1. Calculating Drag
Hello All,
Does any one know how to calculate drag for a projectile.
I know there is coeficiant and the viscosity of air. I think?
Any equation that go along with this. Any help would be great.
roachd_76
2. Re: Calculating Drag
Hi, David.
I'm not sure whether or not you need to know the viscosity of air, but maybe
these relations will help:
For low speeds where laminar flow occurs:
f = kv, that is, the force of air resistance is roughly proportional
to the speed.
For speeds above laminar flow, but below supersonic speeds:
f = k(v^2), that is, the force of air resistance is roughly
proportional to the square of the speed.
As v approaches the speed of sound:
f = k(v^3), that is, the force of air resistance is (very) roughly
proportional to the cube of the speed.
In the above proportions, k is the constant of proportionality and varies
for each body. I assume that it also depends on such things as air
temperature (which would be a factor in determining viscosity, I would
think), humidity, atmospheric pressure, etc.
If I was going to use the above to calculate the position of a projectile,
I'd probably use f=k(v^2) unless the projectile broke the sound barrier. As
I understand it, laminar flow occurs only at very low speeds and probably
wouldn't be worth considering.
Having said that and then trying to derive the equations which describe the
components of velocity of a projectile, the equations are much simpler for
f=kv. (Assuming I've done everything right!)
v_x = vcos(theta)/(1-(kt/m))
v_y = (vsin(theta)-gt)/(1+(kt/m))
where, v_x is the x-component of velocity, v_y is the y-component, v is
the initial velocity, and theta is the angle of projection.
As for f=kv^2, if I did everything correctly, you should be able to solve
the following two equations for v_x and v_y to obtain the appropriate
equations. I've run out of time, but I'll try later.
v_x = k*v_x*t*sqrt((v_x)^2+(v_y)^2)/m + vcos(theta)
v_y = -k*v_y*t*sqrt((v_x)^2+(v_y)^2)/m - gt + vsin(theta)
(m is the mass of the projectile)
I hope this helps,
Ben
>From: David Roach <roachd_76 at YAHOO.COM>
>Reply-To: Euphoria Programming for MS-DOS <EUPHORIA at LISTSERV.MUOHIO.EDU>
>To: EUPHORIA at LISTSERV.MUOHIO.EDU
>Subject: Calculating Drag
>Date: Tue, 8 Feb 2000 04:40:19 -0500
>
>Hello All,
>
>Does any one know how to calculate drag for a projectile.
>I know there is coeficiant and the viscosity of air. I think?
>Any equation that go along with this. Any help would be great.
>
>roachd_76
______________________________________________________
Get Your Private, Free Email at http://www.hotmail.com
3. Re: Calculating Drag
Hi Ben,
I looked on the internet for about 2 hours and couldn't find a thing.
I guess I should of been more specific. I am dealing with the speed
of bullets. So we are definetly talking about over the speed of sound.
But then again in flight they slow down to below the speed of sound.
But I don't believe I will be dealing with them when they get to that
point. What does k stand for? Would that be the coeficient of the bullet?
F is the negative force on the bullet right? Over the speed of sound
does the bullet slow down at vx/vx^3 or something like that? God
wish I had of stayed in college and finished physics now. Know any
good web sites? I apreciate your help.
roachd_7 at yahoo.com
----- Original Message -----
From: Ben Logan <wbljr79 at HOTMAIL.COM>
To: <EUPHORIA at LISTSERV.MUOHIO.EDU>
Sent: Tuesday, February 08, 2000 3:12 AM
Subject: Re: Calculating Drag
> Hi, David.
>
> I'm not sure whether or not you need to know the viscosity of air, but
maybe
> these relations will help:
>
> For low speeds where laminar flow occurs:
> f = kv, that is, the force of air resistance is roughly
proportional
> to the speed.
>
> For speeds above laminar flow, but below supersonic speeds:
> f = k(v^2), that is, the force of air resistance is roughly
> proportional to the square of the speed.
>
> As v approaches the speed of sound:
> f = k(v^3), that is, the force of air resistance is (very) roughly
> proportional to the cube of the speed.
>
> In the above proportions, k is the constant of proportionality and varies
> for each body. I assume that it also depends on such things as air
> temperature (which would be a factor in determining viscosity, I would
> think), humidity, atmospheric pressure, etc.
>
> If I was going to use the above to calculate the position of a projectile,
> I'd probably use f=k(v^2) unless the projectile broke the sound barrier.
As
> I understand it, laminar flow occurs only at very low speeds and probably
> wouldn't be worth considering.
>
> Having said that and then trying to derive the equations which describe
the
> components of velocity of a projectile, the equations are much simpler for
> f=kv. (Assuming I've done everything right!)
>
> v_x = vcos(theta)/(1-(kt/m))
> v_y = (vsin(theta)-gt)/(1+(kt/m))
> where, v_x is the x-component of velocity, v_y is the y-component, v is
> the initial velocity, and theta is the angle of projection.
>
> As for f=kv^2, if I did everything correctly, you should be able to solve
> the following two equations for v_x and v_y to obtain the appropriate
> equations. I've run out of time, but I'll try later.
>
> v_x = k*v_x*t*sqrt((v_x)^2+(v_y)^2)/m + vcos(theta)
> v_y = -k*v_y*t*sqrt((v_x)^2+(v_y)^2)/m - gt + vsin(theta)
>
> (m is the mass of the projectile)
>
> I hope this helps,
>
> Ben
>
> >From: David Roach <roachd_76 at YAHOO.COM>
> >Reply-To: Euphoria Programming for MS-DOS <EUPHORIA at LISTSERV.MUOHIO.EDU>
> >To: EUPHORIA at LISTSERV.MUOHIO.EDU
> >Subject: Calculating Drag
> >Date: Tue, 8 Feb 2000 04:40:19 -0500
> >
> >Hello All,
> >
> >Does any one know how to calculate drag for a projectile.
> >I know there is coeficiant and the viscosity of air. I think?
> >Any equation that go along with this. Any help would be great.
> >
> >roachd_76
>
> ______________________________________________________
> Get Your Private, Free Email at http://www.hotmail.com
__________________________________________________
Do You Yahoo!?
Talk to your friends online with Yahoo! Messenger.
http://im.yahoo.com
4. Re: Calculating Drag
----- Original Message -----
From: David Roach <roachd_76 at YAHOO.COM>
To: <EUPHORIA at LISTSERV.MUOHIO.EDU>
Sent: Tuesday, February 08, 2000 7:48 AM
Subject: Re: Calculating Drag
> Hi Ben,
> I looked on the internet for about 2 hours and couldn't find a thing.
> I guess I should of been more specific. I am dealing with the speed
> of bullets. So we are definetly talking about over the speed of sound.
> But then again in flight they slow down to below the speed of sound.
> But I don't believe I will be dealing with them when they get to that
> point. What does k stand for? Would that be the coeficient of the bullet?
> F is the negative force on the bullet right? Over the speed of sound
> does the bullet slow down at vx/vx^3 or something like that? God
> wish I had of stayed in college and finished physics now. Know any
> good web sites? I apreciate your help.
http://www.dexadine.com/download.htm
This is a ballistics plotting program - draws graphs, taking into account
temp, barometric pressure, humidity & altitude (density of atmosphere),
bullet shapes, etc.
This is a demo, but you might learn from it, or use it to compare flight
paths. (draws nice graphs and breaks out velocity/height into spreadsheet
form)
Regards,
Irv
5. Re: Calculating Drag
On Tue, 8 Feb 2000 04:40:19 -0500, David Roach <roachd_76 at YAHOO.COM> wrote:
>Hello All,
>
>Does any one know how to calculate drag for a projectile.
>I know there is coeficiant and the viscosity of air. I think?
>Any equation that go along with this. Any help would be great.
>
>roachd_76
Take a look at this URL. It appears to be very complete with both
software and theoretical information.
http://www.snipercountry.com/ballistics/
Everett L.(Rett) Williams
rett at gvtc.com
6. Re: Calculating Drag
----- Original Message -----
From: David Roach <roachd_76 at YAHOO.COM>
To: <EUPHORIA at LISTSERV.MUOHIO.EDU>
Sent: Tuesday, February 08, 2000 6:48 AM
Subject: Re: Calculating Drag
> I am dealing with the speed
> of bullets. So we are definetly talking about over the speed of sound.
Not all bullets travel at supersonic speeds, this is why a silencer is much
more effective on a pistol than a rifle, the pistol doesn't keep the
expanding gasses behind the bullet long enough to push it fast enough, basic
physics.
Kat
7. Re: Calculating Drag
Hi,
k is a coefficient which varies for differenct objects. I don't know how
you could calculate it...you'll probably need to come up with an arbitrary
number that causes it to 'look good'. F is the force of air resistance
which tends to slow the bullet. It always acts tangent to the instantaneous
velocity.
Since you're bullet is traveling over the speed of sound, I would use
f=kv^3. However, I'm not sure how to calculate the position of the bullet
under those circumstances. I don't know of any web resources, but if you
find anything, I'd like to know as well.
Regards,
Ben
>From: David Roach <roachd_76 at YAHOO.COM>
>Reply-To: Euphoria Programming for MS-DOS <EUPHORIA at LISTSERV.MUOHIO.EDU>
>To: EUPHORIA at LISTSERV.MUOHIO.EDU
>Subject: Re: Calculating Drag
>Date: Tue, 8 Feb 2000 03:48:37 -0900
>
>Hi Ben,
>I looked on the internet for about 2 hours and couldn't find a thing.
>I guess I should of been more specific. I am dealing with the speed
>of bullets. So we are definetly talking about over the speed of sound.
>But then again in flight they slow down to below the speed of sound.
>But I don't believe I will be dealing with them when they get to that
>point. What does k stand for? Would that be the coeficient of the bullet?
>F is the negative force on the bullet right? Over the speed of sound
>does the bullet slow down at vx/vx^3 or something like that? God
>wish I had of stayed in college and finished physics now. Know any
>good web sites? I apreciate your help.
>
>roachd_7 at yahoo.com
______________________________________________________
Get Your Private, Free Email at http://www.hotmail.com
8. Re: Calculating Drag
Correct. But the majority of bullets do. The speed of sound is 1117 f/s
roughly.
So even a lot of pistols get there.
----- Original Message -----
From: Kat <gertie at ZEBRA.NET>
To: <EUPHORIA at LISTSERV.MUOHIO.EDU>
Sent: Tuesday, February 08, 2000 10:08 AM
Subject: Re: Calculating Drag
> ----- Original Message -----
> From: David Roach <roachd_76 at YAHOO.COM>
> To: <EUPHORIA at LISTSERV.MUOHIO.EDU>
> Sent: Tuesday, February 08, 2000 6:48 AM
> Subject: Re: Calculating Drag
>
>
> > I am dealing with the speed
> > of bullets. So we are definetly talking about over the speed of sound.
>
> Not all bullets travel at supersonic speeds, this is why a silencer is
much
> more effective on a pistol than a rifle, the pistol doesn't keep the
> expanding gasses behind the bullet long enough to push it fast enough,
basic
> physics.
>
> Kat
__________________________________________________
Do You Yahoo!?
Talk to your friends online with Yahoo! Messenger.
http://im.yahoo.com
