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Angle of Wrap of V-Belt given Belt Tension in Loose Side of Belt 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 = \sin (\frac{θ}{2}) \cdot \frac{\ln (\frac{P 1 - m v \cdot {v b}^{2}}{P 2 - m v \cdot {v b}^{2}})}{μ}

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

Angle of Wrap of V-Belt given Belt Tension in Loose Side of Belt Example

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

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

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

160.5987 = \sin (\frac{62}{2}) \cdot \frac{\ln (\frac{800 - 0.76 \cdot {25.81}^{2}}{550 - 0.76 \cdot {25.81}^{2}})}{0.35}

160.5987° = \sin (\frac{62°}{2}) \cdot \frac{\ln (\frac{800N - 0.76kg/m \cdot {25.81m/s}^{2}}{550N - 0.76kg/m \cdot {25.81m/s}^{2}})}{0.35}

160.5987 = \sin (\frac{62}{2}) \cdot \frac{\ln (\frac{800 - 0.76 \cdot {25.81}^{2}}{550 - 0.76 \cdot {25.81}^{2}})}{0.35}

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Angle of Wrap of V-Belt given Belt Tension in Loose Side of Belt Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

α = \sin (\frac{62°}{2}) \cdot \frac{\ln (\frac{800N - 0.76kg/m \cdot {25.81m/s}^{2}}{550N - 0.76kg/m \cdot {25.81m/s}^{2}})}{0.35}

Next Step Convert Units

∴

α = \sin (\frac{1.0821rad}{2}) \cdot \frac{\ln (\frac{800N - 0.76kg/m \cdot {25.81m/s}^{2}}{550N - 0.76kg/m \cdot {25.81m/s}^{2}})}{0.35}

Next Step Prepare to Evaluate

∴

α = \sin (\frac{1.0821}{2}) \cdot \frac{\ln (\frac{800 - 0.76 \cdot {25.81}^{2}}{550 - 0.76 \cdot {25.81}^{2}})}{0.35}

Next Step Evaluate

∴

α = 2.80297658045815rad

Next Step Convert to Output's Unit

∴

α = 160.598728134294°

LAST Step Rounding Answer

∴

α = 160.5987°

Angle of Wrap of V-Belt given Belt Tension in Loose Side of Belt 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

V belt angle

V Belt Angle is defined as the angle included between the side faces of the V cross-section belt.

Symbol: θ

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find V belt angle

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 V Belt

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

Symbol: m_v

Measurement: Linear Mass DensityUnit: kg/m

Note: Value should be greater than 0.

Formulas to find Mass of Meter Length of V 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

sin

Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

Syntax: sin(Angle)

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 V Belt Characteristics and Parameters category

Go Belt Tension in Loose Side of V-Belt

P 2 = \frac{P 1 - m v \cdot {v b}^{2}}{e^{μ} \cdot \frac{α}{\sin (\frac{θ}{2})}} + m v \cdot {v b}^{2}

Go Belt Tension in Tight Side of V-Belt

P 1 = (e^{μ} \cdot \frac{α}{\sin (\frac{θ}{2})}) \cdot (P 2 - m v \cdot {v b}^{2}) + m v \cdot {v b}^{2}

How to Evaluate Angle of Wrap of V-Belt given Belt Tension in Loose Side of Belt?

Angle of Wrap of V-Belt given Belt Tension in Loose Side of Belt evaluator uses Wrap Angle on Pulley = sin(V belt angle/2)*ln((Belt Tension on Tight Side-Mass of Meter Length of V Belt*Belt Velocity^2)/(Belt Tension on Loose Side-Mass of Meter Length of V Belt*Belt Velocity^2))/Coefficient of Friction for Belt Drive to evaluate the Wrap Angle on Pulley, The Angle of Wrap of V-Belt given Belt Tension in Loose Side of Belt 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 of V-Belt given Belt Tension in Loose Side of Belt using this online evaluator? To use this online evaluator for Angle of Wrap of V-Belt given Belt Tension in Loose Side of Belt, enter V belt angle (θ), Belt Tension on Tight Side (P₁), Mass of Meter Length of V Belt (m_v), 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 of V-Belt given Belt Tension in Loose Side of Belt

What is the formula to find Angle of Wrap of V-Belt given Belt Tension in Loose Side of Belt?

The formula of Angle of Wrap of V-Belt given Belt Tension in Loose Side of Belt is expressed as Wrap Angle on Pulley = sin(V belt angle/2)*ln((Belt Tension on Tight Side-Mass of Meter Length of V Belt*Belt Velocity^2)/(Belt Tension on Loose Side-Mass of Meter Length of V Belt*Belt Velocity^2))/Coefficient of Friction for Belt Drive. Here is an example- 9201.629 = sin(1.08210413623628/2)*ln((800-0.76*25.81^2)/(550-0.76*25.81^2))/0.35.

How to calculate Angle of Wrap of V-Belt given Belt Tension in Loose Side of Belt?

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

Can the Angle of Wrap of V-Belt given Belt Tension in Loose Side of Belt be negative?

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

Which unit is used to measure Angle of Wrap of V-Belt given Belt Tension in Loose Side of Belt?

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

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Angle of Wrap of V-Belt given Belt Tension in Loose Side of Belt Formula

Angle of Wrap of V-Belt given Belt Tension in Loose Side of Belt Example

Angle of Wrap of V-Belt given Belt Tension in Loose Side of Belt Solution

Angle of Wrap of V-Belt given Belt Tension in Loose Side of Belt Formula Elements

Other formulas in V Belt Characteristics and Parameters category

How to Evaluate Angle of Wrap of V-Belt given Belt Tension in Loose Side of Belt?

FAQs on Angle of Wrap of V-Belt given Belt Tension in Loose Side of Belt

Variable Name