60 year old problem

Hi HoHun:

Thanks for the links and info. I figured there would be some fairly complex wizardry to reckon with re: air resistance over the trajectory.

I'm actually quite pleased with how the numbers start to pan out. If I take the 39,360 feet (about 12.1km) as the limit of a shell going straight upwards, I get a "composite" deceleration of 25.84 m/s/s. When I plug that back in to the clunky "altitude by time" column, lo and behold the shell tops out at about 30.5 seconds into its flight. In this case, it takes about 12.5 seconds to reach around 25,000 feet.

If I take the 14.7 km absolute height number, I end up with "composite" deceleration of 21.34 m/s/s, a "time to peak" of 37 seconds, and a "time to 25,000 feet" of about 11.5 seconds.

Haven't heard from my mate on the other board yet. Hope he'll either be able to confirm / deny /re-direct: he's a naval buff - worse still he's a Dreadnought fan.

Either way, a rough answer to the original question is starting to look like "more than 10 seconds, but less than 15" (depending of course on horizontal displacement from the battery).

If you contact Delcyros on this forum he can give you the answer.

This site may help, but it makes my brain hurt:

PHYS 251 - Projectile Motion

b17sam said:

Can anyone come up with an answer to a problem that has that has vexed me since 1944? I've had wild guesses, improbable theories, but zip that rings true.
Problem: What is the elapsed time for an 88 flak shell to rise to 25000 feet? Educated guesses accepted.

Click to expand...

I know the Pak-42 75mm shell had a m/v of 3300 ft./sec.
If we can assume the same for the 88, then it would reach 25000 ft. in 7.545 seconds.



Elvis

mhuxt said:

Well, you'd want to compensate for the cumulative effect of gravity - can't remember how many m/s^2 that is though.

I actually used to be able to do ballistics - mark of a mis-spent middle age.

Click to expand...

Rate of Gravity = 9.8 m/s/s.
This is sometimes referred to as "Rate of Acceleration", when used in the context of something in free fall.



Elvis

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1.- Loads of thanks to you guys for all the effort and research expended on this 60 year old problem.
2.- While we don't seem to have come up with a conclusive precise answer, I hope we can all accept the consensus which seems to be 20 to 30 seconds for an 88 shell to rise to 25000 feet including gravity, wind, air resistance, and what the gunners had for breakfast.
3.- If you will forgive me, I am going to start a new thread explaining for the first time ever why I have been seeking the answer to this problem for over 60 years dating back to when we were back in Bassingbourn.

Hi again Sam:

Your thread on the anniversary of your final mission reminded me - I recently read a book on the Hamburg raids, which had a comment on 88mm times.

The USAAF briefing notes for one of the BGs apparently told the crews that they could expect flak shells to explode "twenty to thirty seconds" after they saw the flash of the guns.

I can dig the original reference back out again - the book's in my local library.