3.4.7 · D1Aerodynamic coefficients — CA (axial force), CN (normal forc
Rocket ke paas se guzarti air ek push aur ek twist produce karti hai, aur dono badhte hain jab air jitni fast aur dense hoti hai. Agar hum us push aur twist ko "speed-and-density" wale part se divide kar dein, toh jo bachta hai woh ek pure shape-and-tilt number hai — ek coefficient — jo ek chhote model aur full-size rocket dono ke liye matching conditions pe same hota hai.
Is page par har woh symbol build hoga jis par parent note depend karta hai, un cheezón se shuru karke jo ek 12-saal-ka bachcha already jaanta hai, aur exactly wahin khatam hoga jahan parent note shuru hota hai. Yahan kuch bhi assume nahi kiya gaya ke aapne aerodynamics pehle dekhi hai.
Definition Ek vector — length aur direction wala ek arrowVector bas ek arrow hota hai: uski length batati hai "kitna", uski direction batati hai "kis taraf". Hum velocity, forces, aur axes ko arrows ki tarah draw karte hain. Jab do arrows alag-alag taraf point karte hain, toh unke beech ka angle bahut zyada matter karta hai — yeh single idea is page par sab cheez ka seed hai.
Definition Notation: bold arrow vs plain letterSymbols ke baare mein hume tidy rehna hoga. Ek bold letter jaise V poora arrow (magnitude aur direction). Wahi letter plain , V length (ek plain positive number, jise magnitude kehte hain). Toh V V = ∣ V ∣
Figure 1 mein setup dikhaya gaya hai. Red arrow rocket ki velocity V body axis hai. Dhyan rakhein ke yeh zaroori nahi ke dono same taraf point karein; unke beech ka gap hi Section 5 ki poori kahani hai.
V V V kitni tez rocket air mein move karti hai, metres per second mein (m/s V length . Figure 1 mein red velocity arrow imagine karein: lamba arrow = tez. Air rocket ke paas se usi same speed se guzarti hai (socho tum rocket par baithe ho — duniya ki air tumhare paas speed V Yeh topic isko kyun zaroori karta hai: air jo force deliver kar sakti hai woh depend karta hai ke air body mein kitni zor se takraati hai, aur woh depend karta hai V
ρ ρ har cubic metre mein kitni air packed hai , kg/ m 3 ρ ≈ 1.2 ρ ≈ 0.3 Yeh topic isko kyun zaroori karta hai: wahi speed moti air mein zyada push karti hai baariki air ke mukable.
squared kyun aati hai
Do cheezein tez air ko zyada push karne pe majboor karti hain. (1) Zyada air molecules har second aa rahe hain — yeh V Har molecule zyada speed ke saath aata hai, toh woh zyada zor se marta hai — yeh V doosra factor hai. Dono effects multiply karo toh milta hai V × V = V 2 square ke saath, sirf speed ke saath nahi.
2 1 2 1 ( mass ) × ( speed ) 2 2 1 2 1 m v 2 steadily badhti hai, toh total hota hai half of "full value times full amount" — ek triangle ka area, rectangle ka nahi. Air ki push per unit volume mein exactly yahi 2 1 ρ V 2 2 1 ρ V 2
q q aane wali air ke har cubic metre mein stored kinetic energy — equivalently, woh pressure jo moving air exert kar sakti hai. Iska formula hai
q = 2 1 ρ V 2 . kg/ m 3 × ( m/s ) 2 = kg / ( m s 2 ) = N/ m 2 = Pa Picture: aane wali air ki ek "punch strength" q
2 1 ρ V 2 Dynamic pressure and Bernoulli mein hai. Abhi ke liye q woh single number samjho jo saari speed-and-density scaling carry karta hai . Air kitni fast aur kitni thick hai — yeh sab "boring" information q
S S fixed area hai jis par hum agree karte hain rocket ki size describe karne ke liye, m 2 Yeh topic isko kyun zaroori karta hai: bada body zyada air pakadta hai, toh force area ke saath scale karta hai. q S
d d chosen length hai, almost always body ka diameter , metres mein. Rocket tube ki width socho.
Yeh topic isko kyun zaroori karta hai: ek twist (moment) force times lever arm hota hai — ek extra length. Force-scale ko twist-scale mein convert karne ke liye humein ek length chahiye.
Figure 2 mein rocket ka circular cross-section (area S d S d
F Force ek push ya pull hai, Newtons (N F F Yeh topic isko kyun zaroori karta hai: air rocket ko force se push karti hai; hum us force ko Section 6 mein do useful directions mein split karenge.
M Moment (ya torque ) ek twisting effort hai, Newton-metres (N m lever arm hota hai — pivot se force ki line tak ka perpendicular distance.
M = F ⋅ ( lever arm ) . ⋅ do plain numbers ka ordinary multiplication hai (Newtons mein force times metres mein length) — nahi koi vector cross-product. Hum bas "kitna zor" ko "kitna door" se multiply kar rahe hain.
Picture: ek door push karna. Wahi push door ko zyada twist karta hai jab aap hinges se door push karo (lamba lever arm), kam jab unke paas push karo.
Figure 3 mein ek force F ℓ lever arm , red) par act kar raha hai. Uska twist hai M = F ℓ
Definition Moment ka sign — nose-up vs nose-downHumein agree karna hoga ke konsi twist direction positive count hoti hai. Convention hai: nose-up positive M M Socho nose uthna = + −
Intuition Ek angle itna important kyun haiAgar rocket perfectly apne body axis ke saath fly kare, toh air seedha usse head-on hit karti aur sirf seedha peeche push karti. Jaise hi nose thoda wahan se hat jaata hai jahan woh actually ja raha hai , air side par lagti hai, ek sideways force aur ek twist produce karti hai. Yeh misalignment ek single angle hai, aur almost har interesting effect iske proportional hai.
α α body axis aur velocity arrow V ke beech ka angle hai. Figure 1 mein red velocity arrow aur black body arrow imagine karo: α α = 0 α = 4 ∘ 4 ∘ Sign convention: α positive hota hai jab nose velocity ke upar pitched up ho (body axis V upar hoti hai, jaise Figure 1 mein drawn hai); negative jab nose velocity ke neeche point kare. Positive α Yeh topic isko kyun zaroori karta hai: C N C m α create hote hain. Dekho Angle of attack $\alpha$ .
Definition Radians vs degrees — usi angle ke liye do rulersEk degree ek full turn ko 360 radian use 2 π ≈ 6.283 2 π 18 0 ∘ = π α rad = α deg × 180 π Yeh topic isko kyun zaroori karta hai: slope C N α per radian mein quoted hoti hai. Degrees daaloge toh 180/ π ≈ 57
Intuition "Along" aur "across" mein kyun split kareinEk tilted force arrow ke baare mein reason karna awkward hai. Usse do arrows mein todna kaafi aasaan hai jo right angles par hain: ek body ke saath aur ek body ke across . Yeh do directions natural hain kyunki body-mounted sensor exactly inhi ko measure karta hai.
A N
A nose–tail axis ke saath point karta hai . Sign convention: A positive hota hai jab yeh nose se tail ki taraf point kare (backward "push-back"), jaise feel hota hai haath ko car window se bahar nikaalte waqt.N body axis ke perpendicular ho (sideways). Sign convention: N positive hota hai jab yeh usi side point kare jis taraf positive (nose-up) α — yaani "body se upar wali" side. Is choice se nose-up angle of attack ek positive N Picture: total air-force arrow ek black arrow mein decompose ho body ke saath (A N
Yeh body frame mein hain (axes rocket se chipe hue). Parent note inhe Drag aur Lift se contrast karta hai, jo ek alag frame mein hain — agle mein define kiya gaya.
Definition Wind frame, DragD L Wind frame ek pair of axes hai jo rocket se nahi balki velocity arrow V
Drag D seedha velocity ke against point karta hai (V Lift L velocity ke perpendicular ho (V Picture: wahi total air-force arrow, lekin ab red velocity arrow ke relative split kiya gaya hai, body ke bajaye. Kyunki body aur velocity α A , N D , L α = 0 Drag and Lift in wind axes .
Intuition Woh trick jo sab kuch transferable banati haiKoi force F q × S q S divide karein, toh speed, density, aur size sab cancel ho jaate hain, ek pure number bach jaata hai jo sirf shape aur tilt par depend karta hai. Woh number model se full scale tak transfer hota hai.
C F C F ≡ q S F . N Pa × m 2 = N dimensionless hai (bas ek number). Ek moment ke liye hum ek extra length se divide karte hain: C m = M / ( q S d )
Definition Yeh topic jin teen specific coefficients use karta haiRecipe C F = F / ( q S ) M
C A ≡ q S A axial-force coefficient (A C N ≡ q S N normal-force coefficient (N C m ≡ q S d M pitching-moment coefficient (M C N C m
x c g x c p
x c g balance karta hai (uska saara weight yahan concentrated act karta hai), nose se distance ke roop mein measure kiya gaya.x c p effectively act karti hai , woh bhi nose se measure kiya gaya.
Picture: tube ke saath do marks. Unke beech ki distance, ( x c p − x c g ) Center of pressure and center of gravity .
Yeh topic isko kyun zaroori karta hai: agar CP, CG ke peeche ho, toh air ki sideways shove nose ko seedha ki taraf wapas twist karti hai — ek self-correcting rocket (Static and dynamic stability of rockets ).
Moment M equals force times lever
Aerodynamic coefficients CA CN Cm
Cover the right side and answer aloud before revealing.
Vector kya hota hai, ek phrase mein? Ek arrow — uski length hai "kitna", uski direction hai "kis taraf".
Bold V V V poora arrow hai (size aur direction);
V sirf uski length hai (ek plain number).
Hawa ka push V 2 V Har second zyada molecules aate hain (ek V aur har ek zyada zor se marta hai (doosra V V × V = V 2
q = 2 1 ρ V 2 2 1 Wahi 2 1 2 1 m v 2
Dynamic pressure q q = 2 1 ρ V 2
q Pascals (N/ m 2
S d S q S d q S d
Moment ko words mein define karo. Ek twist = force times perpendicular lever arm pivot tak (plain multiplication, cross-product nahi).
Positive M Nose-up positive hai; nose-down negative hai.
Angle of attack α Body axis aur velocity arrow ke beech ka angle; positive jab nose velocity ke upar pitched up ho.
4 ∘ 4 × π /180 = 0.0698
C N α α α Slope per radian mein quoted hai; degrees 180/ π ≈ 57 ×
Positive A N A N
A , N D , L A , N body ke along/across split hain; D , L velocity ke along/across split hain (wind frame). Yeh sirf α = 0
C A C N C m C A = A / ( q S ) C N = N / ( q S ) C m = M / ( q S d )
Coefficient dimensionless kyun hota hai? Force ÷ q S N ÷ N
≡ "Is defined to be" — hum quantity ko naam de rahe hain.
C N α C N α
CP, CG ke peeche hone se stability kyun milti hai? Sideways air force tab nose ko wapas seedha ki taraf twist karti hai — self-correcting.
Parent: 3.4.07 Aerodynamic coefficients — CA (axial force), CN (normal force), Cm (pitching moment) (index 3.4.7) · Hinglish: 3.4.07 Aerodynamic coefficients — CA (axial force), CN (normal force), Cm (pitching moment) (Hinglish)
Deeper next: Reynolds and Mach scaling .
