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convenient to use a table of squares to find V. A third term in the series for the square can be used for the larger angles.

The values of V, and Vo should be kept closely corrected, as on them depends a good deal of the accuracy of the results. As V is used only to determine r, it is not necessary to find it to a greater approximation than the unit.

For rough results at long ranges, much time is saved, and the great tediousness of the process avoided, by making At larger, say 5 seconds or even 10 seconds.

Calculations have been made of trajectories with time intervals I second, 5 seconds, and 10 seconds. At a nominal range of 30,000 yards, for the 16" gun, the longer interval gives shorter ranges, the differences from that given by the I-second interval being 0.5 per cent for the 5-second interval, and 1.8 per cent for the 10-second interval. When these results are plotted in a curve of percentage error on a base of time interval, it is seen that the error rises rapidly as the interval increases, but the error with intervals between 1 and 5 is small, and the variation in error, at the former figure, is also small. From this consideration it appears that, although the integration with an interval of 1 second gives results that are too small, the error is only of the order of one-tenth of i per cent, or even less, at a range for the 16" gun of 30,000 yards.

Calculations were likewise carried out for the same gun at an angle of elevation of 50°, for intervals of 1 and 10 seconds. The variation was 3.5 per cent; as the time of Aight was io1 seconds, while that for the 30,000 yards range was 54 seconds, it appears that the percentage error with a time interval of 10 seconds is nearly proportional to the time of flight, and the amount of this error, for this gun, is .035 per cent per second of Aight.

It appears, however, from such investigation as has been so far possible, that this error has this value only at the longer ranges. At ranges less than about 30,000 yards the positive error is reduced, and becomes negative at ranges around 10,000 to 15,000 yards.

The amount and character of this error seem also to be nearly the same for the different shells used in this investigation.

A time interval of 2 seconds has also been used considerably, with still further simplification in the mathematical processes, and has given satisfactory results.

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CONCLUSION Sheet C shows the results of calculations made by the mechanical integration process for four actual or possible types of shells, as follows: Caliber

Coefficient 2100

16" ...

.. 2100 2600
1400 2800



Initial velocity

of form

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The following general results are deduced from these curves : Maximum range is obtained at an angle of elevation of nearly 50°, but there appears to be an increase in this angle as the velocity is increased.

At maximum range there is a difference in range of 5000 yards for the 16" shell, due to a difference in initial velocity of 200 f. s.

The high power 14" outranges the low power 16".

The high power 12" outranges both the high power 14" and the low power 16", and has equal range with the high power 16".

Striking velocities of all four shells become minima at about 30,000 yards range, and are practically identical at this range, changing but little between 20,000 and 40,000 yards range.

The angles of fall are nearly the same for all four shells, at any range.

Reducing the coefficient of form from .69 to .60 will increase the maximum range of either the 14" or 16" by nearly 3000 yards, so that, with the same type of shell, the high power 16" will outrange the 12" about 3000 yards, the high power 14" will equal the 12", the low power 16" will still be outranged by about 2000 yards.

This means that the 12" shell must have 200 f. s. more initial velocity to overcome the handicap of smaller weight, as compared to the 14", if the type of shell is the same; but that a small change in the shape of the shell, a reduction of 13 per cent in the coefficient of form, has as much effect.

At ranges above about 30,000 yards, any one of these shells will easily penetrate the armored decks on any ship afloat, and at such ranges the decks offer a target roughly ten times as large as the side armor above water.

Weight of shell has less effect on range than has been commonly supposed, and greater ranges must be obtained by increased initial velocities, or by changes in the type of shell.

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STATEMENT OF BOARD OF CONTROL The “War Notes ” will be discontinued from January, 1919. Such further notes on the war as are included will appear under “Professional Notes.”

The strict censorship enforced during the war made it impossible to obtain official confirmation of naval events. Two courses were open: to publish only the few things that were officially given out, or to publish extracts from papers which appeared to have some foundation of fact. The second course was followed, the authority for the article being given in each case, in order that the reader might form his own judgment of the value of the article.

The strict censorship forbade the printing of any articles on strategy, tactics, material, organization or personnel. Also the small number of articles submitted has not permitted of any choice, but has necessitated the publication of practically all articles on hand at each issue. The board trusts that the members realize the difficulties that have been encountered in the endeavor to continue their publication.

It is hoped and expected that the censorship will in the future be less severe and that members will find it convenient to devote more time to the writing of articles, in order that the PROCEEDINGS may again provide its members with scientific and professional matter which will be of great value and benefit, and this can only be accomplished by the united effort of all members.

COMDR. J. A. FURER, C. C. U. S. N.
Board of Control,

U.S. Naval Institute.

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