No Clear Interpretation
A Mind-Blowing Math Hack

Just The Facts

DOFPro Team

Properties of Saturated Steam: Temperature Table

Nonlinear Interpolation

Saturated Steam: Temperature Table, Pressure Column

Polynomial Interpolation

  • 2nd Order
  • 3rd Order
  • 4th Order

Cubic Spline Interpolation

Variable Transformation

Change of Variable \(\log p^*\) vs \(1/T\)

Saturated Steam: Temperature Table, Pressure Column

Use table value at \(10\ ^\circ \mathrm{C}\ (0.0123)\) as true value.

Linearly interpolate on \(p^*\) and \(T\ (^\circ \mathrm{C})\) and compare with linear interpolation on \(\ln p^*\) and \(1/T\ (\mathrm{K})\). Interpolate with endpoints at

  • \(8\ ^\circ \mathrm{C}\) and \(12\ ^\circ \mathrm{C}\)
  • \(6\ ^\circ \mathrm{C}\) and \(14\ ^\circ \mathrm{C}\)
  • \(4\ ^\circ \mathrm{C}\) and \(16\ ^\circ \mathrm{C}\)
  • \(2\ ^\circ \mathrm{C}\) and \(18\ ^\circ \mathrm{C}\)

Interpolation Fit Plots

The Takeaways

  1. Linear interpolation is adequate with closely spaced tables or low accuracy requirements.
  2. Higher-order interpolation requires more than two data points.
  3. If you have an approximate model for your table data, a change of variables can greatly increase the accuracy of your interpolation.
  4. Having a program or an app with the full model is better than interpolating in a table.






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The DOFPro Team