Ballistics Question

#1
I bought a book on hunting yesterday (Jagt I Norden) and while flicking through it found a statement that seemed odd.

It said that if you fired a horizontal shot along a pefectly flat field, and at exactlythe same moment dropped a bullet from the same height as the muzzle both bullets would hit the ground at the same time.

Is this correct? Surely the bullet fired would be in the air for longer due to it's horizontal momentum.... Or am I mistaken?

Cheers
T_T
 
#2
Assuming no aerodynamic effects, it is absolutely true.

Horizontal momentum acts, by definition, in the horizontal and has no effect whatsoever in the vertical.

It assumes that the barrel is absolutely horizontal, which is rarely the case in the real world.
 
#3
It is true, assuming a whole load of 'ideal' conditions. It's the initial method of aerodynamic assessment that they teach at uni...the real world is different due to lots of non-ideal conditions that exist.

The one that took me a bit of time to absorb was curvature of the earth and earth spin effects on ballistics.

S_R
 
#4
Tartan_Terrier said:
I bought a book on hunting yesterday (Jagt I Norden) and while flicking through it found a statement that seemed odd.

It said that if you fired a horizontal shot along a pefectly flat field, and at exactlythe same moment dropped a bullet from the same height as the muzzle both bullets would hit the ground at the same time.

Is this correct? Surely the bullet fired would be in the air for longer due to it's horizontal momentum.... Or am I mistaken?

Cheers
T_T
The book is correct. Aerodynamic effects may make a tiny difference but nothing from a practical point of view.

You can test it yourself with a couple of marbles etc.
 
#5
The other one that messed with my head for a while was the penny and the feather in the vacuum tube - both fell at the same velocity.
 
#6
There has been a lot in ballistics that has messed with my head. Coriolis effect, the magnus effect, the idiot effect..................
 

Biped

LE
Book Reviewer
#7
It is right. What we are talking about is the rate of acceleration on a free-moving body caused by gravity.

Thus, a feather, in a vacuum will accelerate towards the deck at the same rate as, say, a bullet. The density of air is what slows the feather down, not a reduction of the effect of gravity.

The horizontal momentum matters not . . . . up to a point. If the bullet is travelling at relativistic velocities, it will actually get further away from the ground because of the curvature of the Earth.

If you drop a 1 tonne steel block off the top of the Eiffel tower, at the same time as a marble, they will both hit the deck at the same time.
 
#8
Biped said:
If you drop a 1 tonne steel block off the top of the Eiffel tower, at the same time as a marble, they will both hit the deck at the same time.
As long as its in a vacuum :p
 

Biped

LE
Book Reviewer
#11
roadster280 said:
Carcass said:
Biped said:
If you drop a 1 tonne steel block off the top of the Eiffel tower, at the same time as a marble, they will both hit the deck at the same time.
As long as its in a vacuum :p
While the original hypothesis of the bullet horizontally and vertically is true, the Eiffel tower sketch raises the issue of practical effects.

I'd venture to suggest that the 1 tonne block would hit the sides of the tower and ricochet all the way down (owing to the shape of the tower) whereas the marble would probably hit once, and deflect outwards sufficiently to avoid further contact. Notwithstanding air effects, of course :)

For the mathematically minded, it goes like this

s=ut+(0.5 x at2 ) where t2 means "t squared"

In this equation, s is distance, u is initial velocity, a is acceleration and t is time. Since u is zero, this term goes away. Rearranging the equation for t, it becomes

t=SQRT (2s/a)

s will be the distance the bullets have to fall, say 1.5m (from the standing position). "a" is gravity, which is 9.81m/sec2. So the time of flight will be

SQRT(2 x 1.5 /9.81), or in round figures 550 ms.

This is schoolboy mechanics, air effects etc will have an influence, but not considerably so.
Does it take into account the deceleration of the objects on hitting the girders though?

I would suggest that the marble may actually bounce back up a ways before falling again, whereas the 1 tonne steel block will actually only slow somewhat as it crashes through some of the girders, which would accelerate said girders, along with most of the ones above the POI in a downward direction, at ever-increasing speed through the remaining structure. Depending on which way the wreckage (and the 1 tonne steel block) falls, the marble may, in actual fact keep bouncing off the various bits all the way down and actually arrive on the ground after both the 1 tonne steel block AND the Eiffel Tower. It may be that the marble arrives at ground level a full ten seconds after the steel block, in bits.
 
#12
Biped said:
Does it take into account the deceleration of the objects on hitting the girders though?
....&etc
Isn't he talking about the bullet drop there, rather than your Eiffel Tower analogy?
 

Biped

LE
Book Reviewer
#13
mmmm, could be. I'd rather visualise the process than wrk it out mathematically - I'm cr@p at maths.
 

Biped

LE
Book Reviewer
#14
Thanks for the informative update.

roadster280 said:
Mind you, at some point, all of the above will come to rest around the base of the tower, where it will test the integrity of the French concrete industry.
Are you suggesting that, on facing a force accelerating toward it, the French concrete may, rather than stop the mass, crumble and disappear, allowing the mass to continue through, only to be be stopped by another country's concrete - one made of sterner stuff perhaps?
 
#15
Biped said:
It is right. What we are talking about is the rate of acceleration on a free-moving body caused by gravity.

Thus, a feather, in a vacuum will accelerate towards the deck at the same rate as, say, a bullet. The density of air is what slows the feather down, not a reduction of the effect of gravity.

The horizontal momentum matters not . . . . up to a point. If the bullet is travelling at relativistic velocities, it will actually get further away from the ground because of the curvature of the Earth.

If you drop a 1 tonne steel block off the top of the Eiffel tower, at the same time as a marble, they will both hit the deck at the same time.

(My highlight)


Good grief, Biped — what kind of guns do you sell?? I think this one goes beyond your local civpol: expect a visit from the Men in Black. :eek:
 
#16
Old_Reprobate said:
Biped said:
It is right. What we are talking about is the rate of acceleration on a free-moving body caused by gravity.

Thus, a feather, in a vacuum will accelerate towards the deck at the same rate as, say, a bullet. The density of air is what slows the feather down, not a reduction of the effect of gravity.

The horizontal momentum matters not . . . . up to a point. If the bullet is travelling at relativistic velocities, it will actually get further away from the ground because of the curvature of the Earth.

If you drop a 1 tonne steel block off the top of the Eiffel tower, at the same time as a marble, they will both hit the deck at the same time.

(My highlight)


Good grief, Biped — what kind of guns do you sell?? I think this one goes beyond your local civpol: expect a visit from the Men in Black. :eek:
You don't have to quite go as far as relativistic velocities - an appreciable fraction of escape velocity (~11.2 km/s) will do. A tank shell (APFSDS) travels at up to 1.8 km/s so you might see some effect there, but it will be small.
 
#17
Back to my original question. Unfortunately I can't try this with any of my rifles as it's difficult to find a volunteer who wants to stand in a field a mile away from me with a stopwatch waiting for my bullets to land, so I'll have to try with my air rifle.

Shooting with this, when I fire it says "bang...............thwack!". If I drop a pellet into a tin on the ground it says "Ding!" (if I drop it on the grass it says nothing, so I need the tin for dramatic effect).

Why is that then?
 

Biped

LE
Book Reviewer
#18
Well, when you bullet strikes the ground, it says 'Thwack' because it is a piece of bendy metal hitting the rough, frangible ground, hence 'Thwack' rather than 'twang' or 'peeeyoyng'. When you drop your lead pellet into a tin, it says 'ding' or even 'ting' on the basis of the fact that you are dropping a peace of metal onto metal, which resonates on impact. If the tin didn't have a lip, and thus the base of the tin was resting directly on the ground, and you dropped a pellet in there, it would more than likely go 'thuck'due to the fact that the metal base of the tin being directly supported by the hard-ish but frangible ground would absorb the impact directly, and thus halt the resonation that causes the 'ting' or 'ding'.

I hope that helps.
 
#19
roadster280 said:
Biped said:
Does it take into account the deceleration of the objects on hitting the girders though?

I would suggest that the marble may actually bounce back up a ways before falling again, whereas the 1 tonne steel block will actually only slow somewhat as it crashes through some of the girders, which would accelerate said girders, along with most of the ones above the POI in a downward direction, at ever-increasing speed through the remaining structure. Depending on which way the wreckage (and the 1 tonne steel block) falls, the marble may, in actual fact keep bouncing off the various bits all the way down and actually arrive on the ground after both the 1 tonne steel block AND the Eiffel Tower. It may be that the marble arrives at ground level a full ten seconds after the steel block, in bits.
Indeed. Even more schoolboy mechanics.

If the marble struck a girder surface with an appreciable horizontal component, it would indeed bounce back up to a degree (if it did not smithereen on impact), because the mass of the marble is insignicant wrt to the mass of the tower, thus the conservation of momentum would reverse the acceleration, and it then becomes a trajectory equation. A glancing impact would deflect it outward in the manner I described.
The 1 tonne block may also bounce back up however, since its mass is also relatively small in comparison with the mass of the tower. I would assume that the strength of the rivets holding the girder in place would play a major part here. If the rivets could withstand the impact (quite likely as we're talking about compression strength, not tensile strength), then the block would suffer at least considerable deceleration, possibly even be bounced back up too.

Mind you, at some point, all of the above will come to rest around the base of the tower, where it will test the integrity of the French concrete industry.
The effect is called impulse - and it ain't schoolboy mechanics unfortunately.
http://en.wikipedia.org/wiki/Impulse

Other things that affect the drop-off rate are shape and stability factors
Enjoy :D

http://en.wikipedia.org/wiki/External_ballistics

The last one will scare you if you aren't into maths but check the Bullet Drop bit
 
#20
roadster280 said:
rickshaw-major said:
The effect is called impulse - and it ain't schoolboy mechanics unfortunately.
http://en.wikipedia.org/wiki/Impulse
Well looking at that link, I can definitely say it was schoolboy mechanics at the school I went to. Basic calculus. Mind you, it's going back a while now!

IIRC (from 20+ years ago), it's to do with conservation of energy. The energy (in the form of the object's momentum) has to be dissipated somehow. It ends up being applied to the object in question in a direction opposite to the impact.

ISTR doing sums about individual railway wagons in a hump shunting yard being rolled down the hump at an angle of x degrees with a mass of y kg hitting a train of z kg. Then having to work out the power developed in the locomotive as it pulls the assembled train out of the yard.

Back to the tin and target. If you fired the rifle at the tin, would it make a thwack or a ding? A thwack, obviously. But if you moved the tin sufficiently far away, so the horizontal velocity had decayed, would it then make a thwack or a ding? A ding, naturally. So at what distance is the thwack/ding threshhold?

I knew there was a point to all this maths at school, but I couldnt see it at the time.
It was schoolboy when I was a schoolboy but my cousin (a Chemistry teacher who would, as an aside, get it :D ) tells me that this stuff isn't really taught any more :(

BTW - she is a she!
 

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