| Topic: |
Science > Physics |
| User: |
"Paul Ciszek" |
| Date: |
09 Feb 2005 03:36:43 PM |
| Object: |
Question about Physics of Bullets |
I teach a freshman physics recitation/lab class, and
one of my students came to me with an extracurricular
quesiton: He wanted to know if there was an equation
that would allow him to calculate "drop" for different
shooting distance, bullet mass, muzzle velocity, etc.
We broke it down into the following sub-problems:
1) Is there an empirical equation to describe how a
bullet slows down over time due to air resistance?
2) What rules govern how a bullet "drops" over time?
I know that in a vacuum, you just figure how long
it takes the bullet to travel horizontally to the
target and use freefall equations to calculate the
drop, but I doubt that vertical and horizontal
motion are completely independent when there is
air resistance involved and the horizontal velocity
is so large.
He has some velocity and drop data for certain distances,
so we figure if we can find the equations they are
supposed to obey, we can fit the parameters to the data.
I tried finding a theoretical answer for (1) assuming that
air resistance is proportional to the square of speed, and
I get Vf = Vi / (1+Vi*k*t/m) where k is the constant in the
equation drag = k * V^2, m is the mass of the bullet, and
Vi and Vf are initial and final velocity. I have no idea
if this is anywhere close to what happens in reality,
though.
--
Please reply to: | "When the press is free and every man
pciszek at panix dot com | able to read, all is safe."
Autoreply has been disabled | --Thomas Jefferson
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| User: "willisA40" |
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| Title: Re: Question about Physics of Bullets |
09 Feb 2005 06:27:15 PM |
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"Paul Ciszek" <pciszek@REVERSE_THIS_moc.xinap> wrote in message
news:cudvpb$t95$1@reader2.panix.com...
I teach a freshman physics recitation/lab class, and
one of my students came to me with an extracurricular
quesiton: He wanted to know if there was an equation
that would allow him to calculate "drop" for different
shooting distance, bullet mass, muzzle velocity, etc.
We broke it down into the following sub-problems:
1) Is there an empirical equation to describe how a
bullet slows down over time due to air resistance?
time is not a good thing to relate it to, should be velocity.
2) What rules govern how a bullet "drops" over time?
I know that in a vacuum, you just figure how long
it takes the bullet to travel horizontally to the
target and use freefall equations to calculate the
drop,
yes
but I doubt that vertical and horizontal
motion are completely independent
that is the function you are looking for.
when there is
air resistance involved and the horizontal velocity
is so large.
He has some velocity and drop data for certain distances,
so we figure if we can find the equations they are
supposed to obey, we can fit the parameters to the data.
I tried finding a theoretical answer for (1) assuming that
air resistance is proportional to the square of speed, and
I get Vf = Vi / (1+Vi*k*t/m) where k is the constant in the
equation drag = k * V^2, m is the mass of the bullet, and
Vi and Vf are initial and final velocity. I have no idea
if this is anywhere close to what happens in reality,
though.
This is a typical problem in Dynamics.
--
Please reply to: | "When the press is free and every man
pciszek at panix dot com | able to read, all is safe."
Autoreply has been disabled | --Thomas Jefferson
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| User: "Philip Holman" |
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| Title: Re: Question about Physics of Bullets |
09 Feb 2005 06:52:25 PM |
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"Paul Ciszek" <pciszek@REVERSE_THIS_moc.xinap> wrote in message
news:cudvpb$t95$1@reader2.panix.com...
I teach a freshman physics recitation/lab class, and
one of my students came to me with an extracurricular
quesiton: He wanted to know if there was an equation
that would allow him to calculate "drop" for different
shooting distance, bullet mass, muzzle velocity, etc.
We broke it down into the following sub-problems:
1) Is there an empirical equation to describe how a
bullet slows down over time due to air resistance?
2) What rules govern how a bullet "drops" over time?
I know that in a vacuum, you just figure how long
it takes the bullet to travel horizontally to the
target and use freefall equations to calculate the
drop, but I doubt that vertical and horizontal
motion are completely independent when there is
air resistance involved and the horizontal velocity
is so large.
He has some velocity and drop data for certain distances,
so we figure if we can find the equations they are
supposed to obey, we can fit the parameters to the data.
I tried finding a theoretical answer for (1) assuming that
air resistance is proportional to the square of speed, and
I get Vf = Vi / (1+Vi*k*t/m) where k is the constant in the
equation drag = k * V^2, m is the mass of the bullet, and
Vi and Vf are initial and final velocity. I have no idea
if this is anywhere close to what happens in reality,
though.
There is no closed form solution to this problem. An excel step program
can be created using both the acceleration due to gravity in the
vertical direction and drag per 1/2*Cd*Rho*V^2*A along the line of
trajectory. For vertical and horizontal drag/decelerations Vy and Vx are
proportional to V*Vy and V*Vx and not Vy^2 or Vx^2. For a bullet, the
steps could be set at .01 seconds or smaller. The program will
recalculate a new direction after every step.
Phil H
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| User: "Androcles Androcles@ MyPlace.org" |
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| Title: Re: Question about Physics of Bullets |
09 Feb 2005 06:35:29 PM |
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"Paul Ciszek" <pciszek@REVERSE_THIS_moc.xinap> wrote in message
news:cudvpb$t95$1@reader2.panix.com...
I teach a freshman physics recitation/lab class, and
one of my students came to me with an extracurricular
quesiton: He wanted to know if there was an equation
that would allow him to calculate "drop" for different
shooting distance, bullet mass, muzzle velocity, etc.
We broke it down into the following sub-problems:
1) Is there an empirical equation to describe how a
bullet slows down over time due to air resistance?
No. A musket ball has a compeletely different shape to a pointed
rifle bullet or a snub nose, and lacks spin.
For this reason aircraft shapes are tested in wind tunnels.
2) What rules govern how a bullet "drops" over time?
The same rule, whether it fall out of the chamber onto the ground
or is fired through the barrel. The musket ball or bullet will still
fall the same
height in the same time as Newton's apple
( Unless you wish to consider curvature of the earth or the "lift" from
aerodynamic shape, i.e. the angle of attack, but neither are really
applicable
to a rifle bullet).
I know that in a vacuum, you just figure how long
it takes the bullet to travel horizontally to the
target and use freefall equations to calculate the
drop,
Correct.
but I doubt that vertical and horizontal
motion are completely independent when there is
air resistance involved and the horizontal velocity
is so large.
The horizontal velocity is totally independent of the vertical
acceleration.
He has some velocity and drop data for certain distances,
so we figure if we can find the equations they are
supposed to obey, we can fit the parameters to the data.
I tried finding a theoretical answer for (1) assuming that
air resistance is proportional to the square of speed, and
I get Vf = Vi / (1+Vi*k*t/m) where k is the constant in the
equation drag = k * V^2, m is the mass of the bullet, and
Vi and Vf are initial and final velocity. I have no idea
if this is anywhere close to what happens in reality,
though.
Shape is the controlling factor when considering air resistance.
Androcles.
--
Please reply to: | "When the press is free and every man
pciszek at panix dot com | able to read, all is safe."
Autoreply has been disabled | --Thomas Jefferson
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| User: "Uncle Al" |
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| Title: Re: Question about Physics of Bullets |
09 Feb 2005 07:42:10 PM |
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Androcles wrote:
[snip crap]
Shape is the controlling factor when considering air resistance.
Androcles.
Hopeless idiot. Tell it to a golf ball pocked or smooth. Tell it to
the Magnus effect. Look up ballistics coefficients vs. bullet
velocity - wadcutter, hollow point, round nose, ogive... all the same
if subsonic. Winglets and canards on aircraft.
As for supersonic, your basic cheap jacketed rifle bullet has a
purposely crappy pointy nose to lubricate its way through the air with
a boundary shock layer. A marksman/sniper round is solid alloy with a
precision machined perfect point tip. Uncle Al has a friend can pop
you at 1000 yards no sweat. He loads his own.
Tell it to submarines and torpedoes using Polyox, Sharkskin, bubble
curtains, and cavitation to control the boundary layer.
Idiot.
<http://www.google.com/search?q=Androcles+fumble+site%3Ausers.pandora.be>
<http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/Gibberish.html>
Spewing psychotic idiot troll.
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf
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| User: "Androcles Androcles@ MyPlace.org" |
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| Title: Re: Question about Physics of Bullets |
09 Feb 2005 11:03:13 PM |
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"Uncle Al" <UncleAl0@hate.spam.net> wrote in message
news:420ABBF2.65781F6@hate.spam.net...
Androcles wrote:
[snip crap]
Shape is the controlling factor when considering air resistance.
Androcles.
Hopeless idiot. Tell it to a golf ball pocked or smooth.
Hopeless imbecile. What the ***** do you think the dimples are for?
Is winter still at apogee, moron?
Androcles.
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| User: "Uncle Al" |
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| Title: Re: Question about Physics of Bullets |
10 Feb 2005 10:15:36 AM |
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Androcles wrote:
"Uncle Al" <UncleAl0@hate.spam.net> wrote in message
news:420ABBF2.65781F6@hate.spam.net...
Androcles wrote:
[snip crap]
Shape is the controlling factor when considering air resistance.
Androcles.
Hopeless idiot. Tell it to a golf ball pocked or smooth.
Hopeless imbecile. What the ***** do you think the dimples are for?
Shape is the controlling factor when considering air resistance.
Androcles.
Hopeless imbecile. What the ***** do you think the dimples are for?
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf
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| User: "Gregory L. Hansen" |
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| Title: Re: Question about Physics of Bullets |
09 Feb 2005 08:00:53 PM |
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In article <cudvpb$t95$1@reader2.panix.com>,
Paul Ciszek <pciszek@REVERSE_THIS_moc.xinap> wrote:
I teach a freshman physics recitation/lab class, and
one of my students came to me with an extracurricular
quesiton: He wanted to know if there was an equation
that would allow him to calculate "drop" for different
shooting distance, bullet mass, muzzle velocity, etc.
We broke it down into the following sub-problems:
1) Is there an empirical equation to describe how a
bullet slows down over time due to air resistance?
2) What rules govern how a bullet "drops" over time?
I know that in a vacuum, you just figure how long
it takes the bullet to travel horizontally to the
target and use freefall equations to calculate the
drop, but I doubt that vertical and horizontal
motion are completely independent when there is
air resistance involved and the horizontal velocity
is so large.
He has some velocity and drop data for certain distances,
so we figure if we can find the equations they are
supposed to obey, we can fit the parameters to the data.
I tried finding a theoretical answer for (1) assuming that
air resistance is proportional to the square of speed, and
I get Vf = Vi / (1+Vi*k*t/m) where k is the constant in the
equation drag = k * V^2, m is the mass of the bullet, and
Vi and Vf are initial and final velocity. I have no idea
if this is anywhere close to what happens in reality,
though.
One confounding factor, I have no idea what kind of effect it would have
in real life, is that the bullet, at least at longer ranges, won't point
in the direction of motion. The bullet drops, but the direction it points
is (approximately) constant because it spins. That doesn't just change
the drag, it might provide lift.
--
"Outside the camp you shall have a place set aside to be used as a
latrine. You shall keep a trowel in your equipment and with it, when you
go outside to ease nature, you shall first dig a hole and afterward cover
up your excrement." -- Deuteronomy 23:13-14
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| User: "" |
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| Title: Re: Question about Physics of Bullets |
09 Feb 2005 04:48:56 PM |
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Paul Ciszek <pciszek@reverse_this_moc.xinap> wrote:
I teach a freshman physics recitation/lab class, and
one of my students came to me with an extracurricular
quesiton: He wanted to know if there was an equation
that would allow him to calculate "drop" for different
shooting distance, bullet mass, muzzle velocity, etc.
We broke it down into the following sub-problems:
1) Is there an empirical equation to describe how a
bullet slows down over time due to air resistance?
2) What rules govern how a bullet "drops" over time?
I know that in a vacuum, you just figure how long
it takes the bullet to travel horizontally to the
target and use freefall equations to calculate the
drop, but I doubt that vertical and horizontal
motion are completely independent when there is
air resistance involved and the horizontal velocity
is so large.
He has some velocity and drop data for certain distances,
so we figure if we can find the equations they are
supposed to obey, we can fit the parameters to the data.
I tried finding a theoretical answer for (1) assuming that
air resistance is proportional to the square of speed, and
I get Vf = Vi / (1+Vi*k*t/m) where k is the constant in the
equation drag = k * V^2, m is the mass of the bullet, and
Vi and Vf are initial and final velocity. I have no idea
if this is anywhere close to what happens in reality,
though.
--
Please reply to: | "When the press is free and every man
pciszek at panix dot com | able to read, all is safe."
Autoreply has been disabled | --Thomas Jefferson
Lots of empirical equations around since the topic has been studied
since the invention of artillery.
Most of them you will find to be proprietary.
There are many commercial programs around for small arms.
You will need the ballistic coefficient of the bullet which is basically
a measure of effective drag.
There is free program source of unknown quality here:
http://www.programmersheaven.com/zone3/cat414/16058.htm
--
Jim Pennino
Remove -spam-sux to reply.
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| User: "John T Lowry" |
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| Title: Re: Question about Physics of Bullets |
10 Feb 2005 07:52:57 AM |
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<jimp@specsol-spam-sux.com> wrote in message
news:cue40o$3nt$1@mail.specsol.com...
Paul Ciszek <pciszek@reverse_this_moc.xinap> wrote:
I teach a freshman physics recitation/lab class, and
one of my students came to me with an extracurricular
quesiton: He wanted to know if there was an equation
that would allow him to calculate "drop" for different
shooting distance, bullet mass, muzzle velocity, etc.
We broke it down into the following sub-problems:
1) Is there an empirical equation to describe how a
bullet slows down over time due to air resistance?
2) What rules govern how a bullet "drops" over time?
I know that in a vacuum, you just figure how long
it takes the bullet to travel horizontally to the
target and use freefall equations to calculate the
drop, but I doubt that vertical and horizontal
motion are completely independent when there is
air resistance involved and the horizontal velocity
is so large.
He has some velocity and drop data for certain distances,
so we figure if we can find the equations they are
supposed to obey, we can fit the parameters to the data.
I tried finding a theoretical answer for (1) assuming that
air resistance is proportional to the square of speed, and
I get Vf = Vi / (1+Vi*k*t/m) where k is the constant in the
equation drag = k * V^2, m is the mass of the bullet, and
Vi and Vf are initial and final velocity. I have no idea
if this is anywhere close to what happens in reality,
though.
--
Please reply to: | "When the press is free and every
man
pciszek at panix dot com | able to read, all is safe."
Autoreply has been disabled | --Thomas Jefferson
I suggest you Google "exterior ballistics." Here 'exterior' means 'after
the bullet leaves the barrel.' The major problem is the drag function.
It's coefficients depend on bullet velocity (and the particular shape of
the bullet and several other items.). Therefore a numerical integration
is needed to solve the equations of motion even if done without regards
to rotational motion.
John Lowry
Flight Physics
(former member of Texas State Rifle Team and U.S. Navy Rifle Team)
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| User: "Andy Resnick" |
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| Title: Re: Question about Physics of Bullets |
10 Feb 2005 07:40:37 AM |
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Paul Ciszek wrote:
I teach a freshman physics recitation/lab class, and
one of my students came to me with an extracurricular
quesiton: He wanted to know if there was an equation
that would allow him to calculate "drop" for different
shooting distance, bullet mass, muzzle velocity, etc.
We broke it down into the following sub-problems:
My NRA buddy (also physicist, also has a concealed carry permit...) and
I spent the better part of a morning once discussing this exact
question. It's about as far from simple as you can get. Here's a few
of the complications:
Coefficient of drag (I think a few others noted this point). The bottom
line here is don't believe what the advertisements say.
Spin rate. Bullets also tumble slightly.
Bullet shape- bullets slightly deform upon firing, based on their
constuction.
Weather conditions- wind.
Accuracy: the goal is to predict a target diameter of a couple of inches
over many hundreds of yards.
He had a few of the shooter-enthusiast magazines with semi-rigorous
measurements made for different types of rounds and calibers, the main
result was that the fudge factor dominated any of the rational terms.
In the end, people calibrate their sight empirically. I believe
artillery gunners and the like use trajectories of previous rounds to
make firing corrections to the current round.
We also discussed penetration depth, and that's even more hopeless.
--
Andrew Resnick, Ph.D.
Department of Physiology and Biophysics
CWRU School of Medicine
tanspose 'op' for mail
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