month the horsepower available decreases as a reduction in maximum r.p.m. becomes necessary.
In Fig. 2, a comparison is made between r.p.m. attainable under the two conditions of propeller pitch. With present pitch, the attainable r.p.m. drops off immediately from the clean bottom condition. With reduced pitch the r.p.m. remains constant for the first two months after which it drops off at a somewhat slower rate than before.
In Fig. 3, the horsepowers available for Propulsion under the two conditions are compared. Under present conditions the horsepower decreases at the same rate as the r.p.m. in Fig. 2.
With reduced pitch the tactical horsepower is less for the first month out of dock, the sacrifice varying between 13 per cent with clean bottom and 0 per cent shortly after the end of the first month. From this time °n reduction of pitch results in increased available horsepower, the increase varying from zero to a maximum of 6.5 per cent. Inspection of these two curves immediately discloses that the mean ordinate of the second curve is greater than that of the first. The mean ordinates are determined as 90.6 for the first curve and 94.2 for the second, or a gain of 3.6 per cent in average horsepower for the time out of dock by reducing the pitch.
In Fig. 4, the speeds through the water for these two combinations are compared. The striking feature of these curves is the serious loss of speed due to bottom fouling under any and all conditions. Corresponding to the available power a slight gain in speed after the first month out of dock is obtained at the sacrifice of a slight amount of speed for the first month. The loss of speed for the first month varies from 5 per cent immediately out of dock to zero at the end of the first month. The gain in speed varies from zero at end of the first month to a maximum of 2.5 per cent at the end of the eighth month. Average ordinates of these two curves are 81.1 and 82.1 respectively or a gain of 1 per cent average maximum speed for a reduction in pitch. Corresponding greater average advantage would be obtained when longer periods between dockings are necessary.
These curves for speed were determined by data available for variation of per cent clean bottom speed obtained at various r.p.m. at different times out of dock. These curves (not submitted) also show that fouling is more serious at slow speeds as the percentage reduction of clean bottom speed due to fouling is greater at slow speeds than at high speeds. The curves were drawn on the basis that the propeller efficiency would not be seriously affected by reducing the pitch the necessary amount to effect the change desired.
No attempt has been made to evaluate the effect of sea conditions. With adverse wind and sea the available horsepower will be decreased under all conditions with present propeller pitch and after the second month with reduced pitch. For the first two months with reduced pitch adverse wind and sea would increase the total horsepower available, although, of course, the speed through the water would be reduced from the plotted values.
For purposes of comparison, estimated conditions for an electric drive submarine are depicted on the curves in broken lines on the basis that present propellers are to be used. As engine speed with this type propulsion is independent of propeller speed, 100 per cent rated horsepower is always available. Propeller r.p.m. attainable with 100 per cent power is determined by the intersection of s.h.p.-r.p.m. curves with the 100 per cent horsepower line in Fig. 1.
This comparison is made on the basis of an electric drive installation of the same s.h.p. as the present direct connected one. On the basis of weight per s.h.p. such a plant could probably not be installed. No correction for weight per s.h.p. of the two type installations is made for two reasons. I he first is that no data are available and no fair comparison can be made except on the basis of a complete design for a definite project. Secondly, the writer believes that figures for pounds per horsepower are frequently deceptive.
Figures sometimes quoted for pounds per horsepower are deceptive because of the indefiniteness of both the horsepower and the pounds. The writer is of the firm opinion that Diesel engines should be rated at the horsepower at which they may be operated with reliability. On this basis he believes that many of our submarine engines would have to be re-rated. Also, it is unfair to quote figures for pounds per horsepower on a basis of 100 per cent rating when the engine can develop that rating only for short periods when the bottom is clean.
In comparing weights, the only just comparison is for the weight of the complete plant. Thus, the elimination of engine clutches, propeller clutches, synchronizing clutches, extra shafting, and engine reversing gear would go a long way toward compensation for generator weights, and extra weight of motor and control gear. If high speed engines are used the writer believes that a Diesel-electric drive plant could be designed which would compare well with the best design of direct drive plant.
In this discussion the subject of critical speeds has been avoided. Where critical speed range exists close to the maximum piston speed it frequently occurs that the horsepower available for propulsion drops to 85 per cent rated horsepower a few weeks out of dock. The necessity for such a sacrifice would, of course, not occur in an electric drive installation.
There are other advantages of electric drive such as complete range of operating speeds due to avoidance of critical speeds, multiplicity of smaller primary power units with complete interchangeability of parts, flexibility of control, elimination of troublesome clutches, simplification of control especially on submergence, availability of all units for battery charge without use of propeller clutches, and elimination of the necessity for alignment of long lengths of shafting. These subjects are not discussed at length as they are not directly connected with the subject matter.
Conclusions: 1. Submarine propellers should be pitched with a view to foul bottom operation and not merely for maximum trial speed.
2. A slight increase in average tactical horsepower may be secured by a reduction of the present pitch of submarine propellers.
3. Considering the reduction in tactical horsepower of direct connected Diesel engines due to bottom fouling, Diesel electric drive is under less weight handicap than weight per horsepower figures indicate.