3.3.37 · D1Grain geometry — BATES, star, wagon wheel; neutral - progres
Ek solid rocket ek shaped fuel ka block hota hai jo apni exposed surface par jalta hai, aur abhi kitni surface par fire hai yeh decide karta hai ki rocket abhi kitna hard push kar raha hai . Toh agar tum fuel ke andar ka hollow channel ek clever shape mein kaat do, tum control kar sakte ho ki burning surface time ke saath badhti hai ya ghatati hai — aur isi tarah tum pura thrust-vs-time curve sculpt karte ho bina ek bhi chemical badle.
Yeh page assume karta hai ki tumne kuch nahi dekha . Har letter, har shape, har idea jo parent topic use karta hai, woh sab yahan build hoga, ek aisi order mein jahan har piece pehle wale ke upar tika ho.
Grain solid rocket propellant ka block hota hai — fuel-aur-oxidiser ka mixture ek rubbery-se-hard chunk mein press kiya hua. Socho ek mota grey clay ka cylinder ek metal tube (motor case) ke andar baitha hua hai.
Port woh hollow channel hai jo grain ke beech mein bora jaata hai — woh khaali jagah jahan hot gas collect hoti hai. Socho toothpaste ki tube ke centre mein neeche jaane wala hole.
Neeche di figure dekho: bahari circle propellant ka outer edge hai (case ko touch karta hua), aur andar waali shape port hai. Dono ke beech ka grey ring actual fuel hai jo jalega.
Yeh words kyun chahiye: poora topic us andar waale hole ki shape ke baare mein hai. Hole badlo, rocket badlo. Aage sab kuch port ki shape ka consequence hai.
Intuition Ek candle jo sideways jalti haiCandle ki flame wick ke neeche jaati hai. Solid rocket alag hai: flame fuel ke har exposed face par ek saath baithti hai, aur surface ka har chhota patch propellant ke andar seedha, apne aap ke perpendicular jaata hai. Koi bhi flame fuel ke saath saath nahi chalti — poori surface andar ki taraf peels hoti hai jaise ek siktey seb ki skin.
Definition Burning surface area — symbolA b A b b b urning) propellant ka woh total area hai jo is instant par fire par hai , square metres (m 2
Area ka matlab sirf "surface ki matra" hai, jaise ek divar ka area batata hai ki use kitna paint chahiye. Yahan yeh batata hai ki har second kitna fuel gas ban raha hai.
Definition Normal recession"Normal" ek maths word hai jiska matlab hai perpendicular — 90° ke right angle par surface se. Burning surface ka har point apni khud ki normal direction mein move karta hai, yaani surface se seedha bahar jaise ek divar mein thoka hua nail.
Neeche di figure mein green mein ek curved burning edge hai aur chhote red arrows hain: har arrow surface se 90° par nikalta hai. Iska matlab yahi hai "recede normally" — koi bhi arrow surface ke saath slant nahi karta, sab seedhe bahar shoot karte hain.
Yeh kyun chahiye: agar hum jaante hain ki har surface ek hi speed se apne aap ke perpendicular move karti hai, toh hum kisi bhi amount of burning ke baad port ki nayi shape predict kar sakte hain — pure geometry, koi chemistry nahi.
Definition Web burned — symbolw w woh perpendicular distance hai jitni burning surface fuel ke andar pehle se recede ho chuki hai . Shuru mein, w = 0 w
Port se bahar case tak fuel ki poori thickness ko web thickness kehte hain; w
Intuition Distance burned kyun measure karte hain, time nahi?Same shape wale lekin alag burn speed wale do motors alag rates se recede karte hain — lekin same w shape hamesha same hogi, isliye burning area bhi same. Toh A b w A b ( w ) w
Definition Linear burn rate — symbolr r m/s woh speed hai jis par surface apni normal ke along recede karti hai . Agar r = 5 × 1 0 − 3 m/s 5
r kitna fast samjho, aur w kitna far — dono exactly speed aur distance ki tarah linked hain: distance = speed × time. Ek chhoti time slice d t r d t
Definition Density — symbolρ p ρ p kg/m 3 propellant density hai: har cubic metre mein kitne kilograms fuel packed hain. Paani 1000 ρ p ≈ 1750 kg/m 3 1 m × 1 m × 1 m
Yeh kyun chahiye: burning area batata hai ki kitni surface gas ban rahi hai; density us jale hue fuel ke volume ko bane hue gas ke mass mein convert karti hai. Mass woh cheez hai jise nozzle bahar throw karta hai thrust banane ke liye.
Ab hum teen geometric quantities ko ek physical rate mein combine karte hain.
Definition Mass generation rate — symbolm ˙ m per second " (time mein change ki rate). Toh m ˙ kg/s woh kilograms gas hai jo burning surface har second mein banati hai .
Yahan picture-logic hai, step by step:
KYA: ek chhote instant d t r d t A b KYUN: us skin ka volume = area × thickness = A b ⋅ r d t A t A t CONVERT: volume ko density se multiply karo mass paane ke liye: d m = ρ p A b r d t RATE: per-second version paane ke liye d t
Symbols ka last cluster jo gas ko push se link karta hai. Parent note us chain ko derive karta hai; yahan hum sirf har symbol ko naam lete hain aur picture karte hain taaki kuch bhi surprise na lage.
Definition Chamber pressure — symbolp c p c Pa woh hai jitna hard gas motor ke andar se press karti hai . Socho balloon ki tightness: zyada gas crammed in → zyada p c
Definition Throat area — symbolA t A t m 2 nozzle ke narrowest point ka area hai, woh pinch jahan se gas bahar jaate waqt squeeze hoti hai. Socho bottle ki neck.
K K n K = A t A b K fire kitna bada hai (A b exit kitna chhota hai (A t Chamber pressure & throat area (Kn ratio) topic build hua hai.
Definition Burn-law constants — symbolsa n Saint-Robert burn rate law mein capture hota hai:
r = a p c n a n pressure exponent , usually 0.2 0.5 sensitive hai. n
Definition Thrust aur uske coefficients — symbolsF C F c ∗
F N thrust hai — rocket par actual forward push.C F thrust coefficient ) aur c ∗ characteristic velocity ) near-constant numbers hain jo describe karte hain ki nozzle aur chemistry kitni efficiently kaam karti hai. Abhi ke liye inhe fixed dials samjho.
F = C F p c A t C F A t thrust simply p c , jo A b
Figure teen archetype curves dikhata hai. Horizontal axis ko "kitna far jal chuke hain" (w A b
Mnemonic Teeno ko seedha rakhoPro gressive P oints up. Re gressive Re cedes down. Neu tral ek flat line hai beech mein. (P-upar, R-neeche, N-flat.)
Ratio K equals A_b over A_t
Burn law r equals a p_c to the n
Thrust F equals C_F p_c A_t
Neutral progressive regressive
Ise top to bottom padho: shape → area → gas → pressure → thrust , aur burn class saath saath ride karta hai poori story ki shape ke roop mein.
Right side cover karo aur har answer reveal karne se pehle zyabar se bolو.
What is the grain ? Propellant ka shaped solid block.
What is the port ? Grain ke through hollow channel jahan gas collect hoti hai.
What does A b Total burning surface area jo abhi fire par hai, m 2
What does "recede normally" mean? Surface ka har point apne aap ke perpendicular (90°) move karta hai.
What is the web burned w Woh perpendicular distance jitni burning surface fuel ke andar pehle se recede ho chuki hai.
Why express area as A b ( w ) A b ( t ) Port ki shape — isliye uska area — sirf is par depend karta hai ki woh kitna far jal chuka hai, kitna fast par nahi.
What is the linear burn rate r Woh speed jis par surface apni normal ke along recede karti hai, m/s
What is ρ p Propellant density (kg/m 3 volume ko gas mass mein convert karti hai.
State the mass generation rate in words and symbols. Gas made per second = density × area × speed: m ˙ = ρ p A b r
What is chamber pressure p c Motor ke andar gas kitna hard press karti hai, pascals mein.
What is throat area A t Nozzle ke narrowest point ka area.
Define the ratio K K = A b / A t
What do a n r = a p c n a n
Write the thrust equation and say what tracks what. F = C F p c A t C F , A t p c A b
Name the three burn classes by what A b Neutral (constant), progressive (rising), regressive (falling).
