Body
Hi George,
It's normal to use simplified models for calculations.
By assuming a flat earth and a stationary atmosphere the calculations are made much simpler than by using actual conditions which may not matter much as a plane is extremely small when compared to the earth.
Simplified models are used all the time when calculating electronic circuits. The components are mostly considered ideal even though all components have parasitic values of other components in them. E.g. a resistor has besides its resistance also inductance and capacitance because of its physical dimensions. The inductance is because it has a magnetic field around it when current passes through it. The capacitance is because it is surrounded by dielectrics which has an electric field around the resistor when the resistor has a voltage difference to the ambient.
Capacitors and inductors have the same problem of not being ideal as in simplified mathematical models. Using non-idealized models makes the calculations very complex which is necessary when dealing with high frequencies.
Gabriel Kron made models of plane wings by curving the coordinate system around the wings which made the formulas simpler. The coordinate system then became complex instead. By curving the coordinate system along the curved earth the model becomes much simpler.
This image is taken from here: http://www.quantum-chemistry-history.com/Kron_Dat/Kron-1945/Kron-JAP-1945/Kron-JAP-1945.htm http://www.quantum-chemistry-history.com/Kron_Dat/Kron-1945/Kron-JAP-1945/Kron-JAP-1945.htm to show the idea for solving a non-linear problem.
Regards
Ole
---In [email protected], <canowindracd@...> wrote :
Pardon me Doug for mentioning this report from NASA, but does this make sense to anyone here?
Below is my typed copy as I could not copy and paste it because it was locked. Please see the link below:
https://www.nasa.gov/centers/dryden/pdf/88104main_H-1391.pdf https://www.nasa.gov/centers/dryden/pdf/88104main_H-1391.pdf
NASA Reference Publication 1207 August 1988
Page 35 of 102
3 Concluding Remarks
This report derives a set of linearized system matrices for a rigid aircraft of constant mass, flying in a stationary atmosphere over a flat, nonrotating earth. Both generalized and standard linear system equations are derived from nonlinear six degree-of-freedom equations of motion and a large collection of nonlinear observation (measurement) equations.
This derivation of a linear model is general and makes no assumption on either the reference (nominal) trajectory about which the model is linearized or the symmetry of the vehicle mass and aerodynamic properties. (Emphasis added)
Ames Research Center
Dryden Flight Research Facility
National Aeronautics and Space Administration
Edwards, California, January 8, 1987
On page 6 of 102, it is also a copy of the above in the Summary, and in the Introduction in paragraph 2 it also mentions the stationary atmosphere over a flat, nonrotating earth, and in paragraph 3 it mentions straight and level flight.