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Abstract
The first successful powered and controlled heavier-than-air flight and the subsequent meteoric rise of aviation in the 20th century also brought with it mathematical models to understand the phenomenon of flight. Though successful to a large extent as is obvious from their longevity, these models still suffer from the odd anomalous result. Upon careful examination, the source of this problem can be traced to an inappropriate choice of dynamic stability derivatives that is inconsistent with the aerodynamics. In order to correctly distinguish between the different mechanisms that are responsible for the aerodynamic forces and moments generated due to body angular rates in flight, this paper refines the existing model for flight mechanics by redefining the dynamic stability derivatives with respect to, i) relative rate of rotation between the body and wind axes, and ii) the rate of rotation of the wind axis with respect to the earth axis, sometimes called flow curvature effect. Further, new literal approximations to the longitudinal and lateral-directional modes have been obtained in terms of the redefined dynamic stability parameters. The new approximations, for instance, correctly relate the short-period natural frequency to the longitudinal static stability parameter Cmα.
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References
- Etkin, B., "Dynamics of Atmospheric Flight", J. Wiley and Sons, New York, 1972.
- Nelson, R.C., "Flight Stability and Automatic Control", Mc-Graw Hill, New York, 1998.
- Livneh, R., "Improved Literal Approximation for Lateral-Directional Dynamics of Rigid Aircraft", Journal of Guidance, Control, and Dynamics, Vol.18, No. 4, 1995, pp. 925-927.
- Pradeep, S., "A Century of Phugoid Approximations", Aircraft Design, Vol.1, 1998, pp. 89-104.
- Phillips, W.F., "Phugoid Approximation for Conventional Airplanes", Journal of Aircraft, Vol. 37, No. 1, 2000, pp. 30-36.
- Phillips, W.F., "Improved Closed Form Approximation for Dutch Roll", Journal of Aircraft, Vol. 37, No. 3, 2000, pp. 484-490.
- Ananthkrishnan, N. and Unnikrishnan, S., "Literal Approximations to Aircraft Dynamic Modes", Journal of Guidance, Control, and Dynamics, Vol. 24, No. 6, 2001, pp. 1196-1203.
- Giulietti, F., "Two-Timescale Analysis of Phugoid Mode", Journal of Guidance, Control, and Dynamics, Vol. 26, No. 5, 2003, pp. 827-830.
- Ananthkrishnan, N. and Ramadevi, P., "Consistent Approximations to Aircraft Longitudinal Modes", Journal of Guidance, Control, and Dynamics, Vol.25, No. 4, 2002, pp. 820-824.
- Bryan, G.H., "Stability in Aviation", Macmillan, London, 1911.
- Ananthkrishnan, N., "Small-Perturbation Analysis of Airplane Flight Dynamics - A Reappraisal, 1: Longitudinal Modes", AIAA - 2004-4950, AIAA Atmospheric Flight Mechanics Conference, Providence, RI, Aug 2004.
- Sudhakar, K., Lecture Notes, in Short Course on "Nonlinear Problems in Aerospace Vehicle Dynamics", Ananthkrishnan, N. (ed.), Indian Institute of Technology Bombay, Mumbai, India, Jan 24-25, 2005.
- Theodorsen, T., "General Theory of Aerodynamic Instability and the Mechanism of Flutter", NACA TR 496, 1935.
References
Etkin, B., "Dynamics of Atmospheric Flight", J. Wiley and Sons, New York, 1972.
Nelson, R.C., "Flight Stability and Automatic Control", Mc-Graw Hill, New York, 1998.
Livneh, R., "Improved Literal Approximation for Lateral-Directional Dynamics of Rigid Aircraft", Journal of Guidance, Control, and Dynamics, Vol.18, No. 4, 1995, pp. 925-927.
Pradeep, S., "A Century of Phugoid Approximations", Aircraft Design, Vol.1, 1998, pp. 89-104.
Phillips, W.F., "Phugoid Approximation for Conventional Airplanes", Journal of Aircraft, Vol. 37, No. 1, 2000, pp. 30-36.
Phillips, W.F., "Improved Closed Form Approximation for Dutch Roll", Journal of Aircraft, Vol. 37, No. 3, 2000, pp. 484-490.
Ananthkrishnan, N. and Unnikrishnan, S., "Literal Approximations to Aircraft Dynamic Modes", Journal of Guidance, Control, and Dynamics, Vol. 24, No. 6, 2001, pp. 1196-1203.
Giulietti, F., "Two-Timescale Analysis of Phugoid Mode", Journal of Guidance, Control, and Dynamics, Vol. 26, No. 5, 2003, pp. 827-830.
Ananthkrishnan, N. and Ramadevi, P., "Consistent Approximations to Aircraft Longitudinal Modes", Journal of Guidance, Control, and Dynamics, Vol.25, No. 4, 2002, pp. 820-824.
Bryan, G.H., "Stability in Aviation", Macmillan, London, 1911.
Ananthkrishnan, N., "Small-Perturbation Analysis of Airplane Flight Dynamics - A Reappraisal, 1: Longitudinal Modes", AIAA - 2004-4950, AIAA Atmospheric Flight Mechanics Conference, Providence, RI, Aug 2004.
Sudhakar, K., Lecture Notes, in Short Course on "Nonlinear Problems in Aerospace Vehicle Dynamics", Ananthkrishnan, N. (ed.), Indian Institute of Technology Bombay, Mumbai, India, Jan 24-25, 2005.
Theodorsen, T., "General Theory of Aerodynamic Instability and the Mechanism of Flutter", NACA TR 496, 1935.