Takeoff Performance Calculation - Review

Question 3

Interpolation

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To interpolate means to compute intermediate values between a series of given values. In many instances when performance is critical, an accurate determination of the performance values is the only acceptable means to enhance safe flight. Guessing to determine these values should be avoided.

Interpolation is simple to perform if the method is understood. The following are examples of how to interpolate or accurately determine the intermediate values between a series of given values.

The numbers in column A range from 10 to 30 and the numbers in column B range from 50 to 100. Determine the intermediate numerical value in column B that would correspond with an intermediate value of 20 placed in column A.

A B
10 50
20 X = Unknown
30 100

It can be visualized that 20 is halfway between 10 and 30; therefore, the corresponding value of the unknown number in column B would be halfway between 50 and 100, or 75.

Many interpolation problems are more difficult to visualize than the preceding example; therefore, a systematic method must be used to determine the required intermediate value. The following describes one method that can be used.

The numbers in Column A range from 10 to 30 with intermediate values of 15, 20, and 25. Determine the intermediate numerical value in column B that would correspond with 15 in column A.
A B
10 50
15
20
25
30 100

First, in column A, determine the relationship of 15 to the range between 10 and 30 as follows:

  15 - 10   5
   ------- = -- or 1/4
   30 - 10   20

It should be noted that 15 is 1/4 of the range between 10 and 30. Now determine 1/4 of the range of column B between 50 and 100 as follows:

  100 - 50  = 50
   1/4 of 50 = 12.5

The answer 12.5 represents the number of units, but to arrive at the correct value, 12.5 must be added to the lower number in column B as follows:

  50 + 12.5 = 62.5

The interpolation has been completed and 62.5 is the actual value which is 1/4 of the range of column B.
Another method of interpolation is shown below:
Using the same numbers as in the previous example, a proportion problem based on the relationship of the number can be set up.

The answer 12.5 must be added to 50 to arrive at the actual value of 62.5.
The following example illustrates the use of interpolation applied to a problem dealing with one aspect of airplane performance: