modified Jan 07, 2006, 22:06 by Charles W. Barbour II
Modifications: - got rid of scratch work
Reynolds Number
This section of the model takes the 2D wing airfoil section data and corrects for vortex induced drag effects, a reduction in CLmax, and rereferences the wing to the aircraft angle of attack by adjusting for the wing incidence angle.
wing pitching momemt
Oswald Efficiency
Shed Vortex induced downwash angle, assumes elliptical loading, Ref.: Abbott and Doenhoff pg 7,Prandtl wing theory
relation between wing, fuselage and wing incidence angle:
relation between wing alpha and alpha the wing sees:
combining yields:
Conversion from
Most people want to see data plotted against fuselage AoA, so we will need this inverse function:
wing coefficient of lift:
vortex induced drag:
assumed 5% reduction in CL from 2D to 3D
wing drag:
Wing Max Coefficient of Lift
Wing Min Coefficient of Lift
Stall Angle
Stall Velocity (ft/s)
Horizontal Velocity @ Max Rate of Climb Velocity (ft/s)
Max Rate of Climb Velocity in terms of Stall Velocity
Lift Coefficient for Max Rate of Climb Condition
Angle of Attack Needed for Max Rate of Climb
Angle that the wing section needs to "see".
Corresponding fuselage angle.
approx H tail Reynolds number
This section of the model takes the 2D horizontal tail airfoil section data and corrects for vortex induced drag effects ( both its own and the wings), a reduction in CLmax, and rereferences the tail to the aircraft angle of attack by ajusting for the tail incidence angle.
H tail pitching moment
assumed Oswald Efficiency
assumed 5% reduction in CL
Tail shed vortex induced downwash angle:
method assumes tail is deep in the downwash of the wing and so will see twice the wings downwash on itself, from CalTech
Downwash from the wing onto tail:
downwash at near liftoff conditions:
alpha tranformation from
2D section to fuselage
includes downwash of the wing
Solving for
Solo does not include wing downwash
H tail coefficient of lift, including effect of wing downwash:
H tail coefficient of lift, NOT including effect of wing downwash:
Vortex induced drag:
H tail drag:
Finds new tail incidence such that H tail cancels moment generated by wing at take-off.
If these two numbers do not match then the i.h needs to be reset to the new value in the Layout model.
New Method for calculated d.e.trim.
This should be zero if incedence of H tail is set properly.
Reynold's number
Oswald efficiency factor assumed
Side Slip Angle
vertical tail coefficient of lift:
5% reduction of Cl max assumed
vortex induced drag
Total Vertical Tail Drag
Reynolds Number
Cross Sectional Area of Fuselage
Effective Diameter of Fuselage (For Drag Calc.) see page 502 of Torenbeek, eq F-40
Effective Fuselage Slenderness Ratio, see page 502 of Torenbeek, eq F-39
Fuselage Shape Factor, see page 502 of Torenbeek, eq F-41. This assumes that Ltail divided by Dfeff is greater than or equal to 2, or fuselage has an optimum pointed tail.
Smooth Flat Plate Skin Friction Coeff., assuming turbulent boundary layer, see page 498 Torenbeek, Fig. F-4
15% higher than flat plate, see page 502 of Torenbeek, eq f38.
Streamlined shaped (no seperation)
Assuming zero tail upsweep, page 502 f38, Torenbeek
Assumption made that the gear will not be stream lined -worst case.
Using the discussion on gear drag in REF 2, Pgs. 347-349, and Table 12.5, the below gear drag was calculated.
The dimensions below are taken from the front of the aircraft
Using Table 12.5, the Dq = [(D/q)/Frontal Area] was calculated
Total D/q of 2 main and a slightly smaller nose gear:
This CLmax and CLmin is an approximation but looking at chart below seems to be very close for this A/C Config.
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