what is the necessity of using logarithmic scales in engineering and design?

Answer 1

Logarithmic scales on graphs allow you to compress information into a smaller space than is possible with a linear scale while still being able to see essential information. Many natural processes exhibit logarithmic behavior, the ear’s response to sound levels, the eye’s response to light levels for example. Using a logarithmic scale to represent frequency, the electromagnetic spectrum we commonly use can be represented on a single long graph extending from a few micro hertz to megahertz and beyond through microwaves, infrared, visible light, ultraviolet, x-rays, and gamma rays.

Logarithmic scales also help to visualize that a certain response is indeed logarithmic or exponential because such responses graph as straight lines. Of course seeing is not always believing. Engineers and scientists always try to mathematically analyze the raw data to see if a response is truly logarithmic or exponential, or at least should be approximated as such based on underlying physical principles.

Answer 2

I'll provide an answer in the way of an example.

Take a chart that shows the current-time relationship of a certain fuse, basically the amount of time necessary to blow the fuse at a particular current. At 2 times the rated current, the fuse may not blow for 3 hours, depending on its type. At 100 times the rated current, the fuse may blow in 0.01 seconds. To graph this linearly would not allow any resolution to see the values where it would be most important. By using logarithmic scales, the fuse chart can show 7 or more magnitudes for each scale. So many times, plotting outputs for functions that increase or decrease exponentially may lead to much better interpretation of the data.

Lets say that you wanted to be able to see the difference between 0.01 seconds and 0.02 seconds. So you use a division of 1 mm for each 0.01 second. Then to be able to chart out linearly to 3 hours (from the example above), the time axis would have to be 1,080,000 mm or 1,080 meters wide. Using logarithmic scales allows this to be plotted on a standard 8.5" x 11" paper.

Answer 3

So many functions and relationships in engineering are logarithmic. So, using a logarithmic scale will create a straight line on a graph, and makes it easier to see.

Answer 4

Logs are stable for installation exponentially expanding (super) variety archives to a graph. It fairly purely shrinks the graph length down so which you will discover it. once you have archives that has an excellent exponential variety there is not any genuine thank you to view it w/o plotting by skill of log plot, if plotted in primary linear mode it may be extensive, if scaled it could make an excellent style of the graph appear like a dot. as an occasion, a time vs. reaction plot - you elect to work out the habit of the early area (seconds) AND the late area (DAYS) on the comparable plot. could do a log.

Answer 5

It makes a lot of things a LOT easier to read, and understand. For example, bode plots would make no sense unless you could plot them log scale.