Question

If the wing structure of an aircraft contains ribs of airfoil shape along x-axis, how can we calculate the moment of inertia around x,y,z axes? What formulas we can use and whether any of these moment will be zero?

Answer 1

wing design procedine (performance wing Design requirements , productivity, operational requiements stability cost, flight safety) select Nymber of wings & 누 select wing vertical location ! select/ Design high lift device 누 Select/ Determine sweep and dinedral angles (1,7) Select or design wing airfoil section Determine other wing parametry (ARd, lw, ad) calculation lift, Drag, and pitching moment! No Requnements statisfied yet optimization Calculateb, MAC fr, CA

for a giren materiel, the weight of the wing depends on the airfoil section used for the construction of the wing and also on the design variable Vector X=[xo, X2 X3 ---- x.]* where t= Transpose And Xi = x/CR Wrning where CR root chord different wing cross-section are produced indicating that the choice towing section is also a design pangmeter. The minimization of the dimensionless weight of the wing is an optimization proplem which is posed mathematically- Minimize Wwing (x) = Wspans (X) + Wribs (4) + Wester) Wiringref (Xref) Wspars (Xref) + Wribs/Xreb) tWskin (Xref) I < I critical Max (OR, TR, ok) = (0,2, o critical & equ Ce a cistical performance parameters 27 (2) W bending Non-dimensimlizing subject to Deano S w these stretmas songmetery with the corresponding parameters of the reference wing results in the following equation for the non-dimensional strane performance songmetery of the wing M Spending (Wwingref Wwing Muring Mwing ref

are The coordinates of the centroid to the idealreed wings 1=4 Xo = Ai inn i=4 for i=4 wings YG = Are A E ti Aix i=1 i=4 upper front spar front boony It IT xoz A3 Az (a) mere (b) figne cross section to Actual wi front and rear spans. wing showing the Ai= the virtual area of the spart pont alturned to account for the bending areas of the stungers in the skiny. Ar = Ar actuel + +12 512 (2+8) + 6 6 + & t23823 7 6 Az = Azac And + toaso2 (2+ o) Similarly we can write the area of As and Ay wings second moment of areas of the span caps with reference to a set of orthogonal axes through the centra in (XG MG) at at any cross section of the wing are & Ail Yi - YG)? & Ai (Xi-Xu)? also given by Inx lay

1 I nyx = {Ai (xx-xe) (Yi-Ye) Above equation we can calculate monnentaf inertia in any direction. If the value de orientation is in neutral axis then idealised wing angle calculated formula by following Mх. x = tan IGx My - IGxy My Iny - My My Iuxy