Body
Boy now you've done gone and started a fire storm .
On May 10, 2018 12:21 PM, "[email protected] [EVGRAY]" <
[email protected]> wrote:
>
>
> 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.
> [image: Fig1-large500px.jpg]
> This image is taken from here: 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
>
>
> *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 AdministrationEdwards, 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.*
>
>
>
>
>
>