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Unsteady Aerodynamics Modeling Based on Nonlinear Indicial Response Theory

Practical application of nonlinear indicial response theory is of interest for the rapid, yet high-fidelity, modeling of unsteady aerodynamic phenomena. By representing the build-up of the aerodynamic loads by means of a generalized superposition integral and by accounting for the effects of flow bifurcations, the nonlinear indicial approach provides a theoretical method to understand and address nonlinear aspects of flight mechanics problems.

The present application of nonlinear indicial theory incorporates simplifications which have permitted its implementation in a versatile computer program, the Indicial Prediction System or IPS. These simplifications assume that the indicial and critical-state responses can be parameterized based on the motion state at the time these responses are initiated, which is not to be confused with the relationship between the aerodynamic forces themselves and the prior motion history. Indeed, the present simplifications, which result in a parameterized, nodal representation of the indicial and critical-state response kernel, are entirely compatible with the notion that the nonlinear aerodynamic loads are dependent on the entire motion history.

In general, the indicial and critical-state responses of a nonlinear system can be determined by computational, experimental, or theoretical means, whichever are appropriate or available. Thus, the nonlinear indicial approach addresses the following needs:

    • High-fidelity prediction of nonlinear plant characteristics
    • Ability to include empirical knowledge into the system
    • Ability to be trained on known input-output transfer function characteristics

NEAR's indicial theory based aerodynamic prediction technology was applied to the following problems:
Simulated "cobra" maneuver of a fighter aircraft (nonlinear indicial responses calculated using the Goman-Khrabrov model; prediction of vertical force coefficient)

Rectangular wing in pitch-up motion undergoing dynamic stall (identification of indicial and critical-state responses using a neural network; prediction of lift and moment coefficient)

65-degree delta wing in rolling motion at high incidence (extraction of indicial and critical-state responses from experimental data; prediction of rolling moment, pitching moment and normal force at 30 degrees angle of attack and Mach 0.3).

Commercial Applications: The Indicial Prediction System provides a versatile software environment for solving complex unsteady problems, such as those associated with nonlinear aerodynamic phenomena during aircraft maneuvers. A key feature is the ease with which problem parameterizations may be changed. IPS is capable of arbitrary-dimensional, mixed discrete/continuous parameterizations. Most importantly, the shared object framework upon which the software was built provides a remarkably simple way of adding new capabilities/features to the system. For more information: Click here to go to the IPS webpage.


Reisenthel, P. H., et al., "A Nonlinear Indicial Prediction Tool For Unsteady Aerodynamic Modeling." AIAA Paper 98-4350.

Unsteady Aerodynamics Modeling Based on Nonlinear Indicial Response Theory
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