Would longer lines increase the probability of entanglement (no, not the quantum kind)?
Absolutely yes. I am thinking from a parachute OPENING perspective, the optimum length would be infinite. Obviously infinite isn’t possible, but 10, 50, or even 100 foot lines are POSSIBLE but nobody is gonna do that on a LPR ROCKET. Among the limiting factors are weight of the line, packing room in the rocket for the line, cost of the line, and, as you mentioned, the longer the line the more likely it will get tangled. The same constraints apply to the shock cord. Some experienced rocketeers have given suggestions above. I don’t have empirical knowledge about the difference between 1.5 and 2 diameters, I would hazard a SWAG that going beyond 2 diameters likely buys you much more trouble than any potential incremental efficiency gain is worth,
I will put in a plug for 8 shroud lines over 6 for four reasons.
One is redundancy, shroud lines do break or pull off or through the plastic parasheet type chutes. Losing 3 lines on a 6 line chute is gonna be worse than on 8.
Two is you spread out the opening stress a little more with 8 rather than 6. An additional “insurance” for this is to continue the line over the top center of the canopy and down the other side (making the opposite side shroud line), but that’s a bit messy for me
Three is efficiency, 8 lines gives a slightly more round canopy than 6, although the difference is incremental and I certainly wouldn’t replace a stock 6 shroud chute for that reason.
For all these, you can argue that 10 or 12 or more is better, but you gotta stop somewhere.
Four is if you make your own, I find it is really easy to cut out a perfect octagon than a hexagon. If you ever made paper snowflakes in kindergarten you may remember this.
Start with a square piece of plastic.
Fold in 1/2
Fold in 1/2
Fold in 1/2
Draw or imagine a line bisecting the angle made by the point
Make a single cut along the “near” edge to the point, perpendicular to the line above. (Try it with a piece of paper first)
Open it up, Voila! Perfect octagon.