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Angle of Wrap given Belt Tension in Tight Side Formula

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Wrap Angle on Pulley is the angle between the run-up and run-off of the belt on the pulley. Check FAQs

α = \frac{\ln (\frac{P 1 - m \cdot {v b}^{2}}{P 2 - (m \cdot {v b}^{2})})}{μ}

α - Wrap Angle on Pulley?P₁ - Belt Tension on Tight Side?m - Mass of Meter Length of Belt?v_b - Belt Velocity?P₂ - Belt Tension on Loose Side?μ - Coefficient of Friction for Belt Drive?

Angle of Wrap given Belt Tension in Tight Side Example

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Here is how the Angle of Wrap given Belt Tension in Tight Side equation looks like with Values.

Here is how the Angle of Wrap given Belt Tension in Tight Side equation looks like with Units.

Here is how the Angle of Wrap given Belt Tension in Tight Side equation looks like.

160.3553 = \frac{\ln (\frac{800 - 0.6 \cdot {25.81}^{2}}{550 - (0.6 \cdot {25.81}^{2})})}{0.35}

160.3553° = \frac{\ln (\frac{800N - 0.6kg/m \cdot {25.81m/s}^{2}}{550N - (0.6kg/m \cdot {25.81m/s}^{2})})}{0.35}

160.3553 = \frac{\ln (\frac{800 - 0.6 \cdot {25.81}^{2}}{550 - (0.6 \cdot {25.81}^{2})})}{0.35}

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Angle of Wrap given Belt Tension in Tight Side Solution

Follow our step by step solution on how to calculate Angle of Wrap given Belt Tension in Tight Side?

FIRST Step Consider the formula

α = \frac{\ln (\frac{P 1 - m \cdot {v b}^{2}}{P 2 - (m \cdot {v b}^{2})})}{μ}

Next Step Substitute values of Variables

∴

α = \frac{\ln (\frac{800N - 0.6kg/m \cdot {25.81m/s}^{2}}{550N - (0.6kg/m \cdot {25.81m/s}^{2})})}{0.35}

Next Step Prepare to Evaluate

∴

α = \frac{\ln (\frac{800 - 0.6 \cdot {25.81}^{2}}{550 - (0.6 \cdot {25.81}^{2})})}{0.35}

Next Step Evaluate

∴

α = 2.79872750235192rad

Next Step Convert to Output's Unit

∴

α = 160.355273891985°

LAST Step Rounding Answer

∴

α = 160.3553°

Angle of Wrap given Belt Tension in Tight Side Formula Elements

Variables

Functions

Wrap Angle on Pulley

Wrap Angle on Pulley is the angle between the run-up and run-off of the belt on the pulley.

Symbol: α

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Wrap Angle on Pulley

Belt Tension on Tight Side

Belt Tension on Tight Side is defined as the belt's tension on the belt's tight side.

Symbol: P₁

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Belt Tension on Tight Side

Mass of Meter Length of Belt

Mass of Meter Length of Belt is the mass of 1-meter length of the belt simply mass per unit length of the belt.

Symbol: m

Measurement: Linear Mass DensityUnit: kg/m

Note: Value should be greater than 0.

Formulas to find Mass of Meter Length of Belt

Belt Velocity

Belt Velocity is defined as the velocity of the belt used in a belt drive.

Symbol: v_b

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

Formulas to find Belt Velocity

Belt Tension on Loose Side

Belt Tension on Loose Side is defined as the belt's tension on the belt's loose side.

Symbol: P₂

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Belt Tension on Loose Side

Coefficient of Friction for Belt Drive

Coefficient of Friction for Belt Drive is the ratio defining the force that resists the motion of the belt over the pulley.

Symbol: μ

Measurement: NAUnit: Unitless

Note: Value should be between 0 to 1.

Formulas to find Coefficient of Friction for Belt Drive

The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function.

Syntax: ln(Number)

Other formulas in Introduction of Belt Drives category

Go Wrap Angle for Small Pulley

α s = 3.14 - (2 \cdot (a \sin (\frac{D - d}{2 \cdot C})))

Go Center Distance from Small Pulley to Big Pulley given Wrap Angle of Small Pulley

C = \frac{D - d}{2 \cdot \sin (\frac{3.14 - α s}{2})}

Go Diameter of Small Pulley given Wrap Angle of Small Pulley

d = D - (2 \cdot C \cdot \sin (\frac{3.14 - α s}{2}))

Go Diameter of Big Pulley given Wrap Angle of Small Pulley

D = d + (2 \cdot C \cdot \sin (\frac{3.14 - α s}{2}))

How to Evaluate Angle of Wrap given Belt Tension in Tight Side?

Angle of Wrap given Belt Tension in Tight Side evaluator uses Wrap Angle on Pulley = ln((Belt Tension on Tight Side-Mass of Meter Length of Belt*Belt Velocity^2)/(Belt Tension on Loose Side-(Mass of Meter Length of Belt*Belt Velocity^2)))/Coefficient of Friction for Belt Drive to evaluate the Wrap Angle on Pulley, The Angle of Wrap given Belt Tension in Tight Side formula is defined as the angle between the run-up and run-off of the belt on the pulley. Wrap Angle on Pulley is denoted by α symbol.

How to evaluate Angle of Wrap given Belt Tension in Tight Side using this online evaluator? To use this online evaluator for Angle of Wrap given Belt Tension in Tight Side, enter Belt Tension on Tight Side (P₁), Mass of Meter Length of Belt (m), Belt Velocity (v_b), Belt Tension on Loose Side (P₂) & Coefficient of Friction for Belt Drive (μ) and hit the calculate button.

FAQs on Angle of Wrap given Belt Tension in Tight Side

What is the formula to find Angle of Wrap given Belt Tension in Tight Side?

The formula of Angle of Wrap given Belt Tension in Tight Side is expressed as Wrap Angle on Pulley = ln((Belt Tension on Tight Side-Mass of Meter Length of Belt*Belt Velocity^2)/(Belt Tension on Loose Side-(Mass of Meter Length of Belt*Belt Velocity^2)))/Coefficient of Friction for Belt Drive. Here is an example- 9187.68 = ln((800-0.6*25.81^2)/(550-(0.6*25.81^2)))/0.35.

How to calculate Angle of Wrap given Belt Tension in Tight Side?

With Belt Tension on Tight Side (P₁), Mass of Meter Length of Belt (m), Belt Velocity (v_b), Belt Tension on Loose Side (P₂) & Coefficient of Friction for Belt Drive (μ) we can find Angle of Wrap given Belt Tension in Tight Side using the formula - Wrap Angle on Pulley = ln((Belt Tension on Tight Side-Mass of Meter Length of Belt*Belt Velocity^2)/(Belt Tension on Loose Side-(Mass of Meter Length of Belt*Belt Velocity^2)))/Coefficient of Friction for Belt Drive. This formula also uses Natural Logarithm (ln) function(s).

Can the Angle of Wrap given Belt Tension in Tight Side be negative?

No, the Angle of Wrap given Belt Tension in Tight Side, measured in Angle cannot be negative.

Which unit is used to measure Angle of Wrap given Belt Tension in Tight Side?

Angle of Wrap given Belt Tension in Tight Side is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Angle of Wrap given Belt Tension in Tight Side can be measured.

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Angle of Wrap given Belt Tension in Tight Side Formula

Angle of Wrap given Belt Tension in Tight Side Example

Angle of Wrap given Belt Tension in Tight Side Solution

Angle of Wrap given Belt Tension in Tight Side Formula Elements

Other formulas in Introduction of Belt Drives category

How to Evaluate Angle of Wrap given Belt Tension in Tight Side?

FAQs on Angle of Wrap given Belt Tension in Tight Side

Variable Name