For a friction-driven conveyor, T1 and T2 follow from the effective pull and the Eytelwein relation T1/T2 = e^(μθ), with θ expressed in radians.
The calculation covers drive traction, belt-strength sizing, take-up loading, motor power, and the operating limits imposed by slip and sag.
Separate Effective Pull, T1, and T2
Effective tension, Te, is the net force the drive must apply to move the loaded conveyor at constant speed. It combines resistance from belt and idler friction, material lift, cleaner and skirt-board drag, material momentum, and start-up acceleration [S2]. A simplified conveyor model used by BisonConvey expresses the main resistance as Te = f·L·g·(2·Wb + Wm)·cos α + Wm·g·H, where L is conveyor length, f is the idler friction factor, Wb is belt mass per unit length, Wm is material mass per unit length, α is the inclination angle, and H is vertical lift [S1].
Drive power follows from P = Te·v, with Te in newtons and v in metres per second giving power in watts. Imperial calculations use P(ft-lb/min) = Te(lb)·v(ft/min), followed by division by 33,000 ft-lb/min per horsepower [S2]. A practical motor selection must include gearbox, coupling, startup, acceleration, and material build-up rather than use theoretical shaft power alone [S1].
The relationship between the two pulley-side tensions is T1 - T2 = Te, so once Te and the traction ratio are known, the maximum static tension can be written T1 = Te + T2 [S2]. T1 is the tight-side value and normally governs carcass and splice selection, while T2 is the slack-side value maintained by the take-up.
Apply the Wrap-Angle Friction Relation
The operating tension ratio is T1/T2 = e^(μθ), where μ is the belt-to-pulley friction coefficient and θ is the wrap angle in radians [S1][S4]. Combining that relation with T1 - T2 = Te gives T1 = Te·e^(μθ)/(e^(μθ) - 1) and T2 = Te/(e^(μθ) - 1) [S1]. The smaller wrap angle usually sets the traction limit because it produces the lower available tension ratio [S4].
For equal pulleys, the basic geometry gives 180° wrap on each pulley. For unequal pulley radii, the small-pulley angle is 180° - 2α and the large-pulley angle is 180° + 2α, with α calculated from pulley radii and centre distance [S4]. A plain 180° drive, a 210° snub-augmented arrangement, and a dual-pulley arrangement reaching 240° are practical values used in the calculator [S1].
Published friction values include 0.30 for dry bare steel, 0.20 for wet bare steel, 0.35 for dry rubber lagging, 0.30 for wet rubber lagging, 0.45 for dry ceramic lagging, and 0.40 for wet ceramic lagging [S1]. Surface condition therefore changes the calculated T1/T2 ratio, not just the drive coefficient. Keep θ in radians when evaluating e^(μθ), because treating 180° as the numeric value 180 would produce a meaningless result.
Compare the Main Calculation Methods
The simplified method used by BisonConvey combines idler friction and material lift in one effective-tension expression, then uses the capstan relation to split Te into T1 and T2 [S1]. The CEMA historical method is more granular: Te = LKt(Kx + KyWb + 0.015Wb) + Wm(LKy + H) + Tp + Tam + Tac, with separate terms for friction, gravity, material acceleration, and belt acceleration [S2].
Against calculation depth, the simplified method requires fewer inputs and is suitable for preliminary drive checks. Against auxiliary-load coverage, the CEMA form can explicitly include cleaner drag, skirt-board drag, return-roller bearing friction, material momentum, and acceleration tension. Against traction treatment, the Eytelwein method calculates the ratio from μ and θ directly, while the CEMA historical method specifies T2 slip = Te·Cw, where Cw is a wrap factor [S1][S2].
The CEMA wrap-factor range demonstrates that a single friction coefficient and wrap angle are not a complete replacement for the historical method. Cw can be 0.08 for a dual-drive system with rubber-lagged pulleys, an automatic take-up, and 420° wrap, or 1.2 for a single drive with an unlagged pulley, manual take-up, and 180° wrap [S2]. For a final design, use the project’s selected design method consistently rather than combining a CEMA effective-tension result with an unrelated wrap-factor equation.
Set Idler Friction and Operating Conditions
Idler friction is a major variable in Te and should be selected from operating conditions rather than treated as a universal constant. Published reference values are 0.018 for clean indoor service, 0.020 for standard outdoor service, 0.022 as the default design value, 0.025 for dusty mining environments, and 0.030 for heavy fouling or cold start [S1].
Conveyor geometry changes the result as well. The simplified Te expression includes the cosine of the inclination angle, while Wm·g·H represents the material lift component [S1]. This distinction matters on an incline because belt friction, material lift, and drive traction are not independent. Wrap angle also depends on conveyor type, length, belt width, capacity, and the installed tension arrangement [S5].
Short conveyors can carry a disproportionate end-loss penalty. A design review may apply a 1.05–1.10 multiplier to Te for conveyors shorter than 50 m, while long, heavily loaded systems require an explicit start-up tension check. The published guidance identifies soft starting or a fluid coupling for conveyors longer than 200 m or handling more than 2,000 t/h [S1].
Control Slip, Sag, and Take-Up Load
Drive slip occurs when the required tension ratio exceeds the friction available at the pulley, so μ, wrap angle, belt condition, and wet or dry surface state must all be verified [S1][S3]. Larger wrap angles increase the available ratio, but a snub pulley cannot compensate for contaminated, wet, or damaged lagging. Dual drives can distribute the load, and the cited CEMA example reaches a 0.08 wrap factor with 420° of wrap [S2].
Sag is a separate limit from slip. CEMA historical design permits selection of an acceptable percentage of sag between carrying idlers to prevent material from leaving the belt, with 3% listed as one of the CEMA percentages [S2]. On an inclined conveyor, minimum carrying-strand tension commonly occurs near the loading zone, so the take-up must preserve tension at that location rather than only at the drive pulley.
A gravity take-up uses belt tension to balance the moving mass of the take-up assembly, while a screw take-up sets tension by changing the distance between pulley centres. The January 2026 technical guide identifies both methods and links their sizing to the calculated T1/T2 relationship [S3]. Record the counterweight, travel, belt length, screw pitch, and installed tension so that belt stretch, splice take-up, and wear do not produce an unintended slack-side reduction.
For operating energy context, the drive-side result can be compared with a belt conveyor energy calculation, but kWh per tonne does not replace the mechanical checks for slip, sag, startup, and belt strength.
Apply Belt-Strength and Acceleration Checks
Calculated T1 is an operating tension, not the complete belt specification. Belt selection must also consider rated carcass strength, splice rating, pulley diameter, service factor, and the dynamic tension during startup. The published calculator guidance recommends a 6–10× safety factor over carcass breaking strength for belt selection, while also distinguishing maximum static tension from working tension [S1].
The CEMA effective-tension expression includes Tac, the tension associated with accelerating the material, and Tam, the tension needed to accelerate material from its impact velocity to conveyor speed [S2]. These terms are not automatically captured by a steady-state simplified calculation. A motor sized only from P = Te·v may therefore be under-sized for a loaded start, especially where Q exceeds 2,000 t/h or L exceeds 200 m [S1].
Decline conveyors require a separate sign check. If the gravitational term makes the calculated Te negative, the drive must restrain the descending belt rather than propel it, requiring a holdback or regenerative variable-frequency drive arrangement [S1]. On rising conveyors, verify the loaded-start case, the emergency-stop case, and the static holding case separately. A belt system design also needs a clearer comparison between fabric and steel-cord ratings, which is covered in fabric versus steel-cord belt safety factors.
Build a Traceable Commissioning Check
A defensible calculation sheet should retain conveyor length L, lift H, belt speed v, capacity Q, belt mass Wb, inclination α, idler factor f, pulley friction coefficient μ, wrap angle θ, and every added resistance term [S1][S2]. Record the selected design method, because a CEMA historical result and a simplified CEMA estimate are not interchangeable without reconciliation.
Commission the drive with the calculated Te, T1, and T2 entered as independent checkpoints. Confirm the installed counterweight or screw position, check for pulley slip, inspect belt tracking, and compare measured motor load with the calculated shaft power. Any 1.05–1.15 drivetrain efficiency allowance or 15–25% motor service margin belongs in motor sizing, not in the basic definition of Te [S1].
The next trackable signal is the relationship between installed and calculated slack-side tension. A persistent gap usually points to take-up travel, belt stretch, splice seating, or counterweight errors, while a mismatch on the tight side points to elevation, friction, auxiliary drag, or acceleration assumptions. This closes the calculation loop without treating a single calculator result as a substitute for field verification.
