Terminal Velocity of Bombs

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Thorsten Wahl
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Re: Terminal Velocity of Bombs

Post by Thorsten Wahl »

No problem
Falltimes of Fritz X at drop height
36,8 sec at 6000 m
40,0 sec at 7000 m

according Besprechungsniederschrift from March 20th 1943)
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Dave Saxton
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Re: Terminal Velocity of Bombs

Post by Dave Saxton »

José M. Rico wrote:According to Garzke & Dulin the bombs on Tirpitz were dropped from an altitude of between 430-900 meters. What was the typical diving angle/speed of the Barracuda?

The drop height depends on which strike. During the later Mascot and Goodwood strikes, the release heights were 4000-5000 feet (1220-1525 meters). It was during the final Goodwood strike that the inert bomb in question penetrated to the number 4 switchboard room and came to rest. The max dive speed of the Barracuda was 160 M/s. The min likely dive speed given for the Barracuda is 135 m/s. The typical dive angle was 70*.

Although it is impossible to pin this down exactly, we can arrive at a quite reasonable estimate.

I would like to double check several calculations first though.

In the USAAF bomb data manual it states that this bomb will not exceed 8.2" of homogenous armour penetration at any drop altitude. Since this is the penetration at 270 M/s and striking at the normal previously indicated, this would appear to confirm the 270 M/s terminal V.
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lwd
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Re: Terminal Velocity of Bombs

Post by lwd »

That sounds very reasonable and is in the range of terminal velocities I've read about (that's if my memory is working correctly today)
Mostlyharmless
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Re: Terminal Velocity of Bombs

Post by Mostlyharmless »

Thorsten Wahl wrote:No problem
Falltimes of Fritz X at drop height
36,8 sec at 6000 m
40,0 sec at 7000 m

according Besprechungsniederschrift from March 20th 1943)
This suggests that the average vertical velocity for Fritz X was 312.5 m/s over the last 1000 m. I do not even know if it was still accelerating as the air resistance may increase in the denser air :think: , so the terminal velocity at sea level could be lower than at 1000 m (transonic drag will be less :angel:) We can be absolutely sure that the velocity did not exceed 328.2 m/s from 7000 m and it was probably not far from 312 m/s.

For comparison for any bomb assuming no air resistance

From 5000 m, time = 31.93 seconds, terminal velocity = 313.2 m/s
From 6000 m, time = 34.98 seconds, terminal velocity = 343.2 m/s
From 7000 m, time = 37.78 seconds, terminal velocity = 370.6 m/s
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Dave Saxton
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Re: Terminal Velocity of Bombs

Post by Dave Saxton »

We need to make sure we differentiate between terminal velocity and the end velocity after falling a given height.

Terminal velocity is the velocity were forces of drag balance the forces of gavity and inertia and represtents a limit. Transonic and supersonic velocities greatly complicate matters.

http://www.grc.nasa.gov/WWW/K-12/airplane/termv.html

Determining end velocity from drop time is problematic because the time componant is shrinking as the velocity increases. The start velocity at any given moment is also changing. Here's the better equation to determine drop velocity from a given height:

Vf(sq)=V0(sq) + 2(gs)

Vf=end velocity
V0=starting (vertical) velocity
g=acceleration from gravity (9.8 M/s /s)
s= drop height

perhaps easier:

http://jumk.de/formeln/beschleunigung-weg.shtml

The acceleration due to gravity could be reduced to 9 to estimate the drag but this doesn't make much difference given the relative short drop height in this Tirpitz case. The drop heights during Goodwood were 1220 meters to 1525 meters. Given the max dive speed, and steepest likely dive angle at release, and the highest likely release altitude the end velocity will be about 227 m/s. Given the nominal striking angle the penetration could be as high as 155mm homgenous armour. Given the lowest dive speed, shallowest dive angle, and lowest likely drop height, the penetration will be ~127mm. Given a median; dive speed, dive angle, and drop height, the penetration should be ~140mm. I think its quite reasonable to conclude the penetration in the Tirpitz case should be ~130mm-~140mm.
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Mostlyharmless
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Re: Terminal Velocity of Bombs

Post by Mostlyharmless »

Dave Saxton wrote:We need to make sure we differentiate between terminal velocity and the end velocity after falling a given height.

Terminal velocity is the velocity were forces of drag balance the forces of gavity and inertia and represtents a limit. Transonic and supersonic velocities greatly complicate matters.
....
I must apologise :( . Obviously without air, I should have said "final velocity". However, my point was that the final velocity for the Fritz X must have been close to the final velocity from 5000 m without air of about 313 m/s which is below the speed of sound of 340 m/s and yet the time from 6000 m was only 1.8 s slower than the case without air. Thus I am guessing that we can almost neglect resistance until the velocity starts to cause transonic drag. This is a wave drag and, like the wave drag limiting warship speeds, it rises much faster than frictional drag. Thus bombs dropped from dive bombers will accelerate at roughly 9.81 m/s**2 until they hit while bombs dropped from much higher will accelerate at roughly 9.81 m/s**2 until about 270 m/s and then more slowly approach Mach 1.0
RobertsonN
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Re: Terminal Velocity of Bombs

Post by RobertsonN »

There is a point here that, on further reflection, I do not understand. At an impact angle 12 deg from the normal against a 1600 lb AP bomb, the effective thickness of the Tirpitz 50 + 80 mm deck system was at least 130 mm, probably 130 to 140 mm. However, this is not a shell at oblique impact, so yaw should not be a factor, and as far as I know the 1600 lb AP had no cap, so that decapping was not a factor, therefore what was the performance reducing factor making the deck system add up to slightly more than the sum of the separate thicknesses? I accept that the bomb did have the trajectory and impact velocity given and that the penetration was more or less a bomb that just penetrated, the question is what accounted for the increase in effective thickness over the normal case?
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Re: Terminal Velocity of Bombs

Post by Thorsten Wahl »

if pentration occurs through whether and armored deck(50mm + 80mm) the ballistic resistance is expected to be somewhat lowered compared to an single plate of same thickness(130 mm) as pentration ability of the bomb is probably not affected by the first plate
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Re: Terminal Velocity of Bombs

Post by RobertsonN »

Yes. That is what I thought. This seems to give three possibilities: (1) the bomb was dropped from a lower height than assumed above; (2) The 130 to 140 mm penetration is presumably of US class B, and the target was 50 mm Wh + 80 mm (somewhat harder) Wh: the Wh was of greater effective thickness against bombs than the same amount of Class B; (3) The calculated penetration thickess of the 1600 lb AP bomb was overestimated.
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Re: Terminal Velocity of Bombs

Post by alecsandros »

RobertsonN wrote:Yes. That is what I thought. This seems to give three possibilities: (1) the bomb was dropped from a lower height than assumed above; (2) The 130 to 140 mm penetration is presumably of US class B, and the target was 50 mm Wh + 80 mm (somewhat harder) Wh: the Wh was of greater effective thickness against bombs than the same amount of Class B; (3) The calculated penetration thickess of the 1600 lb AP bomb was overestimated.
I would add:

(4) The actual impact angle of the bomb against the 50mm upper deck was less than ideal

(5) The bomb's fuze was working improperly, either because of faulty production/storage/transport OR because of the spaced-array armor scheme employed on Tirpitz

(6) Metallurgical properties of Wh armor [high tensile strength while retaining very good %EL] caused the bomb to deform during the impact(s) and become useless.

(7) Magic :D
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Re: Terminal Velocity of Bombs

Post by lwd »

Remember also that decks aren't just flat expanses of unsupported steel plate. A bomb hitting on or near a support would face additional resistance. Also air resistance is relative to velocity and in a nonlinear method. That means that a bomb dropped from a dive bomber is not accelerating at 9.81 m/sec*sec immediatly after being dropped but at some lesser rate.
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Re: Terminal Velocity of Bombs

Post by RobertsonN »

Thanks, structure such as beams and brackets may well account for the increase in resistance observed. While I've never seen the detailed plans for the Tirpitz, another very long ship, the Hood, had an extensive system of deck support girders and brackets. Contrariwise, some have suggested in recent times that such stiffening might actually reduce the resistance of the primary deck plating.
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