[swdw]

We hada discussion on range finding among the RFB guys. Here's one of the posts

WARNING_ LONG- but some really good info on this subject

From the fleet boat handbook

The value of the sonar operator to the TDC

By this time it should be apparent why the sonar operator is so important to the TDC. The essential information for TDC comes from various sources:

1. Own ship's course is registered AUTOMATICALLY from the master gyrocompass in the control room.

2. Own ship's speed is also fed AUTOMATICALLY, from the submarine's "log" (actually a speedometer at the keel).

3. Target's course is either estimated by PERISCOPE observation of the angle at which the target ship is traveling, or by plotting from other data. Since this information is only approximate, it is modified as the problem progresses.

4. Target's speed is estimated principally from the turn count obtained by the SONAR operator, or from the periscope identification of the target. This information also is approximate. Therefore, it too is corrected as the problem demands.

5. Target's range can be accurately determined by SONAR single-ping echo-ranging. However, this is used only to supplement estimates from periscope observation,

6. Target's relative bearings can be determined spottily by brief periscope observation. But for a continuous flow of relative bearings, the TDC operator depends on SONAR. (my note, this would be passive sonar which was accurate for bearing in the hands of a good operator)
This is why the sonar operator must give bearings continuously after contact. If he fails to do so, TDC operations are seriously handicapped.

A continuous flow of accurate sonar bearings is important for TDC operation and for a successful torpedo attack.

As you can see, there was actually a very heavy reliance on the sonar (hence the sonar reporting buttons at the attack map and scope positions with the new order bars)

The references I'm seeing with regards to the inaccuracies not only mention the rec manual,but also the stadimeter itself. Remember the lining up of the ships in the stadimeter is a judgement call based on experience of the person manning the scope, the distance to the target, and the visibility. At a longer range accurately lining up the images is more difficult.

Here's some info from another site that talks about an attack approach through the scope:

from http://jtmcdaniel.com/periscope.html

This image shows the view through the periscope with the stadimeter in use. A split prism is used to superimpose a second image of the target over the actual image. The captain adjusts the prism so that the waterline of the second image is set on the masthead of the actual target image. The height of the masthead from the water is entered on the dial, and the reading obtained. The stadimeter actually measures angles, not distance. If the masthead height is entered accurately, the range will be correct. Getting the masthead height wrong gives an incorrect range. (The same principle is used by surveyors, though they have the obvious advantage of basing their ranges on a graduated pole of known length held by an assistant.) In practice, the most accurate ranges were always obtained during exercises, since the subs were operating against units of their own fleet, and masthead heights were always known. Enemy warships and freighters often involved a certain amount of guessing, though recognition books were careful to list masthead heights whenever they were known.

Approach Procedure

Once a submarine finds a target, the approach and attack is essentially an exercise in geometry. The captain needs to determine the precise angle at which to fire his torpedo so that it will hit the target.

In stationary objects, this is easy. You simply point the torpedo directly at the target and, so long as it travels in a straight line, it will hit it. The problem with this, obviously, is that neither the submarine nor the target is likely to actually be stationary. With the rare exception of attacks on anchored vessels—Prien's attack on HMS Royal Oak in Scapa Flow being, perhaps, the best known example—submarines normally encounter their targets at sea, where both the submarine and the target are almost certainly going to be moving.

In this situation, you can't shoot at where the target is. Instead, you have to shoot at where the target will be when the torpedo reaches it.
Bearing
approach01

In this graphic, the approach has begun. The submarine is moving due north at 2 knots. The target is moving due west at 6 knots, and is currently located to the east of the submarine's track, at a range of four nautical miles. (In order to fit everything into the graphic the distances and sizes of the vessels are not to scale. Also, the submarine is shown surfaced for clarity—it would be submerged if this was actually happening.

First, the captain centres the periscope's crosshairs on the middle of the target, or on the point on its hull where he wants the torpedo to hit, calling out, "Bearing." At the moment he has the target exactly centred he then calls out, "Mark!"

The Approach Officer reads the bearing off the bearing ring located on the periscope shaft. This bearing gives the relative angle from the submarine to the target. In this case, 45°. For clarity, the Approach Officer announces the bearing as, "Bearing—zero-four-five." (Target bearings are always given as three numbers, and the digits are always given separately. "Zero-four-five" is less likely to be misunderstood than "forty-five degrees." This is particular so since lookouts call out bearings as "starboard four-five," using two digits and always referring to the side of the ship the sighting is on. Some navies use "red" for port and "green" for starboard in making sighting reports, these being the colours of the navigation lights on those sides.)

Once the target bearing has been determined, it is entered into the Torpedo Data Computer (TDC). This is a highly sophisticated electro-mechanical analogue computer. Two basic types were used during World War II. In most navies, the TDC was an angle solver only, which would give the correct gyro setting for the torpedo based on the data entered at the time of the reading, or at a given time in the future, based on the captain's best guess of where the target would be. The American version added a position keeper, which was capable of keeping track of the target's course in real time. This was a significant advance on the older systems, and made for much more accurate target solutions by eliminating most of the guesswork.

The TDC will always know the submarine's course and speed, as these are constantly updated from the master gyro compass and log. (This log is the submarine's speedometer, by the way, and not the book the captain uses to keep track of daily events.) The TDC now also has the target bearing, but still doesn't have enough information to work out a target solution.
Range to Target

Now the captain needs to determine the range to the target. To do this, he first needs to know just what the target is. Looking through the periscope he can see that it is a large freighter. Submarines carry recognition books which list every enemy warship and merchantman on which information is available. Looking through this book the captain finds the Oyama Maru, a 4,750 ton Japanese freighter, which seems to be the ship he has in his periscope. Since it is mid-1944, and World War II is raging, he decides this is a legitimate target, so he continues with the approach.

Now that he knows—or, at least, believes he knows—the identity of the target, he looks up the masthead height. This is the distance from the waterline to the heighest point on the ship. According to the recognition book, this is 100 feet. This figure is entered into the stadimeter in the periscope.

Range may also be determined by using the active sonar on the single-ping setting. This is one of the two most accurate methods, as it doesn't depend on knowing the target's masthead height. Late war American submarines also incorporated a tiny radar antenna in the search periscope, which would also give an exact range, at the risk of throwing up more spray than the thinner attack periscope.
view through periscope

This graphic shows what the captain sees through the periscope's stadimeter. A split prism is used to place a ghost image of the target so that its waterline is sitting right at the top of the masthead of the "true" image. The stadimeter actually registers the angle above the horizontal to the masthead, not distance. Some basic math is then performed which translates that angle into a distance figure.

The way this works is that, viewed from any particular distance, an object of a given height will be at a particular angle. If you know that the angle of view is 1°, for instance, and the object is 100 feet high, you can calculate that the angle of view and the top of the object will touch only at a distance of one nautical mile. The stadimeter simply does the math for you.

One disadvantage of this, of course, is that accuracy is completely dependent upon knowing the correct height of the object. (In this case, the masthead height of the target.) In our example—but not in the graphic, where the ship is considerably closer than it would be in a true view—the masthead height turns out to be 1/4° above the horizontal. Using the formula R=h/tan(q) this means that the target is four nautical miles from the submarine. The stadimeter does this internally, without the need for the captain or approach officer to calculate it, and indicates that the target is 8,100 yards away.

This figure is read off a dial at the base of the periscope and entered into the TDC, providing another part of the solution.

Also from the fleet boat manual

The second method of obtaining ranges is by means of the stadimeter installed in the Type II periscope. The stadimeter relies for its operation upon the formation of two identical images which can, by means of a handwheel on the periscope, be vertically displaced with relation to each other. Normally the handwheel is at the limit of its counter-clockwise travel. To obtain a range, the handwheel is turned clockwise until the target masthead in one image coincides with the target waterline in the other image. The range is then read on the stadimeter scale opposite the appropriate masthead height. In Plate III, a picture of a stadimeter scale, a masthead height of 60 feet gives a range of 2300 yards. Note that the scale is constructed for high power observation. When ranges are measured in low power the computed value must be divided by four.

(d) The third method of obtaining ranges is by use of the radar installed in the Type IV periscope. In this method the range of the selected target is measured directly by the ST Radar Operator when the periscope is raised and trained on the target.

(e) Of the three methods the radar ranges are the most accurate and depend primarily upon the adjustment of the radar which is usually plus or minus 35 yards. The accuracy of telemeter or stadimeter ranges depend first, upon the skill of the observer and second, upon the accuracy of the estimate of target masthead height.

(f) The value of the masthead height of the target may be obtained by intelligence, estimate, or by a method referred to as "radar stadimeter" (telemeter) estimate. The latter of course is the most accurate and is accomplished as follows; assuming that the target has been tracked using the ST periscope, the Type II periscope is raised immediately following an ST periscope observation, a stadimeter range observation is made as described above, but instead of reading range on the scale, the masthead height is read opposite the value of the TDC generated range.

(g) When radar ranges cannot be obtained the Approach Officer must rely upon his ability to correctly estimate the height of the funnel or masthead, or other prominent mark on the ship's structure above the water line. If the target ship can be properly identified an accurate value may be obtained from intelligence information supplied the ship. If this is not available the following procedure will he of assistance:
(1) Count or estimate the number of decks that are seen above the main deck.

(2) Add to this figure the approximate number of deck heights equal to the observed freeboard.

5-5

(3) Multiply the total by eight to determine the height of the top of the bridge structure above the visible waterline.

(4) Using height of bridge structure above the visible waterline as a yardstick, approximate the masthead height. The masthead heights of merchant ships are on the average about 2.1 times the bridge height (above waterline). A masthead height which appears to be shorter than normal will be about 1.7 to 1.8 times the bridge height, while one which appears to be higher than normal is approximately 2.2 to 23 times the bridge height.

(5) Funnel heights may be estimated by approximating the number of deck heights of the funnel which is seen above the top of the bridge structure and adding this height to the bridge structure height.

(6) At extreme ranges it must be remembered that the waterline is below the horizon. This necessitates estimating the position of the waterline.

5-6

(h) The following points should be kept in mind in height determination:

(1) Masthead heights may be purposely altered by the enemy to cause inaccuracies in periscope ranges.

(2) Tops of masts may be camouflaged in such a manner as to be invisible under average visibility conditions at any except short ranges.

(3) Funnel height is normally sufficient to insure that the smoke which is blown in the direction of the bridge by a tail wind will pass well over the bridge.

(4) Coal burners require taller funnels to insure adequate draft.

(5) Funnels of modern vessels having forced draft do not require as tall a funnel as older vessels without forced draft.

(6) Diesel propelled ships require no draft. Funnels are normally short, are not required, and generally have such dimensions as to provide a good appearance on the ship.

Regardless of the methods employed by the individual Approach Officer, skill in estimating masthead heights, and ability to obtain accurate ranges can be acquired and maintain only by constant practice. Even when radar ranges are available daring an approach the Approach Officer should also obtain telemeter ranges as a means of improving and maintaining his skill.