The question of how long/what kind of shock cord will depend on
what problem you are trying to solve.
What you want to happen: The shock cord and associated parts of the recovery harness keep the parts of the rocket connected to each other and individually intact during the ejection and deployment of the recovery device.
What you
don't want to happen:
Anything else.
Somewhere upthread, Lakeroadster observed that recovery requirements will vary from rocket to rocket. There are also MANY different ways to meet those differing requirements. Lots of different ways to address potential failure modes of the recovery gear.
BABAR's long rumination in #202 gets it right. The job of
every part of the recovery harness is to dissipate mechanical energy.
Some of that energy will be due to the motion of the rocket after motor burn-out but before deployment. Some of that energy will be due to the work done on the rocket parts by expanding gasses expelled by the ejection charge.
The relationship between the energy developed and the forces acting on various parts of the recovery harness is stated most simply as the
work energy equivalence theorem: The change in the kinetic energy of an object is equal to the net work done on the object. The work done is the scalar product of the force acting on the body and the displacement of (distance moved by) that body while the force acts on it.
The mathematical description of this
starts here
https://hyperphysics.phy-astr.gsu.edu/hbase/enecon.html
This is a
lot more physics but it all adds up to the same thing that Random Flying Object said in the
thread that Lakeroadster linked in post #201. It is going to be a lot of math, and there is
no part of this that does not require calculus (at a minimum) to explain.
How deep do you want to go? We can talk about
fluid drag, and
elastic hysteresis, and the dependence of the
elastic coefficient of restitution on strain rate, etc. Its long walk in very tall weeds, and it is no good asking for a simplified, summarized, or condensed version -- handy for comparing different solutions --
until you have a specific problem to solve.
The bridge jumping comment also got me to thinking.. the bridge is fixed and anchored.. just how much of an anchor affect can you really expect from the parachute? There will only be as much force on the recovery materials as the chute can anchor.
The bungee cord comment was on point, but not for the reasons you suggest. The tension (force) on the recovery harness that will be exerted
after the parachute deploys is likely/hopefully going to be small compared to the force exerted between the separable rocket parts by the expanding gas of the ejection charge.
But there is more. It isn't just force that concerns us. As
Nytrunner indicated in #197: it is
shock, which has to do with the rate at which the force increases (in our case) at some point along the recovery harness.
This video demonstrates the difference in behavior on a system undergoing a large shock loading (rapidly increasing force) and a quasi-static load (slowly increasing force).
Again -- there is a
lot more to this. There are other reasons that jumpers, falling at terminal speed, will have very different outcomes if that fall is arrested by an elastic bungee cord rather than a steel cable of equivalent length and mass*. I offer the video
only as an illustration that
strain rate matters, and is
something that can be controlled by using an elastic (or otherwise extensible) tether to attach the rocket parts.
* Edit: In case anybody has read this far, a better explanation than invoking shock would be to note that the work done by the steel cable is the same as the work done by the bungee cord, but that the elasticity of the bungee cord means that a smaller force is exerted over a longer distance to effect the same change in kinetic energy. With the steel cable, it is likely that the larger acceleration due to the larger force will result in stresses internal to the jumper's body which will exceed the yield strength of something the jumper needs to not be dead. Same with the recovery harness: The elastic means a smaller force over a longer distance and -- correspondingly -- smaller stresses applied to the communicating parts of the harness.