Conveyor vertical curve radius calculator
Minimum concave and convex curve radius for a troughed belt: lift-off, edge and centre overstress, buckling and the 30′-per-idler rule.
Result
How it works
Where a conveyor changes slope, the belt follows a vertical curve. In a concave curve (flat run into an incline) a tight radius lets the belt lift off the idlers at start-up and spill material; the belt centre is overstressed and the edges can buckle. In a convex curve (incline to flat, over idlers) the edges are overstressed and the centre can buckle.
Pitcher’s closed-form method (Beltcon 17, 2013) checks each failure mode from the belt width, trough angle, belt modulus, rated tension, the highest and lowest belt tensions at the curve and the belt mass. The required radius is the largest of the checks.
Formula
Concave lift-off: R11 = 1000 · γ · T / B, γ = tan θ / (g · θ) Concave centre overstress: R12 = W · E · sin α / [9 (tr − T/W)] Concave edge buckling: R13 = W · E · sin α / [4.5 (Tlow/W − Tmin)] Convex edge overstress: R21 = W · E · sin α / [4.5 (tr − T/W)]; centre buckling: R22 = W · E · sin α / [9 (Tlow/W − Tmin)] Convex idler angle ≤ 30′: R23 = Ie / 0.5° = 114.6 · Ie; required R = the largest
| Symbol | Meaning | Unit |
|---|---|---|
| W | Belt width | m |
| α | Trough angle (three equal rolls) | ° |
| E | Belt modulus per width (belt maker) | kN/m |
| tr | Maximum recommended tension per width (belt maker) | kN/m |
| T, Tlow | Highest and lowest belt tension at the curve | kN |
| B | Belt mass (belt only) | kg/m |
| θ | Change of slope through the curve | rad |
| Tmin | Minimum tension at edges/centre (CEMA 30 lbf/in) | kN/m |
| Ie | Idler spacing in the convex curve | m |
Worked example
Inputs: Curve type = concave ; Belt width W = 1000 mm; Trough angle α = 35 °; Belt modulus and rated tension = steel ; Belt strength tu = 1000 N/mm; Belt modulus E (belt maker) = kN/m; Max. recommended tension tr (belt maker) = kN/m; Highest tension at the curve = 100 kN; Lowest tension at the curve = 40 kN; Belt mass (belt only) = 30 kg/m; Change of slope θ = 10 °; Convex idler spacing = m; Minimum edge/centre tension = kN/m.
- ST 1000, 1000 mm, 35°, 30 kg/m; 1982 ratios: E = 65 000 kN/m, tr = 150 kN/m; T = 100 kN, Tlow = 40 kN, θ = 10°
- W·E·sin α = 37,282 kN; γ = 0.1030
- Lift-off R11 = 343 m; centre overstress R12 = 83 m; edge buckling R13 = 238 m
- Concave radius ≥ 343 m (lift-off governs); curve length ≈ 60 m
- Same belt convex with 1.2 m idler spacing: edges 166 m, centre 119 m, 30′ rule 138 m → ≥ 166 m
- Hand-calculated with Pitcher’s formulas; the paper gives no numerical example.
Assumptions and limits
- Three equal-length rolls; the belt modulus E and rated tension tr must come from your belt maker for a design decision (the 1982 ratios are dated Dunlop data).
- Use the highest tension at the curve (normally loaded start-up) for lift-off and overstress, and the lowest tension (running empty or stopping) for buckling — from the effective tension calculator at the curve position.
- The convex edge/centre coefficients (4.5 / 9) follow Pitcher’s own strain derivation and CEMA; the paper’s p.6 prints them swapped.
- Minimum edge/centre tension defaults to CEMA’s 30 lbf/in ≈ 5.25 kN/m; MHEA uses 4.4 kN/m.
- Screening only. Long, high-tension or high-speed conveyors need a dynamic (start/stop) analysis and the belt maker’s confirmation.
Screening estimate, not a design approval. Verify measured inputs, current standards, manufacturer limits and site procedures before purchasing, cutting or installation. Isolate and lock out equipment before any hands-on measurement.
Questions
Which case usually governs a concave curve?
On light, high-tension belts the lift-off radius at loaded start-up usually governs. Reducing start-up tension (a soft start) can allow a smaller radius.
What if the belt is overstressed at any radius?
If the tension per width at the curve is at or above the rated tension, no radius will help: the belt is overloaded at that point. Choose a stronger belt or reduce the tension.
Source notes
- R.O. Pitcher, “Calculation of correct radii for vertical curves in troughed belt conveyors”, Beltcon 17 (IMHC, 2013), paper B17-16, pp.3–7 — lift-off, overstress and buckling formulas. Method used with credit.
- CEMA, Belt Conveyors for Bulk Materials — minimum edge tension 30 lbf/in, as quoted by Pitcher.
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