Calculating Depth Charge Lethality

(Created 15 September 2017)
(Updated 15 October 2017)

Primary Reference:

Estimating Depth Charge Peak Pressure

Pmax = k * (W1/3 / R)1.13

Where:

Pmax = Peak pressure at front of shock pulse from an underwater explosion. (in PSI).
K = Proportionality Constant. Dependent on explosive type, but typical variations are minor, and a value of 2.16 x 104 for TNT (or 21,600) is “good enough”.
W = Charge Weight (in pounds)
R = Range from explosion (in feet)
NOTE: For nuclear bursts; it appears that using the power of 1.27 instead of 1.13 in the equation above yields results largely in line with experimental test results.

Example: A 250 pound charge is detonated 50 feet from a target. What is the initial peak pressure of the shock pulse?

K = 2.16 x 104 = 21,600
21,600 * (2501/3 / 50)1.13 = 2,078.939 PSI

Example: A 30 kiloton depth bomb is detonated 5,000 feet (slant range) from a target. What is the initial peak pressure of the shock pulse? (Don't forget to use the power of 1.27!).

K = 2.16 x 104 = 21,600
W = 30 kilotons = 30,000,000 kg or 66,138,678.655 pounds.
21,600 * (66,138,678.6551/3 / 5000)1.27 = 885.97~ PSI

Estimating Percentage of Depth Charge Power At Distance

P = k * (1 / R1.13)

P = Percent of power.
R = Range. (changes according to proportionality constant; see below).
K = Proportionality Constant. Changing this changes the scaling. Known Constants are:

NOTE: If the depth charge is nuclear; it appears that using the power of 1.27 instead of 1.13 in the equation above yields results largely in line with experimental test results.

Example: A conventional HE depth charge is detonated 2 meters from a target. What percentage of power does it have left?

0.261178181 * (1 / 21.13) = 0.119336418 or approximately 11.93%

Example: A nuclear depth charge is detonated 500 feet from a target. What percentage of power does it have left?

1 * (1 / 5001.27) = 0.0003735 or approximately 0.03735%

Estimating Depth Charge First Bubble Pulse Pressure

P1 = K * (W1/3 / R)

Where:

Pmax = Peak pressure at front of shock pulse from an underwater explosion. (in PSI).
K = Proportionality Constant. Dependent on explosive type, but typical variations are minor, and a value of 3300 for TNT is “good enough”.
W = Charge Weight (in pounds)
R = Range from explosion (in feet)

Example: A 200 pound charge is detonated 25 feet from a target. What is the first bubble pulse pressure?

3300 * (2001/3 / 25) = 771.9407 PSI

Historical Depth Charge Lethality


Source #A

Source #B

Source #C

Type

German WBG (Wasserbombe G)

British Mark VII Heavy

British Type F

Charge

60 kg (132 lb)

290 lbs (131.542 kg)

70 lbs (31.8 kg)

Damage Zone

17 to 28 meters (55.77 to 91.86 feet)

At 28 meters, 822~ PSI peak shock front (calculated)

Defined as “splitting a 22mm thick pressure hull at 20 feet (6.1m)”, and “forcing a submarine to surface at twice that distance.”

This equals:

2,829~ PSI peak shock front to “force [a sub] to surface”. (calculated)

and

6,191~ PSI peak shock front to “split a pressure hull” (calculated)

Defined as: “said to be able to sink a submarine if exploded within 14 feet (4 m) or disable it if within 28 feet (8 m).”

This equals:

2,478~ PSI peak shock front to disable. (calculated)

and

5,424~ PSI peak shock front to sink. (calculated)

Danger Zone

5.6 to 17 meters (18.37 to 55.77 feet)

At 17 meters, 1,444~ PSI peak shock front (calculated)

Destruction Zone

0 to 5.6 meters (0 to 18.37 feet)

At 5.6 meters, 5,067~ PSI peak shock front (calculated)

References:

German Destroyers of World War II: Warships of the Kriegsmarine
By Gerhard Koop and Klaus-Peter Schmolke, Page 39

No Room for Mistakes: British and Allied Submarine Warfare, 1939-1940
By Geirr Haarr, pages 74-75

NavWeaps, UK ASW Weapons (LINK)

NavWeaps, UK ASW Weapons (LINK)

From the above sources, we can average out the following “kill states” and extrapolate further:

Conventional High Explosive Depth Charges

State Description

PSI to achieve

D Factor (see below)

90%+ Chance of Destruction

5,560~ PSI peak shock front.

3.324

50% Chance of Destruction, Forced to Surface or Die.

2,650~ PSI peak shock front.

6.402

Good chance of moderate damage to boat.

1,130~ PSI peak shock front.

13.6124

Boat is shaken. Zero Damage except frayed nerves.

500~ PSI peak shock front.

28.011

And then calculate damage ranges from charge weights according to this equation:

RangeDamage = D * W1/3

Example: What's the lethal range for the 250 pound warhead on the RUR-4 Weapon “Able”?

3.324 * 2501/3 = 20.93 feet

For your convenience, here are pre-computed damage distances for a variety of charge weights:

Charge Weight (lbs)

90%+ Chance of Destruction
(feet)

50% Chance of Destruction, Forced to Surface or Die.
(feet)

Good chance of moderate damage to boat.
(feet)

Boat is shaken. Zero Damage except frayed nerves.
(feet)

10

7.2

13.8

29.3

60.3

25

9.7

18.7

39.8

81.9

50

12.2

23.6

50.1

103.2

75

14.0

27.0

57.4

118.1

100

15.4

29.7

63.2

130.0

150

17.7

34.0

72.3

148.8

200

19.4

37.4

79.6

163.8

250

20.9

40.3

85.8

176.5

300

22.3

42.9

91.1

187.5

350

23.4

45.1

95.9

197.4

400

24.5

47.2

100.3

206.4

450

25.5

49.1

104.3

214.7

500

26.4

50.8

108.0

222.3

600

28.0

54.0

114.8

236.3

700

29.5

56.8

120.9

248.7

800

30.9

59.4

126.4

260.0

900

32.1

61.8

131.4

270.4

1000

33.2

64.0

136.1

280.1

1500

38.1

73.3

155.8

320.6

2000

41.9

80.7

171.5

352.9

As you can see, the 90% destruction and 50% destruction ranges remain remarkably flat, explaining how relatively low warhead weight weapons such as Hedgehog were able to be so destructive for their light weights, while on the other hand, the “moderate damage” and “shaken” distances increase more rapidly with heavier charge weights; explaining why depth charges still stuck around for a bit into the 1950s, despite Hedgehog; since they provided area “harassment” fire against submerged submarines.

Nuclear Subsurface Bursts

These are significantly more lethal than conventional subsurface bursts due to two factors:

We only have three datapoints for computing damage distances for nuclear charges from WT-1300 (EX), one report on Operation WIGWAM, which detonated a 32 kt Depth Bomb suspended from a cable at 2,000 ft depth:

SQUAW-29 was later used again in Operation HARDTACK I during Shot UMBRELLA where a 8 kt Mark 7 was detonated on a lagoon bottom at a depth of 150 feet. Damages received at UMBRELLA were:

The following equation was suggested to compute the peak shock pressure required to cause pressure hull collapse:

PS = 1.08 (PC – PH) (1 + e-T/18)

Where:

PS = Peak Shock Pressure required to cause collapse, in PSI.
PC = Static Collapse Pressure of Hull, in PSI.
PH = Hydrostatic Pressure at the depth of the target, in PSI
T = Duration of Shock Pulse, in milliseconds. (Generally 20 msec for a nuclear burst).

Reference: WT-1003(EX) OPERATION WIGWAM Scientific Director's Summary Report, Page 43.

Reducing this further, by pre-calculating the right-most side of the equation and re-arranging it:

PS = 1.08 (PC – PH) * K

Where:

PS = Peak Shock Pressure required to cause Damage Effect.
PC = Static Collapse Pressure of Hull, in PSI.
PH = Hydrostatic Pressure at the depth of the target, in PSI
K = Constant; 1.3292 for 20 msec shock pulse, 1.4346 for 15 msec shock pulse; 1.5427 for 11 msec pulse. (11 msec appears to give the closest with reality based off SQUAW-12 destruction).

Example: A submarine with a pressure hull rated to 500 PSI collapse is at a depth of 400 feet in seawater (193.3 PSI). What is the estimated Peak Shock Pressure to Collapse it?

1.08 (500 – 193.3) * 1.5427 = 510.99~ PSI.

If the same submarine is at periscope depth of 50 feet (37 PSI), what is the peak shock pressure to collapse it:

1.08 (500 – 37) * 1.5427 = 771.4~ PSI.

Damage Distances for Nuclear Subsurface Bursts

Based on the SQUAW-13 data, and the evaluation of “the hull was probably near collapse but did not rupture.”, that is probably our only good datapoint for “Surface or Die”; and running the numbers gives a peak shock pressure for “surface or die” of 70.5% that of the “Kill Zone”.

Known Static Collapse Pressures

Class

Static Collapse Pressure

Notes:

Source

SS-196 Searaven
Sargo
-Class

235 PSI

Test Depth given as 250 ft (126.5~ PSI); so margin of safety is 1.85x.

WT- 1629(EX)
Loading and Response of Submarine Hulls from Underwater Bursts
Page 14

SSK-3 Bonita
(K-1 Class / Barracuda Class)

310 PSI

Test Depth given as 400 ft (193.3~ PSI); so margin of safety is 1.6x.

WT- 1629(EX)
Loading and Response of Submarine Hulls from Underwater Bursts
Page 14, 20.

SQUAW/SS-563
(Tang Class)

655 PSI

Test Depth given as 700 ft (327.3 PSI); so margin of safety is 2x.

WT-1003(EX)
Operation Wigwam Scientific Director's Summary Report
Page 22

WT- 1629(EX)
Loading and Response of Submarine Hulls from Underwater Bursts
Page 15

SSN-593/594
(Thresher/Permit Class)

900 PSI

Thresher imploded at 2,400~ feet; some 400 feet below her designed collapse depth. This works out to 2,000 ft and 907.7~ PSI.

With her test depth of 1,300 feet (594.7~ PSI), that is a margin of safety of 1.5x.

Navy Times Article by Polmar/Rule, April 8, 2013 – PDF Link

Project 685 Plavnik
(K-278 Komsomolets)
MIKE-Class

2,200 PSI.

Crush depth given as 1,500m (4,921 ft) (2,209 PSI) and safe depth given as 1,000m (3,280 ft) (1,477 PSI).

This gives a margin of safety of 1.49x.

Wikipedia on MIKE-CLASS (Link)

Scaling Factors for Underwater Bursts in Deep Water

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

50 PSI Distance= Yield0.342 * 6,769.5
100 PSI Distance = Yield0.342 * 3,705.4
200 PSI Distance = Yield0.342 * 2,028.2
400 PSI Distance = Yield0.342 * 1,110.2
500 PSI Distance = Yield0.342 * 914.4
600 PSI Distance = Yield0.342 * 780.4
700 PSI Distance = Yield0.342 * 682.5
800 PSI Distance = Yield0.342 * 607.7
900 PSI Distance = Yield0.342 * 548.5
1000 PSI Distance = Yield0.342 * 500.5
1500 PSI Distance = Yield0.342 * 352.7
2000 PSI Distance = Yield0.342 * 270
2500 PSI Distance = Yield0.342 * 225.7

Pre Calculated Kill/Force To Surface Distances for various combinations are:

WWII Fleet Boat
310 PSI Collapse Pressure (400 ft test depth)
at 200 ft depth (104 PSI hydrostatic pressure)

PSI To Cause Effect

340~ PSI

240~ PSI

YIELD

90%+ Chance of Destruction
Distance (meters)

50% Chance of Destruction, Forced to Surface or Die.
Distance (meters)

1 kt

1,279

1,731

2 kt

1,621

2,194

5 kT
(UUM-44 SUBROC)

2,217

3,001

10~ kT
(Mk 101 LULU)
(B57 Depth Charge)

2,810

3,804

20 kT
(FAT MAN)

3,562

4,821

30 kT
(Mark 90 Depth Bomb)

4,091

5,539

100 kt

6,176

8,360

1 MT

13,574

18,375

2 MT

17,205

23,291

5 MT

23,537

31,862

10 MT

13,574

40,386

25 MT

40,813

55,249

50 MT

51,731

70,028

100 MT

65,569

88,762

1950s Fleet Boat (Tang SS)
655 PSI Collapse Pressure (700 ft test depth)
at 350 ft depth (171 PSI hydrostatic pressure)

PSI To Cause Effect

800~ PSI

570~ PSI

YIELD

90%+ Chance of Destruction
Distance (meters)

50% Chance of Destruction, Forced to Surface or Die.
Distance (meters)

1 kt

608

816

2 kt

770

1,034

5 kT
(UUM-44 SUBROC)

1,053

1,415

10~ kT
(Mk 101 LULU)
(B57 Depth Charge)

1,335

1,793

20 kT
(FAT MAN)

1,693

2,273

30 kT
(Mark 90 Depth Bomb)

1,944

2,611

100 kt

2,935

3,941

1 MT

6,450

8,661

2 MT

8,176

10,978

5 MT

11,185

15,019

10 MT

6,450

8,661

25 MT

19,395

26,043

50 MT

24,583

33,009

100 MT

31,159

41,840

1960s SSN (Thresher/Permit Class)
900 PSI Collapse Pressure (1,300 ft test depth)
at 650 ft depth (304.8 PSI hydrostatic pressure)

PSI To Cause Effect

990~ PSI

700~ PSI

YIELD

90%+ Chance of Destruction
Distance (meters)

50% Chance of Destruction, Forced to Surface or Die.
Distance (meters)

1 kt

505

682

2 kt

640

865

5 kT
(UUM-44 SUBROC)

875

1,183

10~ kT
(Mk 101 LULU)
(B57 Depth Charge)

1,109

1,500

20 kT
(FAT MAN)

1,406

1,901

30 kT
(Mark 90 Depth Bomb)

1,615

2,184

100 kt

2,438

3,296

1 MT

5,359

7,245

2 MT

6,793

9,182

5 MT

9,293

12,562

10 MT

5,359

7,245

25 MT

16,114

21,782

50 MT

20,425

27,609

100 MT

25,889

34,995

1980s Deep Diver SSN (Pr 685 Plavnik – MIKE)
2,200 PSI Collapse Pressure (3,280 ft test depth)
at 1,640 ft depth (746~ PSI hydrostatic pressure)

PSI To Cause Effect

2,420~ PSI

1,700~ PSI

YIELD

90%+ Chance of Destruction
Distance (meters)

50% Chance of Destruction, Forced to Surface or Die.
Distance (meters)

1 kt

232

315

2 kt

294

400

5 kT
(UUM-44 SUBROC)

402

547

10~ kT
(Mk 101 LULU)
(B57 Depth Charge)

510

693

20 kT
(FAT MAN)

646

879

30 kT
(Mark 90 Depth Bomb)

743

1,010

100 kt

1,121

1,524

1 MT

2,464

3,349

2 MT

3,123

4,245

5 MT

4,272

5,808

10 MT

2,464

3,349

25 MT

7,408

10,070

50 MT

9,389

12,764

100 MT

11,901

16,179