Calculating the optimal radius of your parachute

October Sky Project Lab 4: The Recovery System ______________________________________________________________
Theory: In this lab you will explore these elements of safe recovery. 1. Terminal velocity for safe landing 2. Relationship between drag, terminal velocity, and parachute diameter.
Construction: In this lab you will perform the next 3 steps to completing your rocket: 1. Reinforce fins and launch lug 2. Complete recovery system 3. Prime rockets __________________________________________________________________
Supplies 1. Sheets of light plastic (garbage bags work). 2. Twine 3. Scissors 4. White spray primer 5. Wood glue
1
Name: _____ Partner: _____
I. Calculating the optimal radius of your parachute
A. As we learned this semester, a falling object reaches terminal velocity when the drag force exactly balances its weight. Therefore the whole purpose of a parachute is to create a strong enough drag force such that the terminal velocity is low enough to safely land the object. Recall that the drag force is D = ½ ρv2CdA. When you have reached terminal velocity v becomes vd. Use newton’s second law to derive a formula for vd in terms of ρ, Cd, A, g, and m. (Hint: We did this in lecture)
B. Given that your parachute is a circle, use this fact to express your equation for vd in terms of r, the radius of the parachute.
C. To be sure that your rocket lands safely, it should not hit the ground any faster than vd = 2.5 m/s. Use this terminal velocity to solve for the minimum radius that your parachute will need to be in order to land your rocket safely. Use the values for Cd, air density, and mass that you used in the previous lab report or look them up online.
2
Name: _____ Partner: _____
II. Rocket Construction
A. Fin and launch lug reinforcement.

1. By far the most vulnerable parts of your rocket are the fin connections and the launch lugs. Using the glue nozzle, put a drop of glue on the top edge of both sides of each fin and then use your finger to swipe a nice smooth layer on the seam in order to reinforce it.
   B. Recovery system construction.
2. Using your calculations for part 1 cut out a parachute that will safely land your rockets.
3. Cut 6 18” strings that are attached (evenly spaced) around the parachute and then tie them altogether to the nose cone.
   C. Priming
4. The rocket’s paint coat is more brilliant and sticks better when there is a layer of white primer beneath it.
5. There are three ways to totally mess up your paint job when it comes to spray paint. a) Holding the nozzle down for too long. (If you do this, paint accumulates in one place and you get drips down the side of the rocket.) b) Holding the nozzle too close to the rocket. (Same thing, drips). c) Keeping the spray stream in the same place for too long. (You guessed it, more drips).
6. You can avoid this by: a) Spraying in short 1s bursts. b) Always keeping the nozzle a minimum of 1 foot away from the rocket. c) Always move the nozzle as you paint.
7. Continue until there is one complete opaque white coat over the rocket and nose cone.
   Post Lab Questions:
   3
   Name: _____ Partner: _____
8. Assuming the rocket reaches terminal velocity almost instantly when the parachute is deployed, how long should it take your rocket to careen to the ground?
9. There are currently over a dozen non-military uses for rockets today. These include space tourism, asteroid mining, transporting astronauts to the space station, space exploration, and launching satellites and probes. Pick any three of these (or others that you know of) and write a paragraph describing the