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The Orion reentry vehicle will have a parachute system. Like Apollo, they'll have 3:

   Orion Parachute Drop Test

Orion Parachute Drop Test on May 1, 2013

A model of NASA's Orion spacecraft glides to a successful touchdown during a test of its parachute system on Wednesday, May 1. Orion's three main parachutes, which slow it gradually down for landing, weigh 300 pounds each and can cover almost an entire football field.

Photo and caption source: NASA

They seem so nicely separated in pictures. But from a physics standpoint, the aerodynamic force seems like it should be upward, and that would tend to mush all the chutes together. That would seem quite dangerous, by decreasing the area or making them crumple.

Is there anything about the design of the parachutes and tethers that prevents this? Is there something about the aerodynamics that keeps this from happening? Or is some bumping just not a big deal?

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    $\begingroup$ Another question...why on 2 of the 3 parachutes do the orange/white stripes line up but on 1 of the 3 they are offset checkerboard style... ? Weird... $\endgroup$ – Jimbo Jonny Dec 3 '15 at 14:39
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It's just the aerodynamics. There is high pressure where the air spills out the side that tends to push them apart more than the forces that you mention that pulls them together.

Good thing too. A giant parachute with the same drag would take too long to open.

Clustering is very commonly used for cargo.

cluster another cluster a third cluster

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    $\begingroup$ So each of them is a normal axially-symmetric parachute, and only their locations result in the separation, right? $\endgroup$ – Ruslan Nov 25 '18 at 16:44
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    $\begingroup$ Yes, they are symmetric and identical. $\endgroup$ – Mark Adler Nov 25 '18 at 23:42
  • $\begingroup$ Love the images! $\endgroup$ – uhoh Oct 20 '19 at 12:40
  • $\begingroup$ Also having multiple decreases the risk associated with a single parachute opening. Apollo 15 had a parachute fail and descended safely on its remaining two. $\endgroup$ – Hans Jan 20 at 10:31
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Much more air flows out the top of a round parachute than out the sides - round canopies without vents oscillate rather violently, notice all the openings in that picture. If you see a canopy with no vents it's probably made of porous fabric, nylon woven for the purpose leaks a LOT of air - you could tape it over your mouth and still breathe comfortably.

Round canopies with drive vents ( search for "Para-Commander", a last-generation steerable round parachute) do not cluster as their forward speed will cause collisions, and modern sport-skydiving canopies are very unfriendly to their peers. Any jumper with both canopies out has to land very carefully as the system can collapse with little provocation, and that's usually fatal for the person under it.

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    $\begingroup$ Yes, stability is critical, which requires porosity. Either geometric porosity, material porosity, or both. $\endgroup$ – Mark Adler Jan 25 '14 at 1:19
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While there may be some aerodynamic force in the radial direction pulling the chutes outboard, they probably do not dominate the lateral motion of the parachutes on a space capsule. This corresponds to this paper on the aerodynamic forces, which shows that the L/D values of the chute are quite small.

You can see on this presentation by NASA (slide 35) that the parachutes actually do collide quite a lot, as you already suspected. Furthermore, there is a nice onboard view from the Crew Dragon during their inflight abortion test, where you can observe alternating pairwise collisions of the four parachutes attached to the capsule. So the aerodynamic lift (and resulting lateral force) may reduce the impact force on those collisions but cannot mitigate the collision itself.

It seems like the parachutes are causing some headaches for all of the teams, maybe surviving collisions is one of the concerns. I found this paper looking at asymmetric loads on the chute lines, which also covers the case of chute collisions.

Regarding the pictures I think your are right: there are barely any picture including colliding chutes, but these are probably not the pictures that one would pick for a press release.

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