HEIGHT OVER
LENGTH IS
THE ANGLE.

A rigger who cannot name the angle will still set one. The sling will still do the math. The way to get θ on the ground is not a guess and not a phone photo of a protractor. Measure two lengths. Divide. Take arcsine.

This is a two-leg bridle. Equal legs. Load hanging plumb. θ is the angle between the sling and the horizontal — the same θ GOSPEL uses in the tension formula. It is not the angle between the two legs at the hook.

WHAT YOU MEASURE

L is sling length — along the sling, from the hook saddle to the load connection. Not the tag. Not a memory of last job’s 12-footers if you just choked shorter.

H is vertical height — from the hook centreline down to the load connection. A tape or a known stick. Not ‘it looks about a metre.’ The horizontal run under the sling is the adjacent side. You do not need it for this calculation.

The sling is the hypotenuse. The drop is opposite θ. That is the whole trick.

THE FORMULA

Sine is opposite over hypotenuse. Opposite is H. Hypotenuse is L.

If H is half of L, sin θ is 0.5, and θ is 30°. That is the graphic’s worked lift — 12 ft sling, 6 ft drop, or 4 m and 2 m. Same ratio. Same angle.

WORKED BRIDLE

1. 01

   H / L = 0.500 θ = 30°

   H is half of L. This is the floor the procedure still allows without an engineer. Tension in each leg equals the whole load. GOSPEL-SWP-010.

2. 02

   H / L = 0.707 θ = 45°

   A working bridle. Height is about seven-tenths of the sling. Tension factor 1.41 on each half-share.

3. 03

   H / L = 0.866 θ = 60°

   Steeper. Safer on the hardware. About 15% more than a vertical share. This is where most bridles want to live.

4. 04

   H / L = 1.000 θ = 90°

   Straight up. H equals L. That is a vertical hitch, not a spread. If you needed spread, you do not have it.

THE TABLE YOU SHOULD KNOW COLD

Keep the angle as large as the lift allows. Larger θ, smaller tension. Flattening the bridle to reach pick points is how a tagged sling gets overloaded without the load changing.

USE IT

Phone calculator. Degree mode. H divided by L. Then sin⁻¹. Check: sin⁻¹(0.5) is 30°. If that is not what you get, you are in radians, or you inverted the fraction.

You now have θ. The next number is tension. Two equal legs: T = W / (2 × sin θ). That is the other Wire story. Do not stop at a pretty angle.

WHAT THIS TRIANGLE DOES NOT DO

• It does not replace a measured weight. Garbage W still wrecks T.
• It does not split a 3-leg or 4-leg hitch into equal shares. If the load can tilt, design as if two legs are carrying.
• It does not make a hitch under 30° acceptable because the tape said 29°.
• It does not replace the sling WLL, the hitch factor, or Part 15.
• It does not survive a guess at L. If you shortened the sling in a choke, measure the working length.

If you cannot explain the angle, you cannot use the angle.

That line is already in Proven. This is how you get the angle without lying to yourself. Measure H. Measure L. sin⁻¹(H/L). Then run the tension. If it does not fit the tag, change the hitch.

SIN() FOR SLING TENSION →

SLING SELECTION — GOSPEL-SWP-010 →

06 — RIGGING →