**3.3 AERODYNAMICS**

The aerodynamic values can be estimated very precisely because they differ only by their Reynolds number. To value the aircraft, we need the diagram of the drag polar and the diagram of the lift

curve slope **(C _{Ja}) .**

**3.3.1 The drag polar**

The drag polar is the sum of the resistance factor at **zero **lift cdq, the coefficient of induced drag C_{DI} and the resistance factor of compressible flow C_{DM}.

C_{D} = C_{D0} +* *C_{DI} + C_{DM}

where:

C_{DO} = f (Re)

C_{DI} = f(C_{L}) and

C_{DM} = f (Ma, C_{L}) .

**The theoretical zero lift drag **is calculated by a method called “Group of Six-T-014J”

The formula for this calculation is:

- The skin friction drag coefficient was taken in the first 5% of the profile laminar. The rest of the aircraft has a turbulent flow.
- The form and sweep factors were taken for the wing, fuselage and pylons.
- For parasitic and interference drag, each was taken as 2.8% of the drag at clean flow around the airplane.
- The program for calculating the flight envelope (POP) adapts the values for different Mach numbers and heights by itself,
- varying the values of v/n

A detailed calculation of zero drag C_{DO} at v/n= 7.22*10^{6} 1/m and the effect of the Reynolds number are in the appendix III.3.1.

**The lift dependent drag **C_{DI} is calculated by the following formula from “HFP-R-300-PF2785, HORNER”:

**The compressible drag **is **a **super-critical drag which

consists of the wave drag and viscous effects, that follow the onset of transonic flow with local shocks. It is here defined by the locus in Mach number and lift coefficient for =0.002, also called M_{20}. It is calculated with the “AI/TD 820.315/88” program.

The values for M_{20} were taken for the measurement of the A340, considering of the different sweep and the different relative wing thickness. The values for C_{DM} were taken without changes for the higher Mach number. This is possible, if the Mach effects appear at higher Mach numbers.

To have an impression of the performance, the C_{L}/C_{D} are shown at travelling conditions at a height of 10.7 km.

*Fig.: 3.3.1 Ref.: HL/GoS*

**3.3.2 The lift curve slope**

The lift curve slope ( *CL _{a} ) *is calculated by the classical subsonic theory with a correction for transonic profiles

The correction factor relates to the necessary A340 correction factor between calculation and measured figures. A difference of 4% is added, because the wing is designed for a Mach number of 0.85 instead of Ma = 0.82 (see appendix III.3.2).