3.1.19 · D1Airfoil aerodynamics — camber, chord, thickness
Ek airfoil ek aisi shape hai jiska ek hi kaam hai — guzarne wali hawa ko neeche ki taraf modna taaki hawa wing ko upar dhakele. Parent page ke har symbol — c y c y t θ α c ℓ us shape ko describe karna aur kitni hawa turn hoti hai — woh batana.
Parent note padhne se pehle tumhe ek chhota sa toolbox chahiye. Neeche har woh symbol aur idea diya gaya hai jo woh use karta hai, bilkul zero se build kiya gaya hai, har ek next wale ko earn karta hua. Upar se neeche padhte jao.
Sab kuch ek image se shuru hota hai: ek wing ke through ek slice , jaise bread ki loaf se ek slice kaat lo. Yeh flat 2D shape hai airfoil . Hawa iske past left se right ki taraf flow karti hai.
Definition Leading edge (LE) aur trailing edge (TE)Leading edge slice ka front point hai — woh hissa jo pehle hawa se milta hai. Trailing edge back point hai — woh sharp tail jahan se hawa nikalti hai.
Picture: slice ki naak aur poonch. Kyun zaroorat hai: yeh woh do anchor points hain jinse har measurement pin hoti hai.
Kisi bhi airfoil symbol se pehle, humein points rakhne ke liye ek grid chahiye.
x y
x saath saath, front se back tak ki doori. Hum x = 0 x = c y upar ya neeche ki doori. Upar positive hai, neeche negative.
Picture: x y Kyun: airfoil ka har curve (top skin, bottom skin, skeleton) har position x y
Definition Chord line aur chordc Chord line woh straight line hai jo leading edge se trailing edge tak jaati hai. Uski length chord c Picture: naak se poonch tak kheechi gayi straight ruler (figure mein dashed line).
Topic ko kyun chahiye: c ruler hai. Har doosri length (camber, thickness, positions) c fraction mein boli jaati hai, jaise "0.02 c
c 2% 0.02 c same shape kisi bhi size par. c scale-free hote hain.
Definition Upper aur lower surfaceUpper surface airfoil ki top skin hai; lower surface bottom skin hai. Har x y U y L Picture: shaded slice ko bound karne wali do curved lines — top curve aur bottom curve.
Kyun: actual airfoil inhi do curves se bana hota hai. Baaki sab (camber, thickness) inhe summarize karne ka tarika hai.
t ( x ) y t ( x ) x thickness t ( x ) gap hai — wahan slice kitni "moti" hai. Half-thickness y t ( x ) = t ( x ) /2 aadha hai.
Picture: top se bottom tak vertical (ya skeleton-perpendicular) double-arrow; y t y t t upar + y t neeche − y t
Definition Maximum thicknesst ma x t ma x t ( x ) Thickness ratio t ma x / c t ma x / c = 0.12 Picture: slice ka sabse mota point, ruler c
Definition Mean camber liney c ( x ) Mean camber line un points ka curve hai jo upper aur lower skins ke bilkul beech mein hote hain. Har x y c ( x ) z ( x ) Picture: slice ke middle mein chalne wali "spine" ya skeleton.
Kyun: yeh airfoil ka backbone hai. Agar hum spine y c y t
Camber mean camber line aur chord line ke beech ka sabse bada gap hai, c Picture: curved spine aur straight ruler ke beech ki sabse badi vertical doori.
Agar spine har jagah ruler par bilkul baitha ho, toh camber = 0 symmetric hai.
Common mistake Camber curviness ya fatness NAHI haiEk moti symmetric airfoil curvy aur full lagti hai, lekin agar uski spine chord line par hai, toh uska camber zero hai. Camber sirf spine vs ruler ke baare mein hai — kuch nahi.
Parent d x d y c slope hai — woh tool jo yeh jawab deta hai ki "is point par spine kitna tilted hai?"
Definition Slope = rise over rund x d y c y c x Picture: ek point par spine se tangent ek chhote ramp ki steepness.
Derivative kyun? Humein har point par local tilt chahiye, kyunki tilt airfoil ke saath saath badalta rehta hai. Derivative bilkul wahi tool hai "instantaneous steepness" ke liye.
Parent likhta hai θ = arctan ( d x d y c )
Intuition Kyun humein slope nahi, ANGLE chahiyeThickness ko spine ke perpendicular wrap karne ke liye, humein jaanna hoga konsa direction perpendicular hai . "Perpendicular" ek rotation hai — aur rotations angles se describe hote hain, slopes se nahi. Toh hum slope → angle convert karte hain.
Slope d x d y c ratio hai: rise over run. Chhote tangent ramp ko right triangle ki tarah draw karo: horizontal side "run" hai, vertical side "rise" hai, aur ramp khud hypotenuse hai. Angle θ
tan θ = adjacent opposite = run rise = d x d y c .
tan tan opposite side ki length divided by uske adjacent (paas wali) side se hoti hai. Yeh steepness measure karta hai: steeper ramp → bada tan
arctan arctan tan − 1 tan reverse hai. Hum steepness (slope) jaante hain aur us angle ko jaanna chahte hain jisne yeh produce kiya. arctan tan undo karta hai: isko ek ratio do, yeh angle return karta hai.
arctan arctan
Intuition Yeh airfoils ke liye safe kyun rehta haiCamber lines ke liye slope gentle hota hai aur x θ 0 − 9 0 ∘ + 9 0 ∘ arctan x d x d y c = 0 θ = 0 θ > 0 θ < 0
Definition Angle of attackα Angle of attack α chord line aur aati hui hawa ke beech hota hai.
Picture: poore slice ki naak ko horizontal wind mein upar tilt karo — woh tilt α Kyun: tilting bhi hawa ko neeche turn karta hai, toh α
Definition Zero-lift angleα L 0 Zero-lift angle α L 0 α bilkul lift nahi karta . Symmetric airfoil ke liye α L 0 = 0 negative banata hai (tum naak ko thoda neeche tilt karo aur phir bhi zero lift mile).
Kyun: yeh ek single number hai jo record karta hai "camber pehle se kitna free lift de raha hai".
Definition Lift coefficientc ℓ c ℓ scale-free score hai jo batata hai airfoil kitna lift bana raha hai, jisme raw size, air density aur speed divide ho gayi hain. Bada c ℓ Coefficient kyun? Bilkul waisi tarah jaise length ke liye c c ℓ Lift and Drag Coefficients .
leading and trailing edges
thickness t and half thickness yt
tilt angle theta via arctan
sin and cos give the normal
Har foundation uske neeche walon ko feed karta hai, aur yeh sab parent topic par converge karte hain, airfoil geometry note .
Right side cover karo aur khud test karo. Agar tum yeh sab answer kar sako, toh parent page ke liye tayaar ho.
Chord line kya hai, ek sentence mein? Leading edge se trailing edge tak ki straight line; uski length c
Hum lengths ko c Taaki same numbers kisi bhi physical size par shape describe kar sakein — yeh scale-free hote hain.
Mean camber line kya hai? Un points ka curve jo upper aur lower surfaces ke bilkul beech mein hain.
Camber aur thickness mein kya fark hai? Camber = spine chord line se kitna bow karta hai; thickness = do skins ke beech ka gap. Ek moti symmetric airfoil ka camber zero hota hai.
Slope d y c / d x Har point x
tan θ Tangent triangle ka opposite over adjacent — spine ki steepness.
arctan Ek slope (ratio) leta hai aur woh angle return karta hai jisne use produce kiya — yeh tan
Surface formulas mein sin θ cos θ Yeh perpendicular thickness offset ko uske sideways (sin cos
Angle of attack α Chord line aur aati hui hawa ke beech ka angle.
α L 0 Woh angle of attack jis par lift zero ho; camber ise negative banata hai.
Raw lift force ki jagah c ℓ Yeh size, density aur speed divide kar deta hai taaki shapes fairly compare ho sakein.
Airfoil aerodynamics — camber, chord, thickness — woh parent jiske liye yeh page prepare karta hai.Thin-Airfoil Theory — jahan θ α L 0 c ℓ Lift and Drag Coefficients — c ℓ NACA Airfoil Series — woh naming jo camber, uski position, aur thickness ko digits mein pack karta hai.Reynolds Number — chord c 
