Additional thought, on the bottoms of the spikes put a band of tape a couple inches up. Cut through so that there are many little slips  of paper so that the whole thing resembles a broom. Bend them over, and tape them back so it looks like this
If someone has a problem with me using that image I'll get rid of it, but I just see it as publicity for them.

I'm not sure if the amount of energy it would absorb would be any good, (probably not) but it's just a thought.

Fins would make it look faster and so it would be faster... just kidding. My thought was to replace that voluminous, rear portion of the cone with fins. They'd serve the same purpose -stabilizing flight, ensuring the device lands on the braking contraptions- fins wouldn't create nearly as much drag in the downward direction, and far more in the side to side direction.

P.S. what about concentric cones with crumpled tissue paper between them?

I think several layers would be best. The one closest to the egg being the strongest, the one hitting the ground first being the weakest.

Remember, the name of the game is, "Disperse all energy to anything and anything other than the egg". And the best way to do this is to isolate the egg at as many levels as is possible from the ground.

Right now, I think the the best design would be:
A reinforced cone, made of heavy paper or cardboard lined with tissue paper to cradle egg.
LONG fins to stabilize flight.
A secondary cone (made of two sheets of paper) sliding over the first with shredded paper or kleenex as padding between the two (a crumpled ball of scotch tape placed over the tip of the first cone would be perfect. It should be fitted loosely (at no point directly touching the other cone).
A third cone, longer but not wider, of a single piece of paper, and fully fitted with  spikes should be slid over the second with very little padding between the two. At this point, the bases of all three cones should line up, and taping them togher should be no problem.
The spikes should be construced weaker than those mentioned earlier. They should have many little cuts on them as predetermined beding points - the most severe of which are at the tips. With luck, each spike would bend at several of the points.

Contraption falls. The spikes bend at many points and sometimes sheer off of the sides of the cone. They splay out. This all absorbs energy and slows the egg, which feels nothing at this point. The tertiary cone then impacts and easily deforms. As the secondary cone receives impact, it is compressed against the primary cone (with the kleenex absorbing the energy) and slightly deforms. The egg continues to fall... much slower however. Padding and the primary cond absorb any remaining energy.

Of course this is all assuming that device remains perfectly upright the entire journey... not going to happen. For this reason, more (weak) spikes should be attatched to the sides of the cone, possibly even at angles greater than horizontal. During lopsiding (not a forceful event) spikes and fins will absorb energy.

I suppose I should elaborate on the primary cone for clarification. Lined with fairly compressed tissue paper, then loosely cumpled tissue paper placed towards tip of cone. Egg is placed on that layer and another loosely crumpled layer of tissue on top of that. 10 cm of tape keeps the whole thing nice and safe, and is easily done in under five minutes.

I was thinking of fins something like this.. just longer http://im.edirectory.co.uk/products/1306/i/vortexhowler.jpg" rel="gb_image[nice_pics]" title="...">http://im.edirectory.co.uk/products/1306/i/vortexhowler.jpg" name="post_img_resize_7" alt="..." title="..." border="0" style="display:none" />

O and for a sense of scale I was thinking around eight inches from the back of the first cone to the tip of the third (so excluding spikes and fins). But this could be widely varied. The only concern would be if the egg became placed too far back in the device making stabilized flight and impact more difficult.
I suppose this is more than you ever wanted when posting . I know that I sound 'bossy' but it's just the easiest way to write. (interjecting with, "but i understand that you could do it differently or may not like the blah blah bl-..." would be even more annoying.

Good luck, consider implementing an idea or two of mine

P.S. Altay, just noticed that in three more posts you're a senior member... I think.

Haha, indeed. This is why I stressed that the spikes should be made very weak. All in all, I don't think the spikes would have any impact on the flight, especially with fins attatched, since they'd be very narrow and equally distributed. The way I'm thinking of the design is not to look at it as 'one cone with a bunch of stuff piled around it' but as one cone (the tertiary) with a lot INSIDE of it, and some on the outside. Anyway, spikes, if not for initial impact may be helpful once the cone lopsides. There should be a bonus round from four stories


If a single cone with a bit of padding works, all the better though

So, pretty much like a model rocket flipped upside down?



Something like that flipped over with the egg between the fins?

Interesting design. If it was the winning design it must have worked well. What exactly was the purpose of the paper coils though?