What Swing Fall Does That a Vertical Fall Does Not

Why this matters

If the anchorage is not close to directly above the work, the clearance figure written on your ticket is not describing the fall that would actually happen. Before anyone goes to an edge on a rig anchored off to one side, stand at the work position and look up: if the line to the anchor is closer to horizontal than to vertical, stop and move the anchorage, because nothing downstream of that geometry can be fixed by better hardware.

A vertical fall is a stack of distances added up. A swing fall is a pendulum, and it does two things the stack cannot describe. It drops the worker further than any of the terms in the stack account for, by an amount set by the offset angle rather than by any component's rating. And it delivers the worker sideways into whatever stands between the start of the arc and the bottom of it, at a speed the energy absorber does absolutely nothing about, because an absorber extends along the line and at the bottom of the arc the line is vertical while the motion is horizontal.

The call

A commercial service crew was clearing and re-flashing a line of roof drains along the edge of a 22-foot warehouse roof. One rated stanchion anchor stood on the deck, its attachment eye measured at 5.0 feet above the roof surface and 18.0 feet back from the edge. The tech wore a full-body harness and a self-retracting lifeline clipped to that eye. He had been on the roof three hours.

He slipped on wet membrane while kneeling at a drain and went over the edge. The lifeline locked, he swung, he scraped down the face of the building, and he ended up hanging about nine feet above the loading yard with a broken forearm and abraded ribs. Somebody got a ladder truck to him inside twenty minutes.

The shop's first reading was that the system worked. He fell, the lifeline caught him, he did not hit the ground. That reading survived exactly as long as it took somebody to go up with a tape.

What the crew had actually computed

The tailboard sheet showed a clearance stack. It was arithmetically fine and it was for the wrong fall. The stack assumed a self-retracting lifeline with a short lock-up distance, an anchorage at dorsal D-ring level, and a body dropping straight down beside the anchor. Against 22 feet of available height it cleared comfortably, and everyone on the crew had seen the numbers.

What no line on that sheet described was that the man was 18.0 feet from the anchorage in a horizontal direction, and that his D-ring and the anchor eye were at the same height above the deck, which puts the lifeline dead horizontal at the instant it takes load.

The geometry the sheet had no field for

Once the line goes taut, the worker is on the end of a rope of fixed length swinging about a fixed point. The additional vertical distance the body travels below the point where the line went tight is:

arc drop = L minus (L times the cosine of the offset angle)

where L is the straight-line distance from the anchorage to the attachment point at lock-up, and the offset angle is measured between that line and vertical.

     anchorage
         *
        /|
       / |
    L /  | L x cos theta
     /   |
    /    |
   *     |   worker when the line goes taut
         |
         *   bottom of the swing, directly
             below the anchorage

   arc drop = L - (L x cos theta)
   the worker also travels sideways into
   whatever stands between those two points

That relationship holds the line taut and inextensible, the anchorage a point, and the swing starting from rest at the offset angle. Real lifelines stretch and real absorbers deploy while the swing is happening, both of which lengthen L during the arc, so the computed drop is a floor, never a bound. Round it in that direction and say so.

Four angles worth memorising, because they are exact and they are not intuitive:

The jump from 30 to 90 is not a factor of three. It is a factor of about seven and a half, and it is the reason the common working rule is to keep the offset inside 30 degrees. Note what that rule holds constant: it limits the angle, not the lateral distance. Raise the anchorage and the same 30 degrees buys you more room to work sideways, which is why height and offset are one decision and not two.

Running the incident through it

Measured after the fact, with the anchor eye 5.0 feet above a deck that is 22.0 feet above the yard, so the eye sits 27.0 feet above grade:

Line length at lock-up, L                      18.0 ft
Offset angle from vertical                     90 deg
  (D-ring and anchor eye both at 5.0 ft
   above the deck, so the line is horizontal)
cos 90 degrees                                  0.000
Arc drop = 18.0 - (18.0 x 0.000)               18.0 ft
Anchor eye above grade                         27.0 ft
Bottom of the arc above grade (27.0 - 18.0)     9.0 ft
Lateral speed at the bottom of the arc,
  from the arc drop alone, starting at rest:
  square root of (2 x 32.2 x 18.0)             34.0 ft/s
  which is about                               23 mph

Two honest readings of that block. First, the vertical arithmetic did not fail him: the bottom of the arc is 9.0 feet above grade, so on distance alone the system held. Second, the arc carried him across the face of the building, and the wall is where the injury came from, not the ground. The 23 mph figure is the speed at the bottom of a free swing starting from rest, so it is a ceiling for that arc and a floor for the real event in the sense that it ignores whatever downward speed he already carried when the line took load. He met the wall much earlier in the arc and much slower, which is the only reason this is a near-miss article and not a fatality article.

And the absorber contributed nothing to that part. An energy absorber pays out along the line. At the moment of a lateral strike the line runs one way and the body travels another, so there is no mechanism by which the absorber reduces the impact. This is worth saying out loud to a crew that has been told the absorber protects them, because it protects them from one specific thing.

There is a second hazard hiding in the same setup and it is not the swing. A self-retracting lifeline dragged across a roof edge under load can be cut by that edge unless it is a type specifically rated for leading-edge use. If your work puts the line over an edge, that rating is a separate check with its own device label, not something the swing-fall fix covers.

What the fix cost and what the numbers became

The shop went back with an overhead rigid rail mounted to the mechanical penthouse structure, running parallel to the drain line, attachment height measured at 12.0 feet above the deck, and the rail set 4.0 feet inboard of the edge. Rail design, mounting and load path were signed off by a registered professional engineer, because a horizontal or rail system is not a component you buy and hang: 29 CFR 1926.502(d)(8) requires horizontal lifelines to be designed, installed and used under the supervision of a qualified person, as part of a complete personal fall arrest system maintaining a safety factor of at least two.

With the D-ring still at 5.0 feet, the trolley 7.0 feet above it and the worker 4.0 feet out at the edge:

Vertical from D-ring up to the trolley          7.0 ft
Horizontal offset at the work position          4.0 ft
Line length L, square root of (16 + 49)         8.06 ft
Offset angle, arctangent of 4.0 over 7.0        29.7 deg
cos 29.7 degrees                                0.869
Arc drop = 8.06 - (8.06 x 0.869)                1.06 ft
Lateral speed at the bottom of the arc:
  square root of (2 x 32.2 x 1.06)              8.3 ft/s
  which is about                                5.6 mph

Arc drop went from 18.0 feet to about 1.1 feet. Bottom-of-arc lateral speed went from about 23 mph to about 6 mph. Nothing about the harness changed, nothing about the lifeline's rating changed, and the crew is the same crew. The whole difference is where the top of the line is.

Read the two figures in the same breath rather than only the drop. Cutting the offset angle from 90 to under 30 degrees cut the arc distance by roughly a factor of seventeen and the lateral speed by roughly a factor of four, because speed goes with the square root of the drop while the drop goes with L directly. That is why the angle rule is stated on the angle: it is the variable that moves both terms at once.

What generalises off this roof

A clearance stack computed for a vertical fall is invalidated by offset, not adjusted by it. You do not add the arc drop to a stack and carry on. The arc changes where the lowest point of the body is, which strike surface the body reaches first, and whether the body arrives there moving sideways. The vertical stack in How to Compute Fall Clearance and Why People Get It Short is a necessary calculation and it assumes the anchorage is above the work.

The offset that matters is the one at the far end of the work area, not the one where the tech is standing when you look. A single anchor serving a 40-foot run of work is at 30 degrees in the middle and something much worse at both ends. Walk to the ends before you accept the anchor.

When the anchorage cannot be moved, the work has to move. Two anchorages instead of one, a rail or an engineered horizontal lifeline, or the exposure taken away entirely by working from a platform on the ground side. Accepting a bad angle because the anchor is the only one on the roof is how the anchor's existence becomes the reason somebody gets hurt.

The tell that a crew has never thought about this: the tailboard sheet has a clearance number and no offset measurement anywhere on it. If the sheet cannot answer "how far sideways, and how far up," it has not described the fall.

References

• 29 CFR 1926.502(d), personal fall arrest system criteria for construction, including the qualified-person requirement and safety factor of at least two for horizontal lifelines at 1926.502(d)(8).
• 29 CFR 1910.140, personal fall protection system criteria for general industry.
• Manufacturer instructions for the specific self-retracting lifeline, which own the leading-edge rating and the arrest distance for the configuration in use.
• See related: How to Compute Fall Clearance and Why People Get It Short, What an Anchorage Has to Be Rated For and Who Decides, Why a Self-Retracting Lifeline and a Lanyard Need Different Clearance.