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The science
What is simulated
A walking dragline excavator strips overburden in an open-cast pit: the bucket is dragged across the pit floor, hoisted, swung to the spoil heap, dumped and returned. The page computes the boom geometry, the time of each phase, the rock moved per hour, the swing and hoist power, and whether the machine tips forward about the edge of its tub.
Geometry and motion
The boom pivots at a foot 14 m from the swing axis and 12 m above the bench. A boom of length L at angle β has its tip at radius 14 + L cosβ and height 12 + L sinβ. Swing and hoist use a limited-acceleration profile: over a distance s with acceleration a and top speed v, t = 2 √(s/a) if s ≤ v2/a, otherwise t = s/v + v/a. Hoisting overlaps the loaded swing and lowering overlaps the return swing, so each leg takes the longer of the two.
Payload, power and stability
A bucket of capacity Vb filled to fraction f carries loose volume f Vb, which is f Vb / (1 + swell) of undisturbed (bank) rock of density ρ. The swing moment of inertia sums boom, house, counterweight and loaded bucket, so peak swing power is P = I α ωpeak and the energy per swing is ½ I ωpeak2. Static stability compares the restoring moment of tub, house and counterweight about the front edge of the tub (16 m from the axis) with the overturning moment of boom and loaded bucket hanging at the tip.
Simplifications
- Masses (tub 1500 t, house 1600 t, boom 9 t per metre, bucket 0.5 t per m3) and cycle constants are round illustrative values of the right order for a large dragline, not data for a specific machine.
- The bucket is a point mass at the dump radius, the boom a uniform rod; rope sag, bucket swing, dynamic loads and ground bearing pressure are not modelled, and the 1.5 margin is a rule of thumb, not a design standard.
- The digging force and the fill factor are inputs; the page does not model how the bucket fills in the rock.
- Productivity is output per hour of digging time multiplied by the share of the time the machine digs.
Checks
Five boxes: boom tip and pendant triangle against a rotation matrix, the swing profile stepped in 0.1 ms against the closed form and the kinetic energy, the hoist rope work against m g h, the boom overturning moment by numerical mass slices, and a Monte Carlo shift of 16 000 cycles with random fill and swing angle against the mean-value productivity.