Egg drop physics, making a safe landing.

[Spinnor]

Say we have a rectangular wire frame about 7 inches in size, see:

http://www.schillereng.com/EggDrop1.jpg

Let an egg of mass m, say 40g, be suspended in some type of "seat" as in the above jpg. with rubber bands going from the the eight corners of the frame to the egg seat. Let us say the force acting on the egg when it is displaced a distance x from the center of the frame goes as F = kx. Let us say the drop height is h.

Assume when the frame above hits the ground it maintains its shape. Let us require the egg move only a distance x, about 5 cm when the frame hits the ground.

With this information can we use conservation of energy to get an approximate value of k via:

m*v^2/2 = mgh = k*x^2/2 , energy of the egg gets converted into energy of the stretched rubber? Solving for k gives us an idea of the required force on the egg seat when it is streched 5 cm?

Thanks for any help.

 

[Bob S]

Hi Spinnor-
This egg + frame stores all the downward kinetic energy in the stretched rubber bands as potential energy. There does not appear to be any energy loss, so the "coefficient of restitution" is very high. So after the rubber bands stretch about 5 cm after impact, the egg is launched upward by all the potential energy stored in the rubber bands. How high will the egg go? Is it better to have something that absorbs and dissipates all the downward energy? Would the best choice be a constant retarding force F such that F x 0.05 meters = mgh?
Bob S
[Edit]You need to to consider several things

1) Research
What techniques have been most successful in the past?

2) State of egg
Is a hard-boiled egg more likely to survive than a fresh one?

3) Integrety of shell
The egg has to be supported to uniformly distibute the forces around the shell during deceleration. The pouch is probably not the best choice. Can you control the direction of deceleration forces (orientation of cage)? Could you put the egg in a small cast of plaster of Paris to preserve its shape during deceleration? Would putting it in a small incompressible sealed can of water (or 10wt motor oil or vaseline) provide more uniform pressure on shell during deceleration? Lastly, could you freeze it in an ice cube to preserve its shape during deceleration?

4) Deceleration forces
(deceleration forces outside can or package above)
What force time profile F(t) is best to minimize damage?
If the deceleration in 5 cm from an elevation h has to meet the criteria

∫₀^{5 cm} F(x) dx = mgh

what is the best F(x) profile?

Is making F(x) uniform and constant over 5 cm (in a dissipative foam or equivalent) or using spring force, F(x) = kx (rubber bands) better? In the latter, the maximum force is twice the uniform case. Is a sudden change in deceleration worse or better than a lower maximum deceleration?
Or is it better to consider F(x) profile instead of F(t) profile? Can you relate the F(t) profile to the F(x) profile?

Bob S

 

[Bob S]

See recent changes to previous post in blue.
Bob S