23 replies to this topic

[Potassium chlorate]

To make really good use of at least most of the gas pressure, I've read that the inner mortar lenght should be six times the calibre.

[Peret]

You get diminishing returns after 6 calibers, because the gas pressure falls as the square of the volume - linear with volume but also linear with temperature, and the gas cools as it expands. As a first approximation, if the time from ignition to the shell leaving the mortar is 3T, the acceleration is F for the first period T, F/4 for the second period T and F/9 for the third. Only slow burning powders can take advantage of longer barrels because they keep generating gas to fill the space, while keeping it hot. **

Having some windage probably increases the shell height. I can't find this discussed in any literature, but the mathematics suggests it. Allowing some hot gas to reach the muzzle ahead of the shell both heats the stationary air and lowers its pressure, reducing the initial air resistance for the shell. Since AR is proportional to something between the square and cube of velocity, the AR term in the equations rises so fast that at some fairly modest speed, it becomes so dominant that further increases in velocity are wasted. Any resistance you can save at muzzle velocity is worth having, even at the expense of having to use more lift.

** Lloyd, Hadcock, "Artillery: its Progress and Present Position", 1893. I found a copy in Portsmouth Central Library, Naval History department.

[seymour]

Well, that puts much of what I said in it's place

[Peret]

Well, that puts much of what I said in it's place

Oh, sorry! No offense intended. It's just that I've spent some time and effort recently working out the physics and mathematics of shell flight, since all the available wisdom seems to be fragmentary tribal knowledge based on by-eye guesstimates. I got into it because I had a nagging feeling that "benzolift" was unwise, but didn't have any data to back it up and I wanted to know.

[seymour]

No offense taken at all!

I'm glad to have someone post some real data...

What I said had some value, but more of the 'I'm guessing this from experience type'.

[Potassium chlorate]

I do have slow burning powder for my larger calibres. For my 5" mortars I have an average granule size of 5 mm, and a few of them might even be as big as 10 mm.

I haven't made any really scientific tests, but with a lift 10% of the shell weight, the shells go approximately 150 metres, especially the heavier ones. Newton's laws in practice.

[Peret]

I do have slow burning powder for my larger calibres. For my 5" mortars I have an average granule size of 5 mm, and a few of them might even be as big as 10 mm.

I haven't made any really scientific tests, but with a lift 10% of the shell weight, the shells go approximately 150 metres, especially the heavier ones. Newton's laws in practice.

By "slow burning powder" I wasn't referring to granulated BP but to nitro powders. The big guns at the end of the BP era used powder pressed into quite large prisms several cm across, but it was still considered fast compared to cordite. When cordite was introduced the typical length to calibre ratio doubled overnight to take advantage of it.

Newton's Laws are only part of the equation, because at quite modest speeds the air resistance term becomes much larger than g. The heavier the shell, the higher you can shoot it, because the retardation due to air resistance is inversely proportional to mass. For a spherical shell at speeds up to about 250m/s it's approximately 0.4Av^2/m m/s^2, A in square metres, v in metres per sec, m in kg. This leads to the counter-intuitive situation that you can make a light shell go higher by ballasting it with sand.

[Potassium chlorate]

By "slow burning powder" I wasn't referring to granulated BP but to nitro powders. The big guns at the end of the BP era used powder pressed into quite large prisms several cm across, but it was still considered fast compared to cordite. When cordite was introduced the typical length to calibre ratio doubled overnight to take advantage of it.

I know, but still big granules of BP burn slower than small ones.

Cordite has actually been used for lifting firework shells too, though maybe not big ones. This American boy used it for his fireworks in the 1930's: Spectacular Fireworks

Newton's Laws are only part of the equation, because at quite modest speeds the air resistance term becomes much larger than g. The heavier the shell, the higher you can shoot it, because the retardation due to air resistance is inversely proportional to mass. For a spherical shell at speeds up to about 250m/s it's approximately 0.4Av^2/m m/s^2, A in square metres, v in metres per sec, m in kg. This leads to the counter-intuitive situation that you can make a light shell go higher by ballasting it with sand.

Hm, yes you're right.

Would be fun to fire fireworks on the moon. A 5" shell would go several kilometres, both due to the low gravity as well as the lack of air resistance.

Edited by Pyroswede, 17 May 2010 - 08:32 AM.

[digger]

Oh, sorry! No offense intended. It's just that I've spent some time and effort recently working out the physics and mathematics of shell flight, since all the available wisdom seems to be fragmentary tribal knowledge based on by-eye guesstimates. I got into it because I had a nagging feeling that "benzolift" was unwise, but didn't have any data to back it up and I wanted to know.

Yes I noticed your article on pyroguide regarding shell heights.

I took the liberty of adding a little to it, as I had already done the math myself. As you know the drag on a sphere is a function of the Reynolds number, so I have done a calculator that takes the data for a sphere so you only need to know the shell dimensions and weight along with the total flight time to calculate the shell dynamics. I did this as I find it difficult judging the apogee as it seems to hang about for a while near the top of the flight (dead easy to start and stop the watch at firing and impact).

Edited by digger, 17 May 2010 - 09:52 AM.