What is the purpose of interpolation when reading performance charts, and how is it performed?

• A. To estimate values between charted data points; interpolate linearly by proportion of distance between known values
• B. To extrapolate beyond chart data using a quadratic fit
• C. To ignore chart data and guess
• D. To read only exact values from the chart

Answer: (A)

Interpolation is used to estimate a value between two known data points on a performance chart. Since the chart gives exact values only at specific points, interpolation lets you infer what the performance would be at conditions that fall between those points, assuming the change between them is roughly steady.

To perform it, find the two chart points that bracket the condition you’re interested in. Note the x-values (the condition, like altitude or speed) and their corresponding y-values (the performance parameter, like fuel flow or climb rate). Compute how far your target condition is between the two known x-values as a fraction: f = (x − x1) / (x2 − x1). Then apply that same fraction to the change in the y-values: y ≈ y1 + f × (y2 − y1). In other words, add to the lower-known value the proportional change between the two points.

For example, if at 10,000 ft the chart shows 200 knots and at 15,000 ft it shows 220 knots, and you want the value at 12,000 ft, the fraction is (12 − 10)/(15 − 10) = 0.4. The estimated value is 200 + 0.4 × (20) = 208 knots.

This approach keeps you using the chart data itself to get a reasonable estimate. Extrapolating beyond the chart or guessing would introduce more error, and reading only exact values ignores useful information between the plotted points.