Calculating force of explosion over distance in water

[bjohns5454]

I am conducting research for my Master Thesis. I am a historian focusing on a historic battle between a Navy airship and a German U-boat that occurred just south of Key West on July 19, 1943. The airship was shot down. There is controversy about whether the 4 depth bombs were actually dropped.

A weak explosion was felt by the survivors about 8 hours after the crash. By this time the Gulf Stream had carrier them approximately 36 to 44 miles away from the crash site. I theorize that the bombs sunk to the ocean bottom and then eventually exploded. I need assistance figuring out whether the shock wave eminating from a deep water explosion of 250 lbs of TNT in water 2,500 to 3,000 feet deep could travel far enough and still be strong enough to be felt by swimmers 36 to 44 miles away.

 

[mfb]

I have no idea how to calculate that (test it! test it! :D), but I have an unrelated question: If the swimmers are affected by the gulf stream, why do you expect that the bombs are not? The magnitude and direction of the stream depend on the depth, of course.

 

[bjohns5454]

The depth bombs are heavy, about 325 lbs. I am sure they drifted in relation to the current as they sank. I can't imagine more than a mile if even that much. The surface current is between 4 to 5.5 mph. It is less as you go deeper. I don't think they would move much once they hit bottom given the mud and rocks.

 

[mfb]

Who dropped them at the original location ~8 hours after the battle then, if everything on the surface moved away?

 

[Chestermiller]

The depth bombs are heavy, about 325 lbs. I am sure they drifted in relation to the current as they sank. I can't imagine more than a mile if even that much. The surface current is between 4 to 5.5 mph. It is less as you go deeper. I don't think they would move much once they hit bottom given the mud and rocks.

We could probably estimate the amount of time it took for the bombs to settle to the bottom if we knew the dimensions of the bombs. We could also assume that, at max, the horizontal velocity of the bomb was equal to the stream velocity. This would help us establish a maximum to how far they could have traveled horizontally from splash down.

Chet

 

[bjohns5454]

Let me back up. I did not really list details. There were actually two near simultaneous explosions. They were weak with no sign of water disturbance.the airships carried 4 depth bombs. The theory is that two sunk to the bottom and later exploded. We now now that the other two bombs exploded and damaged the submarine. They often used hydrostatic fuses that armed in two phases, distance airdropped and water depth. Perhaps they were dropped and did not fall far enough to activate the fuzes. Many nose fuses had propellers that had to turn so many times to detonate the bomb. The current could have finished the job by turning them the rest of the way. The depth criteria would area been met and resulted in an explosion. The bombs would have likely been close to each other and the first explosion could triggered the second explosion.The explosions are not in doubt, just the source. There was no other combat documented in the area. Our forces would have known as we flooded the area looking for the survivors and the u-boat.

An alternate theory is that the bombs remained attached to the wreckage and detonated without exploding the main charge in either bomb. the wreckage was slowly sinking as it was carried with the survivors in the current. I spoke to a Navy EOD expert who stated that that scenario is highly unlikely, both main charges failing at the same time. It has been suggested that water intrusion corrupted the charges. The main charges and booster charges in the detonators were impervious to water and the bombs were waterproof. The EOD guy said they would have had to been directly over the detonators to feel them and we know the survivors were in two groups 2000 feet apart. He also said the charges would have created a flash 100 feet across and the shock wave would have been very strong a mile away.

 

[bjohns5454]

17.5 inches wide by approx.4 feet long.

 

[bjohns5454]

I know shock waves travel through water at about 6000 ft per second. Sock waves from explosives go through multiple phases of expansions and contractions with each phase loosing force in relation to a sine function.

I also know underwater sensors can pick up explosions a thousand miles away. The question is what can humans feel?

 

[Bobbywhy]

Here is an equation you might use to figure the distance a depth charge explosion could be felt by those survivors. Were those survivors totally immersed in the sea? Were they aboard a life raft?
Shock factor is a commonly used figure of merit for estimating the amount of shock experienced by a naval target from an underwater explosion as a function of explosive charge weight, slant range, and depression angle (between vessel and charge).
http://en.wikipedia.org/wiki/Shock_factor

Cheers,
Bobbywhy