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{{Infobox Weapon
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|name= Type 91 torpedo
|image= [[Image:Type 91 torpedo.JPG|250px]]
|caption= Type 91 torpedoes aboard an aircraft carrier.
|origin= [[Japan]]
|type= [[Aerial torpedo]]
<!-- Type selection -->
|is_ranged=
|is_bladed=
|is_explosive=yes
|is_artillery=
|is_vehicle=
|is_missile=yes
|is_UK=
<!-- Service history -->
|service= 1931–1945
|used_by= [[Imperial Japanese Navy]]
|wars= [[World War II]]
<!-- Production history -->
|designer= Rear Admiral Shoji Naruse and his team
|design_date=1930–1945
|manufacturer=
|unit_cost= 20,000 yen (in the year 1941)
|production_date=
|number=
|variants=
<!-- General specifications -->
|spec_label=
|weight= {{convert|848|kg|lb|abbr=on}}
|length= {{convert|5.270|m|abbr=on}}
|part_length=
|width=
|height=
|diameter={{convert|45|cm|in|abbr=on}}
|crew=
<!-- Ranged weapon specifications -->
|cartridge=
|caliber=
|barrels=
|action=
|rate=
|velocity=
|range=
|max_range= 2,000 m (2,187 yd)
|feed=
|sights=
<!-- Artillery specifications -->
|breech=
|recoil=
|carriage=
|elevation=
|traverse=
<!-- Bladed weapon specifications -->
|blade_type=
|hilt_type=
|sheath_type=
|head_type=
|haft_type=
<!-- Explosive specifications -->
|filling=
|filling_weight= 323.6&nbsp;kg with high explosive 235&nbsp;kg, (713.4 lb with 518 lb) for Type 91 warhead rev.3
|detonation=
|yield=
<!-- Vehicle/missile specifications -->
|armour=
|primary_armament=
|secondary_armament=
|engine=wet-heater type, 8-cylinder radial engine
|engine_power=200hp
|pw_ratio=
|transmission=
|payload_capacity=
|suspension=
|clearance=
|wingspan= 69 cm (27¼ in. in the air), 66 cm (26 in. in the water)
|propellant=
|fuel_capacity= 4 litres
|vehicle_range=
|ceiling=
|altitude=
|boost=
|speed=42 knots (77.8 km/h, 48.3 mile/h)
|guidance=
|steering=gyrocompass guided vertical rudder control system, gyroscope guided anti-rolling controller system
|accuracy=
|launch_platform=single-engine carrier-based attack aircraft, twin-engine land-based attack aircraft
|transport=
}}
 
The '''Type 91''' was an [[aerial torpedo]] of the [[Imperial Japanese Navy]] which was designed to be launched from an aircraft. It was used in [[naval battles]] in [[World War II]].
 
The Type 91 aerial torpedo  had two unique characteristics:
* Wooden attachments on the tail fins, that acted as aerodynamic stabilizers, which were shed upon water entry.
* An angular acceleration control system ([[PID controller]]) to control rolling movements, which was very advanced for its time.
This system made it possible to release the Type 91 not only at a cruising speed of 180 knots (or 333&nbsp;km/h, 207 mile/h) at an altitude of 20&nbsp;m (66&nbsp;ft), but also in a power-glide torpedo-bombing run at the [[Nakajima B5N|Nakajima B5N2]]'s maximum speed of 204 knots (or 378&nbsp;km/h, 234 mile/h).
 
The Type 91 [[torpedo]] was 450&nbsp;mm (17¾ in) diameter. There were five models put into service, with high explosive warheads weighing 213.5&nbsp;kg to 526.0&nbsp;kg (or 470.7&nbsp;lb to 1160&nbsp;lb) and having effective ranges of 1,500 m to 2,000 m (or 1,640 yd to 2,187 yd) at 42 knots (or 77.8&nbsp;km/h).
 
Since the Type 91 torpedo was the only practical aerial torpedo of the [[Imperial Japanese Navy]], it was simply known as the ''Koku Gyorai'', or '''aerial torpedo'''. Surface warships and submarines used other types of torpedo, namely the [[Type 93 torpedo|Type 93]] and [[Type 95 torpedo|Type 95]] respectively, while the [[Type 97 torpedo]] was designed for use by [[midget submarine]]s.
 
==Thunder fish==
The '''Thunder fish''', type 91 torpedo (modification 2), was a shallow water [[aerial torpedo]] that was designed for and used in the [[attack on Pearl Harbor]] in 1941. Conventional torpedoes when launched from aircraft would dive to 100&nbsp;ft before turning up to hit their targets.  The waters of the lagoon at Pearl Harbor were much shallower so wooden fins <!--and a soft wood breakaway nosecone--> were added to allow for shallow launching at low altitude.<ref name="hellions">{{cite book|last=Gannon|first=Robert|title=Hellions of the Deep|publisher=Pennsylvania State University Press|date=30 April 1996|pages=49–50|isbn=978-0-271-01508-8|url=http://books.google.co.uk/books?id=5pJxc8Je2vsC&pg=RA1-PA49&lpg=RA1-PA49&dq=thunder+fish+torpedo&source=bl&ots=nS3-rDjgWR&sig=Gk9uvlCemjwcDsTfWU6Kl2h59p0&hl=en&ei=Fbl5Sv7hFOLLjAefuuSnBg&sa=X&oi=book_result&ct=result&resnum=1#v=onepage&q=&f=false|accessdate=2009-08-05}}</ref>
 
The name '''Thunder fish''' is a literal translation of the Japanese ''gyorai'', meaning "torpedo" (''gyo'' = fish, ''rai'' = thunder).
 
The tactic was practised at a bay on [[Kyūshū]] island which resembled Pearl Harbor before being used in the attack in December 1941, launched from "Kate" [[B5N]] torpedo bombers.<ref name="hellions"/> The plan for attack was designed by naval air strategist [[Minoru Genda]] for [[Admiral]] [[Isoroku Yamamoto]] in the face of opposition from the majority Japanese navy view that victory could be achieved by the "The Great All-Out Battle" tactic of luring [[United States of America|United States]] [[battleships]] into a major action at sea.<ref>
{{cite web
|url=http://www.ess.uwe.ac.uk/genocide/reviewsw28.htm
|title=Review of Donald M. Goldstein and Katherine V. Dillon, eds.      The Pearl Harbor Papers: Inside the Japanese Plans
|publisher=National Endowment for the Humanities, archived at [[UWE]]
|accessdate=2009-08-05
|last=Kolb
|first=Charles C.
}}
</ref>
 
The torpedo measured {{convert|18|ft|0|in|m}} in length, with a diameter of {{convert|1|ft|5.7|in|m}}, and weighed {{convert|1841|lb|kg}}, with an explosive charge of {{convert|452|lb|kg}}. It had a range of {{convert|2200|yd|m|0}} and a speed of 42 [[Knot (unit)|knot]]s. A slight variant was used to sink [[HMS Prince of Wales (53)|HMS Prince of Wales]] and [[HMS Repulse (1916)|HMS Repulse]], launched from "Betty" [[G4M]] bombers in [[sinking of Prince of Wales and Repulse|an action]] in the [[South China Sea]] three days after Pearl Harbor on December 10, 1941.<ref>
{{cite web
|url=http://www.navweaps.com/Weapons/WTJAP_WWII.htm
|title=Japan Torpedoes of World War II
|publisher=NavWeaps.com
|accessdate=2009-08-05
}}
</ref>
 
== Specifications ==
Here is the list of the series of Type 91 aerial torpedoes, production models.<ref>p.24, Ichikawa, Hidehiko; Table 1-2 List of Aerial Torpedo ''Koku Gyorai Note''</ref>
 
{| class="wikitable"
|+Type 91 Aerial Torpedo, rev.2 Specifications
|-
! Item
! -
|-
| High explosive
| 204&nbsp;kg (449.7&nbsp;lb)
|-
| Speed
| 42 knots (48.33 mile/h)
|-
| Range
| 2,000 meter (2,187 yard)
|-
| Diameter
| 45&nbsp;cm (17¾&nbsp;inch)
|-
| Weight
| 838&nbsp;kg (1,847&nbsp;lb)
|-
| Length
| 5.427 meter (17.81&nbsp;ft)
|-
| Engine
| 200&nbsp;hp, wet-heater type, 8-cylinder radial engine
|}
 
=== Variations ===
{| class="wikitable"
|+Type 91 Aerial Torpedo and Type 91 Warhead, operational models
<!-- Header line -->
|-
! Main body
! Warhead
! High explosive (kg)
! Speed (knots)
! Range (m)
! Total Length (m)
! Diameter (m)
! Total Weight (kg)
! Head Length (m)
! Head Weight (kg)
! Comments
<!-- Row1 line -->
|-
| Type91
| Type91
| 149.5
| 42
| 2,000
| 5.270
| 0.45
| 784
| 0.958
| 213.5
| -
<!-- Row2 line -->
|-
| Rev.1
| Rev.1
| 149.5
| 42
| 2,000
| 5.270
| 0.45
| 784
| 0.958
| 213.5
| Supported shedding wooden tail plates in 1936
<!-- Row3 line -->
|-
| Rev.2
| Rev.2
| 204.0
| 42
| 2,000
| 5.470
| 0.45
| 838
| 1.158
| 276.5
| Body reinforced in 1938, anti-rolling controller in 1941
<!-- Row4 line -->
|-
| Rev.3
| Rev.3
| 235.0
| 42
| 2,000
| 5.270
| 0.45
| 848
| 1.460
| 323.6
| -
<!-- Row5 line -->
|-
| Rev.3
| Rev.3_rev.
| 235.0
| 42
| 2,000
| 5.270
| 0.45
| 848
| 1.460
| 323.6
| Reinforced warhead
<!-- Row6 line -->
|-
| Rev.5
| Rev.3_rev.
| 235.0
| 41
| 1,500
| 5.270
| 0.45
| 848
| 1.460
| 323.6
| Precision forging and stainless cast steel in body
<!-- Row7 line -->
|-
| Rev.5
| Rev.7
| 420.0
| 41
| 1,500
| 5.710
| 0.45
| 1080
| 1.900
| 526.0
| Warhead designed to break bilge
|}
The later, heavier models had a decreased range; this was not an operational problem as close launching was required for accuracy in any case. There were two versions in the Type 91 warhead rev.3,  differing in design maximum launch speeds.
 
=== Other Japanese aerial torpedoes ===
The Type 92 electrical (battery powered) aerial torpedo never made it beyond trial stage.
 
The Type 94 aerial torpedo was based on the highly successful [[Type 93 torpedo]]. The Type 93, called the "[[Long Lance]]" by the Allied press, was a massive (2.8 tonnes fueled) weapon of superior performance, due largely to the use of compressed [[oxygen]] as a propellant instead of compressed air; pure oxygen has approximately five times the reactant capacity in regard to common fuels as the same mass of mixed gasses found in air. The Type 94 emerged from development somewhat smaller, similar to the [[Type 95 torpedo]] - a type also derived from the Type 93 and used successfully as a submarine weapon. It was nonetheless a heavy, unwieldy device and never deployed operationally.
 
[[Yokosuka]] air arsenal began development of a 2 tonne large aerial torpedo for 4-engine [[Nakajima G8N]] land-based [[attack aircraft]], in spring 1944. It was called '''''Shisei Gyorai M''''' (Trial model torpedo M), or simply '''''2 tonne torpedo'''''. This was an enlarged version of Type 91 aerial torpedo, its diameter was 533mm (or 21 in, the diameter of standard Imperial Navy submarine torpedo tubes), length  7.10 m (about 23&nbsp;ft 4in), total weight 2,070&nbsp;kg (4,564&nbsp;lb), with a huge 750&nbsp;kg (1,653&nbsp;lb - about 50% larger than similar weapons of the era) warhead.<ref>p.383, Minoru, Akimoto; "Nihon Gunyoki Kokusen Zenshi, volume 4", Green Arrow sha, June, 1995</ref>
 
But the Type 91 aerial torpedo project members did not regard it as a series of Type 91 aerial torpedo. It would have been the largest aerial torpedo in the Imperial Japanese Navy Air Force, but the since the operating concept became outdated, that torpedo remained uncompleted work. This [[Nakajima G8N|G8N]] or the 18th trial model 4-engine bomber was called "Type 18 prototype land-based attack aircraft".
 
== Tactics  ==
The original Type 91 aerial torpedo entered service in 1931, corresponding to the year 2,591 of the Imperial Japanese calendar, leading to its model designation. This was the beginning of a protracted developing process toward a ''true'' aerial torpedo culminating in 1941.
 
=== Classic tactic ===
The first revision of the Type 91 aerial torpedo needed to be launched carefully, with the airspeed not exceeding 130 knots (or 240&nbsp;km/h, 150 mile/h) and at an altitude no higher than 30&nbsp;m (98&nbsp;ft), with slower airspeeds resulting in better precision. This 'classic' approach was actually easier to carry out in obsolete biplanes or planes with fixed landing gears, whereas the modern, fast Nakajima B5N as used by the IJN carrier strike force's 1st Air Flotilla was not an easy plane to handle at these slow airspeeds.
 
The development project team at [[Yokosuka Naval Arsenal]] of ''Ko-Hon'' or [[Imperial Japanese Navy Air Service]] reasoned that the maximum range of any aerial torpedo could be less than 2,000m (or 2,187 yd, 1.8 nautical mile). When aircraft launches a torpedo in running speed 40 knots, the targeted ship steaming in 30 knots would surely turn hard to maneuver around. It is mandatory for torpedo-bomber pilot ''attacking'', or running into the target as close as possible.
 
=== The second tactic ===
Another approach, called ''the second tactic'', was developed for torpedo-bombing runs in shallow water ports. Here, the aircraft was supposed to fly in at an even slower 100 knots (or 185&nbsp;km/h, 115 mile/h) and at an altitude of 10&nbsp;m (32.8&nbsp;ft) in the midst of intense AA fire. The only way to do this in a B5N2 was to lower the landing gear and flaps to increase drag and lift. The aviators of torpedo-bombing units trained this in the shallow waters of [[Kagoshima Bay]] by late August 1941 but felt uncertain about their chances of success.
 
=== The first tactic ===
The [[Torpedo bomber|torpedo-bomber]] unit of the [[Japanese aircraft carrier Akagi|carrier Akagi]] was the first to receive ten samples of the new rev.2 torpedo in August 1941. It was a marked improvement, allowing an approach in excess of 160 knots (or approx. 300&nbsp;km/h, 185 mile/h) and at 20&nbsp;m (66&nbsp;ft) altitude.
 
Immediately all the torpedo units changed to ''the first tactic'', the gears and flaps are retracted in the wings and flew in faster speed at higher altitude .
 
* A torpedo released at a range of 800 meters (875 yd) from the target at a speed of 300&nbsp;km/h, at height of 60 meters (196&nbsp;ft), would dive into the water entry point 290 meters ahead in 324&nbsp;km/h, at an entry angle of 22 degrees, after 3.5 seconds. That torpedo  runs under the water for 500 meter, and hits the target after 21 second.
 
* A torpedo released at a range of 620 meters (678 yd) from the target at a speed of 300&nbsp;km/h (185 mile/h), at height of 10 meters (33&nbsp;ft), would dive into the water entry point 120 meter (130 yd) ahead in 304&nbsp;km/h (190 mile/h), in entry angle of 9.5 degrees, after 1.4 seconds. The torpedo will then run under the water for 500 meters (547 yd), and hitting the target after 21 seconds.
 
In the morning of the [[Battle of the Coral Sea|Coral Sea]], on May 8, 1942, B5N torpedo-bomber units of ''The 5th Air Flotilla'' penetrated the American defenses at 0910[JST],<ref>Carrier Zuikaku Action Report</ref> swooped to [[USS Lexington (CV-2)]] and [[USS Yorktown (CV-5)]]. USS Yorktown CV-5 was attacked by four B5N2s in one unit of ''[[Japanese aircraft carrier Zuikaku|Zuikaku]] (Lucky Crane)'', led by squadron leader Lt Cmdr Shimazaki, and averted all four torpedoes. Large USS Lexington CV-2 was attacked by 3 units of total fourteen B5N2s, and was struck by the last two torpedoes to port. The Lt Sato unit of ''Zuikaku'' attacked first, followed by the Lt Iwamura unit, and the last was the Lt Ichihara unit of ''[[Japanese aircraft carrier Shōkaku|Shokaku]] (Flying Crane)'', in the crane wings attack formation. Those B5Ns were approaching to the ship in the full speed over 204 knots (or 378&nbsp;km/h, 235 mile/h) faster than known torpedo-bomber aircraft should. Captain Frederick Carl Sherman in the bridge of CV-2 watched a B5N shot down with the torpedo near the ship. He saw that the tail section of the torpedo was covered with box-like attachment. He reported that he had found the reason why the B5N2s could launch Type 91 aerial torpedo at such high speed.
 
=== Fast torpedo-bombing tactic ===
As for a high speed torpedo bombing run in 300 knots (or 556&nbsp;km/h, 345 mile/h), the maximum altitude for release was limited at 300 – 350 m (984 - 1,148&nbsp;ft). The  strength of contra-rotating propeller limited launch height . A torpedo, tested at 100 m in very high speed from [[Yokosuka P1Y|P1Y land-based attacker]] ''Ginga'' at Yokosuka arsenal, veered upon water entry because of a crack in a screw blade. The minimum release height was also limited to 40&nbsp;m (131&nbsp;ft) in a high speed run. If it were released lower than 30&nbsp;m (98&nbsp;ft) in a high speed run, the torpedo might skip on the water's surface.
 
With authorization from the Imperial Japanese Navy Air Force, Army Air Force pilot, Major Hideo Sakamoto established the ''fast torpedo-bombing tactic'', with his [[Mitsubishi Ki-67|Ki-67]] twin-engine bomber aircraft having good maneuverability, at Yokosuka Naval airbase in January 1944. He found the releasing parameters of the tactic after 300 tests. A Ki-67 with 1 tons torpedo starts steep dive at an altitude of 1,500m (approx. 5,000&nbsp;ft) above water level and launches the torpedo in two styles.<ref>pp.196-222, Kyuno Joe Ozawa, "Mitsubishi Type 4 Army Bomber Aircraft", ''Document of Historical Aircraft with Japan Making'' SPECIAL THANKS 600 ISSUE OF AIRREVIEW, last volume, Kanto-sha, 1994.</ref>
# Launch in speed range 370–460&nbsp;km/h, at 30-120m high (or speed 200-248knots (230-285mile/h) at altitude 98–394&nbsp;ft)
# Launch in speed range 460–560&nbsp;km/h at 50-120m high (or speed 248-302knots (285-348mile/h) at altitude 164–394&nbsp;ft)
 
=== Skidding right and left ===
Tactics were needed because the ''killed in action'' rate of aviators in torpedo bombing squadrons was high, 30 - 50% in the beginning of World War II. In the latter stages of the Pacific War, the rate was up to 90% and 100% during daytime operations.
 
Skilled aviators had their own tactics to survive, [[Slip (aerodynamic)|skidding]] right and left with varying speed (180 knots to 70 knots) at less than 10 meters high in the midst of water splashes of AA gunfire, to avoid a curtain of intense AA barrage controlled by the [[Fire-control system]] typical of US Navy warships.<ref>p.105 - p.116, Seko, Tsutomu; "Totsugeki Junbi Taikei Tsukure (or Attack Formation!)", ''Raigeki no Tsubasa (Wings of Torpedo attack)'', Kojin-sha</ref>
 
<!--The above??-->A [http://worldwar2database.com/gallery3/index.php/wwii1247 photo] shows the typical tactic of torpedo bombing, a [[B6N]] ''Tenzan'' in torpedo bombing attack of [[USS Yorktown (CV-10)]]. The original series of photos shows the sequential right and left side-skidding tactic of the crew. In this second photo, the B6N is skidding to its left, or toward the right in the photo, and the flak shell explodes to its right, or to the left in the picture. It was coming up to counterattack near the Truk islands, in the evening of February 17, 1944. It was one of four B6N ''Tenzan'' of a torpedo squadron in 2nd A.G or 582 A.G. Two out of four aircraft ditched on their way back and the crews were rescued. The remaining two aircraft returned safely to base. Original photo is PD, the Property of US Government.
 
== Type 91 history ==
: '''Chronological Table'''
: 1931 Type 91 aerial torpedo is into service, start production.
: 1936 Revision 1. Self-detachable wooden plates are introduced.
: 1937 Launch-tests at 500m and 1,000m with wooden damper.
: 1939 Revision 2 starts production. The sinking level after water entry becomes big problem.
: 1941 Revision 2 cleared the test of shallow water launching by introduction of anti-rolling controller. [[Attack on Pearl Harbor|Battle of Pearl Harbor]], [[Sinking of the Prince of Wales and the Repulse|Battle of offshore Malay]].
: 1941 Revision 3 starts production.
: 1942 [[Indian Ocean raid|Battle of Indian Ocean]], [[Battle of the Coral Sea]], [[Battle of Midway]], [[Battle of the Santa Cruz Islands]].
: 1943 Revision 5 starts production.
: 1944 [[Battle of the Philippine Sea|Battle of offshore the Marianas Islands]], [[Aerial Battle of Taiwan-Okinawa|Aerial Battle of offshore Formosa]].
 
=== Scientists and engineers developing aerial torpedo ===
''Ninety One Association'' includes Rear Admiral Naruse, Lt Cmdr Haruo Hirota, Lt Cmdr Makoto Kodaira (Matsunawa), Naval assistant manager Iyeta, Naval engineer Noma, Naval engineer Moritoshi Maeda, Lieutenant Hidehiko Ichikawa, and Teruyuki Kawada, university student as naval apprentice.
 
Captain Fumio Aiko was assigned in charge of promoting the development project of Type 91 aerial torpedo since 1931. Capt F. Aiko concentrated [[human resources]] to make an aerial torpedo, ordered to analyze the cause and to make anti-rolling controller. He is very proud of the Type 91 aerial torpedo as his great achievement.
 
===Delay of the development===
In the beginning of 1934, ''Kan-Pon'' or [[Imperial Japanese Navy Technical Department]], an operating division of the Ministry of the Navy of Imperial Japanese government, which had the primary responsibility for naval weapon systems, had their own plan and their own project for a Japanese aerial torpedo. In their plan, a big flying boat was to carry heavy Type 93 ''oxygen torpedoes'', to launch at long range, and then turn back towards safety. This soon proved to be an unrealistic desk plan. ''Kan-Pon'' confidentially developed their own Type 94 aerial torpedo, an aerial version of the Type 93 ''oxygen torpedo''. Their original challenge of the latest type of giant [[Kawanishi H6K|H6K Type 97 Large Flying Boat, Mavis]] was just accomplished the test flight successfully in 1934.
 
They even ordered to stop production of Type 91 torpedo, which significantly delayed the development schedule based on Type 91. This frustrated the project members of [[Yokosuka Naval Arsenal]].
 
=== Wooden tail stabilizers ===
The project revised Type 91 aerial torpedoes, as the '''revision 1''' supporting wooden tail plates, taken off on water entry, in 1936. The team demonstrated the launching tests of Type 91 aerial torpedoes wearing wooden ''shock-damper'' objects at altitude 500m (1,640&nbsp;ft) and 1,000m (3,281&nbsp;ft) in the following year, 1937. The project came up again and resumed the development of Type 91 aerial torpedo.
Type 91 aerial torpedo of earlier revision had a frail body.
 
It was revised as the '''revision 2''' by reinforced the frail body structure, in 1938.
 
=== Anti-rolling controller ===
Type 91 aerial torpedoes won the admiration by the anti-[[Yaw, pitch, and roll|rolling]] controller with [[acceleration]] control system of early days. Type 91 already had a shed-off type wooden tail plates as aerodynamic stabilizer. But the running out problem merged as aircraft speed going up from 130 to 180 knots.
 
Before the anti-rolling controller was introduced, the early revision of Type 91 aerial torpedo had a serious problem as other aerial torpedoes had in those days. Roughly released in high speed, it even made double-roll in the air. When it dove into the swelling waves of the heavy sea, it got spinning moment at the hard impact on water entry. It was veering the running direction, going down to stick to the bottom of the shallow basin of a port, crashing at the depth limits 100m by the water pressure, jumping out of the water, skipping water surface, or even running backwards. Only the real razor aviators could make the sure torpedo-bombing run in the calm sea.
 
A tumbled torpedo runs out of control. Though the gyrocompass and the depth meter works well, the torpedo cannot control the running direction by tail rudders unless they are in the neutral position at first. Once the torpedo rolls, the horizontal and vertical rudders lose their positions, or even upside down, result in runaway.
 
Engineers and scientists of the project, led by Lieutenant Hirota, drew one conclusion from their years of tests and numerical analyses, in 1939. Since the specification of launch speed of aircraft was increased from 130knots to 180knots and faster, any aerial torpedo needed an anti-rolling system with not only damping stabilizer function but also acceleration controlling function, otherwise the torpedo would be falling into unstable-state. The idea of acceleration-control, or ''countersteering'' function was thought of as impossible in those days. Two years passed.
 
The breakthrough on aerial torpedo design was made with the anti-rolling controller invented first by Iyeda, Assistant Manager of arsenal workmen, in spring 1941.
 
Ten days later, while the test of Iyeda system was in practice, Naval Engineer Noma invented another system, and it was put into final test in August 1941. It functions all the same with different mechanism. During the prototype tests, the Noma's system found out the better for having less time lags in response, so that the Noma system was adopted for production type of Type 91 aerial torpedo.
 
It looked merely a tiny mechanical air valve object controlling small roll rudders on both sides in the aft of the torpedo, was really the innovation of the torpedo technology world. It was the breakthrough for aerial torpedo. Type 91 rev.2 aerial torpedo first made it possible to use in the high seas.
 
The anti-rolling controller is actually a steering controller to stabilize the rolling motion of the torpedo by roll rudders on both sides. The roll rudders work within angler range +/-22.5 degrees, twisting in ailerons manner.
When a torpedo is rolling or rolls to some degree, the anti-rolling controller twists those rudders in the counter-rolling direction.  When a torpedo is rolling back to its neutral position of 0 degree, the controller sense it and switches roll rudders in the opposite direction to break angular velocity of torpedo rolling back, or ''[[countersteering]]''. They naval engineers called this operation as ''countersteer'' as they modeled it to steer a ship.
 
It enabled to keep Type 91 rev.2 aerial torpedo running under the water no deeper than 20 meter (65.6&nbsp;ft). Actually the cutting-edge pilots of torpedo-bomber squadrons in ''Dai Ichi Koku Sentai'' or ''The 1st Air Flotilla'' of the carrier strike force were able to launch their torpedo so as to sink in the water depth no more than 10 meter (32.8&nbsp;ft) after water entry.
Anti-rolling controller made aircraft possible to torpedo-bomb not only warships anchorage in shallow military port but also warships steam in chopped waves of heavy sea in full speed.
 
=== Increment of the explosive weight ===
The anti-rolling controller also made Type 91 aerial torpedo possible carrying heavier warhead section. Type 91 warhead and Type 91 rev.1 warhead, each weighs 213.5&nbsp;kg (470.7&nbsp;lb) with high explosive 149.5&nbsp;kg (329.6&nbsp;lb) only, but warhead rev.2 weighs 276&nbsp;kg (595.2&nbsp;lb) with high explosive 204&nbsp;kg (449.7&nbsp;lb). Warhead rev.7, which is for twin-engine bomber, weighs 526&nbsp;kg (1160&nbsp;lb) with high explosive 420&nbsp;kg (925.9&nbsp;lb). It was so designed to pierce the reinforced tough armor plates the latest USS warships developed during World War II.
 
=== Aerial torpedo technology of the Allies ===
Engineers and scientists of the Imperial Japanese Navy got a chance to inspect the torpedo technology of [[Allies of World War II|the Allies]], in aerial torpedoes captured at South West Pacific bases in early 1942. The [[United States Navy|US Navy]] aerial torpedo, [[Mark 13 torpedo]] was found at ''Sangley Point'', the military port in the [[Philippines]]. [[Fleet Air Arm]] aerial torpedoes of the [[Royal Navy]] were found at the base ''[[Kota Bharu]]'', northeastern [[Malaysia]], close to the [[Thailand|Thai]] border.
 
There were none like Type 91 aerial torpedo rev.2. They were disappointed with the work of their rivals, because those were as if they had few intentions to deal seriously with the development of aerial torpedo technology. The US Navy's  aerial torpedo had little differences aside from being capable of being loaded in aircraft and looks almost the same as the bigger Mark 13 ship torpedo. The Royal Navy had their traditional type aerial torpedo, which had been originally designed by White Head Company in 1925.
 
== The structure of Type 91 aerial torpedo rev.2 ==
Type 91 aerial torpedo is the first aerial torpedo, which is able to use practically in ocean. The scientific approach consistent with experimental evidence was adopted to lead development.
[[Image:Type91 AerialTorpedo Rev3 StructuralDrawing.svg|360px|right|Type91_aerial torpedo rev3, structural drawing]]
 
=== Warhead ===
Length = 1,460&nbsp;mm (57⅝in)
 
When a torpedo hits a ship, the inertia forces the aft mass in the initiator to thrust forward and ignite the high explosive in the initiator. The high explosive in the warhead will not detonate unless initiated as designed. A 20&nbsp;mm explosive cannon shell can go through the warhead without igniting the stable high explosive in the warhead.
 
The warhead has '''T''' shaped strip parts to reinforce the internal-lower portion of the front shell against the heavy impact on water entry. For the production model, the warhead section needs five reinforced strip bands on the front-bottom of the inner shell, lap welded in a shape of cut lower half star, or the superpose of the letter '''T''' and the letter '''Λ''', instead. The warhead also has two tiny stitch lines aligned on the front-top of the shell to enhance the explosion. The latest version had two hooks on the nose.
 
Type 91 aerial torpedo is to be launched by aircraft power gliding from high in the sky. The aerial torpedo, released at altitude 100m, is falling in speed nearly [[Mach number|Mach]] 0.5 on water entries, and receives over 100[[gravitational acceleration|G]] at the hard impact on the water surface.
 
=== Air chamber ===
L = 1,068&nbsp;mm (42⅛in)
 
The air chamber is a cylinder of thin shell made by alloy of nickel chromium-molybdenum steel. This tough steel alloy was originally developed for steel armor plate of battleship. The chamber is charged with highly compressed normal air at 175 - 215 [[atmosphere (unit)|atm]] (2,500 - 3,000 [[pounds per square inch|psi]]), which burns fuel oil to produce driving power. It loses the pressure down to around 50 atm (710 psi) while running 2,000 m (6,600&nbsp;ft) under the water.
 
=== Front float ===
L = 733&nbsp;mm (28⅞in)
 
Front float section has a pure water tank, a fuel oil tank and a depth meter.
 
The depth meter is placed at the inner bottom of the section to detect the water depth level. It detects the displacement level of the water depth and controls the tail horizontal rudders (or [[Elevator (aircraft)|elevators]]) proportionally, so that the torpedo keeps level running under the water.
 
=== Engine room ===
L = 427&nbsp;mm (16⅞in)
 
This section is constructed free to coming in the water to help a cooling system of the engine in the torpedo.
It has a starter, a ''Chowaki'' or [[pressure regulator]], a wet-heat chamber, a main engine, and a horizontal rudder controller.
 
The ''starter'' starts controllers, one for vertical tail rudders, and another for roll rudders for anti-rolling in both side wing rudders, with horizontal tail rudders being locked at uppermost position, while the torpedo falls down to the water surface. It starts the main engine to propel when the torpedo hits the water. A thick bolt is stuck through the starter during loaded in aircraft as the lock. The bolt is pulled out from the torpedo when it is released. The bolt remains underneath the fuselage of aircraft.
 
The ''pressure regulator'' is called as ''Chowaki'' or ''harmonizing system'' for the engine, it actually is a two-stage pressure regulator with twin pressure-tunable regulation valves. It steps down the pressure of compressed air at 215 - 50 atm (3,000 - 711 psi) in the air chamber to the constant high-pressure air at 10 atm (142 psi). While the air pressure is declining as the torpedo is running under the water, the pressure regulator feeds the constant high-pressure air to the engine intake aspirator and keeps the constant running speed in 43 knots (or 80&nbsp;km/h, 50 mile/h).
 
The ''wet-heat chamber'' is made by heat resistant steel. Type 91 aerial torpedoes use ''[[Torpedo#Wet-heater|wet-heater engine]]'' like almost all other torpedoes in World War II. The general wet heater burning method drastically improved the combustion efficiency of torpedo engines. It burns the mixed gas of fuel oil and the high-pressure air with spraying pure water in the wet-heat block to produce burning steam gas fed to the engine. The high-pressure fuel oil gas is burning at a temperature 800 degrees C (1,500 degF). The sprayed pure water mists into the combustion gas, which produces vapor explosion, results in completely gasified fuel oil combustion.
 
The ''main engine'' is an 8-cylinder single-row radial [[reciprocating engine|piston engine]].
 
The ''horizontal tail rudder controller'' is operated by the rod connection mechanism from the depth meter in the front float section.
 
=== Rear float ===
L = 1,002&nbsp;mm (39½in)
 
A single [[drive shaft]] is going through the section to the tail. This rear float section has a machine oil tank, a rudder controller, an anti-rolling controller, and roll rudders on both sides.
 
The ''machine oil tank'' is center-mounted in the rear float section.
 
The ''rudder controller'' is a general [[gyrocompass]] controlled system, which is steering vertical rudders to keep the longitudinal axis of the torpedo in the sensed direction straight. Both the vertical rudder controller and the anti-rolling controller had their own [[gyroscope]], which is to start rotating when the torpedo is released from aircraft. Each gyro has dual ring support mechanisms to move freely.
 
==== Anti-rolling controller ====
[[Image:USS Lexington under attack at Coral Sea.jpg|thumb|right|Carrier Zuikaku B5N2s in torpedo attacking at Coral Sea on May 8, 1942. Water splashes in front center and left are made by water entries of Type 91 aerial torpedoes.]]
 
[[Image:Guadalcanal-Tulagi Operation, Mitsubishi G4M.jpg|thumb|right|G4M1s in torpedo attacking at Guadalcanal on August 8, 1942.]]
 
[[Image:BB-57 Kates Santa Cruz NAN4-2-43.jpg|thumb|right|B5N2s in torpedo attacking at Santa Cruz on October 26, 1942]]
 
[[Image:B6N2 in formation.jpg|thumb|right|B6N2s in formation flight with torpedoes wearing box type tail stabilizers]]
 
[[Image:B7A-Ryusei torpedo.jpg|thumb|right|Aichi B7A Ryusei carrying torpedo with cross type tail stabilizer plates, 1945]]
 
The ''stabilizer'' or anti-rolling controller is a mechanical control system, whose control design needs [[numerical analysis]] of physical mathematics theory to fit stability. A spinning gyroscope of control system senses the tilt degree of roll, and then the controller is centering the roll of the torpedo.
 
The anti-rolling controller with the gyroscope can steer roll-rudders on both sides in angle range of '''''+/- 22.5''''' ° . When the torpedo tilted, the anti-rolling controller steers roll-rudders (or [[aileron]]s) in twisting ailerons manner to produce counter-rolling moment.
 
When the torpedo tilted over 10 degree and is rolling back the angle toward the neutral center position, the tiny mechanical system in the control air valve works. When it rolls back within the tilt angle 10 degree, the controller now countersteers roll rudders switching back to the reverse angles to break the counter-rolling moment, and to prevent overshoot. The torpedo rolls over the neutral center position and keeps rolling to some degree. The torpedo then stops in opposite tilt at certain degree, and starts rolling back the angle toward the neutral center position. Then the controller senses the angle tilted and countersteers roll-rudders to break the moment. It is rolling over the neutral center position then stops at certain degree, vice versa, like an air cushion is bouncing and settled to the floor. The movement continues but damps to neutral the rolling angle within 2.0 to 3.6 second in the air.
 
In the test, the system working was observed and proved by the developed high-speed movie film, the top-view shot of the falling torpedo tested, taken from the bomb bay.<ref>Fig.4-5, p.68, Ichikawa, Hidehiko; Chap.4-5 The mechanism of roll controller, ''Koku Gyorai Note''</ref> The anti-rolling system also proved the controller functions effectively under the water surface by the running result after the water entry.
 
==== Roll rudders ====
''Stabilizing rudder'', or roll rudders (or [[aileron]]s) are put on both sides of the torpedo, being steered to produce counter-rolling moment. Each rudder is a small 8&nbsp;cm<sup>2</sup> size square metal wing.
Each roll rudder has been covered with a temporal wooden extended wing of 12 × 20&nbsp;cm<sup>2</sup> (4¾in × 7⅞in), tighten with six aluminum sharing pins on both side-edges (three pins each) to get enough aerodynamic force in the air, that is to be shed and broken off when the torpedo gets the hard impact from the water surface on water entry. The remained original metal roll rudders are steering in the water running to converge the rolling movement arisen on water entry.
 
=== Tail section and twin screws ===
L = 530&nbsp;mm (to the tip end of propelling screw hub) (20⅞in)
 
There are [[bevel gears]] driving coaxial contra-rotating double 4 blades screws to propel torpedo running straight under the water. Tail section has vertical and horizontal stabilizer fins in cross. Each fin has a controlling rudder in aft. Horizontal fins and rudders or elevators have wide span in longitudinal direction and work proportionally, while vertical fins are small, and rudders have very short span.
 
==== Shed off aerodynamic wooden stabilizer plates ====
[[Image:Type91 AerialTorpedo TailSection and AeroDynamicTailStabilizer.PNG|thumb|right|Type91 aerial torpedo, tail section and aerodynamic tail stabilizer plates]]
Tail fins are covered with ''Kyoban'' or aerodynamic wooden stabilizer plates. They were introduced in 1936. It is shed off by the impact on water entry. This aerodynamic wooden stabilizer plates in the tail are in the shape of box cover for single-engine carrier-based torpedo-bombers [[Nakajima B5N]] and [[Nakajima B6N]]. In the case for twin-engine land-based torpedo-bombers [[Mitsubishi G3M|G3M]], [[Mitsubishi G4M|G4M]], [[Yokosuka P1Y|P1Y]], and [[Mitsubishi Ki-67|Ki-67]], the torpedo wears another type of aerodynamic wooden stabilizer plates covering tail fins in cross to extend their tail length in the air, which is less in drag resistance loss but needs more clearance heights in the bomb bay underneath the fuselage. In the case of land-based torpedo-bomber aircraft, a plate is needed to be set inside the bomb bay to groom the airflow, because the vortex coming in the bomb bay gives the turbulence behavior to the torpedo released.
 
A torpedo is released at a speed greater than 160 knots (or 300&nbsp;km/h, 184&nbsp;mph) in the air and then follows a parabolic path free-falling to the water. The aerodynamically designed wooden plates stabilize the up-and-down motion of the torpedo in the air keeping it aligned to the diving course. The wooden plates are shed as the torpedo hits the water, and the elevators or horizontal rudders set farthest forward lift the nose of the torpedo after water entry to start level running. The structure is simple and works well. The wooden head cap had been used before the anti-rolling controller system was introduced.
 
==== Screws ====
[[Propeller|Screws]] are coaxial contra-rotating double screw, with 4 propeller blades each.
Each screw is wrought from a cube steel alloy mass into bold cross shape and punched through the center. Hammering punches of 1 tons and 3 tons shape 4 blades.
 
Propel section is compactly designed so that the front screw and the rear screw are put in 5&nbsp;mm close to each other. A trouble happened in 1943, when a P1Y tested the torpedo released at altitude 100 m in high-speed power gliding. That torpedo veered the running direction. The hard impact on water entry made a front blade get cracked by the hit of a rear blade. The project members shared the recognition on the importance of annealing, quench hardening, and normalizing process of the screw blades, and so was done.
 
In the first [[Annealing (metallurgy)|annealing]] process, the metal is left in the oven at 700 °C (or 1,300 °F) for 2 hours then slowly cooled in lime powder. The metal is hammered out and machined in the shape of screw. Then the screw is put in the [[Quench|quench hardening]] process, kept at 850 °C (or 1,560 °F) for 1.5 hours, and is cooled in oil. In the last thermal normalizing process, the screw is put in 180 °C (or 356 °F) hot oil for 2 hours, then is left cooling in the air.
 
: Material: SK chromium-molybdenum alloy steel <ref>The alloy is used as the material for [[Turbine|turbine blade]] in 21st century.</ref>
: Process: Hammer out.
 
=== Rudder steering means ===
: 1. Full steering system
:: Vertical rudder system steers rudders tri-stated to full-right / neutral / full-left as the gyroscope senses. Type 91 aerial torpedo has long time constant period with respect to the longitudinal axis turn moment in the water.
 
: 2. Proportional steering system
::Horizontal rudder system elevates the angle of rudders proportional to the angle of displacement the depth meter detect.  Type 91 aerial torpedo has medium time constant period in longitudinal axis lift moment under the water.
 
: 3. Angular velocity steering system
:: Anti-rolling controller system steers both roll rudders tri-stated to full-up / neutral / full-down in twisting aileron manner. When the controller detect the rolling is coming back to the center position, the system countersteers roll rudders in opposite direction. This system uses countersteering function so as to dump unstable rolling oscillation movement. Type 91 aerial torpedoes has fast period in approx. 0.5&nbsp;s time constant in rolling moment.
 
== Structure of Anti-Rolling Controller ==
: Haruo Hirota, Naval Lieutenant Commander
: Makoto Kodaira, Naval Lieutenant <ref>''Kodaira'' is his adopted family name, his birth name is ''Matsunawa''</ref>
[[Image:Type91 AerialTorpedo RollRudder.svg|thumb|right|Type91 aerial torpedo, roll rudder]]
 
[[Image:Type91 AerialTorpedo MainRollController.svg|thumb|right|Type91 aerial torpedo, main roll controller]]
 
[[Image:Type91 AerialTorpedo RollControllerMovement.GIF|thumb|right|Type91 aerial torpedo, roll controller movement]]
 
The structure of the anti-rolling controller is a set of gyro-controlled air valve system to steer the roll rudders on both sides of a torpedo.
 
The anti-rolling controller is composed with a gyroscope, a main controller, and an output booster. The most significant part is the main controller.
 
=== Gyroscope ===
The [[gyroscope]] senses the rolling tilt degree in real-time. It inputs push-pull control operation force to a pilot valve, sliding it inside the main controller to switch two output valves exclusively to the rudders.
 
=== Main Controller ===
The main controller controls two output air valves exclusively to steer roll rudders.
It steers and countersteers those roll rudders. It steers the rolling-rudders with detecting the tilted degree of the torpedo rolling by the control of pilot valve. It countersteers those roll rudders when the torpedo is rolling back to neutral position, which results in ''detecting'' the acceleration of the rolling angular velocity derivative with respect to time.
<!-- Japanese version has six more paragraphs here -->
 
=== Output Booster ===
The output booster or auxiliary valve has two inlets and two outlets ports. The output booster is working as a pair of air shutoff valves. It is connected in cascade to two output ports of the main anti-rolling controller, switches on and off directly the two powerful high pressure controlling air flows one for clockwise twist and the other for counter clockwise twist of roll rudders, exclusively to each other. It is so as to save the main controller system and to ensure proper operation under the heavy impact condition.
 
== Sequential operation steps in aerial torpedo bombing ==
# A release button is switched on in the cockpit.
# Cartridge is ignited to cut a loading wire band. Torpedo is released and wire is falling freely.
# The torpedo is falling and the safety bolt is pulled out. It starts gyroscopes of both the vertical rudder controller and the anti-rolling controller.
#:  Vertical rudders are kept in straight direction.
#:  Horizontal rudders (or elevators) are locked in uppermost position to prepare the water entry.
#:  Roll rudders start steering by the anti-rolling controller.
#:  ---Water Entry---
# Hard impact to the water surface breaks off wooden air wing covers of side roll rudders and tail aerodynamic stabilizer plates or box.
# Doubly rotate screws are unlocked at propel block.
# Propel engine starts ''cool idling'' while running. (Engine starts rotating with high-pressure air only.)
# Brakes on horizontal rudders (or elevators) are released. Depth meter starts working.
#:  Water pressure after the entry downs a plate to start firing combustion chamber of the engine.
# Propel wet-heater engine starts ''hot'' running by burning fuel air gas, mixed with sprayed water.
# Safety lock in the warhead is released while running.
# High explosive explodes on the hit of the target.
 
----
 
== Theory: Aerial torpedo motion equation ==
[[Image:Type91 AerialTorpedo Vectors of MotionEqs.svg|thumb|right|Vectors of motion equations for aerial torpedo in the air]]
Rear Admiral Shoji Naruse explained in his class as follows.
 
The torpedo motion equation is the set of simultaneous ordinary differential equations, which is to model pitch motion of airborne aerial torpedo as follows.
<ref>Equations in the private book ''Koku Gyorai Note'' has errors in typescript symbol letters in privately printed edition service.</ref>
 
: ''Eq.''1: Falling velocity of the torpedo equation
 
: ''Eq.''2: Horizontal vector velocity of the torpedo mass equation
 
: ''Eq.''3: Vertical vector velocity of the torpedo equation
 
: ''Eq.''4: Vertical vector acceleration of the torpedo mass equation
 
: ''Eq.''5: Angular velocity equation with respect to time
 
: ''Eq.''6: Angular velocity differential equation with respect to time
 
<!-- the aerial torpedo motion equation in 1939 -->
: <math>
\begin{array}{lcll}
dx/dt &= &V_{X} &\cdots(Eq.1)\\
W/g \times \left(dV_{X}/dt \right) &= &- D \cos \varphi - L \sin \varphi &\cdots(Eq.2)\\
dz/dt &= &V_{Z} &\ldots (Eq.3)\\
W/g \times \left(dV_{Z}/dt\right) &= &D \sin \varphi - L \cos \varphi + W  &\cdots(Eq.4)\\
d\theta/dt &= &\omega &\cdots(Eq.5)\\
I \times \left(d\omega/dt\right) &= &57.3M - bV\omega &\cdots(Eq.6)
\end{array}
</math>
 
: where constant '''57.3''' of ''Eq.''6 is the coefficient from '''1''' (radian) = '''57.2958&deg;'''
 
'''''b V ω''''' of ''Eq.''6 is the damping moment, where '''''b''''' is defined as;
 
: <math> b = - (\delta C_{mgH} / \delta \alpha_{H}) \times ( \rho S \mathit{l}/2) \times \mathit{l}_{H}\,</math>
 
Since the angular moment of a torpedo here is the lifting movement as follows;
 
: <math> \omega\mathit{l}_{H} /V = ( \delta C_{mgH} /\delta\alpha_{H}) \times ( \rho S \mathit{l} /2 ) \times \mathit{l}_{H} \times V \times \omega \,</math>
 
:: '''''V''''' : The velocity of the torpedo
:: '''''V<sub>H</sub>''''' : The horizontal axis velocity of the torpedo
:: '''''V<sub>Z</sub>''''' : The vertical axis velocity of the torpedo
:: '''''&phi;''''' : The moving vector angle of the torpedo in reference to horizontal axis
:: '''''&theta;''''' : The posture angle of the torpedo in reference to the horizontal axis
:: '''''&alpha;''''' : The internal angle between '''''&phi;''''' and '''''&theta;''''', which is equal to the lift angle of tail fins of the torpedo
:: '''''W''''' : Weight of the torpedo
:: '''''g''''' : Acceleration of gravity, '''9.8&nbsp;m/s<sup>2</sup>'''
:: '''''I''''' : Inertia coefficient with respect to lift moment at the gravity center of the torpedo
:: '''''&omega;''''' : Lifting angular velocity (radian)
:: '''''D''''' : Drag moment of force
:: '''''L''''' : Lift moment of force
:: '''''M''''' : Roll moment of force around the longitudial axis of the torpedo
:: '''''&rho;''''' : Air density
:: '''''S''''' : Cross-section area of the torpedo
:: '''''l''''' : Total length of the torpedo
:: '''''l<sub>H</sub>''''' : The length between the gravity center and the center of lift moment of tail fins of the torpedo
 
The value '''''l<sub>H</sub>''''' is measured in wind-tunnel test,
as drag moment of force coefficient differences between the torpedoes with and without box type attachment of wooden tail stabilizer plates;
 
: <math> \mathit{l}_{H} = (-C_{mgH}\,\mathit{l}+C_{tHd})/C_{nH}\,</math>
 
where each coefficient is defined as;
 
: '''''C<sub>nH</sub>'' = ''C<sub>XH</sub>'' sin ''&alpha;'' + ''C<sub>ZH</sub>'' cos ''&alpha; '''''
: '''''C<sub>tH</sub>'' = ''C<sub>XH</sub>'' cos ''&alpha;'' + ''C<sub>ZH</sub>'' sin ''&alpha; '''''
 
:: '''''C<sub>X</sub>''''' : Drag moment of force coefficient '''''D'' / (1/2 ''&rho; V''<sup>2</sup> ''S'')'''
:: '''''C<sub>Z</sub>''''' : Lift moment of force coefficient '''''L'' / (1/2 ''&rho; V''<sup>2</sup> ''S'')'''
:: '''''C<sub>mg</sub>''''' : Roll moment of force coefficient around the gravity center of the torpedo '''''M'' / (1/2 ''&rho; V''<sup>2</sup> ''l'')'''
:: '''''C<sub>XH</sub>''''' : Drag moment of force coefficient of tail stabilizer box of torpedo
:: '''''C<sub>ZH</sub>''''' : Lift moment of force coefficient of tail stabilizer box of torpedo
:: '''''C<sub>mgH</sub>''''' : Roll moment of force coefficient around the gravity center of tail stabilizer box of the torpedo
 
Solving ''Eq.''1 through ''Eq.''4 with respect to movement under certain [[Boundary value problem|boundary conditions]], we could derive the set of equations '''''t''''', '''''X''''', '''''Z''''' in definite integral equation form.
 
: <math> X = \int_{\lambda_0}^{\lambda}\,\frac{d \lambda}{gC}\,+\,k\,\varphi(x), \,\, Z = \int_{\lambda_0}^{\lambda}\,\lambda\,\frac{d \lambda}{gC}\,+\,k\,\varphi(x)  </math>
 
: where, '''''&lambda;'' = - tan ''&phi;''''', '''''&lambda;''<sub>0</sub> = - tan ''&phi;''<sub>0</sub>''',  at time '''''t'' = 0 '''
 
[[Integral|Definite integrals]] can be numerically solved by ''[[Simpson's rule|Composite Simpson's rule]]'' in the ordinary differential equations field.
 
Lifting motion ''Eq.''5 can be numerically solved by [[Runge-Kutta methods|The common fourth-order Runge-Kutta method]] to get values of '''''ω'''''.
 
Lifting stability of Torpedo ''Eq.''6 can be numerically solved by [[Moving average|Exponential moving average method]] for exponential equations.
 
=== Practical equation for lift moment ===
Lieutenant Commander Hirota proved the practical torpedo motions by his equations.
 
In the pitching movement, tail stabilizer box has the function not only aligning the longitudinal axis of torpedo in the moving direction or the vector of the center gravity, but also damping the lifting movement or pitching oscillation. The latter effect is the change of lift moment with respect to the angular velocity of the center gravity as follows.
 
:<math> -(1/2) \times 57.3 C_1 \, \rho \, V^2 \, b \, S_1 \, (b/V) \, (d\theta / dt) \,</math>
 
:: '''''&rho;''''' : Air density
:: '''''V''''' : Speed of the torpedo (constant)
:: '''''C''<sub>1</sub>''' : Lift moment coefficient by one degree with respect to the airflow vector to the plates of the aerodynamic tail stabilizer
:: '''''b''''' : The length between gravity center of torpedo and the lift moment center of the plates of the tail stabilizer
:: '''''S''<sub>1</sub>''' : Area sum of the horizontal plates of the tail stabilizer
:: '''''&theta;''''' : Angle of the longitudinal axis of the torpedo to the vector of the center gravity, where the angle is in radian.
 
The 1st [[derivative]] of the lift angle with respect to time, '''57.3 (''b/V'') (''dθ/dt'')''' is the key factor to damp the pitch movement. The characteristics to damp the pitching factor improved the airborne stability and the course of the torpedo.
 
=== Practical equation for roll moment ===
First, the roll moment equation is set, then it is simplified in 2nd derivative of '''''θ''''' with respect to '''''t''''', as follows:
:<math>
\begin{array}{lcll}
I_2(d^2\theta/dt^2)&= &-K-M(d\theta/dt) &\cdots(Eq.7)\\
(d^2\theta/dt^2)+M/I_2(d\theta/dt)&= &0 &\cdots(Eq.8)
\end{array}
</math>
 
Here we set the initial conditions at '''''t'' = 0''' as '''''dθ/dt'' = ''ω''<sub>0</sub>''', '''''θ'' = 0''' to analyze the angular movement on the top neutral point,
then we can simplify ''Eq.''7 and ''Eq.''8 as follows:
 
:<math>
\begin{array}{lcll}
d\theta / dt&= &-(I_2\,/\,M)\,(K\,/\,I_2)\,+\,(\omega_0\,+\,K\,/\,M)\,e^{-(M/I_2)t} &\cdots(Eq.9)\\
\theta &= &-(K/M)t\,+\,(I_2/M)\,(\omega_0\,+\,K/M)\,(1\,-\,e^{-(M/I_2)t}) &\cdots(Eq.10)
\end{array}
</math>
 
:where '''''K''''' and '''''M''''' are defined as follows:
::'''''K'' = - (1/2) ''C''<sub>2</sub> ''&rho; V''<sup>2</sup> ''S''<sub>2</sub> a '''
::'''''M'' = (1/2) × 57.3 ''C''<sub>1</sub> ''S''<sub>3</sub> (''b''<sub>2</sub><sup>2</sup> / 12 )''&rho; V'''''
 
:and the symbols above are the constants and variables as follows:
:: '''''&rho;''''' : Air density
:: '''''V''''' : Speed of the torpedo (constant)
:: '''''C''<sub>2</sub>''' : Lift coefficient of '''22.5&deg;''' with respect to the airflow vector to the side roll rudder plates
:: '''''a''''' : The length between the aerodynamic centers of the lift moment force in two roll rudders
:: '''''S''<sub>2</sub>''' : The area of one roll rudder
:: '''''b''<sub>2</sub>''' : The width of the tail stabilizer
:: '''''C''<sub>1</sub>''' : Lift coefficient by one degree with respect to the airflow vector to the plates of the aerodynamic tail stabilizer
:: '''''S''<sub>3</sub>''' : Area sum of the plates of the tail stabilizer, where '''''S''<sub>3</sub> / 4''' is used in the case of box type aerodynamic tail stabilizer.
:: '''''I''<sub>2</sub>''' : Inertia coefficient with respect to lifting moment at the gravity center of the torpedo
:: '''''&theta;''''' : Roll angle of the torpedo at a right angle with the longitudinal axis
 
In the practical iterative process in analyses, set certain angle value '''''θ''°''' to ''Eq.''10 and gets value '''''t'''''. Put the value '''''t''''' to ''Eq.''9 then we can get the angular velocity passing through the top neutral point.
 
Since numerical calculation analyses are plain and difficult to gain public understanding, Hirota made a very simple alternative qualitative explanation of ''Eq.''7 for the countersteering theory to the outsiders of the project, then. It made sense to all by the characteristics of the equation with respect to roll angle, which was obtained through the results of his numerical analyses. ''Eq.''7 represents the change of the rolling angular velocity of the torpedo, that is the 2nd order derivative of angle with respect to time.
 
The torpedo with anti-rolling controller can converge a big roll angle moment of the torpedo to the small ''to and fro'' rolling motion by the factor '''''K''''' and '''''M''''' of ''Eq.''7. Anti-rolling controller can converge a big roll angle moment of the torpedo to the small to and fro rolling motion by changing '''''K''''' factor in the right hand side in ''Eq.''7, which represents the roll moment produced by twisting the side roll rudders, as follows:
 
When the roll angle is over the range of '''+/-10''' degree, the sign of the first term '''''K''''' factor in ''Eq.''7 works always in positive to steer roll rudders. When the roll angle is coming back within the range of '''+/-10''' degree, the first term '''''K''''' factor in ''Eq.''7 changes the sign of value in negative to countersteer.
 
While the 2nd term '''''M''''' factor of right hand side in ''Eq.''7, which represents the drag force of wooden tail stabilizer plates, always damps the rolling moment.
 
That is how Type 91 aerial torpedo can converge the rolling moment oscillation while falling in the air and running under the water.
 
== Miscellaneous stories ==
 
=== Provision of the aerial torpedo technology to Germany ===
Germany approached Japan to transfer Japanese aerial torpedo technology and [[List of World War II torpedoes of Germany#List of WWII Luftwaffe torpedoes|Type 91 aerial torpedoes]]. The Imperial Japanese Navy accepted that approach, and brought not only the technology but also a number of Type 91 aerial torpedoes to Germany in response, designated the ''Luftorpedo'' '''LT 850''' in German service.
 
Germany needed to know the '''aerial torpedo''' technology because the [[Italian battleship Littorio]] was heavily damaged in the [[Battle of Taranto]] on November 11, 1940, and the [[German battleship Bismarck]] was hit by a single torpedo, which jammed its [[rudder]] and steering gear for hours on May 26, 1941. Germany also needed aerial torpedoes to attack the Allied transport ships steaming in the [[Mediterranean Sea]].<ref>p.13, Fumio Aikō; ''Koku Gyorai Note''</ref> It had previously imported Italian-made aerial torpedoes.
 
=== Kawatana Naval Arsenal: Firm of Type 91 aerial torpedo ===
Kawatana Naval Arsenal was the production firm of Type 91 aerial torpedo.
Type 91 aerial torpedo was first produced at Nagasaki Weapon Factory of [[Mitsubishi Heavy Industries]] in the beginning. Aerial torpedo was researched and developed at [[Yokosuka Naval Arsenal]] in [[Kanagawa Prefecture]].
 
Later, Imperial Japanese Navy established two branch arsenals. One was Suzuka Naval Arsenal in [[Mie Prefecture]]. Another was Kawatana Naval Arsenal, the branch of [[Sasebo Naval Arsenal]] in [[Nagasaki Prefecture]]. [[Kawatana, Nagasaki|Kawatana]] was specialized to torpedo production.
In 1945, a strange map of Japan, carried by aviators of [[United States Army Air Forces]], noted Kawatana Naval Arsenal as a beer factory. Kawatana Arsenal got no air raid. After the war was over, Kawatana could not help but refused the order of rendering beer by the occupied military force.
 
[[Nagasaki]] City and Nagasaki Weapon Factory were perished from the face of the earth by ''[[Fat Man]]''. Casualties and burned citizens were carried over to a small town, Kawatana by rail. Kawatana Naval Arsenal accommodated them all. All high school and junior-high girl students working at the arsenal nursed them. They have fresh memories of Kawatana with killed or burned casualties by ''Fat Man''.
 
=== Postwar ===
The Imperial Japanese Navy was perished in 1945. Japan decleared the no-war commitment. The torpedo technology was prohibited by the war-renouncing [[Constitution of Japan|Constitution]] Article 9. A few scientists got job in some universities, most were working in nonpublic corporations in the chaos of postwar Japan.
 
About 15 years later, Type 91 aerial torpedo project members knew the industrial machineries imported from United States to Japan powered by [[PID controller|proportional-integral-derivative control devices]] at last. They saw those machineries, which proclaimed "high-sounding" title, with mingled feelings.<ref>p.78, Ichikawa, Hidehiko; Chap.4-5 The mechanism of roll controller, ''Koku Gyorai Note''</ref>
 
Some dacades later, they called together at a historic inn named '''Yōshin-tei''', Izu, Kanagawa-prefecture, Japan to establish a small association on January 16, 1978. They decided to raise money to make a tiny book ''Koku Gyorai Note'', or Aerial Torpedo Notebook by private book service.
They selected Yuta Tanaka as the 1st chairman. He soon died in 1979, and the major member Toshimori Maeda, died too. Satoshi Suzuki was selected as the 2nd chairman to publish the private book.<ref>p.278, Ichikawa, Hidehiko; Postface, ''Koku Gyorai Note''</ref>
<ref>''Hotel Yoshin-tei'' was a venerable inn since 1989, famous for its amenity, sanitary modern building, having beautiful scenery by the resort beach of Hayama, Zushi-city, in Kanagawa prefecture, Japan. It located close to the Imperial family resort villa, ''Hayama Goyo Tei''. When [[Emperor Taishō]] had been going to die at Hayama Imperial villa on December 1926, ministors of Imperial Japanese government had stayed at Yoshin-tei to serve Emperor Taishō. Traditional ''Hotel Yoshin-tei'' was closed in 1984 and an Italian restaurant ''Cantina'' is opened at the lot since February, 2004. Only a beach cabana, ''Branch of Yoshin-tei'' is opening on nearby sand beach every summer.</ref>
 
Type 91 torpedoes were now displayed at [[Naval Academy Edashima|Etajima school of Japan Maritime Self-Defense]] (The Maritime Self Defense Force 1st Technical School) and Shimofusa Base. They had lost the roll rudders.
 
Type 91 torpedo retaining original form was once displayed at personal exhibition stand by a small wayside drive-inn cafe, named ''Yoroi-ya'' (armor house), in the pile of other dusty military junk parts the owner had, the engine of [[Nakajima B6N|B6N2]] ''Tenzan'', broken radio communication systems, used cups, and rusted mountain artilleries from the Imperial Japanese army and navy, in Hyogo prefecture, Japan, till 2005. The stand was closed in 2005 and the exhibited junk articles were sold to neighboring farmers or military collectors.
 
An excavated Type 91 aerial torpedo was preserved at Resource Museum in [[Naha Airport|JGSDF Camp Naha]], 1st Combined Brigade of The Western Army, [[Japan Ground Self-Defense Force|JGSDF]], located in [[Naha, Okinawa|Naha]] city, Okinawa, Japan. It is retaining the original form. It was picked up as an [[unexploded ordnance]] by a bomb-disposal Squadron of JGSDF.
 
A captured Type 91 aerial torpedo is displayed at the U. S. Naval Academy, Annapolis, Maryland. It rests on two supports flanking a pathway in a small park in front of the Academy's Dahlgren Hall. Displayed on the other side of the pathway is a Type 93 Japanese Long Lance ship-launched torpedo.
 
==References==
 
===Bibliography===
*{{cite book
| last = Ichikawa
| first = Hidehiko
| coauthors= Kodaira, Makoto; Kawada, Teruyuki
| date = July 25, 1985
| chapter =
| title = "Kyu Ichi Kai - Koku Gyorai Note" or 91 Association - Aerial Torpedo Notebook
| publisher = ''Iyeno Hikari'' Private Publishing Service
| location = Tokyo, Japan
| id = ISBN
}} - text in Japanese, privately printed book.
*{{cite book
| last =
| first =
| authorlink =
|date=July 2002
| chapter = Warship Carrier Zuikaku Action Report No.7, Battle of the Coral Sea
| title = "Kaigun Koku Bokan Sento Kiroku" or Naval Aircraft Carrier Action Reports
| publisher = Athen-shobo
| location = Tokyo, Japan
| id =
}} - photographic print copies of Imperial Japanese Navy Action Reports, text in Japanese.
*{{cite book
| last =
| first =
| coauthors=
| month =  | year = 1994
| chapter = p196 - p222, Ozawa, Kyuno Joe; "Mitsubishi Type 4 Army Bomber Aircraft"
| title = Document of Historical Aircraft with Japan Making, SPECIAL THANKS 600 ISSUE OF AIRREVIEW, last volume
| publisher = Kanto-sha
| location = Tokyo, Japan
| id = ISBN
}} - text in Japanese, Prof. Ozawa is the designer of Ki-69.
*{{cite book
| last = Seko
| first = Tsutomu
| coauthors=
|date=December 1986
| chapter =
| title = "Raigeki no Tsubasa" or Wings of Torpedo Bombers
| publisher = Kojin-sha
| location = Tokyo, Japan
| id = ISBN
}} - text in Japanese, Seko was one of the last torpedo bombardiers of B6Ns.
*{{cite book
| last = Akimoto
| first = Minoru
| coauthors=
|date=June 1995
| chapter =
| title = "Nihon Gunyoki Kokusen Zenshi, Dai 4 kan" or Japanese military aircraft air combat complete history, volume 4
| publisher = Green arrow sha
| location = Tokyo, Japan
| isbn = 4-7663-3174-5
}} - text in Japanese.
* (August, 1945), Resources from Torpedo bombing section, Kawatana branch, Naval aerial technology arsenal, Imperial Japanese Navy.
* (August, 1945), Resources from the 1st torpedo section, Kawatana naval arsenal production firm, Imperial Japanese Navy.
 
=== Notes ===
{{reflist}}
 
== External links ==
*[http://www.navweaps.com/Weapons/WTJAP_WWII.htm A page with many statistics on Japanese WWII torpedoes.]
 
<!--spacing, please do not remove-->
 
{{IJN}}
 
{{DEFAULTSORT:Type 91 Torpedo}}
[[Category:Torpedoes of Japan]]
[[Category:World War II weapons of Japan]]
[[Category:World War II naval weapons]]
[[Category:Aerial torpedoes]]

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