DETERMINATION OF THE ACTUAL TRACK OF A VESSEL DURING TRIALS ON MEASURED COURSES.
By Ivo Chevalier De Benko, Lieutenant, Imperial Austrian Navy.
[Translated by Lieut.-Comdr. 15. H. C. Leutzé, U. S. N., from Mittheilungen am dan Gebiete des Seewesens, Vol. XVII, No. 12.]
In the following we have in view only the cases where the greatest exactness is necessary to determine the actual wake of a vessel and the time required to make it, as for instance in trials for speed.
As the contracts with shipbuilders generally call for premiums or penalties 0.1 of a knot of speed, we will assume that any method which will assure exactness to that limit will be permissible.
Speed trials consist in running the ship over a well known or easily measured course and taking the exact time required to do it.
The exactness of the results will therefore depend, 1st, on the exactness with which the ship is kept on the measured course; 2d, on the exactness with which cither the prescribed or the actually made course can be determined; and 3d, the exactness with which the time is taken.
Under 1 we can omit such faults as would arise from the state of the sea and strong winds, as they are difficult of determination, follow no laws, and would generally be avoided by choosing suitable weather. Their effects could be felt in the difficulty of keeping the vessel on her course, she being exposed to forces which may be considered to act in the same direction as the course and also perpendicular thereto. The harmful influence on the machinery caused by the laboring of the vessel would also have to be taken into consideration.
The first two mentioned causes of error are, however, similar to some which are unavoidable during good weather, namely, the errors due to bad steering and the influence of currents.
The error caused by bad steering can be compared with that made by the surveyor when he chains distances which are to be measured. In that case nearly every link of the chain makes a small, unmeasurable angle with the direction of the actual line to be measured.
We may perhaps assume that as a general thing a ship will run in regular succession three minutes on her course, three minutes on one side and for the same space of time on the other side, and will then return again to her course for another three minutes, etc. The time of a period would therefore be nine minutes, during two-thirds of which the vessel would be on her course. It would be easy to determine, arbitrarily, the length of the curves and their number, and also the angle of deviation from the course. After that a formula could be established for this error. For instance, if the deviation from the course should be ¼ a point and the distance 30 nautical miles, we would have the formula 30 X 1852 (1 — cos ¼ point) =67 m. or 0.1206 per cent. If, then, the speed of the vessel had been 20 knots the error would only amount to 0.024 knot (this would be the maximum error no matter how much of the time the ship is off her course, as long as it is never more than ¼ point).
It will therefore be seen that the error caused by bad steering is small, and by close attention to the steering it would be so reduced as not to be large enough to be taken into consideration. If it is deemed advisable, however, to take this error into consideration, it would be necessary to note the length of the times and the amounts the ship deviates from her course, and also where the deviation reaches the maximum; the amount of the latter must, of course, also be noted.
The following will show how a convenient formula for this calculation can be established.
The curve representing the course of the ship is similar, as far as the error in question is concerned, to the motion of the pendulum.
The angular velocity of the sheering vessel is comparable to the velocity of the pendulum. Supposing then that the steering is regular, the error will then be the difference between the curved course ABCDA and its projection AA, Fig. 1.
[Fig. 1.]
It would therefore only be necessary to establish the formula for the curve and calculate its length.
In actual practice, however, the curve is too irregular to conform to a fixed law, and it would be necessary to observe the deviations (α), noting the time in minutes during which each deviation exists, and then calculate the error due to each α and its corresponding t, as follows:
From Fig. 2 we have
[Fig. 2]
AA1=AA' cos α ∴ f(error) = AA' — AA1
= AA'(1—cos α) = tvX1852/60 2sin2 α/2
=1852/50sin 1"(2sin2 α/2 / sin1") tv = [6.17510—10] vt ,∆
in which the quantity in parenthesis is the logarithm of the actual coefficient, ∆ is the well known number of Delambre of which there are tables, and v the mean velocity obtained by the formula given on the last page of the article. The total error is the sum of the partial errors thus obtained, i.e., F =[6.17510 — 10] v∑tA, and if t be the same for every observed value of a it may be written before the sign of summation, and the calculations can be made by means of tables of the number A which are entered with a to degrees and tenths.
- If so called “measured miles” are not available, it can be presupposed that it is possible to get accurate data for the position of and distances between prominent points on the coasts from the Coast Survey Office. The probable errors which are given by this office, in connection with other data, will determine whether the chosen points are sufficiently accurately located.
In choosing a course its length should be the first consideration (if 1, 2 or 3 miles are wanted). The length will be governed by the requirements of the case. After that the situation and direction can be determined. In regard to situation, it is necessary to choose a location free from strong winds, heavy seas and irregular currents (specially those near the mouths of rivers). In regard to direction, it is desirable that it should be normal to that of the ranges which are to determine the limits of the run, that the marks of these range lines should be distinctly visible, that the marks of each range are not too far apart, and finally that the ranges both have the same relative direction to the measured line. As the ranges should be sharply defined, large objects, such as church steeples, should be chosen; coast lines, etc., which are changeable, should be avoided.
It is not essential that the ranges mentioned above should be perpendicular to the course, but it is necessary to have at each range a third fixed point upon which angles may be taken for determining the exact points at which the line actually cuts the limiting ranges. The moment the limiting range AB is on, the angle between A and C (Fig. 3) should be measured, and it will then be known, the triangle ABC being known, at which point, E or E', the range has been crossed. If A and C are not too high it will not be necessary to reduce the measured angle to the horizon j it is not difficult to prepare tables for this purpose, which are entered with the heights of the objects and the measured angle.
The strict formula would be cos ζ' = (cos ζ — sin α sin β)/(cos α cos β), which ζ represents the measured angle, α and β the height angles of the objects, and ζ' the projection of the angle ξ.
As α and β are generally small, Legendre’s approximation formula can be used,
x=((α + β) / 2)2 tan ζ/2 — ((α — β)/ 2)2 cot ζ/2
to calculate a small table for the required correction. The table would be entered with a and [) for height of eye from 3 to 8 meters and with C to degrees.
But as (Fig. 3) the angle AEC should be chosen as near to go0 as possible, this correction of the observed angles becomes of no importance as long ns A and C are not located too high.
I will now show how it is possible to find without much trouble the correction to be applied when the range is crossed at E' instead of E as required. It has already been mentioned that if the ranges determining the limits of the course are not perpendicular it will be sufficient to have triangles at each end whose position and distance from the course are known. For instance, in Fig. 4 AN is the course and OCM and EGD the known triangles; the angles OAN and ANE and the distance AN are then also known. The lines OMA and EGN represent the limiting ranges. In order to verify if the ranges are passed at the prescribed points A and N, the angles MAC and GND are measured; they are of course known, as the situation of the triangles and their distance from the measured line are known.
The fact that in Fig. 4 the prolonged course AN goes through the triangle point C is irrelevant to the matter, it is only thus indicated to show how easy the reduction of the course becomes when the ranges are perpendicular to the course and its prolongation cuts through one of the points of the triangle.
Let omc and egd represent the sides of the triangles, s the course, and a the verification angle OAC, and v the angle END. If the angle measured on the range EG be EN'D — V' instead of END— V, the vessel will then have
covered the distance AN' — s' meters instead of the distance AN—s meters, and s' — s — c will represent the correction due the difference v'—v in the angles.
As the triangle END can be solved by means of the triangle EGD and the angle V, it is proper to assume that the piece NN' belonging to the triangle ANN' can also be considered as the change in the side EN of the triangle END due to the change in the angle V.
NN'=Dn(sin(V''—V))/sinV'
In this formula only V' is changeable; it is therefore easy to prepare a table for NN' whose argument is the corrected angle V' (corrected for instrumental error and reduced to horizon).
AN' — s' can be found without difficulty from the triangle ANN', as AN — s and the angle END is assumed to be known. We would have
[FORMULA]
where the right side of the equation only contains known quantities, and it would be again easy to prepare a table for the different values of NN'. But as NN' only changes with v' it becomes possible to combine the tables for A'N' and S' into one table for S' with the argument v'. In order to facilitate the computation of the table an auxiliary angle (cos2) is introduced under the sign of the square root.
But it now becomes necessary to mention why the range is crossed at N instead of N'; in other words, which part of the value NN' must be attributed to the engine. It can be considered that NN' is caused by poor steering, incorrect compass error, and finally through the component of the current normal to the course. It has already been shown under I how to eliminate the error due to bad steering; the error due to the normal component of the current can be eliminated by the projection of S' on AN, or by finding the means of calculating the rapidity, namely,
S=s+NN1=s+NN'cosN'NN1,
the error due to the influence of the compass error. There only remains then the error due to faulty compass correction. This can be reduced to a minimum by establishing on the coast a range parallel to AN on which the error can be accurately determined.
It is therefore necessary to make the following calculations for each limit of the measured course:
NN'= Dn(sin(V''—V))/sinV'
and
S=s+NN1=s+NN'cosN'NN1.
Therefore if you let NN'cos N' NN, — Cn and the analogous quantity for the other limit equal Ca,
S=S + Cn + Ca
from which a table with double argument (the verification angles at A and N) can be constructed beforehand and the determination of the speed easily accomplished.
It will be seen that S is sharply defined as the speed maintained by the performance of the engine; it is entirely independent from the “ cross ” component of the current. It furnishes at the same time a good guide for selecting the course; should it, for instance, be a short course that it is repeatedly run over in a comparatively short time, the current can be considered the same in any two consecutive runs, so that the place can be selected without paying any attention to the currents. Should it be a long course, however, then it would be well to select a place where the current sets across, so that it can be accurately determined or eliminated by the method we have above indicated.
If it is certain that the current sets across it is of no importance if its strength is constant or not.
[TABLE]
In conclusion I would call attention to the fact that the mean of several runs over the same short course is not always accurately determined; the first and last run should be only given half weight. Under supposition that the current remains constant during the run in one direction and return, we have
[TABLE]
or in general
Vn=1/2(n-1) V1 + 2(V2+ . . . V(n-1)+Vn).
The assumption that the current does not change in a certain time becomes more tenable as this time is reduced. On the contrary it can therefore not be assumed that the current remains the same during all the runs, but it is perfectly correct to assume this to be a fact during two consecutive runs.
- I have shown under 1 how the error due to bad steering can be calculated, and under 2 I have shown a method to eliminate the compass error and cross current. The time observations remain to be discussed.
It is important the coincidence of the range signals at both ends of the run should be observed by the same person, and it is not immaterial to whom this duty is entrusted. The choice of a proper person becomes more important when the ranges do not cover but pass above and below each other.
It is dangerous to use the sight vane of an azimuth compass, as it may lead to grave errors, as it is very difficult for the observer to judge if the compass is horizontal, that is ii the wire of the sight vane is perpendicular. On the other hand there are persons who have peculiar faculty for judging vertical coincidences. During calm weather a plumb-bob may be of service.
The time is generally noted with chronoscopes (Marenzcller watches); this seems to me to be superfluous unless the watches are repeatedly compared with a well regulated chronometer, as the irregularity of the personal error will certainly be considerably larger than the rate of a good chronometer. I would prefer to mark time by a good chronometer which beats to seconds, the seconds to be counted aloud by an assistant.
An error of 1 second in running over a course of 1 mile at the rate of 20 knots amounts to 1/180 of the observed time or 0.5 per cent, which would give an error of 0.111 in the speed to be determined; it is therefore plain that the times of observations during such run are of the utmost importance. It becomes therefore necessary that the comparison of the chronoscope with the chronometer should be correctly taken, that is, at the same temperature and in the same position.
The valuation of the comparisons is simple.
I will review the methods recommended in the above.
Five persons are required for the observations:
One person to observe ranges.
One person for marking time.
One person for taking the angles.
One person to observe the steering of the vessel at the compass.
One person to assist at the compass (should be provided with a watch).
The next step is to establish the course by means of the verification angles reduced to the horizontal plane; the correction for poor steering is then applied. The preliminary data required for the latter, namely the speed, is obtained by dividing the length of the course by the time according to the formula quoted below.
Finally the observed times must be corrected after comparison, and then the equation
V knots =S Meter/T Sec. X 3600/1852 = (0.28866)S Meter / T Sec. (1852, J. P. M.)
computed. In this equation S— the exact course in meters, T— the exact time in seconds, and V the speed in knots. The number in parenthesis is a logarithm.
The above method is particularly useful on long courses, where steering on a range cannot be resorted to.
SPEED TRIALS OF FAST SHIPS.
A Review.
The Journal of the American Society of Naval Engineers, Vol. II, No. I, contains under the head above, two highly valuable papers on the subject of speed trials, the object of the discussion being to bring out the best method of ascertaining the speed developed by the new protected cruisers, Philadelphia, San Francisco, etc. The idea of the speed trial is to ascertain the exact distance a vessel can cover in four hours, uninfluenced by wind or by current. A scientific standard of comparison being needed, the best speed under the most favorable circumstances is required. The three principal methods proposed are: By a continuous run at sea, the speed being based upon the number of revolutions of the screw found necessary to give a knot in smooth water. By a similar run, the speed being based upon the number of revolutions of a measuring screw, rated in smooth water. By a continuous run at sea past a series of buoys or stations on shore, so arranged as to give the distance that the ship is likely to make, provision being made for accurate determination of the tide and current at frequent intervals along the course.
It is manifestly impracticable to obtain a course free from wind and current, and impossible to steer a vessel without allowing it to deviate from the straight line connecting the terminal points. The last method appears to be the favorite one at present; but each method has its objections, some of which are pointed out clearly in the papers above mentioned. Mr. Isherwood plainly states his doubts as to the accuracy of the measured mile trials, and yet he uses the results of some of these trials to throw doubt upon the method of revolutions of the screw. The paper above, translated by Mr. Leutze, shows clearly the source of inaccuracy in those trials, and in place of taking the slip of the Boston’s screws to discredit the method of revolutions of the screws, the irregular slip, even at such widely varying speeds,should have been sufficient to throw doubt on the distance traveled as determined by the observations. This translation of Mr. Leutzc’s shows how the distance traveled should always be increased more or less to allow for inaccurate steering, and also that although the method of running backwards and forwards over the same course, when only short intervals of time elapse, will correct the error due to the component of the tide acting in the line of the vessel’s keel, it ignores the other component which increases the distance both in going and in coming.
It would seem as if all of the three methods were correct theoretically, the practicable application of them being the great difficulty. The great objection to the last method proposed is the expense. Large signals must be erected and their positions carefully determined, the course must be well buoyed, and a number of vessels anchored at various points along the course so that the strength and set of both surface and sub-surface currents can be observed; then with a smooth sea and little wind the speed could be determined with a near approach to accuracy. There is one point that will always throw some doubt upon the results reached by running over a buoyed course, and that is the error produced by the current. No doubt, with a number of stations and numerous current meters, the strength of the current at various depths can be ascertained and its full effect upon the vessel be calculated; but the resultant direction will be always somewhat in doubt, particularly when it can only be approximately determined by the compass. This may be a small error, but when taken together with the necessary inaccurate steering of the vessel, the results will be further from the truth than if using the simple and less expensive method of taking the number of revolutions made by the screw in a given time.
The advantages of the measuring screw proposed by Mr. Isherwood are that the screw may be rated by means of a medium sized vessel, over a short course at not above medium speeds. Once rated, the course may be set in any direction from the land, keeping in deep water and having the wind abeam. The actual distance over the bottom becomes of no importance; the current, therefore, docs not affect the results, nor docs the course steered, so long as the helm is not put over so as to retard the ship. In other words, if the measuring screw be properly rated, the exact number of revolutions in precisely four hours will give the required speed. If we can obtain the rate of the vessel’s screw we have all the advantages of the measuring screw without the necessity of providing a special instrument, and then there must always be some doubt as to the rigidity of the measuring screw when used on vessels of high speed. There is one point about the vessel’s screws: why rate them at low speeds, when only high speeds will be used? It is obvious that if anything happens to the machinery so as to cut down the speed beyond a very slight amount, the trial will be useless for purposes of comparison, and the contractors would certainly demand another trial. Therefore the screws need be rated only for the best speeds of the vessel and speeds slightly below the best. The vessel can be sent over the measured mile with good way on and with plenty of steam; the mean between two runs made at short intervals apart will eliminate the error made by one component of the current, and by carefully determining the terminal positions, not relying on the ranges alone, the error produced by the other component can be removed. Then by applying the corrections for deviation from course, the exact distance traversed can be obtained. A break-circuit chronometer would give exact time intervals, and an improved counter would record the number of revolutions. A few runs at each speed would suffice to rate the screw. It is possible that the change of load during the four hours’ run would affect the slip, but as the high speeds are within the squatting limit, this does not seem probable, but it might be readily tested on the measured mile.
In spite of Mr. Isherwood’s argument, the revolutions of the vessel’s screws would still appear to be likely to give the nearest approach to accurate results. In fact, for one usually so accurate, Mr. Isherwood has been quite careless in his presentation of the facts. Ills mean of all the slips, in the case of the Boston, should have been 12.75, not 11.75 Per cent, and this would have given a smaller variation between the experimental and the calculated speeds. Again, if he had not been trying to make his facts prove his case, lie would hardly have been willing to assert that the mean slip, ascertained from widely varying speeds, could be the true slip, or that experiments made with unsatisfactory precautions were of use in proving his theory.
In all the methods proposed there are chances of error, in fact none are strictly accurate; but the one that will produce the most regular results, with the nearest approach to accuracy and the least expenditure of money and time, is the one proposed by the Engineer in Chief, if it be so modified as to leave out the lower speeds he proposed, and the contractor be required to run over the measured mile at the highest speed, and if no speed below 18 knots be used to determine the number of revolutions per mile. The distance through the water is what we want; we can ignore the current and avoid the effect of the wind, the number of revolutions and the elapsed time can be noted with precision, and the results must be accepted as a very close approximation to the truth. R. W.
PROPOSED NAVAL MESSENGER PIGEON SERVICE.
Most of the European governments have now fully recognized the practical value of homing pigeons as messengers, and possess a complete system of pigeon stations along their respective coasts, under direct control of the government.
Canada has quite recently followed their example by establishing an organ- ized system of messenger pigeon stations throughout the Dominion, extending from Halifax to Windsor and connecting her principal seaports with the interior.
We advocated in the Proceedings No. 47 (1888) and No. 48 (1889) the establishment of a similar system at our principal seaports of the Atlantic coast and on some men-of-war. So far, no organized service of messenger pigeons has been established in the United States Navy, but some interesting trials have been made at the United States Training Station at Newport. Commander T. J. Higginson, U. S. N., recently in command of the U. S. S. New Hampshire, says, in answer to an inquiry as to advisability of establishing a connected service of messenger-pigeon stations along the Atlantic coast: “ In answer to your letter concerning carrier pigeons, 1 beg leave to state that I would favor a system of stations along the coast, with a central station for breeding, and I think Newport would be the best place for that purpose; breeding the birds here and transferring them while young to the other stations so that their first flight would return them to their permanent homes.
We have at this station erected a pigeon-house and have some choice messenger stock. Although our cote is still in its infancy, we have made some very interesting trials with our birds, and have been much pleased with some of the results. One of the pigeons flew from the Hen and Chicken’s Lightship to our cote, a distance of twelve miles, in 16 minutes and 35 seconds. One of our birds has a famous record and is a sister to the famous homer Akron which won the international gold medal in 1887 for best speed. The brother of one of our flock flew from Washington to Fall River, a distance of 365 miles, in 11 hours and 7 minutes. The parents of several of the carrier pigeons belonging to this station have records of over 400 miles, and some of them are from imported pure Belgian breeds. Pedigree is the principal requisite in a homing bird.
Several of our birds were taken to New York on the Juniata last year, with intention of liberating them along the coast. The weather, however, was thick and they were not flown. While at Brooklyn one of the pigeons escaped from the Juniata and it was considered lost, as it had never flown a greater distance than from Point Judith, but great was our surprise when in a few days the bird arrived at his home here safely and in good condition.
I think it would be a good plan for all naval vessels leaving Newport to be supplied with carrier pigeons for the purpose of sending communications ashore and to train them for long distance flights. The use of carrier pigeons as bearers of dispatches would prove of great use to the naval service, and I am heartily in favor of establishing carrier pigeon lofts along the Atlantic coast. I have no doubt of the success of the undertaking if it were organized and thoroughly executed.”
This is very encouraging and a strong indorsement in favor of establishing a naval messenger pigeon service. The use of homing pigeons in the merchant marine is quite common. It is a well known fact that many captains have pigeons on board for use in communicating with the vessel from the small boats away from it or from shore. These birds, it is said, never mistake any other vessel for their own when at dock or in the harbor. Among the numerous instances of the use of pigeons for sea service we mention that of a bird which, liberated from the steamer Waesland at one o'clock in the afternoon, when three hundred and fifteen miles from Sandy Hook, was at his loft in the evening. Another let go from the Circassia at nine in the morning, when two hundred and fifty-five miles out, brought a message in the afternoon. Major- General D. K. Cameron, Director of the Messenger Pigeon Association, Canada, says in his letter: “I am of opinion that a most important branch of the pigeon service will be connected with coast service. The evidence that these birds can be relied on to cross 400 miles of the ocean is apparently thoroughly reliable.
Amongst the many ways in which pigeons capable of doing so much might be used, not the least interesting to a large and very influential part of the public would be the conveyance of intelligence from the passenger vessels crossing the Atlantic. Reducing the belt within which vessels between Newfoundland and the coast of Ireland are beyond the reach of telegraph stations by 800 or 900 miles, would be a result of the highest importance.” Another writer on the subject says: “It is a wonder to me, after these experiments, that the captain of any vessel should leave the shore without the means of communicating with it.” Among recent experiments in France and Italy the official reports show that during the squadron manoeuvres pigeons were freely used as messengers, and often arrived many days before the dispatch vessels sent at the same time.
A system of lofts to be situated at the principal navy yards along the Atlantic coast could be established at a very small expense to the government, as the homing pigeon fanciers throughout the country are anxious to see the government take hold of the matter and are willing to give their hearty support to the enterprise.
We suggest a connected system of twelve main naval lofts to be situated at the following navy yards and stations:
- Portsmouth.
- Boston.
- Newport. Already established on receiving ship New Hampshire.
- New London.
- New York.
- Philadelphia. Receiving ship St. Louis.
- Washington. (Central Station.)
- Annapolis. (On the Santee.)
- Norfolk.
- Port Royal.
- Key West.
- Pensacola.
The greatest distances being between the last four naval stations, some intermediate points would be needed between them to insure a connected service. Beaufort, N. C. (or Fort Macon), Wilmington, Georgetown, Charleston, Savannah, Jacksonville, Tampa, Cedar Keys, and Apalachicola, would be desirable “points de rel âche.” Several of these stations have already private lofts. Key West has a loft belonging to the Army Signal Service. From these lofts any vessel could be supplied with pigeons and cotes be built on board some men-of-war as in the French Navy.
Advantages of an Organized Service of Messenger Pigeons.
A service of messenger pigeons for naval purposes could not be improvised at short notice, and the birds would require long and careful training before being of any use as bearers of dispatches.* In war time the occasions are innumerable when serious derangement of plans, loss and discomfiture may be involved by the absence of previously organized provision for the rapid transmission of news. The advantage in favor of the side possessing such facilities over an opponent without them is enormous.
War vessels defending a coast are frequently without the means to transmit vital intelligence to the mainland. If provided with trained and reliable messenger pigeons they could send communications ashore over a distance of several hundred miles, signal the approach of the enemy’s fleet and report his every movement.
In peace, vessels leaving and approaching the coast could report the position of disabled vessels needing assistance, and signal their own needs and locate wrecks. At places remote from telegraph stations, light-houses, camps and squadron manoeuvres, interrupted electric communication and many other circumstances afford numerous occasions for employing homing pigeons as messengers.
The fact that homing pigeons can fly several hundred miles a day at sea, that birds can be bred and trained on board ship, that they can be accustomed to the noise of the guns, that they can recognize their own ship among others, that they can be relied upon, as proved by numerous experiments, to carry news from the fleet to the shore (and under favorable circumstances from the shore to the fleet and from one vessel to another), when beyond the range of heliograph and electrograph, should suffice to secure the support of the government to this new enterprise, and encourage the speedy establishment of a permanent system of naval messenger pigeon lofts at the principal navy yards and stations along the Atlantic coast.
H. Marion,
Assistant Professor, U. S. Naval Academ.,
THE TIME AND DISTANCE REQUIRED TO BRING A SHIP TO A FULL STOP AFTER THE ENGINES ARE STOPPED AND REVERSED.
By Assistant Naval Constructor William J. Baxter, U. S. N.
In handling ships in a crowded harbor during fleet drill, in avoiding a friend, or in ramming an enemy, it is of the highest importance for a naval officer to know the time and distance required to bring the ship to a full stop, when moving at varying speeds, after the order has been given to stop and reverse the engines. The captains of merchant steamers, from their constant practice, would be expected to estimate with more accuracy than naval officers, whose opportunities for knowing their ships are much more limited; but the results of investigations by the Office of Naval Intelligence (General Information Series No. VIII) show that even with these merchant captains the tendency to underestimate both the time and the distance is somewhat general.
It would doubtless be a great convenience if every ship carried the means of accurately determining the time and distance required for these manoeuvres, so simply arranged as to be ready for instant use by an officer totally unacquainted with the ship. To determine this data accurately for each ship would require an elaborate series of experiments; but, by the methods suggested below, it can be obtained and put in a shape for ready reference, with but little inconvenience and a small amount of calculation, with so close an approximation to theoretical accuracy as to fulfill all practical requirements.
The following is the principle of the method:
Suppose the curve OAEB to have been constructed, having times, in seconds, as abscissae, and velocities in feet per second as ordinates ; at any point B the velocity in feet per second is represented by Bb and the time in seconds that will elapse from zero velocity is represented by OB = T, if cb represent a unit of time, the distance passed over in this time, dt, will be represented by vdt = cb X cd = area cdBb, and as the same is true of any point in the curve, the whole distance passed over will be represented by ∫Tv dt = total area of the curve OAEBh. The same is true of other points on the curve; thus, the area OAa represents the distance that would be passed over before the velocity is reduced to zero, and Oa represents the corresponding time. These areas can be taken as the ordinates of a new curve; thus, to any convenient scale, A' a represents the area OAa, B'b represents the area OAEBi, so that for any velocity represented by Ee, E'e represents the distance and Oe the time. If, then, a set of these curves is provided for a ship, by an instant's inspection, an officer, knowing the ship's velocity, can tell the distance and time required for her velocity to be reduced to zero and the ship come to a full stop.
To find the data necessary tor constructing these curves two methods are suggested.
First Method.
Let the ship steam at her highest possible speed, having one officer detailed for observing the speeds, and another for observing the corresponding times. At a given signal, whose time is noted, let the order be given to stop and reverse the engines, and as the ship loses speed the observers note the speeds and the corresponding times, continuing these observations as rapidly as possible until the ship comes to rest, and have the data entered on a form, as follows:
[TABLE]
To draw the curves, use zero velocity and the time corresponding for the origin of co-ordinates; convenient scales are 1 inch equals 10 seconds, and ½ inch equals lo feet per second. To plot a point on the curve, say that corresponding to 8 knots, from the above table, the ordinate 12.72 is found in column I, and the abscissa 121 in column 4; other spots are plotted in the same way, and a fair curve is drawn through them. As all subsequent results depend for their accuracy on the accuracy of this curve, it should be checked by an acceleration curve.
To construct this curve, let OABC be a time-velocity curve, Oa, ab, being units of time, since the acceleration
[EQUATION]
and a curveof acceleration can be drawn having Aa = Aa, B’b = Bb2, C’c = Cc2, etc., as ordinates showing the acceleration and velocity at any time. The relation Force – Resistance = Mass x Acceleration is a fundamental one, and it is readily seen that when the ship is moving ahead at uniform velocity the acceleration vanishes and Force = Resistance, but after the engines are stopped and reversed it becomes –Force –Resistance = Mass x Acceleration, or Force + Resistance = Mass x –Acceleration. This negative acceleration is composed of two parts, that due to the resistance offered by the water to the onward motion of the ship, and which varies with a varying power of speed, and will thus quite disappear when the ship comes to a full stop; the other part is that due to the force of the engines acting through the propeller and pulling the ship astern. A few seconds will elapse after the signal is given before the engines can be reversed, and after reversal before they are acting efficiently, but after this time their force is practically constant, and a constant acceleration is produced. It should be noted, however, that these accelerations cannot be exactly evaluated, because “Mass” in the equation consists not only of the known mass of the ship, but also the mass of the water which is drawn after the ship, the value of which is unknown.
The acceleration curve, as used as a check on the velocity curve, must be a fair curve, must be nearly parallel to the axis of abscissae near the origin, and contain no re-entrant curves. If it does not fulfill these conditions there are personal errors or errors of observation in the velocity curve, and the latter must be altered until it and its acceleration curve are fair curves.
Having thus obtained an accurate velocity curve, its integral or curve of areas must be found, and this can be done accurately enough by using the trapezoidal rule with an interval of about one-tenth the total time; thus, from full speed to full stop, 250 seconds later, the distance is
[Equation]
=397.5 feet =1132.5 yards.
Performing the same operation at each interval the distances are found and plotted to convenient scales, and a fair curve drawn as in the accompanying diagram.
To use this diagram it is only necessary to know the speed at which the ship is moving, and the corresponding distance and time are readily found, and a table similar to the following can be made for ready reference.
[TABLE]
Second Method
At convenient opportunities, when the ship’s speeds are different, let the signal be given to stop and reverse the engines, noting the time required to bring the ship to a full stop, after the signal is given, recording the data, thus:
[TABLE]
The velocity curve can then be plotted from its coordinates in columns 2 and 3, and the acceleration and distance curves drawn as in the first method.
In addition to the error due to neglecting the mass of the following water, there is another error due to the assumption that one velocity curve can be made to satisfy all the requirements; thus, let OABC be the velocity curve at 15 knots, and ODAEB that at 14 knots, then these methods assume that the area ODA = area AEB, i.e. area OABK = area ODAEBK, the latter is a little greater, so that ships will slightly overrun the distances as given by these methods. If a complete series of experiments could be carried out on one ship, the probable rate of error could be determined and so tabulated that when applied to the results obtained by these methods, practical accuracy would be obtained.
The data and diagrams described, however, will furnish the necessary information so accurately as to be of great service to officers; and when used in connection with the tactical diameters, precision in fleet manoeuvres can be more easily secured.