Calculate the resultant load from two equal belt-span tensions and a specified change in belt direction. The angle between the two forces acting on the idler is 180° minus that deflection angle. This special-case calculation does not select a bearing or determine actual drive tensions.
Define the belt angle first
A straight belt has zero direction change, so equal tensions on the idler oppose one another. A complete reversal has 180° direction change, so those forces act together. Use the change in belt direction for this calculator, not the included angle between the two outward force vectors.
Idler Wheel Bearing Side Load Interactive Calculator
Explore the vector resultant F=2T sin(theta/2) for equal tensions on both sides of an ideal idler.
Equation Used
- Both belt spans have exactly the same tension magnitude T.
- Entered angle is belt-direction deflection from 0 to 180 degrees, not automatically pulley arc contact under every routing convention.
- Static coplanar forces applied at an ideal point/pulley center.
- No tight/slack-side difference, pretension/transmitted torque, centrifugal tension, pulley radius/width, belt stiffness, misalignment, bearing life, shaft stress, dynamics, vibration or safety factor.
The entered angle is treated as change in belt direction: zero means a straight, undeviated belt and 180 degrees means complete reversal. Calling it wrap angle can be ambiguous; actual idler reactions need the two tension magnitudes and their directions.
Equal-tension vector resultant
Two equal tension vectors acting on an idler combine according to their included geometry. If theta is defined as belt direction change, the resultant magnitude is 2T sin(theta/2).
The rotating wheel is illustrative. Its lines do not define the physical belt routing or the directions of bearing reactions; use the entered deflection convention and numerical load result for this calculation.
Use as a special-case free-body check
The formula can verify the resultant for equal span tensions and a known deflection angle. It cannot calculate real tight/slack tensions, shaft reactions or bearing life.
Angle convention controls the result
At theta=0 the belt remains straight and the equal/opposite forces cancel. At theta=180 degrees the belt reverses direction and the forces add to 2T. The vector acts along the routing-dependent bisector.
The final tile F−T is only arithmetic and has no separate load meaning.
Worked equal-tension example
For equal 200 N span tensions and 90-degree belt deflection, resultant magnitude is 2×200×sin45°≈282.84 N, or 1.414 times one span tension. Half the entered deflection is 45 degrees.
Scope and limitations
Real idler design requires actual belt routing and coordinates, pretension plus transmitted tight/slack tensions, speed and centrifugal tension, belt type/stiffness/minimum bend radius, pulley diameter/profile/width, wrap and traction, alignment and tracking, idler mass/inertia, shaft and support deflection/stress, bearing equivalent dynamic/static load and life, lubrication, environment, vibration and guarding.
Questions
Is wrap angle always the same as deflection angle?
No. Routing conventions differ; this calculator explicitly uses belt direction change.
Are both belt tensions equal in a driven belt?
Usually not while transmitting torque; both magnitudes must then be resolved separately.
Can this select a bearing?
No. Bearing type, duty, speed, life and dynamic factors are absent.
References & Further Reading
- Wikipedia contributors. Idler-wheel. Wikipedia
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