# Aerodynamics. Drag.

Minimum Drag occurs at $(L/D)_{max}$ not at $C_{L}max$. Look at the table to find the airspeed where minimum drag occurs. You may need to estimate between or expand the table to more closely figure airspeed.

Parasite Drag should closely equal Induced Drag at $D_{min}$. This is minimum total drag.

Givens (Questions 1 – 6):
Weight (W)                  10,000 lb         $C_{DP}$               =0.020
Wing Area (S)             100 $ft^{2}$           $C_{L}$ at Stall     =1.3
Aspect Ratio (AR)       9.62                 Note: Assume the drag polar is a parabola
Span Efficiency (e)     0.80                 $C_D =C_{DP} +C_{Di}$   $C_{Di}=[1/(pi*e*AR)]*C_L^{2}$
Temperature               Standard
Altitude                        Sea Level
Complete the following table for this particular typical large transport jet.  Start the table at stall speed, VS.  Then answer the questions at the end.  You can use an excel spreadsheet to create the answers for the table.
 V (KTAS) q (psf) CL CD CL / CD DP (lb) DI (lb) DT (lb) VS 150.64 76.92 1,3 0,09 14,44 153,84 538,44 692,28 160 86,96 1,15 $75*10^{-3}$ 15,33 173,92 478,28 652,2 180 109,89 0,91 $42*10^{-3}$ 21,67 219,78 241,76 461,54 200 135,14 0,74 $42*10^{-3}$ 17,62 270,28 297,31 567,59 205 142,85 0,7 $40*10^{-3}$ 17,5 285,7 285,7 571,4 210 149,25 0,67 $39*10^{-3}$ 17,18 298,5 283,57 582,07 220 163,93 0,61 $35*10^{-3}$ 17,43 327,86 245,89 573,75 240 196,08 0,51 $31*10^{-3}$ 16,45 392,16 215,69 607,85 260 227,27 0,44 $28*10^{-3}$ 15,71 454,54 181,82 636,36 280 263,15 0,38 $26*10^{-3}$ 14,61 526,3 157,89 684,19 300 303,03 0,33 $24,5*10^{-3}$ 13,47 606,06 136,36 742,42

Equations for Table:
$q =sigma*v_k^{2}/295$
$C_L =W/(qS)$
$C_D =C_{DP} +[1/(pi*e*AR)]*C_L^{2}$

$D_p =C_{Dp}*q*S$

$D_i =D_t – D_p=C_{Di}*q*S =[1/(pi*e*AR)]C_L^{2}*q*S$

$D_t =D_i+D_p =C_D*q*S$

1.      Determine VSTALL        (Stall speed in KTAS)
Vstall = 150,64 KTAS
2.      Determine DMIN              (Minimum drag in pounds)
Dmin = 461,54 lb
3.      Determine VDMIN         (Minimum drag speed in KTAS)
Vdmin = 180 KTAS
4.      Determine the parasitic drag at DMIN (pounds)
DP min =219.78 lb
5.      Determine the induced drag at DMIN (pounds)
Dimin = 241.76 lb
6. Find Glide Ratio at VDMIN

Glide Ratio = Cl/Cd=21.67

Givens (Questions 7-11):
Weight (W) = 20,000 lb
Wing Area (S) = 300 $ft^{2}$
Altitude = 5, 000 ft
Temperature Standard

Figure 1.13 from Aerodynamics for Naval Aviators (1965).
7.      What is the Angle of Attack at Stall for the aircraft in Figure 1.13?
AOA at stall = 20 degree
8.      What is the airspeed associated with initial onset of stall? (KEAS)
CLstall = 1.5
$CL = 295*W/(sigma*V^{2}*S)$
V = 114.5 KEAS
9. If the gross weight is increased by 10%, how would the stall speed change?
$V =sqrt{(295*W)/(sigma*CL*S)}$
W =22000 lb

V =120.09 KEAS

The stall speed is increased by (120.09-114.5)/114.5 =0.0488 =4.88%
10. What Angle of Attack is associated with Best L/D?
The best L/D happens at an AOA = 6 degree
11.  What would be the best Glide Ratio for this aircraft?
Best glide ratio = (L/D) max = 12.5