A mast-and-gaff hoist supports a lifting line at the tip of an inclined gaff attached to a vertical mast. Explore the arrangement and calculate tip reach, elevation and the ideal vertical rope distance from the entered geometry.
Mast-and-Gaff Geometry Calculator
Enter gaff length, angle above horizontal, gaff-pivot height above the collar and shaft depth. The calculator reports relative tip geometry and an ideal vertical rope run; it does not size spars, guys, ropes or hoisting machinery.
Equation Used
- The gaff is a straight segment of length L at the entered angle above horizontal.
- The shaft depth datum and mast-pivot height use the same collar elevation.
- Only the vertical tip-to-bottom rope segment is reported; no force or capacity inference is made.
Gaff length and angle determine horizontal reach and tip rise. Adding the pivot height and shaft depth gives an ideal vertical rope run, excluding reeving, drum lead, sag and clearance.
Documented mast-and-gaff arrangement
Historical drawings and the C. W. Hunt catalogue show a vertical mast, an inclined gaff joined by mast fittings, hoisting machinery and a suspended load. Hunt described the form as suitable where business volume was limited, height was not great and loads were moderate. Its mast band could be loosened and the joint adjusted horizontally.
The animation keeps the gaff angle fixed and moves the bucket only along the vertical line below the tip. Horizontal slewing and dumping motion are outside this two-dimensional view.
Geometry screen, not equipment selection
The calculator converts four entered dimensions into tip coordinates and a vertical distance. Use actual engineered drawings, rated fittings, rigging plans and applicable hoisting rules for any real installation.
Explicit planar geometry
x is horizontal reach from the pivot, y is tip rise above it, H is tip elevation above the collar, and R is the ideal vertical distance from tip to shaft bottom.
Arithmetic example
For L=12 ft, theta=45 degrees, h=18 ft and D=45 ft, reach and tip rise are each 8.5 ft, tip height is 26.5 ft and ideal vertical run is 71.5 ft. Those values do not include drum lead, reeving, sag or clearance.
Geometry and load limits
Structural forces depend on the actual hoist-line path, peak support, joints, guys, mast base, load dynamics and three-dimensional geometry.
Mast-and-gaff questions
Does reach determine capacity?
No. It is geometry only.
Why is load not an input?
This calculator determines geometry only. Calculating loads requires the actual rope path, support connections, guys and a complete force analysis of the installation.
Does the animation show horizontal slewing?
No. Hunt notes that the joint could be adjusted horizontally, but the page does not model that three-dimensional motion.
Historical references
- Hiscox, Mechanical Movements, Powers, Devices and Appliances: includes the mast-and-gaff hoist among historical mining and hoisting arrangements.
- C. W. Hunt Company, General Catalogue No. 102 (1910), Mast and Gaff Hoisting: describes the intended limited-height, moderate-load service and horizontally adjustable mast-band joint.
- NBER, Changes in Mechanization: Non-Manufacturing Industries: records mast-and-gaff loaders as historical coal-handling equipment.
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