My Slide Rule Collection

Manual Attack Computers

I used to play a lot of Silent Hunter, an old DOS based submarine game. What a great game.

I eventually got good enough that I raised the difficulty level to make the game more challenging. As I got better and better, I kept raising the difficulty higher and higher, until I maxed out. How to increase the challenge?

I turned off the automatic torpedo data computer (TDC).

Instantly, I went from Sea Ace to Sea Ass. Torpedoes flew everywhere! - except, of course, at the targets. At first I even had a hard enough time just getting in range! I eventually got better at it, but to even further increase realism, I started using genuine WW II technology (actually, the slide rule goes back to the 15th century, but that's another story) to make my attacks. It took some serious trig and some serious thinking, but I made my own manual attack computers.

In this document, I describe the use and construction of two manual attack computers. Each has two functions.

(Slide Rules and Submarines... what next?)

Time-to-Target Calculator

If only there was a fast and easy way to make all the torpedoes strike simultaneously, so there is no warning at all...

You could do the math in your head - a Mark 14 torpedo travels at 46 knots, one knot is 0.562 yards per second, the more distant target is 1214 yards further away... uh... Well, maybe if you're an idiot savant. But when things are happening fast and the destroyers are closing in, there isn't much time to fiddle around, so I created this little thingamabob (a highly technical term if ever there was one) to do the math for me. You can make one too: it's easy, dirt cheap, and uses authentic WW II technology (it is essentially a slide rule).

There are just three simple steps to using the Time-to-Target Calculator.

  1. On the Range (bottom) scale, line up the range of the closer target with the range of the more distant target,
  2. Read the delay off the scale for the proper torpedo type.
  3. Wait that long after shooting at the distant target before shooting at the closer target.

For example: Let's say the closer target is 1100 yards away, and the more distant target is 2000 yards away. In the above image, you'll see that the number 1100 in the Range (bottom) window is lined up with the 2000 underneath the window. Looking at the window labeled M-14, we see that the pointer is pointing at about 35 seconds. If we were firing a Mark 10 torpedo, the delay would be read of the M-10 window, 45 seconds, and the electric Mark 18 torpedo would be read off the M-18 window, about 48 seconds.

There is one thing to remember - the distances used should be to the point of impact, and that is not always easy to figure out. But if you just use the distances given by the TDC, you'll usually do all right, since the targets are usually traveling in formation and their positions relative to each other (and thus the difference in distance) aren't changing much. However, if one target is moving toward you, and the other moving away, the calculator may be way off.

It can also be used for three or more targets, just by calculating the delay between adjacent targets. For a single target, it can be used to calculate the time-to-target directly, just by using zero as the distance to the closer target, but this may not be accurate unless you estimate the point-of-impact correctly.

Using this contraption, I routinely hit two ships within two or three seconds of each other.

Masthead Height Range Calculator

Fine, you can now time your torpedo attack for simultaneous hits. But to do so you need the range to your targets - and how do you get that?

You could simply use the TDC on auto, but for a much more realistic flavor, I've used the Proceedures for Manual Ranging described by Frank Kulick at to calculate range based on masthead height. It seems to work pretty well, but again it involves more math than I can do in my head quickly, so I added a range calculator to my thingamabob (there is that word again).

Again, just three simple steps.

  1. Identify the target and look up the masthead height on the table provided at
  2. Measure the hight of the ship through the periscope.
  3. Plug those numbers into the calculator and read off the range.

For example: If the target is a standard tanker, the masthead height is 120 feet. Looking through the scope, I measure the masthead height to be 1.25 divisions. In the upper window on the calculator, I align 1.25 in the window with 120 under the window, and read the range indicated by the arrow in the bottom window. If I am at 4x magnification, I read it off the arrow to the right (labeled 4x), and if at 1x I read it off the left (1x) arrow. In this case, at 1x the range would be about 1900 yards, and if at 4x, about 7600 yards.

Between 100 and 1000 yards, the divisions are in 100 yards. Between 1000, and 10000, the divisions are 1000 yards. You'll have to estimate where in between, but an estimate is good enough, since the periscope reading is none too precise anyway.

Make sure to read the notes at

Building the Time-to-Target and Range Calculators

Thanks to lil' ol' me, that's even easier than using them.

  1. Download the plan.
  2. Print it, preferably on stiff paper.
  3. Cut it out.
  4. Cut out the windows (use a VERY sharp knife and a ruler).
  5. Fold the frame (top part) along the solid horizontal lines, and tape.
  6. Fold the slide (bottom) along the solid horizontal lines.
  7. Slide the slide into the frame.
  8. Go sink something.

Nasmith Director

The Nasmith Director is a simple angle-solver, using your course, target bearing, and angle on the target's bow (AOB). It's accuracy depends on the accuracy of the estimated AOB.

The Nasmith Director was invented by Martin E. Nasmith, of WW I fame. It was called a Course Finder by the U.S. Navy. I've never seen one - this is my own version which may or may not resemble Nasmith's.

Using the Nasmith Director is really, really easy.

  1. Align the index (at 0 degrees) on the middle wheel with your course on the outer wheel.
  2. Align AOB on the inner wheel with the target bearing on the middle wheel.
  3. Opposite the index (at 0 degrees) on the inner wheel, read off the target course on the outer wheel.

Target Course Calculator, aka The Whiz Wheel

This little device is designed to calculate the course of a target, using two observations of bearing and range.

Using the Whiz Wheel is a lot more complex than using any of the above tools. You start by making two observations of the target, several minutes apart, noting bearing and range. The second observation will also have to include angle on the bow. For example:

Once you've got your observations, you get to work.

Target Speed

You should know know enough about your target's speed and course to stick a torpedo in her innards.

Building the Nasmith Director and the Whiz Wheel

Just print out the plan, cut it out, and mount the wheels through the center cross hairs on a pin or thumbtack. All the L pieces go on one side, and the C pieces go on the other. I mounted mine back-to-back on a piece of cardboard, but you don't have to. For an axle, I used two push pins, one of which I had "depinned" with a pair of pliers.

Some Interesting Notes

The following information is excerpted from U.S. Submarines Through 1945: An Illustrated Design History, by Norman Friedman. A truely fantastic book for anyone interested in submarines.

Click image to for a larger
version fit for printing (485k).

The two key dials of the position-keeper section of a torpedo data computer (TDC) are shown. They model the approach and attack situation. The upper dial shows the target, the lower the submarine; the line between represents the line of sight from submarine to target (postwar systems designed for attacks on submarines called this the line of sound). Outer rings show true bearing; inner ones are relative bearing. The submarine image is aligned to show the angle between the line of sight and the submarine heading; the target shows the angle on the bow, i.e., the angle between the line of sight and the targetís course. The submarine attack officer steered according to true (compass) bearing, but the progress of the approach was reflected in the changing relative bearings of target and submarine, as American submariners learned from the British during World War I.

The small symbol below the target ship symbol represents a torpedo; it shows the track angle, i.e., the angle at which a torpedo fired to hit will approach the target. The similar symbol on the bottom dial shows the corresponding torpedo gyro angle, the angle through which the TDC turns the torpedo to approach the target. The approaching submarine commander sought to minimize gyro angle while obtaining the broadest possible track angle (closest to 90 deg) to make up for possible errors in target course and speed.

Data - target course, target speed, relative target bearing, and range - were entered by hand using cranks. Own-ship data were entered automatically. The odometer dials shown here were added during World War II to existing TDCs as a field change. The TDC contained.separate angle-solver sections. Power switches could energize either the position keeper or the angle solver or both. Typically the angle solver was turned on only after a valid enemy course had been computed by the position keeper. Angle-solver dials showed the ordered gyro angle (at top) and the desired spread; the expected torpedo run was shown. Buttons could be pressed to indicate to the angle solver that the solution in the position keeper was correct.

A real TDC would have white numbers and symbols on a black background, but this version of the display is more legible.

No other navy developed a comparable instrument. The Germans and Japanese used angle solvers without position keepers (at least in the Japanese case, the device also had a timer that allowed it to dead reckon target position for indirect fire through smoke or mist). Probably because the Japanese had no TDC, they abandoned stern torpedo tubes in their later cruiser and fleet submarines on the grounds that they would require excessive gyro angles (Top). (U.S. Navy via Capt. James Patton, USN, Ret.)

These U.S. Navy diagrams show how the TDC was to have been used. At left is the pair of own- and target-course dials, showing the target and the submarine. The officer making the approach had to work out the course needed to obtain a given track angle. If the two dials were mentally superimposed (as at center), they showed the angle between the courses of the submarine and the target. For a stern shot, the necessary course angle appeared opposite the angle on the bow corresponding to the desired track angle. For a bow shot, the necessary course angle was read off 180 deg from the angle on the bow. True (as well as relative) bearings were shown on these dials because they corresponded to directions actually steered. (U.S. Navy via Terry Lindell)

Arrows on the TDC indicated torpedo course and gyro angle, as shown at right (solid arrow for bow tubes, broken arrow for stern tubes). The arrows on the target dial indicated present track angle, the angle at which the torpedo would hit if it were fired at any given moment (i.e., how good a shot was likely to be). Present track angle for a straight shot could be read off the dials by transposing the number on the outer ring opposite the submarineís disengaged axis to the target outer ring, then reading the corresponding inner number. In this example, submarine and target are on converging courses. (U.S. Navy via Terry Lindell)



© 2003 W. E. Johns