OpenEuphoria

Re: Calculating Drag

• Posted by Ben Logan <wbljr79 at HOTMAIL.COM> Feb 08, 2000
• 417 views

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

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