Shell Aerial Performance Detailed.
Feb 14, 2020 12:35:34 GMT -6
director, axe99, and 4 more like this
Post by garrisonchisholm on Feb 14, 2020 12:35:34 GMT -6
I was sifting through the RTW1 board for, well, anything, and found this old thread and was reminded of this superlative and learned post as an answer to a question I had had about heavy naval shells. To wit, when shells are falling on their target are they Decelerating due to atmospheric drag or Accelerating due to gravity?
The thread prompted some very interesting discussion, but Randomizer's reply deserves to be read again by any fans of this genre.
nws-online.proboards.com/thread/1045/long-range-gunfire-physics-query
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.
The thread prompted some very interesting discussion, but Randomizer's reply deserves to be read again by any fans of this genre.
nws-online.proboards.com/thread/1045/long-range-gunfire-physics-query
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.
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