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Basic Aerodynamic Performance Calculations

In the absence of a geometry, at this stage any aerodynamic performance estimates will either be based on very basic physics or simple, empirical equations.

We begin with a very rough estimate of the Oswald span efficiency, only suitable for moderate aspect ratios and sweep angles below 30° (equation due to Raymer):

In [47]: e0 = 1.78*(1-0.045*AspectRatio_**0.68)-0.64 print '{:0.3f} '.format(e0)

0.783

Lift induced drag factor к (Cd = Q0 + kC2):

In [48]: k = 1.0/(math.pi*AspectRatio_*e0) print '{:0.3f}'.format(k)

0.045

Dynamic pressure at cruise

In [49]: q_cruise_Pa = 0.5*CruisingAltDens_kgm3*(CruisingSpeed_mpsTAS**2) print '{:0.1f} Pa'.format(q_cruise_Pa)

544.5 Pa

Dynamic pressure in the climb

In [50]: q_climb_Pa = 0.5*ClimbAltDens_kgm3*(ClimbSpeed_mpsCAS**2) print '{:0.1f} Pa'.format(q_climb_Pa)

352.6 Pa

Dynamic pressure at take-off conditions - for the purposes of this simple approximation we assume the acceleration during the take-off run to decrease linearly with v2, so for the v2 term we’ll use half of the square of the liftoff velocity (i.e., v = vTO/ V2):

In [51]: q_TO_Pa = 0.5*TakeOffDens_kgm3*(TakeOffSpeed_mpsCAS

/math.sqrt(2))**2

print '{:0.1f} Pa'.format(q_TO_Pa)

77.9 Pa

Dynamic pressure at the start of final approach, at stall speed:

In [52]: q_APP_Pa = 0.5*TopOfFinalAppDens_kgm3 *StallSpeedinApproachConf_mpsTAS**2 print '{:0.1f} Pa'.format(q_APP_Pa)

116.2 Pa

 
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