CONSTRUCTION
The instrument consists of two discs and a pointer. The outer or larger disc is constructed by laying off the logs of numbers from one to one hundred around the circumference of the disc. Thus, if the disc is ten inches in circumference, number 2 would be laid off 3.0103 (log) inches from the zero point, etc., number 3 would be laid off 4.7712 (log) inches from the zero point, etc.
The inner disc has three scales, the outer two of which are degree scales and the inner a time scale. The red scale of degrees is laid off by looking up the log cosines of angles for every 5° from 0° to 90° and plotting the line opposite the amount indicated on the outer disc scale. The black degree scale is similarly plotted but taking the log cosecants as factors. The time scale is laid off by dividing 3 by different times from one minute to ten at 15 second intervals. Thus, 3 ÷ 1 =3, so one would be laid off opposite 3 on outer disc; 3 ÷ 2 =1.5, so two would be laid off opposite 1.5 on the outer disc and three opposite one, etc.
The instrument adds and substracts logs automatically or in other words multiplies and divides numbers. Thus, to divide 10,000 by cos 30° place red 30° under 10,000 and read off 11,600 opposite the arrow. Therefore to divide always place dividend and divisor in coincidence and read opposite the arrow. To multiply 10,000 by cos 30°, place arrow under 10,000 and read off opposite red 30°. Therefore to multiply place red arrow under number and read off opposite the degree mark used.
To find "R"
(a) Nautical eye.
(b) Range finder.
(c) Telemeter scale.
The first and second methods require no comment. Range is found by the third method as follows:
After setting enemy abeam (or before) estimate what type of ship it is. Knowing the type, the length will be known within very close limits as ships in all navies are approximately of the same lengths taking them type for type. Then estimate the angle on the bow and also take the number of degrees the enemy subtends on horizontal telemeter scale. If you are not abeam of the enemy you cannot see all of his length, that is the total length of the enemy will not be projected on the telemeter scale. So the telemeter reading must be multiplied by a number depending on the value of To obtain this number put the zero lines of both discs in coincidence and place pointer over black mark agreeing with estimated angle on the bow. The multiplier is picked off the outer disc under the pointer.
For example suppose the C. O. estimates the enemy to be a modern battleship, he knows then that her length is about 600 feet. Angle on the bow estimated to be 30° and enemy subtending 1.2 on the telemeter scale. Place zero lines of discs in coincidence. Place pointer over black 30° and it points to 2. Multiply 1.2 by 2 and get 2.4, the number of degrees the enemy would subtend were you on her beam. Look up range in table. In this case 10,000 yards.
To find T=Distance enemy must run.
Place red 30°, under 10,000 and read 11,600 on the outer disc opposite arrow on inner disc.
To find D.—Distance submarine must run.
Place black 30° under 11,600 on the outer disc and read 5,775 oposite arrow on the inner disc.
To find X=Shortest distance to enemy's track.
Hold arrow on 5,775 and read off opposite red 30°, 5,000 on outer disc.
SPEED
1. To find the speed the enemy must take to stay abeam of the submarine, place the arrow under the speed of submarine, on outer disc and read off opposite the angle on the bow black angle. Thus, if the submarine is making 9 knots and angle being 30°, place arrow under 90 on the outer disc and read off opposite 30° and you will get 18 knots.
2. To find speed if enemy draws ahead or astern.
Method "A"—using red angles only.
Factors used in this method are as follows:
1. Time interval between ranges (known).
2. Change in enemy bearing (known).
3. First and second ranges (approximate).
4. Angle on the bow (estimated).
So far the following data has been used:
Angle on the bow 30°
Range 10,000 yards
Submarine speed 9 knots
and it will be used throughout this explanation. Also the time interval will be taken as 8 minutes.
ENEMY DRAWS AHEAD
Suppose the sub having found the initial range to be 10,000 yds., angle on bow 30°, runs along for 8 minutes and then takes an observation and finds range to be 4,125 yds. and the enemy to have drawn ahead 15° (in getting multiplier for telemeter scale use 45° for angle on the bow has increased 15°). If enemy had maintained an intersecting speed he would have been at E" but he is really at E'. Angle E'S'E"=15°. Place arrow under 4,125 yds. and read off 4,000 yds. opposite red 15° equal to S'O. Subtract this from 10,000 getting EO'=6,000 yds. Place red 30° under 6,000 and read off 25.95 knots opposite 8 minute Mark on time scale.
ENEMY DRAWS ASTERN
If enemy draws astern the procedure is the same. Enemy draws astern 10°, range 8,450 yds. (use 20° in finding multiplier). Place arrow on 8,450 and read 8,400 opposite red 10° mark=EO'. Place red 30° under 1,600 and read 6.95 knots equal enemy speed opposite the 8 minute mark.
3. Method "B"—using black angles only.
The following factors are used:
1. Time interval between observations (known).
2. Increase or decrease bearing (known).
3. Range at second observation (approximate).
4. Angle on the bow (estimated).
5. Submarine average speed during interval( ?)
ENEMY DRAWS AHEAD
Submarine runs 8 minutes at 9 knots and finds the range to be 4,125 and that the enemy has drawn ahead 15°. First find what speed the enemy must make to stay abeam (at E") provided you make 9 knots. Place arrow under 90 and pointer over black 30° reading 18 under pointer on outer disc=E"E. Then place black 15° under 4,125 and put pointer over black 30°. Hold pointer in place and put arrow under pointer. Read off opposite 8 minute mark 7.95=E"E'. Add 7.95 to 18 getting E'E=25.95 knots, the enemy speed. (In placing black 15° under 4,125 the arrow points to 1,070=E'O and the black 30° points to 2150=E'E" in yards.)
ENEMY DRAWS ASTERN
Same as when enemy draws ahead. Place black 10° under 8,450 and hold pointer over black 30°. Turn .arrow under pointer and read off opposite 8 minute mark. Subtract this from 18 getting EE'=6.95.
ADDENDUM
Submarine starts approach with enemy forward or abaft the beam. Take 10° for example.
Find "R" as before.
Find "X" assuming enemy is abeam.
Find “D” from “X” using angle bow equal ? + 10° according to whether enemy is abaft or on forward of the beam.
To find, speed to keep enemy on constant bearing:
Instead of placing arrow under submarine speed and turning pointer over black angle on the bow place (in this problem) black 80° under submarine speed and turn pointer over black angle on the bow. If angle on bow, is 30°, and submarine speed is 9 knots, the enemy would need to make 17.6 to maintain the original bearing constant. If enemy is 20° forward or abaft of submarines beam black 70° would be placed under submarines speed, etc.
To find speed of enemy if he draws ahead or astern. First find enemy's speed to maintain constant the original bearing as explained in the above paragraph. Find E" E' as in method "B" and add or substract from 17.6 as the case might be.
The approach omnimeter will aid the navigator of a submarine or other vessel when it is desired to pass a certain object at a given distance abeam. Suppose for instance, that the captain of a vessel coming into port wishes to pass the end of a dock at a distance of two hundred yards on his port hand vessel on course 0° dock bearing 20° on the port bow. Take range with range finder and at same time observe relative bearing. Suppose range 14,000 yards and bearing now 25° on port bow. Place red arrow of inner disc under 14,000 and read under 200, 82° on red circle. Take complement of 82° which is 8°. Therefore the relative bearing of the dock at the time of taking range should be 8° in order to pass dock abeam distant 200 yards. Hence course will be changed 17° to left immediately and the same operation gone through again until the relative bearing of dock agrees with bearing obtained from omnimeter.
The writer during short range battle practice of the Charleston, spring, 1921, used this method entirely in making approaches for each run. He took his station at the standard compass and had direct communication with the range finder. All his attention was given to maneuvering the ship and seeing proper signals given for commence and cease firing. During the whole practice it was unnecessary to take a pencil or manipulate a parallel ruler. After inspecting the target we would stand down astern for about 2,600 yards and then turn to course paralleling the targets bringing target on the side from which we were to fire. A simultaneous range and relative bearing would be taken and this bearing checked with the bearing obtained from the omnimeter. We endeavored to pass target abeam distant 1,600 yards. Suppose first range was 2,800 bearing 25° port. Place red arrow under 2,800 and pick out under 1,600 55°. 90°—55°=35°. Therefore 35° is what target should bear at this range in order to pass it on parallel course at 1,600 yards range. The observed bearing was 25° so the ship is inside 10° and it will be necessary to sheer off to the right. To find distance inside place black 25° under 2,800 and read 1,180 under red arrow. 1,600—1,180=420 yards.