Angle of Wrap given Belt Tension in Tight Side Calculator

✖Belt Tension on Tight Side is defined as the belt's tension on the belt's tight side.ⓘ Belt Tension on Tight Side [P₁]			+10% -10%
✖Mass of Meter Length of Belt is the mass of 1-meter length of the belt simply mass per unit length of the belt.ⓘ Mass of Meter Length of Belt [m]			+10% -10%
✖Belt Velocity is defined as the velocity of the belt used in a belt drive.ⓘ Belt Velocity [v_b]			+10% -10%
✖Belt Tension on Loose Side is defined as the belt's tension on the belt's loose side.ⓘ Belt Tension on Loose Side [P₂]			+10% -10%
✖Coefficient of Friction for Belt Drive is the ratio defining the force that resists the motion of the belt over the pulley.ⓘ Coefficient of Friction for Belt Drive [μ]			+10% -10%

✖Wrap Angle on Pulley is the angle between the run-up and run-off of the belt on the pulley.ⓘ Angle of Wrap given Belt Tension in Tight Side [α]

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Formula

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Angle of Wrap given Belt Tension in Tight Side

Formula

`"α" = ln(("P"_{"1"}-"m"*"v"_{"b"}^2)/("P"_{"2"}-("m"*"v"_{"b"}^2)))/"μ"`

Example

`"160.3553°"=ln(("800N"-"0.6kg/m"*("25.81m/s")^2)/("550N"-("0.6kg/m"*("25.81m/s")^2)))/"0.35"`

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Angle of Wrap given Belt Tension in Tight Side Solution

STEP 0: Pre-Calculation Summary

Formula Used

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
α = ln((P₁-m*v_b^2)/(P₂-(m*v_b^2)))/μ
This formula uses 1 Functions, 6 Variables

Functions Used

ln - The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function., ln(Number)

Variables Used

Wrap Angle on Pulley - (Measured in Radian) - Wrap Angle on Pulley is the angle between the run-up and run-off of the belt on the pulley.
Belt Tension on Tight Side - (Measured in Newton) - Belt Tension on Tight Side is defined as the belt's tension on the belt's tight side.
Mass of Meter Length of Belt - (Measured in Kilogram per Meter) - Mass of Meter Length of Belt is the mass of 1-meter length of the belt simply mass per unit length of the belt.
Belt Velocity - (Measured in Meter per Second) - Belt Velocity is defined as the velocity of the belt used in a belt drive.
Belt Tension on Loose Side - (Measured in Newton) - Belt Tension on Loose Side is defined as the belt's tension on the belt's 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.

STEP 1: Convert Input(s) to Base Unit

Belt Tension on Tight Side: 800 Newton --> 800 Newton No Conversion Required
Mass of Meter Length of Belt: 0.6 Kilogram per Meter --> 0.6 Kilogram per Meter No Conversion Required
Belt Velocity: 25.81 Meter per Second --> 25.81 Meter per Second No Conversion Required
Belt Tension on Loose Side: 550 Newton --> 550 Newton No Conversion Required
Coefficient of Friction for Belt Drive: 0.35 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

α = ln((P₁-m*v_b^2)/(P₂-(m*v_b^2)))/μ --> ln((800-0.6*25.81^2)/(550-(0.6*25.81^2)))/0.35

Evaluating ... ...

α = 2.79872750235192

STEP 3: Convert Result to Output's Unit

2.79872750235192 Radian -->160.355273891985 Degree (Check conversion here)

FINAL ANSWER

160.355273891985 ≈ 160.3553 Degree <-- Wrap Angle on Pulley

(Calculation completed in 00.004 seconds)

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Osmania University (OU), Hyderabad

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< 15 Introduction of Belt Drives Calculators

Velocity of belt given tension of belt in tight side

Go Belt Velocity = sqrt((((e^(Coefficient of Friction for Belt Drive*Wrap Angle on Pulley))*Belt Tension on Loose Side)-Belt Tension on Tight Side)/(Mass of Meter Length of Belt*((e^(Coefficient of Friction for Belt Drive*Wrap Angle on Pulley))-1)))

Angle of Wrap given Belt Tension in Tight Side

Go 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

Mass per unit length of belt

Go Mass of Meter Length of Belt = (Belt Tension on Tight Side-((e^(Coefficient of Friction for Belt Drive*Wrap Angle on Pulley))*Belt Tension on Loose Side))/((Belt Velocity^2)*(1-(e^(Coefficient of Friction for Belt Drive*Wrap Angle on Pulley))))

Coefficient of Friction in between Surfaces given Belt Tension in Tight Side

Go Coefficient of Friction for Belt Drive = 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))/Wrap Angle on Pulley

Belt Tension in Loose Side of Belt given Tension in Tight Side

Go Belt Tension on Loose Side = ((Belt Tension on Tight Side-(Mass of Meter Length of Belt*Belt Velocity^2))/(e^(Coefficient of Friction for Belt Drive*Wrap Angle on Pulley)))+(Mass of Meter Length of Belt*Belt Velocity^2)

Belt tension in tight side

Go Belt Tension on Tight Side = ((e^(Coefficient of Friction for Belt Drive*Wrap Angle on Pulley))*(Belt Tension on Loose Side-(Mass of Meter Length of Belt*Belt Velocity^2)))+(Mass of Meter Length of Belt*Belt Velocity^2)

Length of Belt

Go Belt Length = (2*Centre Distance between Pulleys)+(pi*(Diameter of Big Pulley+Diameter of Small Pulley)/2)+(((Diameter of Big Pulley-Diameter of Small Pulley)^2)/(4*Centre Distance between Pulleys))

Wrap Angle for Small Pulley

Go Wrap Angle on Small Pulley = 3.14-(2*(asin((Diameter of Big Pulley-Diameter of Small Pulley)/(2*Centre Distance between Pulleys))))

Wrap Angle for Big Pulley

Go Wrap Angle on Big Pulley = 3.14+(2*(asin((Diameter of Big Pulley-Diameter of Small Pulley)/(2*Centre Distance between Pulleys))))

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

Go Centre Distance between Pulleys = (Diameter of Big Pulley-Diameter of Small Pulley)/(2*sin((3.14-Wrap Angle on Small Pulley)/2))

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

Go Centre Distance between Pulleys = (Diameter of Big Pulley-Diameter of Small Pulley)/(2*sin((Wrap Angle on Big Pulley-3.14)/2))

Diameter of Small Pulley given Wrap Angle of Small Pulley

Go Diameter of Small Pulley = Diameter of Big Pulley-(2*Centre Distance between Pulleys*sin((3.14-Wrap Angle on Small Pulley)/2))

Diameter of Big Pulley given Wrap Angle of Small Pulley

Go Diameter of Big Pulley = Diameter of Small Pulley+(2*Centre Distance between Pulleys*sin((3.14-Wrap Angle on Small Pulley)/2))

Diameter of Small Pulley given Wrap Angle of Big Pulley

Go Diameter of Small Pulley = Diameter of Big Pulley-(2*Centre Distance between Pulleys*sin((Wrap Angle on Big Pulley-3.14)/2))

Diameter of Big Pulley given Wrap Angle for Big Pulley

Go Diameter of Big Pulley = Diameter of Small Pulley+(2*Centre Distance between Pulleys*sin((Wrap Angle on Big Pulley-3.14)/2))

Angle of Wrap given Belt Tension in Tight Side Formula

What are theTypes of Belt Drives?

There are five different kinds of belt drive that can be found and those are:
Open belt drive.
Closed or crossed belt drive.
Fast and loose cone pulley.
Stepped cone pulley.
Jockey pulley drive.

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

Angle of Wrap given Belt Tension in Tight Side calculator 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 calculate 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 calculate Angle of Wrap given Belt Tension in Tight Side using this online calculator? To use this online calculator 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. Here is how the Angle of Wrap given Belt Tension in Tight Side calculation can be explained with given input values -> 9187.68 = ln((800-0.6*25.81^2)/(550-(0.6*25.81^2)))/0.35.

FAQ

What is Angle of Wrap given Belt Tension in Tight Side?

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 and is represented as α = ln((P₁-m*v_b^2)/(P₂-(m*v_b^2)))/μ or 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. Belt Tension on Tight Side is defined as the belt's tension on the belt's tight side, Mass of Meter Length of Belt is the mass of 1-meter length of the belt simply mass per unit length of the belt, Belt Velocity is defined as the velocity of the belt used in a belt drive, Belt Tension on Loose Side is defined as the belt's tension on the belt's loose side & Coefficient of Friction for Belt Drive is the ratio defining the force that resists the motion of the belt over the pulley.

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

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 is calculated using 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 calculate Angle of Wrap given Belt Tension in Tight Side, you need 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). With our tool, you need to enter the respective value for Belt Tension on Tight Side, Mass of Meter Length of Belt, Belt Velocity, Belt Tension on Loose Side & Coefficient of Friction for Belt Drive and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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