Archon Engineering has a software program called "Safety Line" that I think will give you the data you need (rope tension, horizontal and vertical end forces, final sag, etc.). The full program can be purchased for $20 and you can download a demo version for free (demo version is limited to a maximum span of 8 feet). The web site is
In lieu of that, it might help you to know that the initial sag is dependant on the initial horizontal component of the rope tension by the following relationship:
Hx = rope wt. per foot x span^2/(8 x sag)
where Hx is the horizontal tension component (span and sag both in feet).
The forces that develop in the life line due to a center concentrated load (during a fall event) depend on the final stretch of the cable, thus making the system statically indeterminate. Outside of a trial and error solution, the horizontal component of the rope tension can be found by application of the formulas in the sixth edition of Roarkes Formulas for Stress and Strain (page 179). In short, the Roarke formula solves for the rope angle with the horizontal, then uses simple geometry to solve for the horizontal component of the rope tension.
For rope angles less than 12 degrees, Roarkes equation for the rope angle is as follows:
angle (in radians) = (W/EA)^1/3
where W is the applied load.
E = modulus of elasticity (29,000,000 psi for steel).
A = rope cross section area.
From this, the horizontal component of rope tension can be found by dividing the applied load by twice the tangent of the above angle. (Vertical component is simply one half the applied load).
All of the above assumes, naturally, that the end supports are at the same elevation (it gets considerably more complicated if they're not).
Of course, a much easier way around all this (which I highly recommend) is to specify a life line system from a manufacturer of such systems who will give you the forces you need to analyze the systems support structure.
Typically these types of systems will include some sort of shock absorbing device at the end(s), turnbuckles, and rope tension indicating device for installation. For long spans, these manufacturers can also provide special rope hangers for intermediate supports that allow 'pass-thru' provisions when used in conjunction with a special carrier attached to the line to which a lanyard can be connected. This eliminates the need for a worker to unhook his lanyard at each intermediate support.
I think most safety harness manufacturers can provide these systems, but I'm most familiar with Miller. These systems aren't cheap by any means, but you do get all the hardware needed for the installation, much of which will come pre-assembled with the cable. (I'm afraid to think what these guys must pay for insurance).
One thing to keep in mind is the potential for a workers lanyard getting caught on some nearby structure or equipment during a fall event. This could result in the loading from the safety lanyard being applied in the horizontal direction rather than the vertical (fall) direction.