Enter the tension on the incoming end, the coefficient of friction, and the wrap angle into the calculator to determine the tension on the outgoing end according to the capstan equation.
Capstan Equation Formula
The following formula is used to calculate the tension on the outgoing end of a rope wrapped around a capstan.
T_2 = T_1</sub> * e^{(μθ)}</sup>Variables:
- T1 is the tension on the incoming end (N)
- μ is the coefficient of friction between the rope and the capstan
- θ is the wrap angle in radians
- T2 is the tension on the outgoing end (N)
To calculate the tension on the outgoing end, multiply the tension on the incoming end by the exponential of the product of the coefficient of friction and the wrap angle.
What is the Capstan Equation?
The capstan equation, also known as the belt friction equation, describes the relation between the tensions on either side of a rope or belt that is wrapped around a cylinder or capstan. The equation is used to calculate the force necessary to overcome friction and pull a rope around a capstan, which is a common scenario in sailing, climbing, and various mechanical systems.
How to Calculate Tension using the Capstan Equation?
The following steps outline how to calculate the tension on the outgoing end using the Capstan Equation.
- First, determine the tension on the incoming end (T1) in newtons (N).
- Next, determine the coefficient of friction (μ) between the rope and the capstan.
- Next, determine the wrap angle (θ) in radians.
- Next, gather the formula from above = T2 = T1 * e(μθ).
- Finally, calculate the tension on the outgoing end (T2) in newtons (N).
- After inserting the variables and calculating the result, check your answer with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge.
Tension on the incoming end (T1) = 100 N
Coefficient of friction (μ) = 0.3
Wrap angle (θ) = 2 radians
