Tugger train: how many carts can I pull?

carts_by_capacity = floor(towing_capacity / (cart_tare + cart_payload)); carts_by_pull = floor((DBP - WT x 98 x G) / ((cart_tare + cart_payload) x (SR + 98 x G))); max_carts = the lower of the two

Derived by Warehouse Machines from Tow Tractors (Supralift materials handling glossary): no single source states this formula, so treat the result as an estimate.

Derived by Warehouse Machines: solves the drawbar pull formula (tow-tractor:drawbar-pull-required) for the towed load and divides by the weight of one loaded cart, and applies the maker's towing capacity; Supralift classifies tow tractors by drawbar pull and by the weight of load to be pulled. Turning, tracking and braking are not modeled.

Worked example: Example inputs (cart weights are ours): carts of 500 lb + 1,500 lb load = 2,000 lb (0.907 t) behind a tractor rated 250 lbf (1,112 N) normal drawbar pull and 10,000 lb rolling load capacity (Crown TR 4500), level smooth concrete (150 N/t rolling): by capacity 10,000 / 2,000 = 5 carts; by pull 1,112 / (0.907 x 150) = 8.2 -> 8 carts; the answer is 5.

level: DBP_N = WL × SR; grade: DBP_N = (WL × SR) + (W_grade × 98 × G) where W_grade = WT + WL (see conditions)

Corrected by Warehouse Machines: the source prints a different form; the conditions below say what changed and why.

Supralift prints the grade term as ((WT x WL) x 98 x G). Multiplying two weights gives tonnes squared, so the 98 N per tonne per % factor cannot apply to it; Warehouse Machines uses (WT + WL), the weight of everything going up the slope. 98 = 9.81 m/s2 x 1,000 kg x 1% (our check). Supralift: for average calculations use 400 N/tonne starting and 200 N/tonne rolling; compare the result with the tractor's maximum DBP (starting from rest) and rated DBP (rolling).

Worked example: Our check: 2 t load on smooth concrete (SR 150 rolling): level DBP = 2 × 150 = 300 N. Same load + 1.5 t tractor on an 8% grade: 300 + 3.5 × 98 × 8 = 3,044 N.

lookup (starting / rolling): smooth concrete 300/150; rough concrete 500/250; good macadam 400/200; smooth brick or tile 360/180; wood 400/200; hard gravel 700/350; steel rails straight 100/50

Supralift lists a starting and a rolling value per surface, in newtons per tonne of towed load.

Worked example: see drawbar-pull-required

rule

Taylor-Dunn Towmaster C4-10 / C4-20 brochure footnote to the towing capacity figures.

Worked example: Taylor-Dunn lists towing capacity 12,500 lb (C4-10) and 20,000 lb (C4-20).

1 mi/h = 0.44704 m/s; 1 km/h = 0.2777778 m/s; 1 lbf = 4.448222 N; 1 lb = 0.4535924 kg; 1 in = 0.0254 m; 1 t = 1,000 kg

NIST SP 811 Appendix B.9. Used by the calculators to show results in both unit systems.

Worked example: 28 mph x 0.44704 = 12.5 m/s.