The following protractor, course indicator, or whatever you may choose to call it, was made to fill the personal need for a quick method of solving the problems of maneuvering and torpedo control, thereby anticipating the prolonged manipulation of dividers and parallel rulers at the chart board, or the no less elaborate fumblings at the torpedo director. The geometry of it is older than Euclid, and the practical use is similar to that of the old Batten- berg protractor and probably to many “gadgets” dear to the heart of their creators.
General Description (See Fig. 1). It consists of a graduated compass circle marked in degrees, with a central spindle on which three arms revolve freely. The narrow target arm and own ship arm revolve around the spindle as diameters of the compass circle. One end of each forms a pointer following the graduated circumference of the compass circle, while the other end, which we will call the Speed End, has marks or Speed Points at distances from the center corresponding to speeds from zero to thirty knots or over.
The broad arm, or bearing arm, revolves about the spindle at the middle of one edge, which edge is also a diameter of the compass circle. The broad part away from the spindle is marked with a series of bearing lines parallel to the edge. When in operation the Speed Ends of the other two arms extend across the bearing arm, and the Speed Points will be interspersed among the bearing lines.
It will be seen that the bearing line connecting any two Speed Points forms one side of a triangle whose other two sides are the distances on the other two arms from the center to those same Speed Points.
Then if these last two sides of the triangle represent the direction and proportionate speed of two ships or moving bodies, and the third side represents the direction or bearing between them, we have the graphic solution for all the problems involving collision courses and constant bearings.
The course and speed of the target must be known or estimated, and the target arm set for them. The other three elements are the target bearing, and our own ship’s (or torpedo’s) course and speed. With any two of these elements known or assumed, the third may be readily found.
Tools and Material. Go to any auto-top repair shop and buy about a square foot and a half of the transparent celluloid used for side-curtain windows. From the moving picture repair shop on the tender or elsewhere procure a small amount of the cement or “dope” used for mending films. This will stick to celluloid much better than ordinary glue and is itself transparent, though glue may be used, lacking anything better.
For the graduations of the compass circle use either the 8-inch compass rose from an old plotting chart or the 10-inch circle from one of the mooring board sheets.
For the spindle use a small bolt and nut, diameter of shank about J^-inch. Flatten or file down the bolt head so that it will lie flat underneath the celluloid circle.
Assemble the following tools and materials: knife, shears, pen and India ink, graduated rule or straight edge, sharp-pointed instrument for scribing lines on celluloid, awl and reamer for boring holes, sheet of cross-section paper, dividers, and fine sandpaper or emery cloth.
Compass Circle. Cut the paper degree circle roughly out of the chart or mooring board sheet, leaving a margin of two or three inches or more outside of the graduations all around to help keep it from distortion while cementing to the celluloid. Mark the graduations with numbers in India ink for every 10°, from 000 around to 360, if they are not already so engraved. Then cut out the inside of the paper circle to within about 1.5 inch from the outside graduations all around. Now scribe and cut out evenly from the celluloid a solid circle slightly larger than the circumference of the outside graduations of the degree circle.
Lay the paper degree circle face up on a flat surface, spread its upper (engraved) side evenly with the cement, then carefully place the celluloid circle upon it, even with the circumference outside the graduations. Press under books or other weights until the cement sets, which will take only a few minutes.
Remove and trim off the paper and celluloid margin flush with the degree circle. The completed compass circle should now be about an even eight inches or ten inches in diameter, with the /-inch ring of the degree circle pasted on its under side and the degree graduations showing through. Find its exact center by scribing cross diameters, punch a small center hole and ream it out to a close working fit on the spindle, using care to keep the hole exactly centered as you enlarge it. Do not try to bore the hole first and then paste on the degree circle concentric with the hole, or you will probably get the whole thing off-center. Accuracy of workmanship is essential to accurate performance of the completed instrument.
Bearing Arm. Cut out a celluloid rectangle, in length equal to the outside diameter of the compass circle (eight inches or ten inches), and in width about Li-inch wider than its radius. (See Fig 1.) Half an inch from one side and midway between the ends, punch and enlarge a center hole to fit the spindle. Put it on the assembled spindle and compass circle, and mark and scribe an accurate diameter from end to end across the center, parallel to the long edge. This line is the first bearing line. Then proceed to scribe a series of other bearing lines exactly parallel to the first one, and at a uniform distance apart of Li-inch if an 8- inch compass circle is being used, or 0.15- inch apart with a 10-inch compass circle. Any distance apart would work so long as the lines are parallel, but these distances are recommended. A simple method which avoids stepping off so many small distances is to lay the celluloid down accurately on a sheet of cross-section paper of the right spacing, and scribe with a straightedge directly over the lines of the paper as they show through.
Scribe every fifth line slightly broader and deeper, and with a pen and India ink darken these fifth lines to make them more pronounced. Trim off the half-inch unruled strip beyond the first bearing line, but leave a semicircular boss of Yi-inch radius around the center hole.
Target Arm and Own Ship Arm. Cut out two celluloid strips about an inch or an inch and a quarter broad, and in length equal to the diameter of tha compass circle. (See Fig. 1.) At the middle point of each strip punch and enlarge a center hole to fit the spindle. Assemble them on the spindle with the compass circle and mark and scribe an accurate diameter lengthwise on each. Narrow an end of each to form a Pointer End. On the opposite ends, which we may call the Speed Ends, step off and mark with light punch marks or scratches a series of Speed Points corresponding to speeds from zero to thirty knots, measuring from the exact center of the hole. The distance between the Speed Points should be the same as that between the lines on the bearing arm, i.e., either Ls-inch or 0.15-inch. The five- knot point will thus be either Li-inch or 0.75- inch from the center, etc. Mark every fifth Speed Point with a longer scratch.
Measuring Scale. Cut from the celluloid a strip about one inch wide and about as long as the diameter of the circle. Along one edge of this mark a scale of distances of the same length as those on the speed scales, Li-inch or 0.15-inch apart. (See Figs. 5 and 8.)
On the other edge mark a scale of Effective Torpedo Range in thousands of yards, each space computed according to the formula:
torpedo speed X length of knot spaces
1000 yds = -------------------------------------------
maximum torpedo range (thousands)
For a 25-knot, 12350-yard torpedo and the knot points Li-inch apart it would be 0.253-inch. For a 6000-yard, 35-knot torpedo, with knot marks 0.15-inch apart it would be 0.875-inch.
Make a hole in one end of the scale whereby to hang it to the bottom of the spindle with a small lanyard, so as to have it on hand when needed.
Save the remains of your celluloid to make other attachments and accessories as they occur to you.
Markings. To put lettering or ink lines on celluloid, the glossy surface should first be dulled by rubbing the place with fine sandpaper or emery cloth, or by first applying talcum powder or powdered soapstone, as you do with tracing cloth.
On the pointer end of one of the arms print Target Course, and on the other arm print Own Ship Course. On the Speed Ends fill in each Speed Point with a dot of ink and also the scratches at every fifth Speed Point, numbering the latter 5, 10, IS, 20, etc., for easier identification.
On the bearing arm close along the inner edge which forms a diameter of the compass circle, print Target Bearing on each side of the spindle. (See Fig. 1.)
Practical Use. The methods of using the instrument may best be explained by examples, as follows:
- Another ship bears 000”, course 250, speed 12. I wish to join her at 18 knots. What will be my collision course?
Set the target arm at 250 and the bearing arm at 000. Then move own ship arm until 18-knot Speed Point is on the same bearing line as the 12-knot point on the target arm, on the side away from the bearing. The Pointer End then indicates 321 on the compass circle, which will be the correct collision course. (See Fig. 1.) Note that in any of these problems the two Speed Points may not fall exactly on a bearing line; but if they are brought by eye the same distance between two adjacent lines, the effect will be the same.
- Data is the same as in (a), but I wish to open out on the target ship instead of closing, while maintaining the same bearing as before.
Set the target arm and the bearing arm as before. Then move own ship arm until its 18-knot Speed Point is on the same bearing line as the 12-knot point of the target arm, but on the side towards the bearing. The Pointer End then is at 219, which course will keep us on the same true bearing of 000. (See Fig. 2.)
Note that in using the instrument for problems in opening distance, on diverging courses, it is merely necessary to set it as though dosing from the opposite bearing. Or perhaps a more perfect picture of the problem if given by setting the reverse or Speed Ends of the target and own ship arms in the direction of the two courses, with the bearing arm on the side towards which we are going instead of the one from which we are coming. Both methods are illustrated in Fig. 4.
- The target ship bears 030, course 280, speed 11. (See Fig. 3.) I wish to join her on course 330, keeping her 60° on my starboard bow, but on the same true bearing of 030. What speed must I make?
Set bearing arm at 030 and target arm at 280 as before. Set own ship arm at 330, and pick out on it the Speed Point which lies on the same bearing line as 11 knots on the target arm. It will be about 12 knots, which will be the required collision speed.
- Target data is the same as in (c), but I wish to open out on course 255, keeping her 45° on my starboard quarter, but on the same true bearing. (See Fig. 4.) What speed must I make?
Set target and bearing arms as before. Set ozvn ship arm at 255. Then pick out the Speed Point on it matching the 12-knot point on target arm, or about 14.5 knots.
(e) The target bearing is 100, target course 350, and speed 11; and I wish to hit her with a 25-knot torpedo. What are the torpedo track, sight angle, target angle, track angle, and maximum effective torpedo range? (See Fig. 5).
Set target and bearing arm at 350 and 100. Bring Torpedo Speed Point, 25, on own ship or torpedo arm, to match the 11- knot point on the target arm. The pointer end then comes to 075.5 which is the direction of the required torpedo track, and if using curved fire ahead will be the correct firing course. The difference between the torpedo track, 075.5, and the target bearing, 100, is the sight angle, 24.5. The difference between the reverse end of the bearing arm, 280, and the target course, 350, is the target angle, 70° on the target’s port bow. The difference between the target course, 350, and the torpedo track, 075.5, is the track angle, 85.5° on the target’s port quarter.
To find the maximum effective torpedo range, merely measure the distance between the respective Speed Points involved, using the maximum torpedo range scale. (See Fig. 5.) In this case it comes to about 14,300 yards.
(f) The target data is the same as in (e), but I can choose my own bearing for firing, and wish to know which one will give me an exact 90“ track angle.
Set target arm at 350, and torpedo arm 90° from it, or at 080 as shown in Fig. 6. Then move bearing arm until some bearing line passes through both the torpedo and target Speed Points, which will give a bearing of 103.5 on which to bring target before firing.
(g) From my present station on a screen, bearing 180 true from the fleet guide, distant 14 miles, I am to take another station bearing 060 true from the guide and distant 21 miles from same. What is the distance and bearing of the new station from my present one?
Set the Speed End of own ship arm at 180 and Speed End of target arm at 060. Then their 14- and 21-knot points respectively are in the same relative positions from the center, as the old and new stations are
from the fleet guide. (See Fig. 7.) Shift the bearing arm around until a bearing line passes through these two speed points. It will come to 036.5 which is the true bearing of the new station from the old. To find the distance between the two stations, take the distance scale and measure the distance between the 14- and 21-knot Speed Points. It comes to about 30.6 miles in this case.
(h) In case (g) above, the guide’s course is 280, speed 10; what course shall I steer to reach the new station at 20 knots; and for how long?
Proceed as in example (a), setting the target arm at 280, and the bearing arm at 036.5, and adjusting the own ship arm until its 20-knot point matches the 10-knot point on the target arm. The own ship arm now points to 009.5 which is the correct course.
Leaving the arms in this position, take the distance scale and move it up between the Speed Ends of the two arms, keeping it parallel to the bearing lines and adjusting it until the distance from 0 to 30.6 exactly spans the distance between the two speed scales, as shown in Fig. 8. The knot points which it touches represent the distance in miles to be traveled by our own ship and by the new station, up to the point of meeting. For our own ship it comes to about 27.5 miles, and we will get there by steaming 1 hr. 22.5 min., at 20 knots on course 009.5.
(i) In examples (b) and (d) I wish to know how long to run in order to open out 10 miles from the target ship.
With the arms set for the solution of the original problem, (Fig. 2 or 4), take the distance scale and use it as in example (h) ; adjusting it until the distance from 0 to 10 spans the distance between the speed scales, at points corresponding to the distances to be steamed. The distance may then be converted into time to run.
In these problems involving distance, it may happen that the numbers to be used are beyond the limits of 0 to 30 on the speed scales, as for example a distance of 40 miles. The obvious procedure is to multiply or divide it by a factor which will bring it within the limits of the speed scale; and then to reverse the process to get the final result.
Variations and Refinements, (a) For convenient use in torpedo control alone, make an extra own ship arm marked torpedo arm, and scribe on it only the speed of the particular mark of torpedo you are equipped with. The one point is then less easily confused and is easier to handle. See Fig. 5.
With fine sandpaper roughen slightly the celluloid surface on the arms near the Speed Points; you can then mark with a pencil the Speed Points to be used on each arm in a particular case, and more easily identify and match them. Also, roughen similarly a space near the Pointer End of each arm. You can then use it to write down the target’s known or assumed course, its bearing, and your own course, as memoranda if required. The pencil marks erase easily.
Use ordinary wire paper clips to clamp the ends of the various arms in place, so that you will not have to hold your fingers on them. If you are mechanically minded, devise some sort of clip to attach permanently to the end of the arms.
In place of the target arm for torpedo control, use a whole circle of celluloid. Scribe a heavy diameter to use as target arm and engrave the speed points on it as before. In addition scribe, or draw with pencil the outline of a ship or battle-line, with relative bearing lines on it, or sector limits, or anything else that may be helpful to the particular job in hand.
In place of own ship arm {or torpedo arm) use a complete celluloid disc as above. Scribe on it a heavily marked diameter to function as torpedo arm and engrave the Speed Point as before. This line represents the torpedo track, and also the torpedo tube when curved fire is not used. Draw on the disc pencil marks to represent ship’s head in proper relation to the torpedo track, tube angle, and gyro angle to be employed.
This will help considerably in handling the ship when firing otherwise than with curved fire ahead. Note, however, that if you are going to fire one broadside and then turn and fire the other, you must draw a separate mark for the ship’s head for each salvo.
Summary. The instrument is perfectly accurate in theory, and if carefully made, will be more than sufficiently accurate for maneuvering and torpedo control. It might be well to satisfy yourself by working out the same problem both on the mooring board or universal drafting machine and on this instrument you have made. Check it also against the torpedo director and note that were the latter put out of action you could still solve the sight angle and fire by pelorus. A flash light, held low behind the bridge shield, will enable you to use it at night without disclosing your presence.
It is speedier than any other standard mechanism, even the universal drafting machine. Speed and accuracy require practice always, and it is recommended that after making your instrument, you compose and write down a series of problems with the answers, and spend a few minutes every now and then practicing them in your room.
You will soon be ready to use it with confidence in handling the ship; or at the very least, to annoy the navigator and torpedo officer by announcing the answer to problems with which they are still struggling!