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This process of ascertaining axial loads from non-axial vector forces is a process commonly found in entry-level trigonometry and introductory physics courses. The process, specifically, is known as decomposing vector forces.

Axial load is the amount of force exerted in either the vertical or horizontal direction. Though this load may seem straightforward to calculate when dealing with forces that are directly up and down or side to side, it is not so straightforward to calculate when the force vector is pointed in a direction between these two absolute poles. Using trigonometry, you can calculate the force applied in the up-and-down and back-and-forth direction by a force that is moving in both directions simultaneously.

Measure the total horizontal distance traversed by the load (e.g., the total distance in the horizontal direction of a cable holding up a sign).

Measure the total vertical distance traversed by the load.

Divide the distance in the vertical direction by the distance in the horizontal direction. The resultant figure is the Tangent of the load.

Determine the "arc Tangent" of the Tangent from Step 3 using a scientific calculator. Press the "arc Tangent" button (normally marked as "tan–1", "inverse Tan", or "aTan"). Enter the "Tangent" value from step 3. The value returned is the angle of the load.

Find the Cosine of the force. Press the "Cosine" or "Cos" button on the calculator and enter the angle of the force from Step 4.

Find the Sine of the force. Press the "Sin" key on the calculator and enter the angle of force from Step 4.

Determine axial load in the vertical direction. Multiply the magnitude of the force (the weight of the object or force applied by the machine in question) by the Cosine value determined in Step 4.

Determine the axial load in the horizontal direction. Multiply the magnitude of the force (the weight of the object or force applied by the machine in question) by the Sine determined in Step 5.

References

- "Trigonometry"; Margaret Lial, John Hornsby, David Schneider; 2009
- "Physics"; Douglas C. Giancoli; 2005

About the Author

Gabriel Dockery began writing in 2009, with his work published on various websites. He is working toward a Bachelor of Science in neuroscience in a transfer program between Ivy Tech College and Indiana State University.