Although some of the restrictions for the classic egg drop project vary, some of the same prinicples found in this design might be applied to your own device.
The winner for our competition was determined based on the highest P-score. Where the P-score is equal to the below equation (h being the maximum height survived, m being the mass in grams and V being the volume in cubic centimeters). I think my device ended up with a score of about 430 (more than four times the second place score).
Step 1: Materials
2 toilet paper rolls
1 manila paper folder (any kind of thicker paper would work just as well)
5 yakitori skewers (long thin sticks)
some thread (optional)
hot melt glue gun (not totally necessary but helpful)
x-acto knife (again not necessary but helpful)
Step 2: Assemble the body
Take the un-modified roll and cut it in half. This is easiest with an x-acto knife but scissors will work too. Make about 1 inch vertical cuts all the way along the perimeter of one of the halves. Leave about 3/4 inches of space between the cuts.
Step 3: Assemble the rotors
Step 4: Cut out and attach the blades
Once you have all your blades, attach them to the skewers at slight angles. I used electrical tape to attach mine to reduce weight but I'm sure hot glue or other kinds of tape would work just as well. Make sure all the blades are approximately equidistant from the center of the tube (this ensures that it is the most stable as it gracefully spins downward).
Step 5: Putting it all together
Poke another pair of holes in both the bottom of the roll of the rotor assembly and top of the roll that was slightly widened. This attaches the propeller assembly to the base while also allowing you to easily take it off for transporting or checking the egg.
Create two more pairs of larger holes on the bottom of the widened toilet paper roll to fit the two straws through. Ideally they would be perpendicular to eachother but as long as it's able to support the egg it should be fine.
Insert the bottom half of the role (the one with vertical cuts) into the bottom of the widened tube. I didn't need to secure this because mine was a relatively tight fit but if it falls out when you hold it vertically you should use tape to secure it in place.
Step 6: Finishing touches
First get a small ziplock bag and cut the top off (about one third down). Wrap your egg in the bag and insert it into the top of the device prior to dropping it. It should be a pretty snug fit. If it's not fitting make sure the bulk of the excess plastic bag is under the egg when you place it in and the egg is sitting vertically in the tube (eggs are much stronger in this orientation).
Also slightly curl out the bottom cuts so that when the device lands it acts as a sort of spring or shock absorber and spreads out.
You can also attach a thread to the top rotor assembly. This makes dropping the device easier. This is very helpful if you're not the one dropping it.
Step 7: Drop Time!
If it's working well it should spin gracefully down and land lightly on the springy cardboard cuts.
That's it! Good luck with your egg drop.