Enter the horizontal force, distance between supports, and weight per unit length into the calculator to determine the sag of a catenary curve.
Catenary Equation Formula
The following formula is used to calculate the sag of a catenary curve.
S = {w* d^2}/{8* H}Variables:
- S is the sag of the catenary curve (unit of length)
- w is the weight per unit length (force per unit length)
- d is the horizontal distance between the supports (length)
- H is the horizontal force (force)
To calculate the sag of a catenary curve, multiply the weight per unit length by the square of the distance between supports, and then divide by eight times the horizontal force.
What is a Catenary Curve?
A catenary curve describes the shape of a flexible chain or cable that hangs between two points under its own weight and is acted upon by gravity. The curve has a specific mathematical form and is relevant in various engineering and architectural applications, such as the design of suspension bridges and overhead power lines. Understanding the sag of a catenary curve is crucial for ensuring the structural integrity and functionality of such systems.
How to Calculate Sag in a Catenary Curve?
The following steps outline how to calculate the sag in a Catenary Curve.
- First, determine the horizontal force (H) in the cable or chain.
- Next, determine the horizontal distance between the supports (d).
- Next, determine the weight per unit length (w) of the cable or chain.
- Next, gather the formula from above = S = (w * d^2) / (8 * H).
- Finally, calculate the sag (S) in the catenary curve.
- 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.
horizontal force (H) = 500 N
distance between supports (d) = 100 m
weight per unit length (w) = 2 N/m
