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

Question

How is logarithm used in engineering and design?

Answer 1

Engineering and design are based on modeling known laws of physics and chemistry and applying them to the real world. Many times, the physical is modeled with mathmatics. Many of the mathmatics have terms that are x squared/ x cubed/ x fourth or even a higher exponent. Also, many times in engineering the subject is graphed for presentation to laymen. Terms that go to the fourth or higher exponent require a graph on a scale so large that it quickly becomes meaningless. If you see the 48 inch I-beam to the 4th power, the 6" I-beam to the 4th power looks bad or vice versa. However, the log scale allows both items to be placed on a graph for comparison.

48 to the 4th power is 5308416
6 to the 4th power is 1296

These two extremems may not even look good on a log scale graph but it gives the idea of the differences of equations with parameters that get raised to some power. the bottom line is that log scales make it easier than normal scales.

Answer 2

Well back in the dark ages I used a slide rule which used logarithmic scales to multiply or get the answer of any number to any power (with precision of 3 to 4 places).

Hope this helps.

Answer 3

i'm going to grant an answer interior the way of an occasion. Take a chart that shows the present-time relationship of a definite fuse, basically the quantity of time mandatory to blow the fuse at a particular modern-day. At 2 circumstances the rated modern-day, the fuse won't blow for 3 hours, consistent with its variety. At one hundred circumstances the rated modern-day, the fuse could blow in 0.01 seconds. To graph this linearly does not enable any decision to verify the values the place it may well be maximum mandatory. by using utilising logarithmic scales, the fuse chart can tutor 7 or greater magnitudes for each scale. a brilliant number of circumstances, plotting outputs for purposes that advance or cut back exponentially could carry approximately lots greater helpful interpretation of the help. we could say which you had to be waiting to verify the version between 0.01 seconds and 0.02 seconds. so which you employ a branch of one million mm for each 0.01 2d. Then to be waiting to chart out linearly to 3 hours (from the occasion above), the time axis might could be one million,080,000 mm or one million,080 meters huge. utilising logarithmic scales helps this to be plotted on a properly-known 8.5" x 11" paper.

Answer 4

Multiplication is linear on a log-log plot. That is, the length between 1 and 2 is the same as 2 and 4, etc. For example, circuit breaker characteristics are plotted on log-log scales. The graph of a typical 100A breaker compares to a 20A breaker of the same type by a factor of 5 on a time-current characteristic plot. Taking a 50A breaker by a factor of 2 would result in the same curve as a 20A breaker multiplied by a factor of 5--a 100A breaker.

Answer 5

Drawings print in a small papers so far