Calculating Depth Charge Lethality(Created 15 September
2017)

Primary Reference:
NOLTR 73103: The Effects of Underwater Explosions on Swimbladder Fish (27 July 1973) (2.1 MB PDF)
NRL Memorandum Report 6181: A Review of the Propagation of Pressure Pulses Produced by Small Underwater Explosive Charges (2.4~ MB PDF)
Underwater Explosion Phenomena and Shock Physics by Frederick A. Costanzo, Proceedings of the IMACXXVIII February 1–4, 2010, Jacksonville, Florida USA (1.1~ MB PDF)
An Evaluation of Various Theoretical Models for Underwater Explosion Bubble Pulsation (15 April 1971) (3.1~ MB PDF)
U.S. Underwater Nuclear Testing and Derived Effects Data (Alternatewars.com)
P_{max} = k * (W^{1/3} / R)^{1.13}
Where:
P_{max} = 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 10^{4} 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 10^{4} = 21,600
21,600 * (250^{1/3} / 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 10^{4} = 21,600
W = 30 kilotons = 30,000,000 kg or 66,138,678.655 pounds.
21,600 * (66,138,678.655^{1/3} / 5000)^{1.27} = 885.97~ PSI
P = k * (1 / R^{1.13})
P = Percent of power.
R = Range. (changes according to proportionality constant; see below).
K = Proportionality Constant. Changing this changes the scaling. Known Constants are:
1 = Range in Feet.
0.288970149 = Range in Yards (Good from 0.333333 yards and above).
0.261178181 = Range in Meters (Good from 0.3048m and above).
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 / 2^{1.13}) = 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 / 500^{1.27}) = 0.0003735 or approximately 0.03735%
P_{1} = K * (W^{1/3} / R)
Where:
P_{max} = 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 * (200^{1/3} / 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 No Room for Mistakes: British and Allied
Submarine Warfare, 19391940 
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:
Range_{Damage} = D * W^{1/3}
Example: What's the lethal range for the 250 pound warhead on the RUR4 Weapon “Able”?
3.324 * 250^{1/3} = 20.93 feet
For your convenience, here are precomputed damage distances for a variety of charge weights:
Charge Weight (lbs) 
90%+ Chance
of Destruction 
50% Chance
of Destruction, Forced to Surface or Die. 
Good chance
of moderate damage to boat. 
Boat is
shaken. Zero Damage except frayed nerves. 
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.
These are significantly more lethal than conventional subsurface bursts due to two factors:
The pulselength of a nuclear burst is significantly compressed compared with a conventional burst's pulselength. (see graph below).
Rather than creating intense overpressure over a small area, a nuclear subsurface burst raises the surrounding pressure around the submarine instead.
We only have three datapoints for computing damage distances for nuclear charges from WT1300 (EX), one report on Operation WIGWAM, which detonated a 32 kt Depth Bomb suspended from a cable at 2,000 ft depth:
“The results indicated that SQUAW12 was at a horizontal range of 5150 ft and a depth of 290 ft; the peak shock pressure at the hull was about 850 psi, and the target was destroyed, probably within 10 msec.” (Slant range 5,158 ft)
“SQUAW13 was at a horizontal range of 7200 ft and a depth of 260 ft; the peak dynamic pressure at the hull was about 615 psi, and the hull was probably near collapse but did not rupture.” (Slant range 7,407 ft) – SQUAW 13 was later lost while under tow seven days later when the tow line parted, causing the loss of all scientific data on board.
SQUAW29 was surfaced at a radial distance of 10,200 feet (slant range 19,394 ft) and received about 430 to 440 PSI.
SQUAW29 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:
SQUAW29: Submerged at depth of 52 feet, stern towards device at a distance of 1,680 feet – severe dishing in of frames and ballast tanks. (Slant Range of 1,682 ft).
SSK3 Bonita: Submerged unmanned at depth of 54 feet, bow on towards device at a distance of 2,880 feet – little if any damage. (Slant Range of 2,881 ft).
The following equation was suggested to compute the peak shock pressure required to cause pressure hull collapse:
P_{S} = 1.08 (P_{C} – P_{H}) (1 + e^{T/18})
Where:
P_{S} = Peak Shock Pressure required to cause collapse, in PSI.
P_{C} = Static Collapse Pressure of Hull, in PSI.
P_{H} = 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: WT1003(EX) OPERATION WIGWAM Scientific Director's Summary Report, Page 43.
Reducing this further, by precalculating the rightmost side of the equation and rearranging it:
P_{S} = 1.08 (P_{C} – P_{H}) * K
Where:
P_{S} = Peak Shock Pressure required to cause Damage Effect.
P_{C} = Static Collapse Pressure of Hull, in PSI.
P_{H} = 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 SQUAW12 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 SQUAW13 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 
SS196 Searaven 
235 PSI 
Test Depth given as 250 ft (126.5~ PSI); so margin of safety is 1.85x. 
WT 1629(EX) 
SSK3 Bonita 
310 PSI 
Test Depth given as 400 ft (193.3~ PSI); so margin of safety is 1.6x. 
WT 1629(EX) 
SQUAW/SS563 
655 PSI 
Test Depth given as 700 ft (327.3 PSI); so margin of safety is 2x. 
WT1003(EX) WT 1629(EX) 
SSN593/594 
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 
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 MIKECLASS (Link) 
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
Pre Calculated Kill/Force To Surface Distances for various combinations are:
WWII Fleet Boat


PSI To Cause Effect 
340~ PSI 
240~ PSI 
YIELD 
90%+ Chance of
Destruction 
50% Chance of Destruction, Forced
to Surface or Die. 
1 kt 
1,279 
1,731 
2 kt 
1,621 
2,194 
5 kT 
2,217 
3,001 
10~ kT 
2,810 
3,804 
20 kT 
3,562 
4,821 
30 kT 
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)


PSI To Cause Effect 
800~ PSI 
570~ PSI 
YIELD 
90%+ Chance of
Destruction 
50% Chance of Destruction, Forced
to Surface or Die. 
1 kt 
608 
816 
2 kt 
770 
1,034 
5 kT 
1,053 
1,415 
10~ kT 
1,335 
1,793 
20 kT 
1,693 
2,273 
30 kT 
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)


PSI To Cause Effect 
990~ PSI 
700~ PSI 
YIELD 
90%+ Chance of
Destruction 
50% Chance of Destruction, Forced
to Surface or Die. 
1 kt 
505 
682 
2 kt 
640 
865 
5 kT 
875 
1,183 
10~ kT 
1,109 
1,500 
20 kT 
1,406 
1,901 
30 kT 
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)


PSI To Cause Effect 
2,420~ PSI 
1,700~ PSI 
YIELD 
90%+ Chance of
Destruction 
50% Chance of Destruction, Forced
to Surface or Die. 
1 kt 
232 
315 
2 kt 
294 
400 
5 kT 
402 
547 
10~ kT 
510 
693 
20 kT 
646 
879 
30 kT 
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 