Torpedo Data Computer The Torpedo Data Computer ( TDC ) was an early electromechanical analog computer used for torpedo fire - control on American submarine s during World War II . Britain , Germany , and Japan also developed automated torpedo fire control equipment , but none were as advanced as the US Navy ' s TDC , as it was able to automatically track the target rather than simply offering an instantaneous firing solution . This unique capability of the TDC set the standard for submarine torpedo fire control during World War II . Replacing the previously standard hand - held slide rule - type devices ( known as the " banjo " & " is / was " ) , the TDC was designed to provide fire - control solutions for submarine torpedo firing against ships running on the surface ( surface warships used a different computer ) . It had an array of handcranks , dials , and switches for data input and display . To generate a fire control solution , it required inputs on The TDC performed the trigonometric calculations required to compute a target intercept course for the torpedo . It also had an electromechanical interface to the torpedoes , allowing it to automatically set courses while torpedos were still in their tubes , ready to be fired . The TDC ' s target tracking capability was used by the fire control party to continuously update the fire control solution even while the submarine was maneuvering . The TDC ' s target tracking ability also allowed the submarine to accurately fire torpedoes even when the target was temporarily obscured by smoke or fog . The TDC was a rather bulky addition to the sub ' s conning tower and required two extra crewmen : one as an expert in its maintenance , the other as its actual operator . Despite these drawbacks , the use of the TDC was an important factor in the successful commerce raiding program conducted by American submarines during the Pacific campaign of World War II . Accounts of the American submarine campaign in the Pacific often cite the use of TDC . Some officers became highly skilled in its use , and the navy set up a training school for its use . Two upgraded World War II - era U . S . Navy fleet submarines ( and ) with their TDCs continue to serve with Taiwan ' s navy and U . S . Nautical Museum staff are assisting them with maintaining their equipment . The museum also has a fully restored and functioning TDC from , docked in San Francisco . Background . History . The problem of aiming a torpedo has occupied military engineers since Robert Whitehead developed the modern torpedo in the 1860s . These early torpedoes ran at a preset depth on a straight course ( consequently they are frequently referred to as " straight runners " ) . This was the state of the art in torpedo guidance until the development of the homing torpedo during the latter part of World War II . The vast majority of submarine torpedoes during World War II were straight running and these continued in use for many years after World War II . In fact , two World War II - era straight running torpedoes — fired by the British nuclear - powered submarine — sank the ARA " General Belgrano " in 1982 . During World War I , computing a target intercept course for a torpedo was a manual process where the fire control party was aided by various slide rule s ( the U . S . examples were colloquially called " banjo " , for its shape , and " Is / Was " , for predicting where a target will be based on where it is and was ) or mechanical calculator / sights . These were often " woefully inaccurate " , which helps explain why torpedo spreads were advised . During World War II , Germany , Japan , and the United States each developed analog computer s to automate the process of computing the required torpedo course . In 1932 , the Bureau of Ordnance ( BuOrd ) initiated development of the TDC with Arma Corporation and Ford Instruments . This culminated in the " very complicated " Mark 1 in 1938 . This was retrofitted into older boats , beginning with " Dolphin " and up through the newest " Salmon " s . The first submarine designed to use the TDC was , launched in 1940 with the Mark III , located in the conning tower . ( This differed from earlier outfits . ) It proved to be the best torpedo fire control system of World War II . In 1943 , the Torpedo Data Computer Mark IV was developed to support the Mark 18 torpedo . Both the Mk III and Mk IV TDC were developed by Arma Corporation ( now American Bosch Arma ) . The problem of aiming a straight - running torpedo . A straight - running torpedo has a gyroscope - based control system that ensures that the torpedo will run a straight course . The torpedo can run on a course different from that of the submarine by adjusting a parameter called the gyro angle , which sets the course of the torpedo relative to the course of the submarine ( see Figure 2 ) . The primary role of the TDC is to determine the gyro angle setting required to ensure that the torpedo will strike the target . Determining the gyro angle required the real - time solution of a complex trigonometric equation ( see Equation 1 for a simplified example ) . The TDC provided a continuous solution to this equation using data updates from the submarine ' s navigation sensors and the TDC ' s target tracker . The TDC was also able to automatically update all torpedo gyro angle settings simultaneously with a fire control solution , which improved the accuracy over systems that required manual updating of the torpedo ' s course . The TDC enables the submarine to launch the torpedo on a course different from that of the submarine , which is important tactically . Otherwise the submarine would need to be pointed at the projected intercept point in order to launch a torpedo . Requiring the entire vessel to be pointed in order to launch a torpedo would be time consuming , require precise submarine course control , and would needlessly complicate the torpedo firing process . The TDC with target tracking gives the submarine the ability to maneuver independently of the required target intercept course for the torpedo . As is shown in Figure 2 , in general , the torpedo does not actually move in a straight path immediately after launch and it does not instantly accelerate to full speed , which are referred to as torpedo ballistic characteristics . The ballistic characteristics are described by three parameters : reach , turning radius , and corrected torpedo speed . Also , the target bearing angle is different from the point of view of the periscope versus the point of view of the torpedo , which is referred to as torpedo tube parallax . These factors are a significant complication in the calculation of the gyro angle and the TDC must compensate for their effects . Straight running torpedoes were usually launched in salvo ( i . e . multiple launches in a short period of time ) or a spread ( i . e . multiple launches with slight angle offsets ) to increase the probability of striking the target given the inaccuracies present in the measurement of angles , target range , target speed , torpedo track angle , and torpedo speed . Salvos and spreads were also launched to strike tough targets multiple times to ensure their destruction . The TDC supported the firing of torpedo salvos by allowing short time offsets between firings and torpedo spreads by adding small angle offsets to each torpedo ' s gyro angle . Before the sinking of South Korea ' s ROKS " Cheonan " by North Korea in 2010 , the last warship sunk by a submarine torpedo attack , the ARA " General Belgrano " in 1982 , was struck by two torpedoes from a three torpedo spread . To accurately compute the gyro angle for a torpedo in a general engagement scenario , the target course , range , and bearing must be accurately known . During World War II , target course , range , and bearing estimates often had to be generated using periscope observations , which were highly subjective and error prone . The TDC was used to refine the estimates of the target ' s course , range , and bearing through a process of Estimating the target ' s course was generally considered the most difficult of the observation tasks . The accuracy of the result was highly dependent on the experience of the skipper . During combat , the actual course of the target was not usually determined but instead the skippers determined a related quantity called " angle on the bow . " Angle on the bow is the angle formed by the target course and the line of sight to the submarine . Some skippers , like the legendary Richard O ' Kane , practiced determining the angle on the bow by looking at IJN ship models mounted on a calibrated lazy Susan through an inverted binocular barrel . To generate target position data versus time , the TDC needed to solve the equations of motion for the target relative to the submarine . The equations of motion are differential equations and the TDC used mechanical integrators to generate its solution . The TDC needed to be positioned near other fire control equipment to minimize the amount of electromechanical interconnect . Because submarine space within the pressure hull was limited , the TDC needed to be as small as possible . On World War II submarines , the TDC and other fire control equipment was mounted in the conning tower , which was a very small space . The packaging problem was severe and the performance of some early torpedo fire control equipment was hampered by the need to make it small . TDC functional description . Since the TDC actually performed two separate functions , generating target position estimates and computing torpedo firing angles , the TDC actually consisted of two types of analog computers : Angle solver . The equations implemented in the angle solver can be found in the Torpedo Data Computer manual . The Submarine Torpedo Fire Control Manual discusses the calculations in a general sense and a greatly abbreviated form of that discussion is presented here . The general torpedo fire control problem is illustrated in Figure 2 . The problem is made more tractable if we assume : As can be seen in Figure 2 , these assumptions are not true in general because of the torpedo ballistic characteristics and torpedo tube parallax . Providing the details as to how to correct the torpedo gyro angle calculation for ballistics and parallax is complicated and beyond the scope of this article . Most discussions of gyro angle determination take the simpler approach of using Figure 3 , which is called the torpedo fire control triangle . Figure 3 provides an accurate model for computing the gyro angle when the gyro angle is small , usually less than 30° . The effects of parallax and ballistics are minimal for small gyro angle launches because the course deviations they cause are usually small enough to be ignorable . U . S . submarines during World War II preferred to fire their torpedoes at small gyro angles because the TDC ' s fire control solutions were most accurate for small angles . The problem of computing the gyro angle setting is a trigonometry problem that is simplified by first considering the calculation of the deflection angle , which ignores torpedo ballistics and parallax . For small gyro angles , " θ ≈ θ - θ " . A direct application of the law of sines to Figure 3 produces Equation 1 . where Range plays no role in Equation 1 , which is true as long as the three assumptions are met . In fact , Equation 1 is the same equation solved by the mechanical sights of steerable torpedo tubes used on surface ships during World War I and World War II . Torpedo launches from steerable torpedo tubes meet the three stated assumptions well . However , an accurate torpedo launch from a submarine requires parallax and torpedo ballistic corrections when gyro angles are large . These corrections require knowing range accurately . When the target range was not known , torpedo launches requiring large gyro angles were not recommended . Equation 1 is frequently modified to substitute track angle for deflection angle ( track angle is defined in Figure 2 , " θ = θ + θ " ) . This modification is illustrated with Equation 2 . where A number of publications state the optimum torpedo track angle as 110° for a Mk 14 ( 46 knot weapon ) . Figure 4 shows a plot of the deflection angle versus track angle when the gyro angle is 0° ( " i . e " . , " θ = θ " ) . Optimum track angle is defined as the point of minimum deflection angle sensitivity to track angle errors for a given target speed . This minimum occurs at the points of zero slope on the curves in Figure 4 ( these points are marked by small triangles ) . The curves show the solutions of Equation 2 for deflection angle as a function of target speed and track angle . Figure 4 confirms that 110° is the optimum track angle for a target , which would be a common ship speed . There is fairly complete documentation available for a Japanese torpedo fire control computer that goes through the details of correcting for the ballistic and parallax factors . While the TDC may not have used exactly the same approach , it was likely very similar . Position keeper . As with the angle solver the equations implemented in the angle solver can found in the Torpedo Data Computer manual . Similar functions were implemented in the rangekeepers for surface ship - based fire control systems . For a general discussion of the principles behind the position keeper , see Rangekeeper .