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Osmania University (OU), Hyderabad
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Length of the Belt Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)
B = 2*C+(pi*(D+d)/2)+((D-d)^2/4*C)
This formula uses 1 Constants, 3 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
Center Distance - Center Distance is the distance in between the centers of the big pulley and the small pulley. (Measured in Millimeter)
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)
STEP 1: Convert Input(s) to Base Unit
Center Distance: 300 Millimeter --> 0.3 Meter (Check conversion here)
Diameter of Big Pulley: 100 Millimeter --> 0.1 Meter (Check conversion here)
Diameter of Small Pulley: 50 Millimeter --> 0.05 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
B = 2*C+(pi*(D+d)/2)+((D-d)^2/4*C) --> 2*0.3+(pi*(0.1+0.05)/2)+((0.1-0.05)^2/4*0.3)
Evaluating ... ...
B = 0.835806949019234
STEP 3: Convert Result to Output's Unit
0.835806949019234 Meter -->835.806949019234 Millimeter (Check conversion here)
FINAL ANSWER
835.806949019234 Millimeter <-- Belt Length
(Calculation completed in 00.016 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

Length of the Belt Formula

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)
B = 2*C+(pi*(D+d)/2)+((D-d)^2/4*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 Length of the Belt?

Length of the Belt calculator uses 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) to calculate the Belt Length, The length of the Belt formula is defined as the pitch length is measured at the pitch diameter of the sheaves. Both effective length and pitch length are measured with the belt tensioned by a specified amount. Belt Length and is denoted by B symbol.

How to calculate Length of the Belt using this online calculator? To use this online calculator for Length of the Belt, enter Center Distance (C), Diameter of Big Pulley (D) and Diameter of Small Pulley (d) and hit the calculate button. Here is how the Length of the Belt calculation can be explained with given input values -> 835.8069 = 2*0.3+(pi*(0.1+0.05)/2)+((0.1-0.05)^2/4*0.3).

FAQ

What is Length of the Belt?
The length of the Belt formula is defined as the pitch length is measured at the pitch diameter of the sheaves. Both effective length and pitch length are measured with the belt tensioned by a specified amount and is represented as B = 2*C+(pi*(D+d)/2)+((D-d)^2/4*C) or 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). Center Distance is the distance in between the centers of the big pulley and the small pulley, Diameter of Big Pulley is the distance from side to side of the flat of the Big pulley and Diameter of Small Pulley is the distance from side to side of the flat of the Small pulley.
How to calculate Length of the Belt?
The length of the Belt formula is defined as the pitch length is measured at the pitch diameter of the sheaves. Both effective length and pitch length are measured with the belt tensioned by a specified amount is calculated using 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). To calculate Length of the Belt, you need Center Distance (C), Diameter of Big Pulley (D) and Diameter of Small Pulley (d). With our tool, you need to enter the respective value for Center Distance, Diameter of Big Pulley and Diameter of Small Pulley 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 Belt Length?
In this formula, Belt Length uses Center Distance, Diameter of Big Pulley and Diameter of Small Pulley. 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 Length of the Belt calculator used?
Among many, Length of the Belt calculator is widely used in real life applications like {FormulaUses}. Here are few more real life examples -
{FormulaExamplesList}
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