I don't have any answers for you but as an avid climber - you also want to be taking into account the material you are tying knots in. Super static material lik

I don't have any answers for you but as an avid climber - you also want to be taking into account the material you are tying knots in. Super static material like dyneema really doesn't like being bent at a tight angle and will lose a lot more strength in a knot than something like nylon. Also thicker material tends to lose less strength (bigger bend radius). But yeah... beyond that my usual method of understanding a knot is to find the places where one part of the knot constricts another under load, because that generates the friction. For instance the reef knot in the linked article has two collars that bite on two strands of the rope each when pulled, so lots of friction there and it makes sense to me it's very syrong. On the other hand I can't work out how the granny knot is stronger than the thief! Very subtle stuff.