References:
WT-1003(EX) Operation Wigwam, Scientific Director's Summary Report. (12.8 MB)
DNA 6038F Operation Hardtack I – 1958 (35~ MB)
WT-1608: Operation Hardtack – Project 1.3 Surface Phenomena from Underwater Bursts
WT-1629(EX) Operation Hardtack – Project 3.5: Loading and Response of Submarine Hulls from Underwater Bursts. (3.6 MB)
Effects of Nuclear Weapons, Chapter 6; 1977

Operation Crossroads

Shot Baker was fired from a depth of 90 feet in water only 180 feet deep. Yield was 23.5 kilotons.

Operation Wigwam

On 14 May 1955, at 126°16' W 28°44' N (~560 miles off the coast of Baja California) in water about 16,000 feet deep, the US Navy tested a Mark 90 “Alias Betty” Nuclear Depth Bomb with a yield of 32~ kilotons.

The device itself was suspended at a depth of 2,000 feet under the barge YC-473 via a cable for the test, and around the device at varying distances to measure the effects of the NDB in the anti submarine role were three instrumented sub-scale submarine models dubbed SQUAWs.

The SQUAWs

The SQUAWs were simplified 4/5^th scale models of SS 563 Tang class submarines 134 feet long, with 14.5 foot diameter pressure hulls constructed of 1” thick HTS plate with a yield strength of 56,000 PSI, using one dimensional bends only for economy of production. Pressure hull end caps were constructed of STS. Total beam was about 22' 12”, and displacement was about 400~ tons. Engine-Generators were simulated with 4/5^th scale cast iron weights weighing 11,900 lbs each. Motors were also 4/5^th scale cast iron weights, weighing 25,000 lbs each. Batteries were simulated by concrete weights. Three were constructed by Long Beach Naval Shipyard and designated SQUAW 12, 13, and 29 respectively.

The Test

The following effects on the subsurface targets were observed:

• SQUAW-12: 5,150 ft (1,570m) from Hypocenter, submerged at an up angle of 36 degrees at a depth of 290 ft (88m); with a slant range of 5,428 ft (1,654m) from the device, received a peak shock pressure of about 850 psi and was probably destroyed within 10 milliseconds, with the loss of all data recorded from its internal sensors.

• SQUAW-13: 7,200 ft (2,195m) from Hypocenter, submerged at a depth of 265 ft (80m); with a slant range of 7,408 ft (2,258m) from the device, received a peak shock pressure of about 615 psi and was damaged, but did not sink. However, as it was being towed to the salvage area, it sank, causing the loss of all data recorded from its internal sensors.

• SQUAW-29: 10,200 ft (3,109m) from Hypocenter on the Surface; with a slant range of 10,394 ft (3,168m) from the device, received a peak shock pressure of about 440 PSI and little, if any damage was inflicted.

The shockwave from the device at 2,000 feet produced a spray dome on the surface with a 7,000 foot radius and a central height of 170 feet. This was followed by a second spiky dome from the bubble pulse which rose to about 900 feet.

The following radiological effects on the ocean were observed after the Wigwam shot.

Statements made after Wigwam concerned what had been learned concerning weapons effects.

As well as one semi-humorous finding regarding the excellent transmission of the sound of the shot:

Operation Hardtack I

Video of Operation Hardtack I can be found at the Internet Archive HERE

Shot Wahoo

Fired at 1330 on 16 May 1958 at Eniwetok Atoll. The device was suspended 500 feet below a target barge via cable.

With a water depth of 3,000 feet, and with an estimated yield of 9 kilotons, Wahoo produced a spray dome some 3,800 feet in diameter, with a central height of some 840 feet.

• SSK 3 Bonita was at periscope depth some 18,000 feet from surface zero, manned by her crew. Originally she was to be moored in an unmanned condition at periscope depth some 10,500 feet from surface zero. However, heavy seas caused this plan to be reconsidered due to uncertainty over whether the Bonita could be moored between the two YC barges safely. Thus, a change of plans proposal was introduced, in which the Bonita would instead be manned by her crew at periscope depth some 12,500 feet from surface zero. In the interests of safety 5,500 more feet were added between the Bonita and surface zero, probably to the immense relief of her crew. Calculations indicated that the peak pressure received by Bonita was less than 100 PSI; and no damage was recorded.

• On DD 886 Orleck, some 10,300 yards from surface zero, “no significant personnel reactions were noticed” from the shot.

• On DD 727 De Haven, some 5,900 yards from surface zero, things were quite different, with the following reactions recorded:

Engineering Spaces: Personnel were generally calm, though considered it violent. In some cases personnel were frightened.

Lower Sound Room: Shock wave sounded like water rushing by the ship. Shock wave shook ship violently with a loud cracking noise. Personnel were somewhat frightened.

Bosun's Locker: Ship vibrated violently, first fast then slow. Sounded like water pouring into the ship. Personnel were considerably frightened.

Shot Umbrella

Fired at 1115 on 8 June 1958 at Eniwetok Atoll. The device was fired from the bottom of Eniwetok lagoon at a depth of 150 feet.

With an a estimated yield of 8 kilotons and in very shallow water, Umbrella produced a spray dome that was truly massive, with a maximum height of about 5,000 feet.

• SSK 3 Bonita was submerged 2,900 ft (884 meters) from surface zero at apparently periscope depth. No permanent hull deformations were caused, presumably because the short duration of the shock pulse did not allow pressure to build up enough to damage the boat. During recovery of Bonita at H+1 post-shot, Radiac probes gave readings of 2 roentgens at 140 feet, and 30 roentgens on the bottom. Despite this, divers were sent over the side from USS Grasp to manipulate the air tanks on Bonita to surface her.

• SQUAW-29 was submerged 1,600 ft (488 meters) from surface zero at apparently periscope depth. It suffered pressure hull deformation, mainly dishing in of the hull between frames. Heavy damage was sustained in the main ballast tanks, with 1,340 PSI peak pressure being recorded. This was probably due to the presence of air pockets within the ballast tanks amplifying the shock pulse. Despite this, damage was considered as being significantly shorter than lethal.

Conclusions

From the above tests previously detailed, the following was learned:

• The peak total pressure needed to violently rupture the hull and cause virtually-instant loss of the submarine was about 1.5 to 1.9 times the maximum static pressure resistance for that submarine. As an example, a submarine which had a collapse rating of 390 PSI would need to be hit with between 585 and 741 PSI to kill it with reliability.

• As an addendum to the above, pressure had to remain at high levels for more than 4 milliseconds to cause significant damage.

• The orientation of the submarine with regards to the initiation point was not a significant factor in the vulnerability of the hull to the pressure wave.

• The hull damaging radius for nuclear weapons in shallow water are small compared to the hull damaging radius of equivalent weapons detonated in deep water.

Calculations/Math

Surface Wave Motions From Deep Underwater Bursts

Peak to Peak Wave Height (ft) = 40,500 * ( (Yield^0.54) / Range_Burst

Yield is in kilotons and the Range_Burst is in feet. Accuracy of the above equation is ±35%.

Thus, a ship 5,000 feet from a 32 kiloton device initiated in deep water would encounter peak waves between:

40,500 * ( (32^0.54) / 5,000 = 52.63 feet

52.63 feet * 0.35 = 18.4 feet

52.63 + 18.4 = 71.03
52.63 – 18.4 = 34.23

34 and 71 feet in height.

Other equations are available for computing the Peak Wave length and period. They are:

Length of Peak Wave (ft) = 1010 * Yield^0.288
Period of Peak Wave (Sec) = 14.1 * Yield^0.288

In both cases, yield is again in kilotons.

Scaling Factors for Underwater Bursts in Deep Water:

Notes: Yield is in Kilotons, and Distances are in meters.

50 PSI Distance= Yield^0.342 * 6,769.5
100 PSI Distance = Yield^0.342 * 3,705.4
200 PSI Distance = Yield^0.342 * 2,028.2
400 PSI Distance = Yield^0.342 * 1,110.2
500 PSI Distance = Yield^0.342 * 914.4
600 PSI Distance = Yield^0.342 * 780.4
700 PSI Distance = Yield^0.342 * 682.5
800 PSI Distance = Yield^0.342 * 607.7
900 PSI Distance = Yield^0.342 * 548.5
1000 PSI Distance = Yield^0.342 * 500.5
1500 PSI Distance = Yield^0.342 * 352.7
2000 PSI Distance = Yield^0.342 * 270
2500 PSI Distance = Yield^0.342 * 225.7