Air pressure effects on impact velocity

[alecsandros]

Hello,

Inspired by Cuttlefish's project, I started thinking about the effects the air parameters have upon a battleship shell.
My question: How much do you think severe air parameters differences can influence the velocity of a large, spinning projectile ?

For instance, in the northern hemisphere "normal" air conditions (at 0m altitude) are:
Pressure: 760 mmHg
Temperature: Medditeranean annual average: 20*C
Density:: 1.22 kg/m3@15*C

Let's take the German Sk34 38cm gun: the normal m-v would be 820m/s, and impact velocity at 20km - 510m/s

But what would happen if pressure at ground level would be very low (< 680) or very high (> 800), and the incremental decrease with altitude would mantain the same pattern normal air pressure does ?

[Thorsten Wahl]

In(de)creased air density by 10% in(de)reases range by about 700m at 20,000m.(~3,5%)

[alecsandros]

In(de)creased air density by 10% in(de)reases range by about 700m at 20,000m.(~3,5%)

That's very interesting...
Any thoughts on the effects of very powerfull winds (> 30m/s) on shell velocity ? (Presuming the direction of the wind to be perfectly parallel to that of the trajectory, either from the front or from the rear of the shell)

[Thorsten Wahl]

some ballistic information you can take from
GENE SLOVERS
US NAVY PAGES -AMMUNITION DESIGN AND TESTING
Rangetables for different projectiles
http://www.eugeneleeslover.com/USN-GUNS ... STING.html

[RNfanDan]

Don't forget that humidity plays a small role in the ballistic calcs, too.

[CuttleFish]

Hi,

Though I am in no - let's say - tactical situation of knowledge and information to exchange fire with experts on the topic, I can look at this from an atmospheric persepctive and add my commentary. Indeed, the variables of temperature and pressure are on the cards already for inclusion in the simulation model. I was motivated as yourself to wonder, once I had a basic model working, how these factors affected gunnery during battles in atmospherically different locations such as Barents Sea or North Atlantic and, for example, the South China Sea. That, and whether these factors were considered significant enough to be incorporated in the gunnery calculations or computers of the day. I honestly do not know anything about that last statement.

What I can say, and it is already confirmed in the posts above, is that pressure and temperature will certainly have an effect on the range a shell travels, all other factors aside. When you ask...

and the incremental decrease with altitude would mantain the same pattern normal air pressure does ?

...you are referring to the lapse rates of temperature, pressure, and as a product of these, density. The answer is they most certainly do not follow a simple "one fits all" pattern, but they are predictable to a great extent. They are in fact closely related to the altimetry "problems" of true versus indicated altitudes that pilots (and airline Operations Engineering departments, I hasten to add) have when flying in regions where the temperature differs widely from ISA conditions.

Please pardon me if this is all known stuff here, but the post also serves me as a reference in what I was thinking on a particular date in relation to my gun model progress. The problem is generally broken down into two related subjects; Indicated Altitude and Density Altitude. The first of these does not really concern us, but it helps to understand what is happening to air pressure in regions of different sea level ambient temperatures;

In ISA conditions, a gain of 1,000 ft entails a drop of pressure of approximately 3607 Pascals. In warmer temperatures (let's say, ISA +20º C), that drop of 3607 pascals does not occur until you have gained about 1,075 ft, and in colder temperatures (ISA -20º C) a gain of 935 ft is enough to cause that same pressure change. In essense, what is happening is that the higher temperature is vertically expanding the pressure gradient, and vice versa.

Now it is plainly obvious that air pressure is going to affect its density, simply by cramming more kg's worth of air molecules into a cubic metre. But it is not the full story. The very temperature that causes the expanding temperature gradient itself also affects the density, albeit to a smaller measure than the pressure. As expected, higher temperatures will tend to reduce the density. The best way to think of it is that temperature "fine tunes" the density that is predominantly set by the air pressure. Pilots generally use a rule of thumb here;

Each degree of difference of temperature from an ISA value for a given Pressure Altitude is equivalent to a change of 120 feet in Density Altitude. For example, at a pressure altitude of 8,000 ft, the ISA temperature would be about -1º C, but the real outside air temperature is 21º C. So; 8,000 + 22 x 120 = 10,640 ft. The density of the air would be equivalent to the ISA value for 10,640 ft, or 0.902 kg / m³, and not 0.963 kg/m³, as it would normally be at ISA at 8,000 ft.

It is rough, yes, as it assumes a constant gradient, and is certainly not what I am going to do in the gun model. But it does give an idea of what is happening. It also becomes obvious that it will affect the range of a shell, bearing in mind that density is one of the main variables in the dynamic pressure calculation, which in turn is a component of the drag calculation.

It will be exciting to see the results in the model. Sorry, I prattled on a bit as I got somewhat carried away in a subject that interests me!

Thanks!

PS:
Humidity reduces air density, and is calculable. As far as wind is concerned, it will obviously affect the trajectory of a shell, both in range and azimuth, much the same way it affects an aircraft's ground track and ground speed. The important thing here would be wind directions and strengths at different altitudes, as even that is not constant, and a shell goes through them in short order.

And that is definitely IT, from me, now.

[lwd]

Some of those effects simply could not be dealt with directly in fire control computers as there was no way to measure them at the time one shot. On the otherhand that's why one observed the fall of shot and corrected. The preceding rounds to some extent measured the conditions and allowed for a correction to be applied. Where I would expect wind or similar things (rain?) to be a more serious problem is if they are rapidly changing. I'll caveat this by saying I'm no expert on these matters.

[alecsandros]

Some fascinating insights guys... Thanks a lot...

I still can't figure out if the impact velocity of a BB shell would be bigger, or smaller, and consequently if plate perforation would be affected by weather.

For instance, if the wind blows from the rear of the shell at 30m/s, and the "usual" impact velocity of the shell at a given range is 500m/s, how much would the impact velocity be in such a case ?

[lwd]

.. For instance, if the wind blows from the rear of the shell at 30m/s, and the "usual" impact velocity of the shell at a given range is 500m/s, how much would the impact velocity be in such a case ?

As a rough estimate the speed loss over the distance would be the same as if the muzzle velocity was 30 m/s less than for the time of flight involved. I.e if the muzzle velocity was 500 m/s and the target was 1 second away calculate the speed lost for 470m/s over 1 second and apply it to the final velocity. In an example where any relationship to reality is completely accidental.
Say the muzzle velocity is 600 m/s and it take 40 seconds to reach 18000 meters and the terminal velocity is 500 m/s
We woudl then take a muzzle velocity of 570m/s and see what the terminal velcoity is after 40 seconds. Say it's 490 m/s. Then you would expect the terminal velocity of the round with the head wind to be ~520m/sec instead of 500 m/s. This of course ignores a bunch of things one of them being the force of friciton is iteslf velocity dependent (thus the real effect may be some what greater) and the trajectory will be different (I don't even want to guess which effects will dominate here).

Have I succeeded in confusing things and making afool of myself or is this close to right?

[Thorsten Wahl]

I dont have ballistic data for the SK 38
using rangetable for US 2700lb 2500fs AP projectile
500m/s =1640fs
wind 30m/s = 58,3 knots
http://www.eugeneleeslover.com/USN-GUNS ... 770-2.html

normal range for 1640 impact speed~ 24500 yards
column 13 change for 10knot windcomponent in plane of fire 73 yards*5,83 --->426 yards the target will be overshot by 426 yards

24500 yards - 426 yards = 24074 yards---> aiming point ~24100 yards
impact speed 1650fs and AOF 19° 56 minutes

to hit the target at 24500 yards point with correction for 58,knots wind in plane of flight you have to use a decreased elevation of 15° 12.5 minutes instead of 15° 34.2 minutes

[alecsandros]

Thanks Lwd, Thorsten, Cuttlefish !

So the effects of wind over striking velocity are very small... 10fps... 3m/s...

What about air density ? IF the shell travels through thinner air (let's take the 10% less density Thorsten mentioned), how much more impact velocity does it have at the end of the trajectory ?

[lwd]

As a very crude first estimate. I'm pretty sure air friction is a function of density so I'd exect a 10% decrease in air friction to mean ~10% less velocity loss. However since it's also a function of velocity that will likely overestimate the effect somewhat so say less so exect velocity loss to decrease by less than 10%.