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What is a Cosine Weighing Error?

A cosine weighing error is an error that results from the load not aligning perfectly with the weight axis. The weight axis is a component that is perpendicular (at 90-deg) to the scale/load cells (see black arrow in diagram below).

Cosine errors result from 2 possible conditions:

1) the load has a slight sideways force being applied to it, or

2) the load cells (scale) are not on level ground

Let’s take a look at an example with no cosine error.


This illustration shows how our cosine error is zero when the weight is aligned perfectly with the weight axis. Since they are both parallel, the angle between them is 0. The cosine(0) is 1, which means there is no cosine weighing error. This is the ideal scenario for weighing.

Now let’s look at when the load has a slight sideways force on it.


When a sideways force is present on the load, it causes the load not to be aligned with the weight axis. Load cells cannot account for a sideways force, only a downward force. This sideways force results in an “angle” between the two. The actual force on the load cell, is now represented by a cosine error. In this case an angle of 1-deg results in a cosine error now being introduced into all weighments. Instead of the weight being multiplied by 1 [from a cosine(0)], it will now be multiplied by 0.99985, which can give an artificially low weight.

It should be noted that the same cosine error can be introduced when the scale is not on a level surface. The scale/load cells should always have a force that is perpendicular to their orientation.

So what type of conditions can induce a cosine error?

There are several type of conditions to watch out for.  They are

  1. A sideways force acting on the load being weighed
  2. Deflection on a monorail
  3. Expansion, or contraction, of a truck scale

Make sure your scale provider thoroughly understands all conditions affecting your weighments.

Contact us at 712-722-1181 to learn more.