Best rope for main halyard

all this is confusing and im struggling to understand.

I mean Peaky, since when has a halyard been used in compression? rope would buckle almost immediately in compression. i know, you mean the mast has compressive forces. Yes, it's the mast in compression, under load from the halyard/sail, not the halyard; that's what I understand Peaky to be saying.

with 100kN acting downwards on a mast from the sail you then have 50kN running down the mast in the halyard (if 2:1) therefore to resist the force the deck must produce a reaction, of 150kN, or the sail and mast will come out the bottom of the boat. the mast acts as a compressive member. thats all very well and good. Yes, except unless you run your halyard to the deck rather than to a cleat on the mast, all the main halyard loads are internalised in the mast. The mast foot/deck is oblivious to the halyard set-up, and feels only the weight of the mast, sail etc and the standing rigging, jib halyard etc. loads.

but what about the 50kN acting downwards at the dead end of the knot at the top of the mast, that brings the total downward force to 200kN thus the compression in the mast must be 200kN which is the same as a 1:1. the 2:1 will be easier to pull up and would require less of a reaction to hold it up there (think of a mainsheet and the difference of 1:1 and multiple purchases), but mast compression does not change. The 50N in the two parts of the 2:1 halyard connected to the sail head are merely transferring the sail load to the mast head - they are how the 100N from the sail get to load the mast at all - what the mast-head experiences is the pull of those two runs of halyard, plus of that going down the mast to the cleat, all loaded to 50N, thus the compressive force is 150N

locking the sail at the top of the mast reduces the compression as you can neglect the halyard loads acting downwards and therefore a smaller reaction is needed. Yes

I think thats all right, my head is spinning to be honest.

Lol ive just confused myself even more.

in reality though, though the compression forces acting down do not run down the centre of the mast. they are offset (the sail at the top) causing a moment and initiating a buckle in the mast and thus the trailing edge of the mast carries compressive load and the front edge will be under tension. You're right, but we've simplified it for the sake of discussion - by and large our conclusions are valid

plus there are many many more factors to think of, such as the fact the force on the sail is a vector not just a parrallel force Again, you're right, but it's a relatively small effect on compression that doesn't invalidate the simplified argument, but does indeed induce bend and very significant effects.