Vitsas Modified Transient Peak Ratio Method

For dynamic stability data reduction in flight testing, the traces of various raw data can be used in order to determine the damping ratio and undamped natural frequency of the oscillations. These two parameters are important in consideration of flying qualities.

One of the most used methods for this type of data reduction is the Transient-Peak-Ratio (TPR) method as defined in textbooks [1]. The TPR method, as well as its modified versions [2], always include the use of a given chart in order to derive damping ratio out of TPR.

Using the logarithmic decrement relation as a start, a new formula has been derived that connects TPR explicitly to damping ratio. While the derivation of this formula is not very sophisticated, it has never been included in Flight Test Handbooks. The new method is named Vitsas Modified Transient Peak Ratio Method (VMTPR) after the author of this blog and the derived formula can be seen below:

Comparing of VMTPR to the standard TPR method chart gives almost a perfect agreement.

VMTPR method makes dynamic stability data reduction faster, easier and more accurate. The limitations of the method are the same as for standard TPR.

Use the above method referenced as:

Vitsas, Panagiotis A., “Vitsas Modified Transient Peak Ratio Method”,, September 2012.


[1] USAF Test Pilot School, “Flying Qualities Textbook, Volume II Part 1”, Edwards AFB, California, April 1986.

[2] Ward, Donald T., and Strganac, Thomas W., “Introduction to Flight Test Engineering”, Second Edition, Kendall/Hunt Publishing Company, Dubuque Iowa, 2001.

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