Smoothbore or Rifle?
I will start with the premise that a spinning projectile has a more accurate trajectory over a non-spinning one.
Now, the debate went into fin-stabilization and using canted fins for spinning. Then there was the loss of energy due to drag.
Drag is a force that pulls an object moving in a fluid backwards.
F[SUB]D[/SUB] = (1/2)Ïv[SUP]2[/SUP]C[SUB]D[/SUB]A. (eq. 1)
where,
v is the velocity and
A is the area. We can ignore the rest for now.
A moving projectile will have kinetic energy as such:
E[SUB]KIN(t)[/SUB] = (1/2)mv[SUP]2[/SUP]. (eq. 2)
where
m is the mass.
Now, as the projectile moves in a fluid, it loses Kinetic Energy, by virtue of the drag (among other causes). The loss of kinetic energy over a small distance
δs in unit time
t is:
E[SUB]LOSS(t)[/SUB] = F[SUB]D[/SUB]δs(t). (eq. 3)
So, after covering this distance, the projectile ends up with a remaining energy:
E[SUB]KIN(t+1)[/SUB] = E[SUB]KIN(t)[/SUB] - E[SUB]LOSS(t)[/SUB]. (eq. 4)
All this comes from [ref: 3], [ref: 4], and [ref: 5].
Now, if we see eq. 1, drag force is proportional to the square of the velocity. So, if a projectile moved twice as fast, loss of energy would be quadrupled. As per eq. 2, we cannot reduce mass, nor the area. So, the only way the energy loss occurs is by reduction in velocity.
[HR][/HR]
So far so good. Now, let us see how a smoothbore fired projectile can behave under two types of fins, not canted and canted. Note, both will offer drag stabilization:
Fins not Canted:
The projectile is not spinning, so it will wobble [ref. 2]. Every time it wobbles, the body of the projectile and the fins produce drag. Only the fins help push the centre of pressure back from the centre of gravity. So, while the force, being a function of mass, acts as per the centre of gravity, the fins push the centre of pressure backwards, and causes a lift, that brings the projectile aligned with the direction of motion. However, the projectile will continue to wobble, and the fins will continue to correct it, thus causing continuous loss of energy, and therefore, velocity.
Fins Canted:
This is very similar to the above scenario, but the fins are canted, and so it imparts spin, due to torque applied by the canted trailing edges of the fins, which also creates drag, and loss of energy, and velocity. However, the canting is very small, because, the fins being further away from the centre of the projectile, can exert enough torque on the body of the projectile. Once it starts spinning, there is very little chance of wobble, and the only loss of energy is by virtue of the cantings.
In either case, we see that there is loss of energy, and when this energy is lost in flight, whatever remains, is transferred into power. Let us assume the projectile hits the armour after
n seconds, and it takes
k seconds to come to stop, the average power transferred into the armour is:
P = E[SUB]KIN(n)[/SUB]/k.
where,
E[SUB]KIN(n)[/SUB] is the energy left after losing velocity over
n seconds of flight.
Now, what if we actually used a rifle to spin the projectile?
We would need no fins (canted or otherwise), and there will be no wobbling, and hence, the drag will be limited to the area i.e. the cross section of projectile (note, if it wobbled, the drag is more than the cross section [ref: 1], [ref: 2]).
Thus, much less loss in energy (proportional to square of velocity).
Another way to look at it is if we look at the instantaneous power:
P(t) = Fv = mv[SUP]2[/SUP]/t.
So, if we can preserve the velocity, i.e. reduce its loss (which we can if we eliminate fins altogether), we can deliver a bigger punch on the armour.
Therefore, looking at the equations, it looks like fins are necessitated if a smoothbore is used, but the disadvantages of fins are well overcome by rifling.
[HR][/HR]
I don't believe drag stabilized projectiles will have canted fins
IIRC viscous force opposes motion. So yes, it'll be against flight direct but also prevent wobbling and other undesirable effects
In drag stabilization, it is actually the lift that corrects the wobbling. Whether there will be any lift or not, will depend upon the centre of gravity and centre of pressure. See the right-most diagram in [ref: 2].
It's because you said,
and are trying to lump the APFSDS and HEAT at the same levels of spin as HESH.
No, I am not trying to lump anything together. I have not even mentioned APFSDS. All I am talking about is the projectile actually reaching the target accurately, and why a rifle is desired over smoothbore.
Now, if you want to talk specifically about Armour Piercing projectiles (since you mentioned APFSDS), I must say, it is in the interest of APFSDS to preserve as much energy as possible, so, better keep the fins out, and use rifling to spin the projectile.
[HR][/HR]
References:
[ref: 1]
http://www.apogeerockets.com/education/downloads/Newsletter325.pdf
[ref: 2]
Rocket Stability
[ref: 3]
Power (physics) - Wikipedia, the free encyclopedia
[ref: 4]
Energy - Wikipedia, the free encyclopedia
[ref: 5]
Drag equation - Wikipedia, the free encyclopedia
