Overhead Crane & Mine Hoist Engineering, Wire-Rope Winch Fleet Angle & D/d Fatigue
Wire-Rope Winch Fleet Angle & Sheave D/d Ratio Formula
Calculate Maximum Winch-Drum Fleet Angle ATAN((W/2)/L) (deg), Minimum Lead-Sheave Stand-Off Distance for 1.5° Limit (m), Sheave-to-Rope Bending Ratio D/d, and Spooling Audit.
Mount a lead sheave too close OR too far from a winch drum and wire rope either scrubs drum flanges or piles up in the center!
Proper multi-layer wire-rope spooling onto a hoist drum of Flange-to-Flange Width `W` (m) from a centered fixed Lead Sheave at perpendicular Stand-Off Distance `L` (m) depends critically on **Maximum Fleet Angle `alpha_fleet = ATAN((W / 2) / L)`**! Counter-intuitively, fleet angle has BOTH an upper AND a lower bound: if `alpha_fleet > 1.5°` on smooth drums (`> 2.0°` on Lebus helical-grooved drums!), excessive side scrub abrades adjacent wraps and crushes strands against the drum flange; if `alpha_fleet < 0.5°`, insufficient lateral return force prevents the rope from rolling away from the flange, causing dangerous "piling" and snap-drop shock loads! Simultaneously, wire-rope outer-strand bending fatigue requires **Sheave Pitch-to-Rope Diameter Ratio `D / d >= 24`** (`>= 18–30` per ASME B30 / CMAA crane service class)!
Verify on a Lebus-Grooved Harbor Hoist Winch—Drum_Between-Flanges_Width `W` = 0.90 m (B2), Fixed_Lead-Sheave_Distance `L` = 18.00 m (B3 -> Max Fleet Angle = `1.43°` in E2, vs `17.18` m minimum stand-off for a `1.5°` smooth drum in E3), Wire-Rope_Diameter `d` = 22.0 mm (B4), and Lead-Sheave_Pitch_Diameter `D` = 660.0 mm (B5 -> `D / d = 30.00` in E4): Spooling & Bending Gate confirms `"GROOVED DRUM & SHEAVE OK"` (E5)!
| Crane Hoist Wire-Rope KPI (Drum W=0.90 m, Lead L=18.0 m, d=22 mm, Sheave D=660 mm) | Formula | Verified Output |
|---|---|---|
| Maximum Winch Fleet Angle (deg) | ATAN((Drum_W_m / 2) / Lead_L_m) * (180/PI()) | 1.43° (3.22° > 2.0° @ cramped L=8.0 m!) |
| Min Lead Distance @ 1.5° (m) | (Drum_W_m / 2) / TAN(1.5 * PI()/180) | 17.18 m |
| Sheave Bending Ratio (D / d) | Sheave_Pitch_D_mm / Wire_Rope_d_mm | 30.00 (>= 24 heavy-duty crane spec) |
| CMAA / Lebus Spooling Gate | 0.5° <= Fleet <= 2.0° AND D/d >= 24 | GROOVED DRUM & SHEAVE OK |
Winch-Drum Fleet Angle Window & Sheave D/d Bending Fatigue Formula
Validate `Drum_Width W > 0` m, `Lead_Distance L > 0` m, `Rope_Diam d > 2` mm, and `Sheave_Diam D > d` mm right on `E2` (checking `ISTEXT(E2)` on `E3..E4` so text pass/violation labels in `E5` stay decoupled)!
=LET(wd_m, B2, ld_m, B3, dr_m, B4, ds_m, B5, fl_d, ATAN((wd_m / 2) / ld_m) * (180 / PI()), dd_r, ds_m / dr_m, IF(OR(wd_m <= 0, ld_m <= 0, dr_m <= 2, ds_m <= dr_m), "Invalid Hoist Input", IF(AND(fl_d >= 0.5, fl_d <= 2, dd_r >= 24), "GROOVED DRUM & SHEAVE OK", "FLEET OR BENDING VIOLATION")))Cramped Deckhouse 8.0 m Lead-Sheave Fleet Scrubbing Violation Check (Set Lead Distance B3 = 8.0 m)
Crowd the lead block onto a cramped `8.0` m deck (`B3 = 8.0`): Fleet Angle E2 jumps to `3.22°` (`> 2.0°` grooved ceiling!), triggering `"FLEET OR BENDING VIOLATION"` in E5 until a traversing level-wind or Fleet-Angle Compensator (`FAC`) sheave is installed!
=IF(ISTEXT(E2), E2, ROUND(B5 / B4, 2))Try the example
Use the original values or change them to test your understanding.