Crane Load Radius and Boom-Tip Height from Boom Geometry
Turns the boom-angle-indicator reading into the load RADIUS the load chart is indexed by.
Example
You enter
- Boom length (ft) 30
- Boom angle from horizontal (deg) 60
- Boom-foot offset from center pin (ft) 4
- Boom-foot height (ft) 6
- Target load radius (ft) 25
You get
- Load radius 19 ft
- Boom-tip height 31.98 ft
- Angle for target radius (deg) 45.573
No published worked example is on file for this calculation. It is checked against a hand-worked derivation of its method and an independent reference test.
Details, formula, and sources
Scoperadius = boom-foot offset from the center pin + boom length x cos(angle); tip height = boom-foot height + boom length x sin(angle). A 30 ft boom at 60 degrees off a foot 4 ft out and 6 ft up puts the hook at a 19 ft radius and 32 ft tip height; lowering to 45 degrees swings it out to 25 ft. The inverse gives the angle for a target radius, acos((target - offset)/length), and flags a target beyond reach. RIGID-BOOM GEOMETRY ONLY -- boom deflection under load, rope stretch, and an out-of-level machine all INCREASE the real radius and cut capacity. The load chart, the load-moment indicator, and a qualified operator/lift director govern.
Formula or tableload_radius = boom_foot_offset + boom_length x cos(boom_angle); boom_tip_height = boom_foot_height + boom_length x sin(boom_angle); angle_for_target_radius = acos((target_radius - boom_foot_offset)/boom_length).
Source and editionCrane boom geometry (load radius and tip height from boom length and angle), by name; the manufacturer's load chart and the load-moment indicator govern the rated capacity.
Free accessThe radius/height relations are public plane trigonometry; the boom length, angle (off the boom-angle indicator), and geometry offsets are the operator's measured values.
What governsEstimate. Head rigger and manufacturer working-load-limit charts govern. Inspect every piece of hardware before the show.
API field namesboom_length_ft, boom_angle_deg, boom_foot_offset_ft, boom_foot_height_ft, target_radius_ft, load_radius_ft, boom_tip_height_ft, angle_for_target_radius_deg
- Rigid-boom geometry radius = offset + L cos(angle); tip height = foot height + L sin(angle); inverse angle = acos((target - offset)/L)plane trigonometry
- Deflection excluded boom deflection, rope stretch, and out-of-level all INCREASE the real radius; the load chart and load-moment indicator governcrane manufacturer load chart