Watched “Wanted” the other night (dont bother, not a particularly good film) and in it was a conceit that a multi-stage bullet slug would travel great distances.

Ignoring the effect of curvature of the earth, but taking into account air resistance and gravity, if you had a bullet of a particular mass and projected with a particular force, if that bullet were at stages to lose mass (but retain it’s velocity at the exact point of losing mass) would it travel further than the same bullet that retained the same mass and initial impulse?

Maybe.

No.

Show your working or its a C-

How does it ‘lose mass’? Do bits somehow magically detach themselves and veer off the ballistic trajectory with no additional force being applied?

Do bits somehow magically detach themselves and veer off the ballistic trajectory with no additional force being applied?

Well, in the film they had sections un threading and then falling away. But for the purpose of this thought exercise, lets just say that they detach from the rear of the ballistic mass and apply no acceleration in any direction to the residual mass at the front.

In which case the answer is no.
I’d say that it would travel less far as the air resistance would remain the same (+-) but the inertia & mass of the reduced slug would be less.

Right.

If you throw a projectile on say the moon, a light one would go the same distance as a heavy one if both launched at the same velocity, but the light one would have less energy. On Earth, assuming the same size and shape, air resistance losses would be fixed so the lighter one would lose more of its energy PROPORTIONALLY and hence slow down more.

So lighter projectiles don’t go as far launched at the same velocity. If you are firing from a gun then it’s slightly different since you’re launching at the same ENERGY (sort of but probably not in a real life gun situation) not the same velocity. The same energy into a smaller projectile gives greater velocity and hence further travel provided it’s not too light to lose too much to air resistance.

If a projectile split in mid air, you have to ask how is it splitting? If there’s some kind of charge in the middle of it firing half backwards and half forwards, then the forward part would gain the momentum of the backwards part so would go faster. But the charge would add energy into the system.

As thepurist suggests, if the projectile simply broke up they’d both describe the same trajectory so nothing would change – provided one part was not so small to experience significant losses to air resistance. If it was a small bullet sized projectile and it broke into equal parts you’d have two pretty small projectiles and the above mentioend effect of air resistance on small projectiles would make them BOTH travel less distance.

OK. Got you.

Now what if it lost mass and, through changes to it’s form factor in flight, air resistance simultaneously?

Can you describe to an idiot like me the relative effects of changes in resistance and changes in inertial mass?

I think they probably decided to do this because it’s what rockets do when leaving the earths atmosphere.

The difference is that the rocket is continually accelerating under the action of it’s thrusters, whilst the bullet has finished accelerating and is behaving as a projectile.

In the former case, the rocket can accelerate faster by losing mass (the empy fuel/thruster modules). In the latter case the bullet would not travel faster by losing mass.

In fact, I suspect that if we ignored unsteady forces/effects (like turbulence), in an idealised situation if you magically split the bullet in two without perturbing it, it would continue on the same trajectory as if it had not been split.

Air resistance depends on the shape of the thing. If you make a thing heavier but the same shape, then it’ll have more energy. The forces of air resistance will scrub off some of that energy depending on the shape, but if it’s heavier there’s more energy to begin with, and hence it will lose less as a percentage of what it has.

Thought experiments are handy for these Newtonian physics situations. Imagine falling out of a plane holding two sparrow wings. Flap them all you like you’re still in trouble. If a sparrow falls out of a plane equipped with its two wings, it can not only slow its descent completely but fly off wherever it likes.

Can you describe to an idiot like me the relative effects of changes in resistance and changes in inertial mass?

Not me

as a guess though:

I reckon the initial bullet would have to be either incredibly unaerodynamic for a major advantage to apply (and why would you do that ?) or else some sort of dual density thing with a very dense core that becomes the final projectile. Not sure why that would work though, unless it allowed a bigger initial force to be applied when the gun’s fired. It’s also have to separate almost instantly – like cannonballs and wadding ??

bastard sparrows. Flaunting their wings in my face like that.

So we can assume then that a projectiile that adopted a more aerodynmaic shape, but retained its mass, during it’s flight would travel further than a similarly massed projectile that remained in its original shape.

So in order to travel further with less mass than something with more mass, the bullet would have to change shape to a much more aerodynamic profile to compensate for the loss in energy of shedding mass. Yep?

A simple example of ballistics with the projectile separating mid flight are all those sick & rad gnaarly videos of da yoot doing stupid things like letting go of their bike in mid air after riding off a huge ramp. If you believed hollywood the lighter part (the bike) would then accelerate off and leave the heavier rider behind. Fortunately for such stuntsters this sort of thing doesn’t happen.

PS Yep.

Fortunately for such stuntsters this sort of thing doesn’t happe

fortunately? Id say Id rather have my bike bugger off out the way of my controlled landing zone! 😉

Yep.
Perhaps a bullet with a pointed cylindrical tungsten core and a less dense sheath would benefit from shedding the sheath.

So we can assume then that a projectiile that adopted a more aerodynmaic shape, but retained its mass, during it’s flight would travel further than a similarly massed projectile that remained in its original shape

Yes.

So in order to travel further with less mass than something with more mass, the bullet would have to change shape to a much more aerodynamic profile to compensate for the loss in energy of shedding mass. Yep?

Yes but only because it would be slowing down less. It wouldn’t actually accelerate.

FWIW there is already research into using piezo-electrics to make ‘morphing’ wing profiles.

What if you fired said bullet from an aeroplane? On a treadmill, of course.

“There’s a reason they never made a military variant of concorde. At its fastest, Concorde can do Mach 2.02 or 1,350 mph. There’s no gun that fires bullets that fast, so were an armed Concorde to open fire, it would promptly shoot itself down.”

A favourite line taken from the very funny http://www.amazon.co.uk/What-Goes-Might-Come-Down/dp/B00002MOJK

Silly rather than funny.. a) wrong and b) guns do fire bullets faster than that anyway.

I think you forgot to suspend your disbelief for a moment there molgrips 🙄

Humour has to be more than saying something wrong and daft 🙂

There’s nothing to make the bullet accelerate, so it can only slow, and if its mass decreases, it will slow more, albeit its wind resistance may decrease too which may mitigate that.