Long Range gunfire physics, query.

[garrisonchisholm]

So, I had a question.  When a large caliber shells are falling towards their target, are they accelerating due to gravity or decelerating due to air resistance?  I was surprised to realize I did not know.

I could Google it of course, but I always prefer talking to people about such things, the answers and unexpected directions of conversation are much more interesting.  :]

[director]

Um... some of both? With the exact numbers depending on the angle of descent... I think. Shells are pretty aerodynamic (the V-2 rocket was designed to the shape of a German artillery shell - it was the only practical experience they had with something going past the speed of sound) so I think their terminal velocity would be quite high. I'm using 'terminal velocity' to mean maximum speed attainable in atmosphere, not as in how fast they are going when they hit. Given the short time of flight I'm not sure their final velocity would be much affected by atmosphere or gravity, other than gravity forming their downward arc, but I won't swear to that.

[skyblazer]

I believe it would be losing energy as it goes from air resistance. The round would already be travelling past terminal volcity (can't spell) thus it would continue to lose energy till it hits terminal or hits the ground.

[garrisonchisholm]

I suppose that would make the most sense, as if it was at its slowest at its apex then logically that would explain why a 16 inch shell could be stopped by 7 inches of deck armor, if it was constantly slowing. I also warrant 9.8 m/sec from gravity doesn't contribute a great deal when its starting energies were so high.

[oldpop2000]

What you are asking about is of course, exterior ballistics. The first force on a shell is the acceleration due to the propellant in the chamber and the resulting movement through the barrel. The longer the barrel, the greater the acceleration.

The next force is gravity acting downward on the shell. Remember however, that gravity is not the same throughout the earth. Gravity changes with altitude. Gravitation force is proportional to 1/R squared. The farther you are from the center of the earth, the less gravity has an effect. You weigh about .5% more at the poles than at the equator.

You now have two vector quantities, the force of the propellant acting on the shell's direction and the force of gravity acting downward.

The next force is what in my world, we call form drag. The drag caused by the form of the shell passing through the atmosphere. As the shell climbs in altitude, the atmosphere's density changes, so does form drag. No two shells have the same ballistic coefficient which is the measure of the air drag. There are standards, but as I said, no two are the same.

The last force is the force of the meteorological conditions that the shell is traveling through. This would be wind speed and direction, humidity or how much water vapor is in the atmosphere and barometric pressure. These forces can act in various ways and can change during the travel of the shell.

As the force of the propellant begins to decrease, form drag, gravity and environmental conditions will begin to have more effect. Generally this is after the apogee is reached and the shell begins its decent in which case the effects of gravity on the weight of the shell will now have a greater effect.

This is the best I can do without books near me and I am certain there are better people on this forum to explain it. Where is Randomizer when you need him?


Just another bit of info: Barrel wear, droop and differences in powder from one bag to another are other variables that can change the acceleration of the shell. I know there are more, but will let someone else explain them.

[axe99]

From memory from reading the tables in Campbell, for longer ranges there's definitely acceleration from plunging fire. No way I can provide any background on the physics beyond what's above though. Terminal velocity for a shell will depend on aerodynamics, but I imagine it's pretty quick.

For examples (and no more memory here, I've tottered off to the bookshelf)....

Here we go (and interestingly) - it's worth noting that it depends a bit on range. At 30km, a shell from Yamato's 46cm guns is still decelerating (and on a descent angle of 31.4 degrees). Same for a shell from a Japanese 41cm gun - and the Japanese tables only to to 30km (and, to be fair, it's unlikely many/any hits are going to be scored outside that distance!)

If we go to the US 16in Mk 6 gun, though, the table has velocity increasing again at 36,000 yards, with a descent angle of around 48 degrees.

For smaller calibre shells, it's more marked - the US 6in with a muzzle velocity of 762m/s drops to 336 m/s at 20k yards, but by 26k yards (pretty much maximum range) has sped back up to 376m/s (faster than it is at 16k yards - but now at an angle of 62 degrees instead of 24 degrees).

Again from memory (I'm not looking at all the ballistics tables now ) once the angle of descent goes over around 45 degrees, the speed of the shell increases (but at an angle far more suited to deck than belt penetration). There'll be some physics going on here that it's far, far too long from high school for me to explain!

[oldpop2000]

Here is good link to page at the San Francisco Maritime National Park website which explains using drawing etc. interior and exterior ballistics.

maritime.org/doc/firecontrol/index.htm

I am going to read it again after babysitting.

[randomizer]

Fredrik sent me the OP and suggested that my reply to him should be posted here. Having spent several years teaching ballistics and ammunition, I have tried below to explain without resorting to formulae and calculus (that would probably escape me anyway) but this greatly simplified version is necessarily incomplete.

The short answer is that a projectile fired at an elevation consistent with battle ranges would not be accelerating significantly due to gravity but its rate of drag-induced deceleration is reduced. That said what follows is from memory since my ballistics manual seems to have vanished.



Terminal velocity of a projectile is a function of a number of factors with initial velocity and projectile weight as major components. Lighter shells (having less mass) retain less velocity at impact and this is an important reason why the lighter German shells did less damage to the British ships at Jutland than the bigger RN shells did to the better armoured HSF ships despite the German guns generally having greater muzzle velocities. The angle of fall and so the effects of gravity at battle ranges actually had relatively little to do with the remaining velocity; defined as the projectile velocity at impact. In high-angle trajectories (> greater than 45 degrees with maximum range being achieved at typically 50-56 degrees angle of departure) the effects of gravity on velocity become more pronounced and there may indeed be gravity induced acceleration in the terminal phase.



Oldpop2000's post is reasonably accurate even if he does conflate some terms and effects. External ballistics (everything that happens from shot-ejection to fuze-function OR projectile impact) is complex and the theoretical underpinnings is still not fully understood even by the experts (and I am certainly not one of those). My specialty was internal ballistics (everything from the firing of the primer to shot ejection) but in addition to these there is terminal ballistics (everything that happens between fuze-function OR impact and when all related movement ceases) and a rather arcane "intermediate ballistics" that is used when muzzle brakes are present to account for the interaction between the expelling propellant gases as they change direction and the projectile at shot ejection and the initial in-air shot travel.



On the ascending branch of the trajectory the principle drag components are base-drag and skin drag, the former being far greater than the latter. For projectiles travelling greater than mach 1 these drag components were exacerbated by the projectile's square bases, short ogives and full body bourolettes found in early 20th Century projectiles. Modern projectiles have long, complex ogives and short bourolettes and boat tail shaped bases that are often hollow. Some projectiles utilize base-bleed where a propellant is burned inside the base, filling the partial vacuum that produces the base drag. Base bleed can increase range by up to one-third just by reducing base drag on the ascending branch. As I recall it was a Swedish innovation. Sometimes projectiles transition into and out of the supersonic regime due to atmospheric conditions and these "transonic" conditions tend to greatly increase the probable errors and round to round variations even if the trajectory remains theoretically rigid. Fortunately all long-range artillery projectiles (> 18,000 m in US/CA/UK usage) are supersonic throughout the trajectory.



The latter is an important point since since a descending projectile traveling at supersonic speed and relatively shallow angle of fall gets relatively little velocity help from gravity. The velocity at maximum ordinate the highest point in the trajectory and the exact point where the projectile transitions from ascending to descending is still supersonic but has reached the point where drag has reduced velocity to where gravity can now begin to act on it and cause it to descend. Gravity will be the major component acting on the projectile during the descending branch of the flight but its principle effect at shallow angles of fall is to reduce the rate of deceleration caused by drag rather than adding any significant velocity. The main drag component in the descending branch is skin-drag while base drag becomes largely irrelevant. This is why the descending branch of an in-air trajectory is always steeper than the ascending branch, why particularly at long range, the angle of fall is always greater than the angle of departure and why maximum ordinate is always closer to the point of impact than to the gun. The gravity effect on velocity increases at higher angles of departure, which provide steeper angles of fall and longer times of flight, the latter being important because gravity now has more time to act on the descending projectile. The math being pretty complex for this small-brained primate but as I recall, there is no in-air situation where a shell's terminal velocity would equal or exceed its muzzle velocity with a conventional propellant gun firing a ballistic projectile. There's no escape here from Newtonian physics and the tyranny of atmospheric drag.



A descending projectile in air also benefits from lift due to Bernoulli's principle since gyroscopic precession tends to keep the nose of the projectile above the trajectory and so producing some aerodynamic lift on both branches of the trajectory. This is why absolute maximum range is typically achieved at angles of departure >45 degrees in air for ultra-long range guns firing at >30,000 m or so. The Paris Guns of 1918 were fired at a fixed elevation of 55 degrees to achieve maximum range (~115,000 m) while the GC-45/GHN-45 and G-5 family of howitzers reach maximum range ~40,000 m at 53 degrees (860 mils). Transient effects such as meteorology, rotation of the earth, and round to round variations are not considered to affect the trajectory but do affect the point of impact. Droop has essentially zero effect in a well designed gun (although this seems counter-intuitive to the uninitiated) and is disregarded in trajectory and non-standard conditions calculations. The oft repeated canon that German built-up guns were superior to British wire-wound guns because they had less "droop" is entirely wrong in every sense. Wire wrapping was used to provide hoop strength reinforcement and was generally employed outside the breach and chamber (typically in place of the B or C tubes) where girder strength was less important. All big guns were built up with the outer tubes providing girder strength to minimize droop.



Definitions:



Ogive - The conical shape of the forward part of the projectile. The shape may be simple or complex and is a function of calibre and projectile length and is defined by a set of formulae that produces a "caliber radius head" or CRH.
Complex CRH projectiles tend to have lower drag coefficients than those made with simple CRH ogives.


Bourolette - The portion of the projectile that has been machined to the exact inside diameter of the gun tube. In the early 20th Century, most projectiles had full-body bourolettes which greatly increased skin drag. Later through empirical testing it was determined that only a short bourolette was necessary to stabilize the projectile in the bore and the projectile external diameter between the bourolette and driving bands could be slightly less. This reduces drag by invoking the area-rule principle of aerodynamics in the transonic and supersonic regimes.



Base - The portion of the projectile behind the driving bands. May be square, so that the diameter is the same as the projectile body or boat tail where the base is tapered and the diameter is less than the projectile body. Bases may also be solid or hollow. Projectiles designed for base ejection of contents or those fitted with base fuzing typically use square bases.


Angle of departure - The ballistic angle measured through the centre of the bore and long axis of the projectile in relation to the horizontal plane at the instant of shot ejection. It incorporates all mount variables, angle of site and range corrections and in the case of naval guns, roll and pitch. Angle of departure does not necessarily equal elevation.

There's lots of conflicting ballistic data on the Internet and merely examining firing tables without some theoretical understanding of why things happen as they do while attempting to infer cause and effect can lead to confusion. You may find conflicting sources or different terminology used elsewhere, caveat emptor.

[oldpop2000]

Jan 26, 2017 16:34:39 GMT -6 randomizer said:

Fredrik sent me the OP and suggested that my reply to him should be posted here. Having spent several years teaching ballistics and ammunition, I have tried below to explain without resorting to formulae and calculus (that would probably escape me anyway) but this greatly simplified version is necessarily incomplete.

The short answer is that a projectile fired at an elevation consistent with battle ranges would not be accelerating significantly due to gravity but its rate of drag-induced deceleration is reduced. That said what follows is from memory since my ballistics manual seems to have vanished.



Terminal velocity of a projectile is a function of a number of factors with initial velocity and projectile weight as major components. Lighter shells (having less mass) retain less velocity at impact and this is an important reason why the lighter German shells did less damage to the British ships at Jutland than the bigger RN shells did to the better armoured HSF ships despite the German guns generally having greater muzzle velocities. The angle of fall and so the effects of gravity at battle ranges actually had relatively little to do with the remaining velocity; defined as the projectile velocity at impact. In high-angle trajectories (> greater than 45 degrees with maximum range being achieved at typically 50-56 degrees angle of departure) the effects of gravity on velocity become more pronounced and there may indeed be gravity induced acceleration in the terminal phase.



Oldpop2000's post is reasonably accurate even if he does conflate some terms and effects. External ballistics (everything that happens from shot-ejection to fuze-function OR projectile impact) is complex and the theoretical underpinnings is still not fully understood even by the experts (and I am certainly not one of those). My specialty was internal ballistics (everything from the firing of the primer to shot ejection) but in addition to these there is terminal ballistics (everything that happens between fuze-function OR impact and when all related movement ceases) and a rather arcane "intermediate ballistics" that is used when muzzle brakes are present to account for the interaction between the expelling propellant gases as they change direction and the projectile at shot ejection and the initial in-air shot travel.



On the ascending branch of the trajectory the principle drag components are base-drag and skin drag, the former being far greater than the latter. For projectiles travelling greater than mach 1 these drag components were exacerbated by the projectile's square bases, short ogives and full body bourolettes found in early 20th Century projectiles. Modern projectiles have long, complex ogives and short bourolettes and boat tail shaped bases that are often hollow. Some projectiles utilize base-bleed where a propellant is burned inside the base, filling the partial vacuum that produces the base drag. Base bleed can increase range by up to one-third just by reducing base drag on the ascending branch. As I recall it was a Swedish innovation. Sometimes projectiles transition into and out of the supersonic regime due to atmospheric conditions and these "transonic" conditions tend to greatly increase the probable errors and round to round variations even if the trajectory remains theoretically rigid. Fortunately all long-range artillery projectiles (> 18,000 m in US/CA/UK usage) are supersonic throughout the trajectory.



The latter is an important point since since a descending projectile traveling at supersonic speed and relatively shallow angle of fall gets relatively little velocity help from gravity. The velocity at maximum ordinate the highest point in the trajectory and the exact point where the projectile transitions from ascending to descending is still supersonic but has reached the point where drag has reduced velocity to where gravity can now begin to act on it and cause it to descend. Gravity will be the major component acting on the projectile during the descending branch of the flight but its principle effect at shallow angles of fall is to reduce the rate of deceleration caused by drag rather than adding any significant velocity. The main drag component in the descending branch is skin-drag while base drag becomes largely irrelevant. This is why the descending branch of an in-air trajectory is always steeper than the ascending branch, why particularly at long range, the angle of fall is always greater than the angle of departure and why maximum ordinate is always closer to the point of impact than to the gun. The gravity effect on velocity increases at higher angles of departure, which provide steeper angles of fall and longer times of flight, the latter being important because gravity now has more time to act on the descending projectile. The math being pretty complex for this small-brained primate but as I recall, there is no in-air situation where a shell's terminal velocity would equal or exceed its muzzle velocity with a conventional propellant gun firing a ballistic projectile. There's no escape here from Newtonian physics and the tyranny of atmospheric drag.



A descending projectile in air also benefits from lift due to Bernoulli's principle since gyroscopic precession tends to keep the nose of the projectile above the trajectory and so producing some aerodynamic lift on both branches of the trajectory. This is why absolute maximum range is typically achieved at angles of departure >45 degrees in air for ultra-long range guns firing at >30,000 m or so. The Paris Guns of 1918 were fired at a fixed elevation of 55 degrees to achieve maximum range (~115,000 m) while the GC-45/GHN-45 and G-5 family of howitzers reach maximum range ~40,000 m at 53 degrees (860 mils). Transient effects such as meteorology, rotation of the earth, and round to round variations are not considered to affect the trajectory but do affect the point of impact. Droop has essentially zero effect in a well designed gun (although this seems counter-intuitive to the uninitiated) and is disregarded in trajectory and non-standard conditions calculations. The oft repeated canon that German built-up guns were superior to British wire-wound guns because they had less "droop" is entirely wrong in every sense. Wire wrapping was used to provide hoop strength reinforcement and was generally employed outside the breach and chamber (typically in place of the B or C tubes) where girder strength was less important. All big guns were built up with the outer tubes providing girder strength to minimize droop.



Definitions:



Ogive - The conical shape of the forward part of the projectile. The shape may be simple or complex and is a function of calibre and projectile length and is defined by a set of formulae that produces a "caliber radius head" or CRH.
Complex CRH projectiles tend to have lower drag coefficients than those made with simple CRH ogives.


Bourolette - The portion of the projectile that has been machined to the exact inside diameter of the gun tube. In the early 20th Century, most projectiles had full-body bourolettes which greatly increased skin drag. Later through empirical testing it was determined that only a short bourolette was necessary to stabilize the projectile in the bore and the projectile external diameter between the bourolette and driving bands could be slightly less. This reduces drag by invoking the area-rule principle of aerodynamics in the transonic and supersonic regimes.



Base - The portion of the projectile behind the driving bands. May be square, so that the diameter is the same as the projectile body or boat tail where the base is tapered and the diameter is less than the projectile body. Bases may also be solid or hollow. Projectiles designed for base ejection of contents or those fitted with base fuzing typically use square bases.


Angle of departure - The ballistic angle measured through the centre of the bore and long axis of the projectile in relation to the horizontal plane at the instant of shot ejection. It incorporates all mount variables, angle of site and range corrections and in the case of naval guns, roll and pitch. Angle of departure does not necessarily equal elevation.

There's lots of conflicting ballistic data on the Internet and merely examining firing tables without some theoretical understanding of why things happen as they do while attempting to infer cause and effect can lead to confusion. You may find conflicting sources or different terminology used elsewhere, caveat emptor.

You're telling me, read each site and get many different answers. Thanks for clarifying all this.

[garrisonchisholm]

Wow. THIS is exactly why I wrote a post this morning rather than simply try to google an answer. Thank you, all, for taking the time to relay such a depth of knowledge and in such an interesting manner.

I wish I could generate a reply of wit, worthy of this education, but in short (from both Randomizer and Oldpop's Maritime National Park link) it seems that whether a shell is undergoing acceleration or deceleration at impact is dependent upon the mass of the shell and the range fired at- the higher both of these are, the more energy carried to impact.

Axe99's quotations are interesting as well, as it seems to imply that speed at impact could vary by as much as 15%, depending upon range alone. I had not expected the differences would be so marked.

[axe99]

Cheers for the great post randomizer (and your info as well Oldpop, always helpful , hugely informative .

[ikahime]

I'm not as well informed as other people who have posted here before me, but I know from KSP that a projectile traveling in a Ballistic arc will be decelerating as it approaches it's apex, and accelerating afterwards. That however is assuming a vacuum. In atmosphere, deceleration seems to be dependent on density. Smaller heavier objects will have less drag, and thus slow down less, while bigger lighter ones will slow down more. Early game capsules traveling in sub-orbital flights often come down so fast that they won't be able to safely engage chutes, and impact the ground much like artillery shells. On the other hand, larger spacecraft with empty fuel tanks sometimes don't even need heat shields. In both cases the re-entry angle matters a lot.

[elouda]

To the best of my knowledge, the answer to this is yes, but only for larger shells at long distances.

Plugging the numbers for the 16in/50 Mk7 with the Mk8 AP @ 762m/s into my own ballistics calculator (which is designed to reproduce that gun based on its ballistic tables, and does so within a few tenths of a % error) says that at 45 degrees elevation, it tops out at around 11.1km altitude with velocity down to around 410m/s, and then accelerates to around 515m/s for impact at its 39km maximum range.

This same case plays out (to a lesser degree) all the way down to around 26-27 degrees, at which point impact velocity (around 475m/s) is about the same as the lowest velocity in the flight path.

[chz]

Well that got me reading quite a bit.
I know it's slightly off the original topic, but it made me realise that I *still* don't understand how Gerry Bull's ERFB guns work. (and was amazed to see that - officially at least - no-one seems to know who killed him)

[oldpop2000]

Feb 7, 2017 3:32:38 GMT -6 chz said:

Well that got me reading quite a bit.
I know it's slightly off the original topic, but it made me realise that I *still* don't understand how Gerry Bull's ERFB guns work. (and was amazed to see that - officially at least - no-one seems to know who killed him)

Well, I will leave the physics of his gun designs to randomizer, but as to his assassination, I would bet it was accomplished by the Israeli Mossad. I don't think the Israeli's thought that having his guns pointed at them was a really good idea so "cut off the head, the body dies". Which it did. My guess is that the US and other nations sanctioned the hit.