Moving a Skid Up a Ramp: Cable Tension, Geometry, and Anchor Capacity
A 1,500 kg equipment skid is being pulled up a 15° steel ramp on dry steel ways. The static friction coefficient is 0.15 and the kinetic coefficient is 0.12. The winch cable is initially rigged parallel to the ramp surface. The skid has been sitting on the ramp overnight, and the rigging crew wants to know the minimum hold tension needed before they release the mechanical chock. During the lift the winch can accelerate the skid at up to 0.4 m/s² up the ramp. The cable anchors to a cast-in eye bolt with a rated working load of 12 kN. The site procedure requires a minimum factor of safety of 2.0 on the rated working load for lifting and pulling operations. A supervisor suggests rerouting the cable horizontally from a snag point at the top of the ramp because it is a shorter run.
1. Calculate the minimum hold tension while the skid is stationary, and the steady-state tension needed to pull it up the ramp with the cable parallel to the surface.
Read the worked answer
Weight: W = 1,500 × 9.81 = 14,715 N Components on a 15° ramp: W sin15° = 14,715 × 0.2588 = 3,807 N (down the ramp) W cos15° = 14,715 × 0.9659 = 14,211 N (normal to the ramp)
Holding it stationary: Maximum static friction available = μs N = 0.15 × 14,211 = 2,132 N The gravity component (3,807 N) exceeds the maximum friction (2,132 N), so the skid will slide down on its own once the chock is removed. The cable must supply the difference: T_hold = 3,807 − 2,132 = 1,675 N (about 170 kg equivalent) Any tension above this holds the skid; below it, the skid accelerates down the ramp. Do not release the chock until the winch is loaded to at least this value plus a margin.
Pulling up at steady speed (kinetic friction acts down the ramp, opposite to motion): Friction = 0.12 × 14,211 = 1,705 N T_pull = 3,807 + 1,705 = 5,512 N
Note that the hold case uses static friction and the pull case uses kinetic friction; mixing them is a common error and understates the pull tension.
2. Evaluate the supervisor's suggestion to run the cable horizontally. Recalculate the pull-up tension and explain the effect on the skid.
Read the worked answer
With a horizontal cable, only its component parallel to the ramp pulls the skid, and its perpendicular component presses the skid into the ramp, increasing normal force and therefore friction.
Resolve parallel and perpendicular to the ramp (pulling up, at impending motion, using μs): Parallel: T cos15° = W sin15° + μs N Perpendicular: N = W cos15° + T sin15°
Substitute: T cos15° = W sin15° + μs (W cos15° + T sin15°) T (cos15° − μs sin15°) = W (sin15° + μs cos15°) T (0.9659 − 0.15 × 0.2588) = 14,715 (0.2588 + 0.15 × 0.9659) T (0.9659 − 0.0388) = 14,715 (0.2588 + 0.1449) T × 0.9271 = 14,715 × 0.4037 = 5,941 T = 6,408 N
That is about 16% more than the 5,512 N parallel case, not less, despite the shorter cable run. The horizontal pull also introduces a downward normal component of T sin15° ≈ 1,658 N, which increases friction and adds load to the ramp and ways. Check that the skid is not being lifted: 1,658 N is far below the 14,211 N normal weight component, so it stays seated.
Conclusion: reject the horizontal routing for pulling. If geometry forces it, re-rate the cable, winch, and anchor for 6.4 kN, and monitor the snag point for side load - a snag point loaded off-axis is itself a rigging hazard and should be engineered, not improvised.
3. Check the eye bolt against the site's 2.0 factor of safety, including the dynamic case, and state your recommendation.
Read the worked answer
Dynamic case, cable parallel to the ramp: When the winch accelerates the skid at a = 0.4 m/s² up the ramp, the cable must also accelerate the mass:
T_dyn = W sin15° + μk W cos15° + (W/g) a = 3,807 + 1,705 + (1,500 × 0.4) = 3,807 + 1,705 + 600 = 6,112 N
This is the worst credible steady load for the parallel rigging (the horizontal rigging gives about 6.4 kN plus dynamic allowance, roughly 6.8 kN).
Check against the eye bolt: Required capacity = 2.0 × 6,112 = 12,224 N ≈ 12.2 kN The eye bolt is rated 12 kN, so 12.0 < 12.2 - it does not meet the site's 2.0 factor of safety, even before considering shock loading from starting the winch, slight misalignment, or the horizontal-rigging case.
Recommendation:
- Do not use this eye bolt as the sole anchor for the pull. Select an anchor rated at least 14–15 kN working load to satisfy 2.0 on the dynamic tension with margin, or use a properly rated sling around a structural member with a softener.
- Verify the anchor's load direction rating - eye bolts are often rated for axial load only, and the pull here may be at an angle, which reduces capacity substantially.
- Confirm the concrete or embedment capacity, not just the hardware.
- Soft-start the winch to reduce the dynamic increment, and keep personnel out of the line of the cable and downhill of the skid.
- Re-check the ramp's capability for the increased normal load from any angled rigging.