Projectile fire questions

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CuttleFish
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Projectile fire questions

Postby CuttleFish » Fri Sep 23, 2011 5:41 am

Hello again.

I am here with some questions, as I think there will probably be someone here who knows this matter. The subject is (roughly) the venerable Royal Navy 15" gun.

What altitude did the shell reach at the top of its loft, if fired at about a 22º elevation angle, for example?

What might the velocity of the shell have been upon impact?

Why I am asking. I just knocked up some code on C++ for fun to simulate an 870 kg projectile with a muzzle velocity of 785 m/s (about the 15" gun's specs, yes?). I am getting, with a 22º elevation a range of 29,700 meters, with a maximum altitude of 3,708 meters, and a final impact velocity of 481 m/s. The velocity at the top of the loft, at maximum altitude, has already fallen to 536 m/s. The time to the fall of shot is 55 seconds.

The frontal area of the shell is 0.1148 square meters. The drag coefficient I am estimating at 0.22, and I am not adjusting the air density as the shell's altitude changes (ie, it is constant at 1.225 kg/m³). The effect would not be too significant, anyway.

Any data? Does this sound about right? Thanks in advance.

lwd
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Re: Projectile fire questions

Postby lwd » Fri Sep 23, 2011 4:03 pm

Some here don't like it but I find a good place to start with this kind of question is:
http://www.navweaps.com/Weapons/index_weapons.htm
in particular for this case:
http://www.navweaps.com/Weapons/WNBR_15-42_mk1.htm
Down near the bottom of the page are tables with striking velocities and angles at various ranges.

dunmunro
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Re: Projectile fire questions

Postby dunmunro » Fri Sep 23, 2011 6:51 pm

lwd wrote:Some here don't like it but I find a good place to start with this kind of question is:
http://www.navweaps.com/Weapons/index_weapons.htm
in particular for this case:
http://www.navweaps.com/Weapons/WNBR_15-42_mk1.htm
Down near the bottom of the page are tables with striking velocities and angles at various ranges.


What you really need is a 15"/42 range table. However, the 15/42 has a similar trajectory to the USN 16"/50, when fired at similar MVs:

http://www.eugeneleeslover.com/USN-GUNS ... 770-2.html

I would suggest that you tweak your code using the 16"/50 range tables, and then adjust your code to match the known data points for the 15"/42:

30 degs elevation = 33550 yds at mv = 2458fps with 1938lb MK 17B.
20 degs elevation = 26650 yds at MV =2458 fps with 1938lb MK 17B

30 degs elevation = 37870 yds at mv = 2638fps with 1938lb MK 17B.
20 degs elevation = 29930 yds at MV =2638 fps with 1938lb MK 17B

CuttleFish
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Re: Projectile fire questions

Postby CuttleFish » Sat Sep 24, 2011 8:04 am

Well, well! Thanks for those links, they are very helpful. It seems, by the results, that my physics were about right. The main "problem", if I can call it that, is that the coefficient of drag was a bit low at 0.22. Values between 0.25 to 0.27 hit it on the money.

Thanks again!

Mostlyharmless
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Re: Projectile fire questions

Postby Mostlyharmless » Sat Sep 24, 2011 9:57 pm

It would appear that the Germans at least believed that the reduction in air density at high altitude could give a useful increase in range as their coastal defence mountings allowed 52 degrees elevation. Examples are http://www.navweaps.com/Weapons/WNGER_15-52_skc34.htm and http://www.navweaps.com/Weapons/WNGER_16-52_skc34.htm.

CuttleFish
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Re: Projectile fire questions

Postby CuttleFish » Sun Sep 25, 2011 12:22 am

Thanks for that detail, Mostlyharmless. I was already thinking of working that variable into the computations, as experimenting subsequently with angles of elevation revealed that the shell could easily be lofted to over 11 km altitude, even with higher drag coefficients (more on that in a moment), and 45º - 50º elevations. The density ratio at these altitudes IS significant, about 29% of what it is at sea level, or 0.355 kg/m³. That certainly is going to make a difference. That said, too, I think I remember reading once that it was the Hipper class cruiser's main guns that had a pretty high elevation capability, with a ridiculous range to go with it, for an 8 incher. It has been a (long) while since I used to pour over ship's data in such detail, and I am too lazy (tired from work atm) to go browsing around for it right now. However, if I am wrong, I am sure someone will put me right. My thanks to who does!

I had actually popped in to add to my last post, regarding the drag coefficient. I actually get the best results with even higher drag coefficients (over 0.35). Now that is high, considering a streamlined projectile. BUT, I was not considering aerodynamic's wild card. Mach drag coefficient increase. In reality, the subsonic coefficient of drag WAS probably about 0.22 to 0.25. To get my demo up to scratch, I am going to have to work this drag coefficient modifier feature in, too. Something for when I am rested properly. Right now, <yawn>, and goodnight all!

Mostlyharmless
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Re: Projectile fire questions

Postby Mostlyharmless » Sun Sep 25, 2011 11:05 am

Just to help you keep the code simple, I should mention another minor effect. Because the shell is spinning, there will be a gyroscopic effect keeping the nose of the shell pointing slightly above its actual course. This will initially cause lift and then during the descent will slightly increase the range. I hope it doesn't get complicated by precession.

CuttleFish
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Re: Projectile fire questions

Postby CuttleFish » Sun Sep 25, 2011 4:57 pm

<Chuckle>

One small step at a time! This is beginning to look like a good thesis project for mega-geek (with all due respect and hats off to the species) doing a university course in kinetic physics, not a middle aged chap with a distant interest in the subject and a hobby of fiddling with C++ every now and then, current schedule permitting, who once upon a time took an automobile engineering college course.

That said, I do see what you mean. Precession of the spinning shell IS going to cause it to cant sideways as its nose dips to follow the trajectory curve, which will present a side of the shell at an angle to the relative airflow and generate a side aerodynamic force, which in turn will cause the shell to drift, in the direction of its rotation (right hand spin, right hand drift). All of that is going to mean calculating the principal moments of inertia of the shell, which first, is going to define the angle of difference you mentioned of the shell's center-line to the trajectory flight path (as its aerodynamic longitudinal stability characteristics tend to try and keep it aligned with that flight path), then the magnitude of the side angle induced by the precession. In essence, it is not difficult to calculate the number of spins the shell is theoretically going to do during its voyage, but the effects are going to be a different kettle of fish. However, the effect of precession is a 3D consideration, and my model is (as yet) 2D.

That does not discount the effect, however, of the shell's resistance to change its orientation, because of the gyroscopic stability of the spinning, relative to the changing flight path, even on the 2D planes, generating that "angle of attack" which will create the aforementioned lift. The "lift" (actually, total resultant force) is also going to cause some additional drag (induced drag), which basically is going to be the sine of the angle of attack times that total resultant force, at least in this case of a symmetrical shell. The lift itself is no problem to calculate, but again we come back to the problem of its coefficient. And I am still stuck on the changing coefficient of drag due to compressibility at supersonic speeds. I have dug out a couple of books and am delving through formulas, with calculator and pen in hand. Good way to use up my one day off, when there were things to do around the house. This is going to make me popular...

CuttleFish
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Re: Projectile fire questions

Postby CuttleFish » Sun Sep 25, 2011 6:09 pm

Oh, I can cheat now. A table on this page shows some curious Cd behavior of a "bullet" that approximates what my "experimentation" has been revealing. To simplify, I can map these points to velocity in Mach, calculate the Mach speed variation at different altitudes, and interpolate for the required Cd.

The page is interesting, as it also goes into the other topics discussed above.

http://en.wikipedia.org/wiki/External_ballistics

CuttleFish
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Re: Projectile fire questions

Postby CuttleFish » Mon Sep 26, 2011 3:59 am

Okay, with the data tweaked for the USN 16" gun, at a projectile mass of 1224.7 kg, a muzzle velocity of 762.2 m/s, the air density according to ISA per altitude (interpolated off an array table), and Mach number off ISA temperatures, starting at 340.278 m/s, with a decrease of 0.61 m/s for every -1º C (at 15º C SL and with a lapse rate of -1º C per every 152.39 meters), and the Coefficient of Drag model as per the page I linked earlier (with 12 points for linear interpolation), a nominal Coefficient of Lift of 0.015, and gravity acceleration at 9.807 m/s², I get at 20º elevation, as a sample;

Time to fall of shot; 48 seconds
Range: 26,694 meters
Striking angle: 25.68º
Velocity at impact: 491.2 m/s (a tad high, by about 11 m/s)
Highest altitude: 2,741 meters
Velocity at top: 560.25 m/s

That's as near I can really hope for, at this stage. Other angles of elevation are checking out similarly, according to the range tables linked by dunmunro for the 16".

Thanks, it has been a fun little project.

All the best.

delcyros
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Re: Projectile fire questions

Postby delcyros » Mon Sep 26, 2011 10:48 am

You may be intetested in Rick Robinsons BIG GUN freeware. The source code should be aviable, too.

CuttleFish
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Re: Projectile fire questions

Postby CuttleFish » Mon Sep 26, 2011 3:48 pm

Thanks, delcyros.

I just had a quick look at the source code, but have not run the program (yet) as I am on Linux. It is interesting, though there are three main differences (apart from the fact that his has armor penetration calculations); the air density is calculated by a constant formula, and I extract mine from references in a table of ISA values, as the atmosphere density lapse is not constant. Another is the calculation of variable coefficient of drag, by Mach number. And finally, my energy / drag model is calculated off momentum (m = vel * mass) and not kinetic energy factor (kf = vel²/2). The really outstanding feature of it, however, is that it appears to calculate the muzzle velocity of the shell by the energy released from the charge. That's neat.

Thanks for that.

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tommy303
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Re: Projectile fire questions

Postby tommy303 » Mon Sep 26, 2011 5:24 pm

This article by Bill Jurens should be useful for you was well, specifically since it deals with long range artillery.

http://www.navweaps.com/index_tech/tech-043.htm

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They stood and Earth's foundations stay;
What God abandoned these defended;
And saved the sum of things for pay.

CuttleFish
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Re: Projectile fire questions

Postby CuttleFish » Tue Sep 27, 2011 3:38 am

@tommy303;

All good reading, thanks!

PS: Isn't that Seydlitz's motif, the BC of BC's, if I am not mistaken?

Bill Jurens
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Re: Projectile fire questions

Postby Bill Jurens » Tue Sep 27, 2011 4:17 am

Cuttlefish wrote:

"I am here with some questions, as I think there will probably be someone here who knows this matter. The subject is (roughly) the venerable Royal Navy 15" gun.

What altitude did the shell reach at the top of its loft, if fired at about a 22º elevation angle, for example?

What might the velocity of the shell have been upon impact?"

The official Royal Navy Range tables for this gun, 1920lb 4CRH projectile at I.V. of 2450 f/s and angle of departure of 22 degrees 4 minutes, gives a range of 26000 yards, a maximum ordinate of 9970 feet about 14531 yards downrange. Angle of fall is 32 degrees 51 minutes, striking velocity 1352 f/s.

Hope this helps...

Bill Jurens


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