Question bank — Pitch program — open-loop pitch-over

False — ideal gravity turn mein nose velocity ke saath aligned rehta hai ($\alpha \approx 0$); gravity velocity vector ko bend karti hai aur nose sirf follow karta hai, isliye kick ke baad almost koi active steering nahi hoti.

False — ek attitude loop actively vehicle ko commanded angle par hold karta hai; jo open-loop hai woh sirf ==command ${\theta }_c(t)$== hai, jo ek fixed time schedule hai, measured state se compute nahi hota.

False — kyunki $\dot{\gamma }=-g\cos \gamma /v$, turn rate $\propto 1/v$ hai; zyada speed ka matlab zyada inertia hai, isliye gravity velocity vector ko kam bend karti hai, zyada nahi.

False — $\gamma =90^{\circ }$ par, $\cos \gamma =0$ isliye $\dot{\gamma }=0$; turn rate exactly zero hai aur hamesha zero hi rahega. Tumhe nonzero $\cos \gamma$ seed karne ke liye initial kick chahiye.

False — pitch-over isliye exist karta hai taaki thrust ko orbital speed ke liye horizontal ki taraf redirect kiya ja sake, jo drag se independent hai; drag sirf yeh change karta hai ki kab aur kitne gently tum turn kar sakte ho.

False — bahut bada kick over-rotate karta hai: vehicle bahut jaldi horizontal ki taraf turn ho jaata hai, high dynamic pressure wali ghani hawa mein ghus jaata hai, aur bade loads aur losses suffer karta hai.

True — thrust body axis ke saath hai, aur body axis velocity ke saath hai ($\alpha =0$), isliye uska normal component zero hai; sirf gravity ka normal component $mg\cos \gamma$ hi path ko turn karta hai.

True (roughly) — open-loop atmosphere mein precisely isliye use hota hai kyunki wahan active closed-loop maneuvering dangerous $\alpha$ build karne ka risk rakhti hai; ek gentle fixed schedule max-Q ke through $\alpha \approx 0$ maintain karta hai.

Error: ideal turn mein engine seedha body axis ke saath point karta hai aur gravity turning karti hai; continuous gimballing $\alpha$ aur side loads create karega. Gimbal sirf brief kick aur stabilization ke liye use hota hai.

Error: jaldi turn karna low $v$ aur high dynamic pressure par hota hai, jisse bada $\alpha$ aur aerodynamic loads bante hain → structural risk aur steering loss. Tum dheere aur neeche pitch karte ho taaki max-Q ke through $\alpha \approx 0$ rakho.

Error: correct law hai $\dot{\gamma }=-g\cos \gamma /v$ (multiply nahi, divide karo). Speed denominator mein hai, isliye zyada $v$ tumhe slower turn karti hai.

Error: minus sign ka matlab hai $\gamma$ decrease hota hai — yahi bilkul woh cheez hai jo path ko vertical se horizontal ki taraf bend karti hai. Iske bina koi turn hi nahi hogi.

Error: yeh alag phases mein use hote hain — open-loop schedule ghani atmosphere ke through, phir closed-loop guidance upper stages par jahan aero loads khatam ho jaate hain aur precise orbit targeting matter karta hai.

Error: climb karte waqt thrust ko partially gravity ke against point karna phir bhi gravity loss incur karta hai; gravity turn steering loss minimize karta hai ($\alpha \approx 0$ rakhke), saari losses nahi.

Kyunki sabse ghani hawa pad ke paas hoti hai; $\alpha \approx 0$ ke saath seedha body axis ke saath fly karna aerodynamic load minimize karta hai, aur pre-tilt wahan angle of attack create karega jahan dynamic pressure badh raha hota hai.

Kyunki $\dot{\gamma }$ sirf current state par depend karta hai ($g,v,\gamma$); ek baar ${\gamma }_0$ set karne ke baad (aur thrust-to-weight $n$ ke saath), wahan se equation integrate karna poora $v(\gamma )$ curve fix kar deta hai — nudge ke baad ascent self-determined hai.

Kyunki $\dot{\gamma }\propto 1/v$ aur $v$ flight ke through badhta hai; jab tak $v$ chhota hai turn rate sabse bada hota hai, isliye vehicle apna zyaatar angle change early mein sweep karta hai.

Slow vehicle ka $v$ chhota hota hai, isliye $\dot{\gamma }=-g\cos \gamma /v$ bada hota hai — yeh apne aap quickly gravity-turn karta hai; upar se bada kick use over-rotate kar dega, isliye use gentler nudge chahiye.

Aerodynamic side force $\alpha \cdot q$ ki tarah scale karta hai; high dynamic pressure par ek modest $\alpha$ bhi aisi loads produce karta hai jo vehicle tod sakti hai, isliye structural survival tab tak dominate karta hai jab tak hawa patli nahi ho jaati.

Tsiolkovsky mass ratio se total achievable $\Delta v$ deta hai, lekin time ke saath direction ke baare mein kuch nahi bolta; pitch program decide karta hai ki woh $\Delta v$ gravity se ladne aur horizontal speed build karne ke beech kaise split hoga.

$\cos \gamma$ near zero rahta hai, isliye $\dot{\gamma }$ tiny rehta hai aur vehicle kabhi enough nahi turn karta — burnout par woh abhi bhi steeply climb kar raha hota hai, gravity ke against $\Delta v$ waste kar raha hota hai aur near-horizontal orbital condition reach karne mein fail hota hai.

$\cos \gamma \to 1$, isliye turn rate apne maximum magnitude $\dot{\gamma }\to -g/v$ tak pahunchta hai; lekin tab tak $v$ bada hota hai, isliye practice mein actual angular change per second abhi bhi chhoti hoti hai. Yahi woh jagah bhi hai jahan tum chahte ho ki turn almost ruk jaaye.

$\cos \gamma$ negative ho jaata hai, isliye $\dot{\gamma }=-g\cos \gamma /v$ positive ho jaata hai — gravity $\gamma$ ko wapas upar $90^{\circ }$ ki taraf push karegi; vertical point ek unstable balance hai jisse kick ko decisively door karna padta hai.

Nahi — kick khud ek active maneuver hai (chhota gimbal deflection) jo briefly nonzero $\alpha$ create karta hai; pure gravity turn ($\alpha \approx 0$) immediately baad mein shuru hota hai, ek baar velocity aur nose realign hone ke baad.

Law $\dot{\gamma }=-g\cos \gamma /v$ diverge karta hai (division by zero), jo sirf signal karta hai ki model rest par invalid hai — tum ek aisi velocity vector ko bend nahi kar sakte jiska koi length hi nahi. Gravity turn tabhi sense karta hai jab vehicle ke paas real speed ho.

Necessarily nahi — aero loads ke bina $\alpha$ ki koi penalty nahi hai, isliye closed-loop guidance jo optimally thrust steer kare preferred ho jaati hai; gravity turn atmospheric constraint ka response hai.