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Wrap Angle for the Small Pulley Solution

STEP 0: Pre-Calculation Summary
Formula Used
wrap_angle_for_small_pulley = 3.14-2*asin((Diameter of Big Pulley-Diameter of Small Pulley)/2*Center Distance)
αs = 3.14-2*asin((D-d)/2*C)
This formula uses 2 Functions, 3 Variables
Functions Used
sin - Trigonometric sine function, sin(Angle)
asin - Inverse trigonometric sine function, asin(Number)
Variables Used
Diameter of Big Pulley - Diameter of Big Pulley is the distance from side to side of the flat of the Big pulley. (Measured in Millimeter)
Diameter of Small Pulley - Diameter of Small Pulley is the distance from side to side of the flat of the Small pulley. (Measured in Millimeter)
Center Distance - Center Distance is the distance in between the centers of the big pulley and the small pulley. (Measured in Millimeter)
STEP 1: Convert Input(s) to Base Unit
Diameter of Big Pulley: 100 Millimeter --> 0.1 Meter (Check conversion here)
Diameter of Small Pulley: 50 Millimeter --> 0.05 Meter (Check conversion here)
Center Distance: 300 Millimeter --> 0.3 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
αs = 3.14-2*asin((D-d)/2*C) --> 3.14-2*asin((0.1-0.05)/2*0.3)
Evaluating ... ...
αs = 3.12499985937144
STEP 3: Convert Result to Output's Unit
3.12499985937144 Radian -->179.049302920993 Degree (Check conversion here)
FINAL ANSWER
179.049302920993 Degree <-- Wrap Angle for Small Pulley
(Calculation completed in 00.031 seconds)

10+ Design of Belt Drives Calculators

Belt Tension in the Tight Side
belt_tension_in_tight_side = (e^Coefficient of Friction*Angle of Wrap)*(Belt Tension in loose Side-Mass of Meter Length of Belt*Belt Velocity^2)+Mass of Meter Length of Belt*Belt Velocity^2 Go
Length of the Belt
belt_length = 2*Center Distance+(pi*(Diameter of Big Pulley+Diameter of Small Pulley)/2)+((Diameter of Big Pulley-Diameter of Small Pulley)^2/4*Center Distance) Go
Center Distance from Small Pulley to Big Pulley When Wrap Angle of Small Pulley is Given
center_distance = (Diameter of Big Pulley-Diameter of Small Pulley)/(2*sin((3.14-Wrap Angle for Small Pulley)/2)) Go
Center Distance from Small Pulley to Big Pulley When Wrap Angle of Big Pulley is Given
center_distance = (Diameter of Big Pulley-Diameter of Small Pulley)/(2*sin((Wrap Angle for Small Pulley-3.14)/2)) Go
Wrap Angle for the Small Pulley
wrap_angle_for_small_pulley = 3.14-2*asin((Diameter of Big Pulley-Diameter of Small Pulley)/2*Center Distance) Go
Diameter of Small Pully When Wrap Angle of the Big Pulley is Given
diameter_of_small_pulley = Diameter of Big Pulley-2*Center Distance*sin((Wrap Angle for Small Pulley-3.14)/2) Go
Diameter of Big Pulley When Wrap Angle for the Big Pulley is Given
diameter_of_big_pulley = Diameter of Small Pulley+2*Center Distance*sin((Wrap Angle for Small Pulley-3.14)/2) Go
Diameter of Small Pulley When Wrap Angle of Small Pulley is Given
diameter_of_small_pulley = Diameter of Big Pulley-2*Center Distance*sin((3.14-Wrap Angle for Small Pulley)/2) Go
Diameter of Big Pulley When Wrap Angle of Small Pulley is Given
diameter_of_big_pulley = Diameter of Small Pulley+2*Center Distance*sin((3.14-Wrap Angle for Small Pulley)/2) Go
Wrap Angle for the Big Pulley
wrap_angle_for_big_pulley = 3.14+2*asin((Diameter of Big Pulley-Diameter of Small Pulley)/2*Center Distance) Go

Wrap Angle for the Small Pulley Formula

wrap_angle_for_small_pulley = 3.14-2*asin((Diameter of Big Pulley-Diameter of Small Pulley)/2*Center Distance)
αs = 3.14-2*asin((D-d)/2*C)

Define a Wrap Angle?

The wrap angle is defined as the angle between the run-up and run-off of the belt on the pulley. In addition, the greater curvature causes greater bending stresses in the belt, which also limits the transmittable belt force. So-called idler pulleys can be used to increase the wrap angle.

How to Calculate Wrap Angle for the Small Pulley?

Wrap Angle for the Small Pulley calculator uses wrap_angle_for_small_pulley = 3.14-2*asin((Diameter of Big Pulley-Diameter of Small Pulley)/2*Center Distance) to calculate the Wrap Angle for Small Pulley, The Wrap Angle for the Small Pulley formula is defined as the angle between the run-up and run-off of the belt on the pulley. Wrap Angle for Small Pulley and is denoted by αs symbol.

How to calculate Wrap Angle for the Small Pulley using this online calculator? To use this online calculator for Wrap Angle for the Small Pulley, enter Diameter of Big Pulley (D), Diameter of Small Pulley (d) and Center Distance (C) and hit the calculate button. Here is how the Wrap Angle for the Small Pulley calculation can be explained with given input values -> 179.0493 = 3.14-2*asin((0.1-0.05)/2*0.3).

FAQ

What is Wrap Angle for the Small Pulley?
The Wrap Angle for the Small Pulley formula is defined as the angle between the run-up and run-off of the belt on the pulley and is represented as αs = 3.14-2*asin((D-d)/2*C) or wrap_angle_for_small_pulley = 3.14-2*asin((Diameter of Big Pulley-Diameter of Small Pulley)/2*Center Distance). Diameter of Big Pulley is the distance from side to side of the flat of the Big pulley, Diameter of Small Pulley is the distance from side to side of the flat of the Small pulley and Center Distance is the distance in between the centers of the big pulley and the small pulley.
How to calculate Wrap Angle for the Small Pulley?
The Wrap Angle for the Small Pulley formula is defined as the angle between the run-up and run-off of the belt on the pulley is calculated using wrap_angle_for_small_pulley = 3.14-2*asin((Diameter of Big Pulley-Diameter of Small Pulley)/2*Center Distance). To calculate Wrap Angle for the Small Pulley, you need Diameter of Big Pulley (D), Diameter of Small Pulley (d) and Center Distance (C). With our tool, you need to enter the respective value for Diameter of Big Pulley, Diameter of Small Pulley and Center Distance and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Wrap Angle for Small Pulley?
In this formula, Wrap Angle for Small Pulley uses Diameter of Big Pulley, Diameter of Small Pulley and Center Distance. We can use 10 other way(s) to calculate the same, which is/are as follows -
  • wrap_angle_for_small_pulley = 3.14-2*asin((Diameter of Big Pulley-Diameter of Small Pulley)/2*Center Distance)
  • center_distance = (Diameter of Big Pulley-Diameter of Small Pulley)/(2*sin((3.14-Wrap Angle for Small Pulley)/2))
  • diameter_of_small_pulley = Diameter of Big Pulley-2*Center Distance*sin((3.14-Wrap Angle for Small Pulley)/2)
  • diameter_of_big_pulley = Diameter of Small Pulley+2*Center Distance*sin((3.14-Wrap Angle for Small Pulley)/2)
  • wrap_angle_for_big_pulley = 3.14+2*asin((Diameter of Big Pulley-Diameter of Small Pulley)/2*Center Distance)
  • center_distance = (Diameter of Big Pulley-Diameter of Small Pulley)/(2*sin((Wrap Angle for Small Pulley-3.14)/2))
  • diameter_of_small_pulley = Diameter of Big Pulley-2*Center Distance*sin((Wrap Angle for Small Pulley-3.14)/2)
  • diameter_of_big_pulley = Diameter of Small Pulley+2*Center Distance*sin((Wrap Angle for Small Pulley-3.14)/2)
  • belt_length = 2*Center Distance+(pi*(Diameter of Big Pulley+Diameter of Small Pulley)/2)+((Diameter of Big Pulley-Diameter of Small Pulley)^2/4*Center Distance)
  • belt_tension_in_tight_side = (e^Coefficient of Friction*Angle of Wrap)*(Belt Tension in loose Side-Mass of Meter Length of Belt*Belt Velocity^2)+Mass of Meter Length of Belt*Belt Velocity^2
Where is the Wrap Angle for the Small Pulley calculator used?
Among many, Wrap Angle for the Small Pulley calculator is widely used in real life applications like {FormulaUses}. Here are few more real life examples -
{FormulaExamplesList}
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