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docs/documentation/analysis/aerodynamic_analysis/aerodynamic_principles.md

 
 # Aerodynamic principles {#aerodynamicprinciples}
 
-All methods for calculationg the properties of an aircraft include a trade off between accuracy on one hand and complexity and computing effort on the other hand.
-Due to the iterative process in the preliminary design process, it is favourable to use fast methods for rapid calculation in the sizing loop.
-**aerodynamic_analysis** contains a set off different methods and will be expanded in future. 
+All methods for calculationg the properties of an aircraft face a trade off between accuracy on one hand and complexity and computing effort on the other hand.
+
+A typical aircraft in UNICADO takes roughly 20 to 30 iterations to converge in the design loop.
+For each iteration, the full aerodynamic properties have to be calculated.
+To enable extensive design space exploration and optimization studies in a reasonable time frame, the whole design process in UNICADO should takes less then an hour.
+The aerodynamic analysis therefore should be finished in under a minute.
+As a consequence of this requirement, the preliminary aircraft design in general, including UNICADO, is limited to lower fidelity methods, ranging from semi-empirical formulas to analytical approaches.
+
+**aerodynamic_analysis** contains a set off different methods and will be expanded in future.
 
 
 ## Methods
@@ -12,8 +18,8 @@ Currently there are **methods** with differing levels of fidelity implemented. T
 
 | Aerodynamic value                               | Methods                       | Fidelity level                    | Application                               |
 |-------------------------------------------------|-------------------------------|-----------------------------------|-------------------------------------------|
-|Lift, induced drag and pitching moment                           | Lifting Line                  | analytical                        | Lifting surfaces in general               |
-|Lift, induced drag and pitching moment with corrections for TAW   | Lifting Line                  | analytical/semi-empirical         | Wing and stabilizer for TAW               |
+|Lift, induced drag and pitching moment           | Lifting Line                  | analytical                        | Lifting surfaces in general               |
+|Lift, induced drag and pitching moment with corrections for TAW   | Lifting Line | analytical/semi-empirical         | Wing and stabilizer for TAW               |
 |Viscous drag                                     | According to Raymer           | semi-empirical                    | Lifting surfaces, fuselages and nacelles  |
 |Wave drag                                        | According to Mason            | semi-empirical                    | Lifting surfaces                          |
 |High lift adaptions                              | According to Raymer and Howe  | semi-empirical                    | TAW configuration                         |
@@ -43,6 +49,7 @@ This simplified geometry is divided into trapezoidal elementary wings, which are
 A system of equations is constructed from the vortex system and the boundary conditions, the solution of which is used to calculate the lift distribution.
 For a more in-depth discussion, the  dissertation by Horstmann (Horstmann 1987: Ein Mehrfach-Traglinienverfahren und seine Verwendung für Entwurf und Nachrechnung nichtplanarer Flügelanordnungen) is recommended.
 
+The following picture shows the lifitng surfaces of a typical TAW aircraft discretized into elementary wings according to the lifting line method:
 ![A wing and horizontal tailplane broken down into elementary wings](img/ll_geom.png)
 
 The Prandtl-Glauert transformation is applied to the polars from Lifting Line.
@@ -50,23 +57,27 @@ Lift coefficients, induced drag and pitch moment coefficients are thus transform
 The lift distribution calculated using lifting line agrees well with CFD results for both the conventional wing and the blended wing body.
 The calculated induced drag cannot be validated by CFD methods.
 Several semi-empirical corrections are integrated into the lifting line methodology in UNICADO.
-Based on Roskam, induced drag are calculated for the fuselage and nacelles.
+Based on Roskam, induced drag is calculated for the fuselage and nacelles.
 The pitching moment is corrected for fuselage and nacelle influences based on Torenbeek (Torenbeek, E. - Advanced Aircraft Design, 2013, ISBN: 9781119969303).
 
 ### Viscous drag according to Raymer
 The frictional drag/viscous drag/zero lift drag is calculated based on the method of Raymer (Raymer 1992: Aircraft Design: A Conceptual Approach, page 280 ff).
-Contrary to what the name suggests, the viscous drag also "captures" influences of the boundary layer, which makes validation by CFD calculations difficult.
+Contrary to what the name suggests, the viscous drag also regards influences of the boundary layer, which makes validation by CFD calculations difficult.
+
+For this purpose, the aircraft is broken down into its individual components, whose drag is calculated from a form factor, interference factor, friction coefficient and the wetted area:
 
-![Formula for viscous drag](img/visc_drag.png)
+$
+    C_{D0} = \frac{\sum(C_{fc}FF_{c}Q_{c}S_{wet,c})}{S_{ref}}+C_{Dmisc}+C_{DLP}
+$
 
-For this purpose, the aircraft is broken down into its individual components, whose drag is calculated from a form factor, interference factor, friction coefficient and the wetted area.
 The form factors are calculated using semi-empirical formulas, the interference factors are derived from the recommendations in the text (page 284 f).
 The friction coefficient is derived from the flow around a flat plate and depends on the Reynolds number and the surface roughness.
+
 In addition to the drags for the individual components, a 'miscellaneous drag' is calculated.
 This includes resistance caused by gas entering and leaving the hull through leaks and resistance caused by antennas, protrusions and the like.
 In total, the viscous drag depends only on the geometry, Reynolds number and Mach number and is thus constant over an entire aircraft polar.
-BUT there is still a calibration method built in which the viscous drag is calibrated using an exponential function based on the lift coefficient.
-Thus, the viscous drag slightly increases with increasing lift coefficient.
+But a calibration method is built in which the viscous drag is calibrated using an exponential function based on the lift coefficient.
+Thus, the viscous drag slightly increases with increasing lift.
 
 ### Wave drag according to Mason
 The wave drag is the pressure drag generated by the occurrence of a shock wave.
@@ -75,6 +86,7 @@ The wave drag therefore only occurs when a compression shock occurs.
 From flight data it could be deduced that with increasing Mach number the wave drag is only between 0 and 10 drag counts and increases slightly linearly up to a Mach divergence number, above which the wave drag increases exponentially.
 This behavior of the wave drag is approximated by a fourth degree polynomial.
 
+The following picture shows the drag creep in the flight test data of a DC-9-30, according to Gur, Full-COnfiguration Drag Estimation, 2010:
 ![The rise of the wave drag for a typical aircraft](img/Drag_creep.png)
 
 To calculate the wave drag, the critical Mach number is required, which is calculated according to the Korn-Mason equation (Mason 1990: Analytic Models for Technology Integration in Arcraft Design).
@@ -82,21 +94,30 @@ To calculate the critical Mach number, the wing sweep, the profile thickness rat
 Two values ​​are given for the profile technology factor, 0.87 for conventional and 0.95 for transonic profiles.
 Since the local lift coefficient is included in the formula for the critical Mach number, the wing is divided into individual strips for the drag calculation.
 
-For each strip, the local critical Mach number and the local wave resistance are calculated and then summed.
-In [Gur 2010: Full-Configuration Drag Estimation] a simple, area-weighted summation over all wing strips is proposed.
+For each strip, the local critical Mach number and the local wave drag are calculated and then summed up.
+In Gur 2010: Full-Configuration Drag Estimation a simple, area-weighted summation over all wing strips is proposed.
 The wave drag is then calibrated like the viscous drag using an exponential function based on the lift coefficient.
 
 ### High lift polars
+Analysis of the aircraft in high lift configurations, with extended leading and trailing edge high lift devices, poses difficulties, even in numerical or experimental setups.
+In the interest of saving computing time and ressources in the aerodynamic analysis, the only valid option is to rely on semi-empirical calculations.
 
 The high lift polars are calculated for the following cases:
+
 - Take Off
+
 - Take Off landing gear retracted
+
 - Climb
+
 - Approach
+
 - Approach with landing gear
+
 - Landing
 
-For this, the number, type postions and aera of all leading and trailing edge devices are read in.
-Based on smei-empirical formulas, a maximum lift coefficient and shifts of the drag and moment are calculated, based on the read in wing devices.
+For this, the number, type, postions and areas of all leading and trailing edge devices are read in.
+The geometric parameters of the high lift devices are used to calculate a maximum lift coefficient and shifts of the drag and moment coefficients, based on a set of semi-empirical formulas.
 
+The following picture shows the shifts in lift and drag in the high lift polars for a typical short medium range passernger aircraft according to the method:
 ![An example of a clean polar and transformed high lift polars at Mach 0.2](img/high_lift_shift.png)
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