OT: Question regarding gravity

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Date: 09 Oct 2006 20:44:13
From: nawt2smart
Subject: OT: Question regarding gravity

Long time lurker and I know you guys/gals will be able to answer this
easy,

No I am not a trolling. I was talking to my dad on the phone tonight
and somehow the concept of gravity came up.

Scenario: I am shooting a high powered rifle at eye level directly
parallel to earth. The round is travelling at 3000 fps from the
barrel. Say 308 win. No wind, but air friction. This is a flat
ground area, say salt flats.

At the same exact time I drop a marble at eye level.

Which will hit first?

I said the marble because velocity throws the equation out of balance.
Thanks for the help!

Date: 10 Oct 2006 03:50:51
From: Sam Wormley
Subject: Re: OT: Question regarding gravity

Date: 10 Oct 2006 00:56:21
From: Brian Tung
Subject: Re: OT: Question regarding gravity

Sam Wormley wrote:
> They hit the ground at the same time... ignoring air friction all
> objects fall at the same rate. Flat is not required... works
> around the curvature of the Earth.

First of all, OP is explicitly *not* ignoring air friction. He wants it
taken into account. Secondly, what you say obviously cannot work around
the curvature of the Earth, or else satellites could not orbit. I know
you know this, so you must mean something other than what you wrote, but
I can't figure out what.

Taking into account air friction is difficult, especially with rifling.
My guess is that the marble might beat the bullet by just a little, but
I really don't know. Anyone else have any bright ideas?

--
Brian Tung <brian@isi.edu >
The Astronomy Corner at http://astro.isi.edu/
Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/
The PleiadAtlas Home Page at http://astro.isi.edu/pleiadatlas/
My Own Personal FAQ (SAA) at http://astro.isi.edu/reference/faq.html

Date: 10 Oct 2006 09:10:53
From: John Banister
Subject: Re: OT: Question regarding gravity

This is an old "gotcha" from the shooting world. If you take the problem
simply, i.e. the horizontal plane is flat and the bullet is fired perfectly
levelly, then there is only one force causing both to drop: gravity. And
gravity works equally on both so both hit the ground at the same time.

In high school physics we did an experiment to "prove" this: We had a
simple machine that dropped a ball bearing at the same time that it shot
another (via a spring) horizontally off of a table. Both hit the ground at
the same time.

However, if you think too much about this, you will miss the simple message.
For instance, any bulllet fired at 3000 fps will have some instablity in
yaw. This will cause the point of the bullet not to be in line with the
flight path for some of the time. During that time there will be a bit more
lift on one side of the bullet than the other, causing it to rise or fall
due to air pressure. If the initial yaw is upward (positive lift) the
bullet path will be slightly above horizontal, increasing the time of fall.

There are many other things which make this problem not so simple, but the
simple problem does indicate the counter-intuitivity (?) of the basic
physics.

BTW, rifle bullets are rarely fired horizontally. Normally, they are fired
so that they cross the line of sight a few yards downrange and remain above
the line of sight for a while before dropping below.

-John

"Brian Tung" <brian@isi.edu > wrote in message
news:egfjn5$30k$1@praesepe.isi.edu...
> Sam Wormley wrote:
>> They hit the ground at the same time... ignoring air friction all
>> objects fall at the same rate. Flat is not required... works
>> around the curvature of the Earth.
>
> First of all, OP is explicitly *not* ignoring air friction. He wants it
> taken into account. Secondly, what you say obviously cannot work around
> the curvature of the Earth, or else satellites could not orbit. I know
> you know this, so you must mean something other than what you wrote, but
> I can't figure out what.
>
> Taking into account air friction is difficult, especially with rifling.
> My guess is that the marble might beat the bullet by just a little, but
> I really don't know. Anyone else have any bright ideas?
>
> --
> Brian Tung <brian@isi.edu>
> The Astronomy Corner at http://astro.isi.edu/
> Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/
> The PleiadAtlas Home Page at http://astro.isi.edu/pleiadatlas/
> My Own Personal FAQ (SAA) at http://astro.isi.edu/reference/faq.html

Date: 11 Oct 2006 01:32:17
From: Sam Wormley
Subject: Re: OT: Question regarding gravity

Brian Tung wrote:
> Sam Wormley wrote:
>> They hit the ground at the same time... ignoring air friction all
>> objects fall at the same rate. Flat is not required... works
>> around the curvature of the Earth.
>
> First of all, OP is explicitly *not* ignoring air friction. He wants it
> taken into account. Secondly, what you say obviously cannot work around
> the curvature of the Earth, or else satellites could not orbit. I know
> you know this, so you must mean something other than what you wrote, but
> I can't figure out what.
>
> Taking into account air friction is difficult, especially with rifling.
> My guess is that the marble might beat the bullet by just a little, but
> I really don't know. Anyone else have any bright ideas?
>

Sorry--The point I wanted to make was both objects are subjected to
the same force of gravity and, taking away any atmosphere, they would
fall at the same rate. That is true even for objects in orbit to a
first approximation, but as Brian correctly points with horizontal
velocity great enough such that the curvature of the earth comes into
play, time-to-impacting the surface lengthens.

-Sam

Date: 10 Oct 2006 09:18:09
From: Shawn
Subject: Re: OT: Question regarding gravity

Date: 10 Oct 2006 07:52:36
From:
Subject: Re: OT: Question regarding gravity

nawt2smart wrote:
> Scenario: I am shooting a high powered rifle at eye level directly
> parallel to earth. The round is travelling at 3000 fps from the
> barrel. Say 308 win. No wind, but air friction. This is a flat
> ground area, say salt flats.
>
> At the same exact time I drop a marble at eye level.
>
> Which will hit first?

Both hit at the same time. Even when you add aerodynamic drag to the
equations. Even when you use the rotational-stability of the bullet to
keep the nose of the bullet above the plane of flight--this only ends
up contributing to drag. Even when you use nutation carve some latteral
distance due to aero and spin on the bullet.

The only thing that would make the bullet hit later is the curvature of
the earth over the path of the bullet (over the salt flats).

Date: 10 Oct 2006 15:07:53
From: Chris L Peterson
Subject: Re: OT: Question regarding gravity

On 10 2006 07:52:36 -0700, MitchAlsup@aol.com wrote:

>Both hit at the same time. Even when you add aerodynamic drag to the
>equations. Even when you use the rotational-stability of the bullet to
>keep the nose of the bullet above the plane of flight--this only ends
>up contributing to drag. Even when you use nutation carve some latteral
>distance due to aero and spin on the bullet.
>
>The only thing that would make the bullet hit later is the curvature of
>the earth over the path of the bullet (over the salt flats).

I agree if you consider the _average_ result over many trials. But in
any individual, real-world trial the two will not land at the same time
because the bullet will experience lift as its flight isn't perfectly
stable. The lift may be upwards or downwards, so it may either increase
or decrease the time it takes the bullet to hit the ground.

_________________________________________________

Chris L Peterson
Cloudbait Observatory
http://www.cloudbait.com

Date: 10 Oct 2006 14:47:26
From: Jim Klein
Subject: Re: OT: Question regarding gravity

Same time.

Sometimes it is caused by gravity, except in Guam.

In Guam there is no gravity, the Earth just Sucks there. :-)

It Sucked harder the longer I was stationed there. :-)

Jim

Date: 10 Oct 2006 09:33:20
From: Shawn
Subject: Re: OT: Question regarding gravity

Jim Klein wrote:
> Same time.
>
> Sometimes it is caused by gravity, except in Guam.
>
> In Guam there is no gravity, the Earth just Sucks there. :-)
>
> It Sucked harder the longer I was stationed there. :-)

LOL!
Had the same experience when I lived in Dallas for a year.

Shawn

Date:
From: Martin Brown
Subject: Re: OT: Question regarding gravity

Date: 10 Oct 2006 22:49:39
From: Al
Subject: Re: OT: Question regarding gravity

"Martin Brown" wrote
>
> My instinct is that the bullet will see ground effect forces from its
> own reflected shockwave when it gets near to the ground (provided that
> the surface is very smooth - like a salt flat) and so skim along on a
> cushion of air for a little bit longer. Since it is spin stabilised by
> rifling it shouldn't tumble until it finally touches something. The
> marble will drop like a stone.
>

I think I see what you're getting at but, by the same token, the bullet is
also "falling like a stone" from a certain frame of reference. The effect of
the world (and all its atmosphere) rushing past shouldn't change the fact
that that it is falling like a stone...

This link won't help, but it is on-topic ;-)

http://www.phys.unsw.edu.au/exploratorials/flash/projectiles/hunter.html

Al

Date: 10 Oct 2006 09:25:09
From: Greg Neill
Subject: Re: OT: Question regarding gravity

"Al" <null@null.com > wrote in message
news:452b96e9$0$22937$afc38c87@news.optusnet.com.au...
> "Martin Brown" wrote
> >
> > My instinct is that the bullet will see ground effect forces from its
> > own reflected shockwave when it gets near to the ground (provided that
> > the surface is very smooth - like a salt flat) and so skim along on a
> > cushion of air for a little bit longer. Since it is spin stabilised by
> > rifling it shouldn't tumble until it finally touches something. The
> > marble will drop like a stone.
> >
>
> I think I see what you're getting at but, by the same token, the bullet is
> also "falling like a stone" from a certain frame of reference. The effect
of
> the world (and all its atmosphere) rushing past shouldn't change the fact
> that that it is falling like a stone...
>
> This link won't help, but it is on-topic ;-)
>
> http://www.phys.unsw.edu.au/exploratorials/flash/projectiles/hunter.html

The usual high-school analysis of the horizontally
fired projectile versus the dropped one makes
certain simplifying assumptions, the primary one
being that the gravitational field is uniform
and vertical. It also assumes that the "playing
field" is flat and horizontal and of unlimited
extent (with respect to the experiment at least).

This leads to the conclusion that the horizontally
fired projectile will trace out a parabolic arc with
respect to the fixed horizontal ground surface, with
the vertical and horizontal components being entirely
independent. If these simplifying assumptions are not
made, the arc is instead a section of an elliptical
orbit, and the ground is a curved surface (section of
a sphere).

It thus becomes possible to fire a projectile
horizontally with sufficient velocity that it can
escape the Earth entirely, or go into an orbit that
would not strike the surface barring energy lost
due to air friction. The reality will, of course,
be something in between, with the projectile
traveling much further and longer than it would
in the simplified model.

Date: 10 Oct 2006 01:50:23
From: jeffery.m.thompson@gmail.com
Subject: Re: OT: Question regarding gravity

>From the frame of reference of the bullet, the marble or the eye at eye
level?

Brian Tung wrote:
> Sam Wormley wrote:
> > They hit the ground at the same time... ignoring air friction all
> > objects fall at the same rate. Flat is not required... works
> > around the curvature of the Earth.
>
> First of all, OP is explicitly *not* ignoring air friction. He wants it
> taken into account. Secondly, what you say obviously cannot work around
> the curvature of the Earth, or else satellites could not orbit. I know
> you know this, so you must mean something other than what you wrote, but
> I can't figure out what.
>
> Taking into account air friction is difficult, especially with rifling.
> My guess is that the marble might beat the bullet by just a little, but
> I really don't know. Anyone else have any bright ideas?
>
> --
> Brian Tung <brian@isi.edu>
> The Astronomy Corner at http://astro.isi.edu/
> Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/
> The PleiadAtlas Home Page at http://astro.isi.edu/pleiadatlas/
> My Own Personal FAQ (SAA) at http://astro.isi.edu/reference/faq.html

Date: 10 Oct 2006 15:37:32
From: Bob May
Subject: Re: Question regarding gravity

In the scenario, the marble hits first but not for the reason that you'd
suspect.
The thing is that you're shooting the bullet around a round object. As a
result, the bullet won't be hitting beside the marble bur rather at some
distance away around the round object. If you shot the bullet fast enough,
the bullet would never hit the round object bur rather just orbit it.
Of course, I haven't taken into consideration the atmosphere here but that
would only take and shorten the bullet's path length providing that it
doesn't provide any lift to the bullet.

--
Yeppie, Bush is such an idiot that He usually outwits
everybody else. How dumb!

Date: 10 Oct 2006 16:43:42
From: Brian Tung
Subject: Re: Question regarding gravity

Bob May wrote:
> The thing is that you're shooting the bullet around a round object. As a
> result, the bullet won't be hitting beside the marble bur rather at some
> distance away around the round object. If you shot the bullet fast enough,
> the bullet would never hit the round object bur rather just orbit it.
> Of course, I haven't taken into consideration the atmosphere here but that
> would only take and shorten the bullet's path length providing that it
> doesn't provide any lift to the bullet.

Again, the OP specifically wants air resistance to be taken into
account. One cannot assume that no lift will be provided to the bullet.
Even in an ideal experimental setup, I suspect there will be quite a
bit of variance, but as to what the distribution would be, I have no
good idea.

Of course, one does not have to drop the marble each time. I'd like to
think there wouldn't be that much variance in the marble's drop. :)

--
Brian Tung <brian@isi.edu >
The Astronomy Corner at http://astro.isi.edu/
Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/
The PleiadAtlas Home Page at http://astro.isi.edu/pleiadatlas/
My Own Personal FAQ (SAA) at http://astro.isi.edu/reference/faq.html

Date: 11 Oct 2006 00:22:07
From: Chris L Peterson
Subject: Re: Question regarding gravity

On Tue, 10 2006 16:43:42 -0700 (PDT), brian@isi.edu (Brian Tung)
wrote:

>Of course, one does not have to drop the marble each time. I'd like to
>think there wouldn't be that much variance in the marble's drop. :)

Since this is a "real world" question and not so much a purely
theoretical one, that may not be the case. It's actually really hard to
drop a marble consistently. You need to build some sort of automated
dropper, and presumably you want to make sure that you don't impart any
spin. After all, we may only be talking about millisecond differences
here.

While you probably don't need to drop the marble at the same time as you
shoot the bullet, you probably _do_ want to drop it many times and
average the results.

Other factors to consider in the real world: obviously any wind changes
will affect the result if you don't drop both together, but so will the
air temperature and pressure. These may even change for the bullet over
its long flight. Also, the aerodynamic profile the marble and the bullet
are different. You'd like them to be the same, but there's really no way
to make that so.

_________________________________________________

Chris L Peterson
Cloudbait Observatory
http://www.cloudbait.com

Date: 11 Oct 2006 16:32:35
From: Bob May
Subject: Re: Question regarding gravity

From my last paragraph, it is quite obvious that the only action by an
atmosphere would be to slow down the bullet along it's path and this means,
quite obviously, that the bullet will hit the surface closer to where it was
shot from, thus shortening the time of the travel. Please note that this
shortening of time doesn't mean that it hits before the marble but rather
that the time difference is just less.
Please also note that if air currents force the bullet off of it's natural
path, all bets are off.

--
Yeppie, Bush is such an idiot that He usually outwits
everybody else. How dumb!

Date: 11 Oct 2006 17:09:32
From: Brian Tung
Subject: Re: Question regarding gravity

Bob May wrote:
> From my last paragraph, it is quite obvious that the only action by an
> atmosphere would be to slow down the bullet along it's path and this means,
> quite obviously, that the bullet will hit the surface closer to where it was
> shot from, thus shortening the time of the travel. Please note that this
> shortening of time doesn't mean that it hits before the marble but rather
> that the time difference is just less.

Even assuming it's obvious that you meant that, it's not clear that
your reasoning is right. The bullet is not a sphere, and it is also
rotating. I don't agree that the things you say are "obvious" are in
fact obvious.

--
Brian Tung <brian@isi.edu >
The Astronomy Corner at http://astro.isi.edu/
Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/
The PleiadAtlas Home Page at http://astro.isi.edu/pleiadatlas/
My Own Personal FAQ (SAA) at http://astro.isi.edu/reference/faq.html

Date: 12 Oct 2006 20:32:10
From: Bob May
Subject: Re: Question regarding gravity

Brian, from my time at Fire Control B school, the only effects of a rotating
projectile is that the facing side of the round moves the round in the
direction that the round's surface is moving away from - basically if the
round is rotating so that the ground side of the round is moving to the
left, the round will be going to the right. This is assuming that the round
is still in the orientation that it was shot in. Since rounds often nutate
a bit as they go down the range, the motion will be an average to the axis
of the nutation. The energy for the sideways motion is taken from the
downrange energy for the most part. This motiion doesn't change the time of
impact from gravity.
I'll also note that when you put the effects of the air into any gravity
drop question like this, you then start running into the problem of the
feather vs. the iron ball in such a test. The one pound ball will fall
faster than the ten tons of feathers.

--
Yeppie, Bush is such an idiot that He usually outwits
everybody else. How dumb!

Date: 10 Oct 2006 13:30:28
From: Willie R. Meghar
Subject: Re: OT: Question regarding gravity

"nawt2smart" wrote:

>Scenario: I am shooting a high powered rifle at eye level directly
>parallel to earth. The round is travelling at 3000 fps from the
>barrel. Say 308 win. No wind, but air friction. This is a flat
>ground area, say salt flats.
>
>At the same exact time I drop a marble at eye level.
>
>Which will hit first?

1) The marble and bullet will each (initially) fall at the same rate.
Thus, if they both had to fall the same distance before encountering
the ground they would both hit at the same time.

2) But the 'flat' surface of the earth is curved away from the initial
(at the muzzle) instantaneous, straight line trajectory of the bullet.
This means (at a distance further from the muzzle) the bullet has
further to fall before reaching the ground.

3) This also means that the bullet's downward acceleration is slower
than the marble's through the earth's gravitational field (another way
of looking at the earth's surface curving away from the bullet's
initial path).

For most practical purposes, at typical small arms ranges, the effects
in the above two paragraphs would be quite small. it would be a
reasonable approximation, on reasonably level ground, to say that the
marble and the bullet would hit the ground at the same time; but if
one wanted to split hairs, it is the marble that would hit first.

Willie R. Meghar
Observational Notes at:
http://meghar.blogspot.com/

Date: 11 Oct 2006 11:33:05
From: Chris McMahan
Subject: Re: OT: Question regarding gravity

A good question.

If you discount the air resistance, then the two will hit the ground
at the same time since the initial vertical velocity of both is 0.

Taking air resistance into account, however, complicates the problem.

You have the stabilized spin, heavy mass, and aerodynamic shape of the
bullet the help it cut through the air. But relative to the marble, it
has to cut through a LOT more air.

You have a marble that offers little or no resistance in the short
distance (eye level) that it travels to hit the ground.

There has also been some discussions in other circles that the spin of
the bullet coming out of a rifle actually serves to provide a small
amound of lift to the round on exiting the barrel.

The density of the air might also be an issue.

Hmmm.... might be worth the standard "the solution is left as an
exercise to the student"...

- Chris

"nawt2smart" <nawt2smart@excite.com > writes:

> Long time lurker and I know you guys/gals will be able to answer this
> easy,
>
> No I am not a trolling. I was talking to my dad on the phone tonight
> and somehow the concept of gravity came up.
>
> Scenario: I am shooting a high powered rifle at eye level directly
> parallel to earth. The round is travelling at 3000 fps from the
> barrel. Say 308 win. No wind, but air friction. This is a flat
> ground area, say salt flats.
>
> At the same exact time I drop a marble at eye level.
>
> Which will hit first?
>
> I said the marble because velocity throws the equation out of balance.
> Thanks for the help!
>

--
(. .)
=ooO=(_)=Ooo=====================================
Chris McMahan

Date: 11 Oct 2006 08:05:01
From: moorthy
Subject: Re: OT: Question regarding gravity

nawt2smart wrote:
> Long time lurker and I know you guys/gals will be able to answer this
> easy,
>
> No I am not a trolling. I was talking to my dad on the phone tonight
> and somehow the concept of gravity came up.
>
> Scenario: I am shooting a high powered rifle at eye level directly
> parallel to earth. The round is travelling at 3000 fps from the
> barrel. Say 308 win. No wind, but air friction. This is a flat
> ground area, say salt flats.
>
> At the same exact time I drop a marble at eye level.
>
> Which will hit first?
>
> I said the marble because velocity throws the equation out of balance.
> Thanks for the help!

Let me be clear with your conditions:
1.your are considering air friction effects
2.your are assuming a flat surface(it means the distance travelled by
the bullet is assumed to be small ,so the earth's curvature doesnot
come in to picture)

under this conditions,we want to know the relative time ,when they hit
the ground.
Since both are thrown from the same point(i.e same distance from the
ground).the distance travelled by both the bodies in vertical axis will
be same.This is turn is nothing but the relative velocity or relative
acceleration.
since both starts with 'zero' initial velocity in vertical
direction(bullet initial velocity is in horizontal direction).they both
should arrive at the same time due to gravity effect.
But considering the air resistance,although the shape of the object
plays crucial role,the mass plays siginificant role(not much of
scientific explaniation ,more of intution).
So mass should dictate the time.

Date: 11 Oct 2006 19:05:43
From: Stuart Chapman
Subject: Re: OT: Question regarding gravity

nawt2smart wrote:
> Long time lurker and I know you guys/gals will be able to answer this
> easy,
>
> No I am not a trolling. I was talking to my dad on the phone tonight
> and somehow the concept of gravity came up.
>
> Scenario: I am shooting a high powered rifle at eye level directly
> parallel to earth. The round is travelling at 3000 fps from the
> barrel. Say 308 win. No wind, but air friction. This is a flat
> ground area, say salt flats.
>
> At the same exact time I drop a marble at eye level.
>
> Which will hit first?
>
> I said the marble because velocity throws the equation out of balance.
> Thanks for the help!
>

I don't know what effect air friction has on a rifle bullet v. a marble.
Assuming the effect is the same, they will hit the ground at the same
time. Most people imagine this problem in a 'side-on' view. Try
imagining the scenario from a 'behind the shooter' viewpoint. That can
clarify things.

Its possible that air resistance to a rifle bullet generates lift,
although I can't imagine the mechanism. Dimples on a golf ball, together
with its backspin, generate lift.

Stupot

Date: 11 Oct 2006 11:39:43
From: nawt2smart
Subject: Re: OT: Question regarding gravity

Date: 13 Oct 2006 16:39:25
From: Llanzlan Klazmon the 15th
Subject: Re: OT: Question regarding gravity

"nawt2smart" <nawt2smart@excite.com > wrote in news:1160591983.238426.306770
@i3g2000cwc.googlegroups.com:

>
> nawt2smart wrote:
>> Long time lurker and I know you guys/gals will be able to answer this
>> easy,
>>
>> No I am not a trolling. I was talking to my dad on the phone tonight
>> and somehow the concept of gravity came up.
>>
>> Scenario: I am shooting a high powered rifle at eye level directly
>> parallel to earth. The round is travelling at 3000 fps from the
>> barrel. Say 308 win. No wind, but air friction. This is a flat
>> ground area, say salt flats.
>>
>> At the same exact time I drop a marble at eye level.
>>
>> Which will hit first?
>>
>> I said the marble because velocity throws the equation out of balance.
>> Thanks for the help!
>
> Thanks all for the replies. It seems the air friction and aerodynamics
> of the projectile come into play. Maybe I can forward this to Myth
> busters so they can try it out. :)
>
> Again, thanks for the time.
>
>

In a lot of these cases, the answer depends on the assumptions made. When
you start throwing in other variables like aerodynamic lift, wind etc
things get tricky depending on how much accuracy you need. In the real
case, nature itself automatically takes all factors into account. That is
why experiment always trumps theory ;-). It reminds me of the old physics
joke about assuming a spherical cow.

Klazmon.