There are times when I've wanted to calculate drag through the air for a variety of reasons. Most recently I wanted to calculate how much force a parachute would be subjected to in the event of a high speed deployment. The formula for calculating drag is fairly simple:
Fd = .5 * rho * V^2 * Cd * Af
Where:
Fd = Drag Force in Pounds
rho = Air Density in Slugs per cubic foot (See note 1)
V^2 = Velocity * Velocity in feet per second
Cd = Drag Coefficient (See note 2)
Af = Frontal Area in square feet
Note 1: Air Density is usually given in pounds per cubic foot, to convert pounds to slugs multiply pounds by .0310809502.
Here's a link to an air density calculator http://www.denysschen.com/catalogue/density.asp
Note 2: Drag Coefficient must be calculated or derived experimentally. For sub sonic flow, here are a few example Cd's:
Flat Sheet Circular Parachute: .75
Round Disk: 1.12
Model Rocket: .75
High Performance Rocket: .35 to .55
For example, I wanted to know the approximate force a 48" diameter drogue chute would be subjected to if it deployed at a speed of 500 feet per second (340.9 mph) at an attitude of 25,000'. First I used the calculator from the link above to calculate the air density at 25,000' at a temperature of 0 degrees. The value was 0.0318 pounds per cubic foot. To convert to slugs per cubic foot, multiply by .0310809502 to get .000988374 slugs per cubic foot. Now to the formula.
Fd = .5 * .000988374 * 250,000 * .75 * 12.56
Fd = 1,163.81 pounds force
So at 500 fps I'd have over 1,100 pounds of force acting on the chute and recovery system.
Here's another way we can use this formula. I can check to see if the descent rate calculator I'm using is accurate.
The calculator I'm using tells me I'll have about a 75 fps descent rate under the drogue. I'm going to assume this
rate is calculated near the main deployment altitude of 1,000' above ground level. I'm launching from 1250' above
sea level. So I'll calculate the descent rate at an altitude of 2,250'. Air density is .07 pounds per cubic foot
at 60 degrees F. Converting to slugs we get .00217566 slugs per cubic foot.
Fd = .5 * .00217566 * 5625 * .75 * 12.56
Fd = 57.64 pounds force
On the descent rate calculator I used a rocket weight of 60 pounds. So you can see the 57.64 is pretty close to the weight I used.
You could also calculate a rockets altitude using the same formula if you knew the thrust profile, weight, Cd and threw in a few more calculations.
One thing that initially threw me when I tried to make these calculations was that no one bothered to mention you needed to convert pounds to slugs for the formula to work. Once I figured that out, it was easy...