In reply to David Coley:
Well I´ve made plenty of curves and boring it is too!
If we only consider the rope dynamics then it is clear that reducing the friction at the top point is never going to reduce the load on the gear, that´s the case for any reasonable climber weights, rope characteristics and all Fall Factors.
There is an optimum desirable friction on the top point for the lowest force which varies with all the other parameters but seems to be in the region of 0,5 up to 1 depending.
For example with a FF of 0.1, 100kg climber and an 8kN rated rope the forces on the various parts are:-
No friction (0) Climber 3.11kN Belayer 3.11kN Total 6.22kN
Normal Karabiner (0.333) Climber 3,44kN Belayer 2.29kN Total 5.73kN
Optimum (0.58) Climber 3.89kN Belayer 1.63kN Total 5.52kN
Fixed (1) Climber 9.05kN Belayer 0kN Total 9.05kN
I´m seeing the same effect with different rope factors and climber weighs, just the optimum point moves around a bit, for the same as above but a 50kg climber the optimum friction is 0.51.
Over Fall Factors of about 0.5 you´d be better off tied to the top karabiner rather than have the rope slide through it!
HOWEVER!!!! This doesn´t take into account the belay itself, in the example above the 3.11kN felt by the belayer is certainly in the range of force one could apply through a normal device but for higher fall factors I´d have to start changing the forces felt at the belayer end as he couldn´t normally hold them.
For examplöe if the belayer in the case above gave a soft catch or used a weak plate and held only 2.5kN then with a frictionless top point the force on the top is only 5kN which is better than the optimum friction value of 5.52kN (unless of course there is too much slip and the belayer drops you with rope burns or you hit the ground).
So with soft belaying reducing the friction may well be beneficial (covering myself here a bit) but with hard belaying reducing the friction is of no benefit. Time to find a fool to jump off a cliff a few times I guess!