Ballistic trajectory and rifled barrels

[Asolepius]

Any ballistics experts out there? I have been wrestling with a thought experiment for some while without success.

The purpose of rifling is to impart spin to a projectile, which gives it gyroscopic stability. My interpretation of that is that as soon as it leaves the barrel it will carry on pointing in the same direction. Hence a small bore rifle bullet will arrive at its target point first. Smooth bore weapons are less accurate because the ammo wavers and tumbles, unless it's stabilised some other way(eg by aerodynamic fins on a sabot round).

That's all fine and dandy for an infantry rifle with a very shallow trajectory, but what about an artillery piece? To take an extreme case, let's consider a howitzer firing at 45 degrees to horizontal. Well that's not really extreme judging by WW1 footage I've seen. Anyway, off goes the shell at 45 degrees. At the top of the parabolic trajectory it's travelling horizontally, as it transitions from going up to going down. But if the gyroscopic forces are still working, it's still pointing 45 degrees upwards. That's the whole point of a gyroscope, as the rotational inertia resists changes in orientation of the axis.

The shell now goes down the other half of the parabola, all the time still pointing up 45 degrees. Ignoring air resistance for the moment, you can see where I am going - the shell hits the target going sideways.

Cartoons usually portray shells orientating themselves along the trajectory, so they hit the target nose first. If they do, what forces act on them to affect the gyroscopic stability? I can't find any articles online that explain this, or even consider what actually happens to projectile orientation. I have the feeling that I have missed something fundamental. If I have, what is it?

 

[The Don]

I'm not sure how different this is from throwing an American football with a spiral or punting a rugby ball with a spiral kick. The ball rotates about an axis which is in the same direction as the travel but the orientation of the nose of the ball is up-level-down unless the ball stalls in flight.

 

[erwinl]

That's why you don't want the rifling to be too much. Or else this is exactly what will happen.
See this part of Wikipedia

As it stands the point of a projectile is indeed somewhat above the line of travel, when coming down again.

 

[Asolepius]

That's why you don't want the rifling to be too much. Or else this is exactly what will happen.
See this part of Wikipedia

As it stands the point of a projectile is indeed somewhat above the line of travel, when coming down again.

The forces I am looking for are aerodynamic? That means that the centre of pressure for the shell must be well behind the centre of gravity, ie it is very nose-heavy.

 

[casebro]

A bullet out of a modern rifle barrel spins 180,000 rpms. Fired straight up, it will come down butt first, still spinning about 100,000 rpms. In thousand yard competitions, the bullets do make oval holes in the paper targets. The peak apogee is 35 feet above line of sight to target.

My guess is that explosive rounds have to be able to detonate when the rear of the shell strikes first. Hmm, newest tank guns went back to smooth bore sabots.

 

[WhatRoughBeast]

The forces I am looking for are aerodynamic? That means that the centre of pressure for the shell must be well behind the centre of gravity, ie it is very nose-heavy.

It's complicated. For a head-on flight, the standard ogive shape (pointy-nose) has a center of mass behind the center of pressure, and in the absence of spin it will yaw to 180 degrees (tail first). The denser the medium it penetrates, the greater the upset forces. This is why all small-arms bullets tumble when they hit flesh - the stability produced by spin is adequate for the forces encountered in air, but not in (effectively) water. See, for instance, http://www.ar15.com/ammo/project/Fackler_Articles/wounding_patterns_military_rifles.pdf

However, for a high-angle artillery shell, after a while its initial orientation gets increasingly sideways to its flight path, and for sideways motion the center of pressure is behind the center of mass. The resulting motion is not as simple as for a non-spinning body (the correcting forces act in 2 dimensions rather than one), but the result is the same - the shell aligns its orientation with its flight path and hits nose-first.

During WWI there was a variety of mortar which fired a cylindrical shell. This did not stabilize, and an "all-angles" fuse had to be developed.

 

[patchbunny]

A bullet out of a modern rifle barrel spins 180,000 rpms. Fired straight up, it will come down butt first, still spinning about 100,000 rpms. In thousand yard competitions, the bullets do make oval holes in the paper targets. The peak apogee is 35 feet above line of sight to target.

My guess is that explosive rounds have to be able to detonate when the rear of the shell strikes first. Hmm, newest tank guns went back to smooth bore sabots.

IIRC smoothbores were developed as the spin imparted by rifling has a negative effect on the plasma jet from a HEAT round.

 

[catsmate]

A bullet out of a modern rifle barrel spins 180,000 rpms. Fired straight up, it will come down butt first, still spinning about 100,000 rpms. In thousand yard competitions, the bullets do make oval holes in the paper targets. The peak apogee is 35 feet above line of sight to target.

My guess is that explosive rounds have to be able to detonate when the rear of the shell strikes first. Hmm, newest tank guns went back to smooth bore sabots.

IIRC smoothbores were developed as the spin imparted by rifling has a negative effect on the plasma jet from a HEAT round.

In WW2 saboted penetrators (of the 'long rod' type) were developed along with Munroe effect shaped/hollow charge rounds. Rifled weapons suited neither of these types of ammunition well.
Saboted penetrators were far narrower that the cannon's bore (encased with a 'sabot' that engaged with the cannon barrel) and thus rotated far faster than a full bore projectile; thus (before ballistic computers) they were less accurate than expected.
With shaped/hollow charge projectiles a spinning projectile tends to dissipate the penetrating jet via centrifugal force. It's possible to overcome this by clever tricks, e.g. contra-rotating warhead used in the Carl Gustav.

After WW2 the standardisation of APDS for tank cannon led to smoothbores (which have the advantage of marginally higher projectile velocity over rifled guns) and long rod penetrators with fins for aerodynamic stabilisation being the preferred tank armament in some countries (APDS-FS) with HEAT used for long range shots.
The UK stuck with rifled cannon, using a contra-rotating sabot system and preferred HESH to HEAT anyway.

Nitpick: the jet from a shaped/hollow charge warhead is hot but not plasma hot, based on spectrophotography. It's basically a high velocity jet of molten metal particles.

 

[erwinl]

In WW2 saboted penetrators (of the 'long rod' type) were developed along with Munroe effect shaped/hollow charge rounds. Rifled weapons suited neither of these types of ammunition well.
Saboted penetrators were far narrower that the cannon's bore (encased with a 'sabot' that engaged with the cannon barrel) and thus rotated far faster than a full bore projectile; thus (before ballistic computers) they were less accurate than expected.
With shaped/hollow charge projectiles a spinning projectile tends to dissipate the penetrating jet via centrifugal force. It's possible to overcome this by clever tricks, e.g. contra-rotating warhead used in the Carl Gustav.

After WW2 the standardisation of APDS for tank cannon led to smoothbores (which have the advantage of marginally higher projectile velocity over rifled guns) and long rod penetrators with fins for aerodynamic stabilisation being the preferred tank armament in some countries (APDS-FS) with HEAT used for long range shots.
The UK stuck with rifled cannon, using a contra-rotating sabot system and preferred HESH to HEAT anyway.

Nitpick: the jet from a shaped/hollow charge warhead is hot but not plasma hot, based on spectrophotography. It's basically a high velocity jet of molten metal particles.

Technically it isn't molten either.
The metal of the armour and the projectiles (whether HEAT or inert penetrator) do act like fluids when interacting at those energy levels though.

 

[catsmate]

Technically it isn't molten either.

In general I agree, though it depends on the liner material and the design of the charge; jets using steel, copper, tungsten or molybdenum aren't generally hot enough to be considered molten in their entirety, though part of the jet may be. Tin, aluminium, magnesium or glass liners generally are molten, in the sense of being hotter than their melting point. [/quote]

The metal of the armour and the projectiles (whether HEAT or inert penetrator) do act like fluids when interacting at those energy levels though.

Agreed. With all the complex physics that fluid mechanics implies...........