What would make the egg from a team with a slower/longer flight drop time break as compared to a team with a faster/shorter drop time.
Several variables determine whether or not the egg breaks.
The first thing that comes to mind is the egg itself. Eggs are not uniform and some have weaker shells or internal membranes. For this reason, teams are allowed to inspect and chose their egg from several provided by the event supervisor.
Another variable is the instantaneous vertical velocity (and horizontal to a lesser degree) at the moment of impact. Overall time reflects the average vertical velocity during the drop. Several factors cause instantaneous velocity to be greater than the average.
.....1. Swinging of the egg increases velocity at points in the swing. Lack of stability caused many of the devices to oscillate from side-to-side,
........much like the stalls exhibited by an improperly trimmed glider.
.....2. When the rotor tips to one side, the lift vector is not vertical, and both vertical and horizontal velocities can increase.
.....3. When a helicopter encounters a downdraft, it's vertical velocity is increased.
.....4. If the rotor is in "ground effect" at the moment of impact, the velocity may decrease.
.....5. Any dirt/dust or irregularity on the floor can concentrate the force of impact to a very small area of the shell.
Depending on how the helicopter is constructed, the egg will have varying amounts of energy to absorb on impact.
Several eggs had cracked shells, but the membrane inside remained intact, thus passing the "paper towel" test.