The same balance-of-moments principle as the 3D flagship crane, seen from the side. Instead of a trolley sliding along a horizontal jib, this is a luffing boom: raising or lowering the boom angle θ changes how far out the load hangs. Every torque is measured about the crane's central pivot:
reach = L_boom · cos(θ) (horizontal distance, boom tip from pivot)
M_load = m_load · g · reach (tips toward the load, forward)
M_cw = m_cw · g · d_cw (fixed counterweight arm, resists forward tip)
overload_fwd = M_load − M_cw − M_struct (> 0 → tips forward, over the load side)
overload_bwd = M_cw − M_load − M_struct (> 0 → tips backward, over the counterweight side)
Simplifying assumptions (stated explicitly): the counterweight sits at a fixed horizontal arm from the pivot — only its mass changes, matching how real counterweight blocks are added or removed rather than repositioned. M_struct is a constant resisting moment standing in for the chassis's own dead weight and outrigger footprint — real capacity also depends on how far apart the outriggers are set, which this model holds fixed. The boom's own weight and any dynamic (swinging or accelerating) loads are ignored — only the static load and counterweight moments are balanced, which is why a real crane's load chart also derates for wind and lift speed but this one does not.
- Load mass — the mass hanging from the boom tip.
- Boom angle — steeper (larger θ) pulls the load in and shrinks the overturning moment; shallower reaches further out and grows it.
- Counterweight mass — more mass at the fixed rear arm adds resisting moment, but too much with too little load can tip the rig backward instead.