Formulaes

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  Hereafter a few formulaes which may proved usefull when designing your models: 
NB: Foam = "Mousse" on graphics.
pt_plan.gif (2912 octets) Input data to be given by user:
  • Segment length (L. segment)
  • root chord.
  • tip chord.
  • leading edge tilt angle
  • tilt angle ("Flèche")
  • Dihedral (optional).
  • leading edge thickness
  • trailing edge width
  • skin thickness
  • spar(s) position(s)
  • spar(s) size
tan Alpha = tilt ("Flèche") / segment length ("L segment") 

Recul E = tan Alpha * Decalage E ---> Defines the starting point at root location.

Recul S = tan Alpha * Distance

tan Beta = (Corde E - (Corde S + Fleche)) / L segment

Course E = Corde E + Recul E + (tan Beta * Decalage E)

Course S = Course E - (Recul S + (tan Beta * Distance))
ba.gif (2479 octets) Leading Egdge ("Bord d'attaque") withdrawal.

RBA = epBA / cos Alpha

Trailing edge ("Bord de fuite") withdrawal.

RBF = epBF / cos Beta
coffrage.gif (2068 octets) Skin withdrawal at point (X0,Y0).

Slope = (Yb - Ya) / (Xb - Xa) = tan Gamma

For EXTRADOS

X = X0 + ep * sin Gamma

Y = Y0 - ep * cos Gamma

For  INTRADOS

X = X0 - ep * sin Gamma

Y = Y0 + ep * cos Gamma
L' = L/cos Delta

longeron.gif (2919 octets)

We assume that the spar is located in a portion of the airfoil where the tangeant is roughly horizontal. 

 Spars ("longerons") withdrawal

L : spar width

H : spar height

P : Position of the spar(s) axis(es) over the chord (mm or en %)

With a single spar, located at Intrados ou Extrados:

From X = (P - (L'/2) we adjust Y = Y - H at Extrados up to location where X = P + (L/2)

At Intrados, from X = (P - (L'/2), we adjust Y = Y + H up to location where X = P + (L/2)
vrillage.gif (2157 octets)
 Wing twist angle Alpha.
We rotate the wing section around coordinate (0,0) point. 

r = square root(X² + Y²)

Teta = arcsin (Y/r)

X' = cos(Teta + Alpha)

Y' = sin(Teta + Alpha)

 
Modifying the section relative thickness. Abandonned! (for the first version...)
  • The original thickness is delivered after the section name : Epr.
  • Calculation of the medium line of the section: 
Foreach  X, Ysup et Yinf : Yligne = (Ysup + Yinf) / 2   (Detail to check!) True for symetrical section.  The spline module should be aapplied before this step.
  • Epr2 : desired thickness.
Foreach X, Ysup' = (Ysup - Yligne) * Epr2 / Epr

Foreach X, Yinf ' = (Yinf + Yligne) * Epr2 / Epr
Computation of the apparent wire diameter change as a functionof the wing taper (tip chord/root chord)...