Solid propellants — fuel + oxidizer in polymer matrix: Foundations

3.3.35 · D1 · Physics › Rocket Propulsion › Solid propellants — fuel + oxidizer in polymer matrix

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0. Do ideas jo kisi bhi symbol se pehle chahiye

Symbols se pehle, do everyday pictures.

Picture A — ek aag ko teen cheezein chahiye. Ek campfire ko fuel (lakdi), oxygen (hawa), aur ek spark chahiye. Ek solid propellant bilkul waisa hi hai siwaaye is baat ke ki woh apni khud ki oxygen block mein bake karke rakhta hai. Yeh dhyan mein rakho — yahi explain karta hai ki block empty space mein bhi kyon jal sakta hai.

Picture B — mass ko peeche phenkne se tum aage jaate ho. Skateboard par khade ho aur ek bhaari ball aage phenko: tum peeche roll karoge. Ek rocket hot gas ko peeche phenkta hai, isliye woh aage roll karta hai. Woh "phenk" hi thrust ka poora source hai.

Figure — Solid propellants — fuel + oxidizer in polymer matrix

Neeche har symbol in dono pictures mein se kisi ek se attached ek number hai: ya toh block kaise jalta hai (Picture A) ya exhaust kitna zor se dhakka deta hai (Picture B).

1. Grain aur port — shapes

Socho ek gunpowder-dough ki candle jisme poori lambai mein ek ched drilled hai. Dough grain hai; ched port hai. Hum ched ki andar ki wall ko jalate hain, to aag port se grain ke andar ki taraf baahir phailti hai.

2. "Block kaise jalta hai" ke liye symbols

Ab hum Picture A ko describe karne wale numbers ko naam dete hain.

2.1 Density $ρ_{p}$

Picture: propellant ka ek $1 m \times 1 m \times 1 m$ cube. Use weigh karo. Agar usme $1800 kg$ hai, toh $ρ_{p} = 1800 kg/m^{3}$ . Bas yahi density hai: space ke ek box mein mass per unit.

Topic ko yeh kyon chahiye: hum jaanna chahenge ki aag kitna mass gas mein badal deti hai. Aag solid ka ek certain volume khaati hai; density woh exchange rate hai jo khaaye gaye volume ko khaaye gaye mass mein convert karti hai.

$mass = ρ_{p} \times volume$

2.2 Burning surface area $A_{b}$

Port ki andar ki wall ko glowing imagine karo. Agar tum us glowing wall ko flat unroll karke measure kar sako, toh woh flat patch ka square metres mein size $A_{b}$ hai.

Topic ko yeh kyon chahiye: zyada burning surface = har second zyada solid gas mein badal raha hai. Yeh sabse important geometric quantity hai. Ek choti burning patch kam gas banati hai; ek badi burning wall bahut zyada banati hai.

2.3 Linear burn rate $r$

Burning wall par ek point socho. Ek second mein flame andar kuch depth tak chab gayi hai — maano $8$ millimetres. Tab $r = 8 mm/s = 0.008 m/s$ . Yeh hai kitni tez aag andar tunnel karti hai, surface ke perpendicular.

Topic ko yeh kyon chahiye: $A_{b}$ batata hai kitni wall jal rahi hai; $r$ batata hai har bit of wall kitni tez recede hoti hai. Inhe multiply karo aur tum paate ho kitni tez volume gayab hoti hai.

2.4 Mass burn rate $\overset{m}{˙}$

Dot ka matlab: physics mein kisi symbol ke upar dot "rate of change per second" ka shorthand hai. Toh $\overset{m}{˙}$ "m-dot" bola jaata hai aur matlab hai "mass per second." Yeh waisi hi idea hai jaisi speed distance-per-second hoti hai.

Ab pichle teen symbols combine karo. Volume-per-second $A_{b} r$ hai; volume ko mass mein convert karo density $ρ_{p}$ se:

$\overset{m}{˙} = ρ_{p} A_{b} r$

Topic ko yeh kyon chahiye: yeh geometry aur chemistry (density, area, burn speed) se kitna exhaust motor se nikalta hai tak ka bridge hai. Yeh directly aage thrust mein jaata hai.

3. "Exhaust kitna zor se dhakka deta hai" ke liye symbols

Ab Picture B: mass ko peeche phenkna.

3.1 Exhaust speed $v_{e}$

Rocket par khade hoke socho aur gas ko peeche se whoosh karte dekho. Woh tumhare paas se tumhare relative (ground ke relative nahi) kitni tez nikalti hai woh $v_{e}$ hai. Ek typical value $2400 m/s$ hai — yeh gas $8000 km/h$ se zyada tez nikalti hai.

Topic ko yeh kyon chahiye: mass ko tez peeche phenkne se tum aage zyada zor se dhakke jaate ho. $v_{e}$ measure karta hai ki hum kitni tez phekte hain.

3.2 Momentum $p$ aur thrust $F$

Skateboard wali picture phir se socho. Jab tum ball phenkते ho, ball momentum lekar jaati hai (uska mass times uski speed). Newton's Third Law se (har push ka ek equal opposite push hota hai), momentum ki equal amount tumhare andar enter karti hai, opposite direction mein. Woh momentum-per-second jo tumhare andar aa raha hai wahi tumpar force hai.

$F = \frac{d p}{d t} = \overset{m}{˙} v_{e}$

Yeh padhna: $d p / d t$ ka matlab hai "momentum change ki rate per second." Exhaust $\overset{m}{˙}$ rate (kg per second) se nikalta hai, har kilogram $v_{e}$ speed carry karta hai, toh backward momentum $\overset{m}{˙} v_{e}$ rate se jaata hai — aur usi rate se forward momentum rocket mein banta hai. Momentum principle ke liye Newton's Third Law dekho, aur $v_{e}$ aur $\overset{m}{˙}$ finally rocket ki top speed kaise tay karte hain ke liye Tsiolkovsky Rocket Equation dekho.

4. Pressure aur burn-rate law ke liye symbols

4.1 Pressure $p_{c}$ , $p_{e}$ , $p_{a}$

Gas molecules ko ek wall se bounce karte socho; jitna zyada aur jitni tez woh hit karte hain, utna zyada pressure. Jalta hua motor ke andar gas tight packed hoti hai → high $p_{c}$ .

Topic ko yeh kyon chahiye: pressure control karta hai ki block kitni tez jalta hai (aage), aur exit par koi bhi leftover pressure thoda extra push deta hai (full thrust formula mein $(p_{e} - p_{a}) A_{e}$ term, jahan $A_{e}$ nozzle-exit area hai). Gas ko De Laval Nozzle se supersonic speed tak compress kiya jaata hai.

4.2 Burn-rate law: $a$ , $n$ , aur exponent kyun

Exponent kyun aur seedhi line kyun nahi? Kyunki experiments dikhate hain ki burn rate pressure ke saath simple proportion mein nahi badhta — woh zyada gently badhta hai. Expression $p_{c}^{n}$ (" $p_{c}$ raised to the power $n$ ") jab $n < 1$ hota hai to exactly woh shape hai jo grow karti hai par flatten hoti hai: pressure double karne par rate $2^{n}$ se multiply hoti hai, jo doubling se kam hai. Woh gentleness hi motor ko stable rakhti hai.

4.3 Specific impulse $I_{s p}$ (ek aage ki jhalak)

Tumhe thrust samajhne ke liye yeh abhi nahi chahiye, par yeh woh figure hai jisse sabhi engines compare kiye jaate hain — Specific Impulse dekho. Zyada $v_{e}$ → zyada $I_{s p}$ → har kilogram mein zyada mileage.

5. Sab kuch ek saath kaise fit hota hai

Ise do nadiyaan milte hue samjho: baayaan branch (area, density, burn rate, pressure) compute karta hai har second kitni gas; daayaan branch (exhaust speed, Newton's third law) us gas ko push mein badalta hai. Woh thrust par milte hain.

6. Numbers se sanity check

Equipment checklist

Daayaan side cover karo aur khud test karo — jab har line instant ho tab tum parent note ke liye ready ho.

ρ_{p}

ka kya matlab hai aur uski units kya hain?

Propellant density, mass per cubic metre,

kg/m^{3}

A_{b}

kya hai?

Solid surface ka total area jo abhi jal raha hai,

m^{2}

mein.

Linear burn rate

r

kya measure karta hai?

Woh speed (m/s) jis par flame front solid ke seedha andar tunnel karta hai.

\overset{m}{˙}

mein dot ka kya matlab hai?

"Rate per second";

\overset{m}{˙}

har second kitne kilograms solid gas mein badalta hai.

Mass burn rate formula likho.

\overset{m}{˙} = ρ_{p} A_{b} r

(density × burning area × burn rate).

v_{e}

kya hai?

Exhaust gas speed rocket ke relative, m/s mein.

Ideal thrust formula likho aur batao yeh kyon kaam karta hai.

F = \overset{m}{˙} v_{e}

; backward pheka gaya momentum per second aage ki push ke barabar hai (Newton's third law).

p_{c}

p_{e}

p_{a}

kya hain?

Chamber pressure, nozzle-exit pressure, ambient (baahri) pressure.

Burn-rate law batao aur har symbol ka naam lo.

r = a p_{c}^{n}

;

a

= chemistry/temperature constant,

n

= pressure exponent.

n < 1

kyun hona chahiye?

Warna ek pressure spike khud ko feed karti hai (zyada pressure → faster burn → zyada gas) aur motor runaway ho jaata hai aur explode ho jaata hai.

Ek solid propellant vacuum mein kyun jalta hai?

Woh apna khud ka oxidizer grain mein chemically bound karke rakhta hai, isliye use baahri hawa ki zaroorat nahi.

Connections

Yeh note Hinglish mein → — woh parent topic jiske liye yeh page tumhe prepare karta hai.
Newton's Third Law — $F = \overset{m}{˙} v_{e}$ ke peeche momentum principle.
Tsiolkovsky Rocket Equation — jahan $v_{e}$ aur $\overset{m}{˙}$ final velocity decide karte hain.
De Laval Nozzle — chamber gas ko supersonic $v_{e}$ tak kaise compress kiya jaata hai.
Specific Impulse — $I_{s p} = v_{e} / g_{0}$ , efficiency score.
Liquid Propellants — throttleable contrast.
Combustion Chemistry — heat ke peeche reactions.