Spanned Cable Sag and Tension
The tension a horizontally spanned cable (a tramline, highline, span set, or messenger) develops from its sag: H = w L^2 / (8 d), the support tension H sqrt(1 + (4d/L)^2), and the developed length. A 100 ft span at 1 lb/ft sagging 2.5 ft runs 500 lb; pull it to a 0.5 ft sag and the tension jumps to 2,500 lb - five times the load for the same span, because tension is inversely proportional to the sag. Shallow parabola (sag under ~1/10 span), uniform load, level supports; a concentrated load is the sling-angle case. A planning screen; the rope WLL, the anchors, and the head rigger govern.
Formula and source
H = w x L^2 / (8 x d); T_support = H x sqrt(1 + (4 d / L)^2); length = L + 8 d^2 / (3 L); slack = length - L; sag_ratio = d / L.
Shallow-cable parabola statics (by name) with ASME B30.9 / Wire Rope Users Manual rigging practice; first-principles, no edition cycle.
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