Acceleration due to air resistance?

[evilmigit14]

a friend of mine asked if i could help him work out some equations for a (fairly) long range projectile, to go no farther than 2 miles or so. i have everything reasonably worked out except for acceleration due to air resistance. I'm using the equation from https://www.physicsforums.com/showthread.php?t=9066" thread to calculade Fd, and Cd=.295, rho=1.22752kg/m^3, A=pi.2^2m^2, v=240m/s, firing an object with a mass of .23kg. (Cd and rho both came from the Nasa website) I did the calculations and got an estimated acceleration of about (-)5698 m/s^2, which obviously cannot be right.

I was also wondering if there is any way to get a more accurate velocity by factoring in acceleration of gravity and air resistance. I'd assume it'll take some nasty algebra/calculus, but i can't figure it out on my own.

any help is greatly appreciated.

 

[AlephZero]

Area = 4pi square meters and a mass of only 0.23 kg? That sounds pretty much like a 2 meter diameter balloon to me.

If you tried moving something as big and light as that at 240 m/s (mach 0.7), the deceleration would indeed be large.

 

[SGT]

Area = 4pi square meters and a mass of only 0.23 kg? That sounds pretty much like a 2 meter diameter balloon to me.

If you tried moving something as big and light as that at 240 m/s (mach 0.7), the deceleration would indeed be large.

I think the area is 0.04pi m^2. Still very large. A projectile with a 20 cm diameter with a mass of only 0.23 kg can´t fly at 240 m/s.

 

[denverdoc]

Its not a wieldy problem, first Cd is not a constant at all but varies with velocity in a complex fashion, making this impossible to find an exact closed form solution. However, you could approximate a soln using a fixed Cd and initial V that's only subject to drag and gravity. But check the diameter, this is as pointed out much too low a ballistic coefficient to go anywhere due to whiffle ball effect.