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{{Short description|Electromechanical analog computer}}
[[Image:TDCfullview.jpg|thumb|right|U.S. Navy Mk III Torpedo Data Computer, the standard US Navy torpedo fire control computer during World War II. Later in World War II (1943), it was replaced by the TDC Mk IV, which was an improved and larger version.]]
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===History===
The problem of aiming a [[torpedo]] has occupied military engineers since [[Robert Whitehead (engineer)|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]].<ref name=othertorps>There were other forms of torpedo guidance attempted throughout WWII. Notable are the Japanese human-guided ''[[Kaiten]]'' and German [[G7e#G7e/T3|pattern running]] and [[acoustic homing]] types for attacking convoys. Today, most submarine-launched torpedoes are wire-guided with terminal homing.</ref> 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.<ref name=USMk14his>{{cite web|url = http://www.geocities.com/Pentagon/1592/ustorp5.htm|title= Part Five: Post WW-II Submarine Launched/ Heavyweight Torpedoes|access-date=2006-07-26|author= Frederick J Milford|date= October 1997|work= US Navy Torpedoes|archive-url=https://web.archive.org/web/20060523064716/http://www.geocities.com/Pentagon/1592/ustorp5.htm|archive-date=2006-05-23}}</ref> In fact, two World War II-era straight running torpedoes — fired by the British nuclear-powered submarine {{HMS|Conqueror|S48|6}} — sank {{ship|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<ref name=fleetsub>{{cite web | title = Torpedo Data Computer | work = FleetSubmarine.com | year = 2002 | url = http://www.maritime.org/tdc.htm | access-date = 2006-07-03 | archive-date = 2012-07-17 | archive-url = https://web.archive.org/web/20120717035001/http://maritime.org/tech/tdc.htm | url-status = dead }}</ref> (the U.S. examples were the [[Mark VIII Angle Solver]] (colloquially called the "banjo", for its shape), and the "Is/Was" circular sliderule ([[Nasmith Director]]), for predicting where a target will be based on where it is now and was)<ref>Holwitt, Joel I. ''"Execute Against Japan"'', Ph.D. dissertation, Ohio State University, 2005, p.147; Beach, Edward L., Jr. ''Run Silent, Run Deep''.</ref> or mechanical calculator/sights.<ref name = dread>{{cite web |title = Firing a Torpedo Using A Mechanical Computing Sight |work=The Dreadnought Project |url =http://www.dreadnoughtproject.org/tfs/index.php/Torpedo_Director|year=2000
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In 1932, the [[Bureau of Ordnance]] (BuOrd) initiated development of the TDC with [[Arma Corporation]] and [[Ford Instruments]].<ref name="Holwitt, p.147">Holwitt, p.147.</ref> This culminated in the "very complicated" Mark 1 in 1938.<ref name="Holwitt, p.147"/> This was retrofitted into older boats, beginning with {{USS|Dolphin|SS-169|2}} and up through the newest {{sclass|Salmon|submarine|5}}s.<ref name="Holwitt, p.147"/>
The first submarine designed to use the TDC was {{USS|Tambor|SS-198|2}},<ref name=Tambor>{{cite web | last = Mohl | first = Michael | title = Tambor (SS-198) |
In 1943, the Torpedo Data Computer Mark IV was developed to support the [[Mark 18 torpedo|Mark 18]] torpedo.<ref name=Mk18>The Mark 18 was electric and therefore wakeless and difficult for surface forces to trace. On the downside, it was slower than the Mark 14. This made it more difficult to aim accurately because larger gyro angles were involved. Even so, thousands of them were fired during WWII.</ref><ref name=clearMk18>{{harvnb|O'Kane|1977|p=221}}</ref>
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Straight running torpedoes were usually launched in salvo (i.e. multiple launches in a short period of time)<ref name="spread">{{harvnb|COMSUBATL|1950|loc=§ Definitions pp 1–9}}</ref> or a spread (i.e. multiple launches with slight angle offsets)<ref name="spread"/> 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.<ref name = doctrine>{{cite book | title = Current Submarine Doctrine | editor = Commander Submarine Force, Pacific Fleet | orig-year = 1944-02 | date = 2006-02-17 | pages = paragraph 4614 | chapter = Attacks -- General (Chapter IV, Section 1) | chapter-url = http://www.history.navy.mil/library/online/ss-doc-4.htm | url = http://www.history.navy.mil/library/online/sub_doctrine.htm | archive-url = https://archive.today/20121212215116/http://www.history.navy.mil/library/online/sub_doctrine.htm | url-status = dead | archive-date = December 12, 2012 | access-date = 2006-07-02 }}</ref> 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 [[ROKS Cheonan sinking|sinking]] of [[South Korea]]'s {{ship|ROKS|Cheonan|PCC-772|6}} by [[North Korea]] in 2010, the last warship sunk by a submarine torpedo attack, ARA ''General Belgrano'' in 1982, was struck by two torpedoes from a three torpedo spread.<ref name=belgrano_attack>{{citation| url=http://www.geocities.com/nmdecke/Submarines.html| title = Submarines 1950-2000, a study in unused potential| access-date = 2006-08-20| author = Nathan Decker | date = July 2005|archive-url=https://web.archive.org/web/20070317172208/http://www.geocities.com/nmdecke/Submarines.html|archive-date=2007-03-17}}</ref>
[[Image:Torpedo Data Computer, interior.jpg|thumb|right|A look inside the TDC showing the motors driving the Position Keeper
To accurately compute the gyro angle for a torpedo in a general engagement scenario, the target course, speed, 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
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===TDC functional description===
Since the TDC
*Angle solver: This computer calculates the required gyro angle. The TDC had separate angle solvers for the forward and aft torpedo tubes.
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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.<ref name="clear"/><ref name = "wahoo"/> Figure 3 provides an accurate model for computing the gyro angle when the gyro angle is small, usually less than 30°.<ref name = SmallGyro>{{harvnb|COMSUBATL|1950|loc=§ "Theory of Approach and Attack", pp. 8-8, 8-9}}</ref>
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.<ref name = Doctrine>{{cite book | editor = Commander Submarine Force, Pacific Fleet | title = Current Submarine Doctrine | orig-year = 1944-02 | url = http://www.history.navy.mil/library/online/sub_doctrine.htm | archive-url = https://archive.today/20121212215116/http://www.history.navy.mil/library/online/sub_doctrine.htm | url-status = dead | archive-date = December 12, 2012 | access-date = 2006-08-19 | publisher = Department of the Navy | date = 2006-02-17 | id = USF 25(A) | pages = paragraph 4509 | chapter = Attacks -- General (Chapter IV, Section 1) | chapter-url = http://www.history.navy.mil/library/online/ss-doc-4.htm. }}</ref>
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.<ref name = Deflection>{{harvnb|COMSUBATL|1950|loc=§ "Definitions", p. 1-2}}</ref>
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:{{math|''θ''<sub>Deflection</sub>}} is the angle of the torpedo course relative to the periscope line of sight.
Range plays no role in Equation {{EquationNote|1}}, which is true as long as the three assumptions are met. In fact, Equation {{EquationNote|1}} is the same equation solved by the mechanical sights of [https://web.archive.org/web/20060902191228/http://www.history.navy.mil/photos/images/h41000/h41761.jpg 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.<ref name = AccurateRange>{{harvnb|COMSUBATL|1950|loc=§ "Theory of Approach and Attack" p. 8-10}}</ref>
Equation {{EquationNote|1}} is frequently modified to substitute track angle for deflection angle (track angle is defined in Figure 2, {{math|1=''θ''<sub>Track</sub>=''θ''<sub>Bow</sub>+''θ''<sub>Deflection</sub>}}). This modification is illustrated with Equation {{EquationNote|2}}.
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