Mass budgets — dry mass, wet mass, margin: Question bank

3.6.24 · D5 · Physics › Spacecraft Structures & Systems Engineering › Mass budgets — dry mass, wet mass, margin

Cards se pehle, chaar pictures har us symbol ko fix kar deti hain jinpar ye questions tike hain. Jab bhi koi card abstract lage, inpar wapas aao.

Ek nazar mein variable map

Is bank ki har quantity do stacks mein se ek mein hoti hai: jo rehta hai (dry) aur jo kharcha hota hai (wet minus dry). Neeche ki figure inhe stack karke dikhati hai taaki tum split dekh sako.

Figure — Mass budgets — dry mass, wet mass, margin

Rocket equation kahan se aati hai — ek visual proof

$m_{wet} = m_{dry} e^{Δ V / v_{e}}$ ka relation is deck mein baar baar aata hai, isliye yahan ek picture mein kyun sahi hai woh bataya hai. Rocket sirf mass ko peeche phenk kar speed badhata hai: propellant ka har chhota slug $d m$ jo speed $v_{e}$ se nikalta hai, ship ko $d V = - v_{e} d m / m$ aage push karta hai (momentum conservation — thrust equals mass-flow times exhaust speed).

Exponential penalty curve

Poora "1 kg dry ke liye kaafi kg fuel chahiye" wala story ek hi curve hai: penalty $e^{Δ V / v_{e}} - 1$ ko ratio $Δ V / v_{e}$ ke against plot kiya gaya hai. WHY aur edge-case cards ka jawab dene se pehle ise padho.

Margin kaise stack hota hai — aur ghatta hai

CBE, MEV aur system margin teen layers hain, teen alag numbers nahi. Left bars stack dikhate hain; right panel wahi reserve dikhata hai jo ek review cycle ke khaane par ghatta hai.

True or false — justify karo

TF1. "Wet mass ek fixed number hai jo tum pure mission ke liye ek baar lookup kar sakte ho."

False — wet mass ek function of time

m_{wet} (t)

hai; launch pe maximum hota hai aur propellant jalane par dry mass ki taraf girta hai (figure s01). Rocket equation ko instantaneous value chahiye.

TF2. "Agar do spacecraft ka dry mass same hai, toh unhe same propellant chahiye."

False — propellant required

Δ V

aur exhaust velocity

v_{e}

par depend karta hai

m_{wet} = m_{dry} e^{Δ V / v_{e}}

ke through; identical dry mass ke saath bada mission

Δ V

exponentially zyada fuel maangta hai. Tsiolkovsky Rocket Equation dekho.

TF3. "End of life par wet mass essentially dry mass ke barabar hota hai."

True — design ke hisaab se lagbhag sab propellant kharcha ho jaata hai, isliye

m_{wet, EOL} \approx m_{dry}

hota hai, sirf kuch small unusable residuals chhod ke jo tanks aur lines mein band rahte hain.

TF4. "Khaali propellant tanks dry mass mein aate hain."

True — tank hardware vehicle ke saath hamesha rehti hai aur kabhi nahi jalti, isliye dry mass mein count hoti hai; sirf andar ka fluid propellant hota hai. Yeh ek classic bookkeeping trap hai.

TF5. "Flight hardware par 5% margin early design mein 20% margin se zyada dangerous hai."

False — tight percentage appropriate hai kyunki program ke late stage mein masses measure hote hain, estimate nahi, isliye uncertainty khatam ho chuki hai. Margin ko baaki bachi unknowns track karni chahiye, constant nahi rehni chahiye.

TF6. "Kyunki propellant consume hota hai, isliye yeh launch mass limits mein count nahi hota."

False — liftoff par propellant ka har kilogram physically vehicle par hota hai, isliye woh fully launcher capacity ke against count hota hai; consumption tab hota hai jab mass already lift ho chuka hota hai.

TF7. "Pressurant gas negligible hai aur wet-mass budget mein ignore kiya ja sakta hai."

False — pressurant (jaise helium) ek real consumable hai jo

m_{wet}

mein listed hoti hai; ise ignore karna ek chhota par systematic under-estimate hai jo margin khaata hai. Propellant Management dekho.

TF8. "Dry mass badhaana aur propellant badhaana budget ko equally hurt karte hain."

False — ek kilogram dry mass ko khud har burn mein carry karna padta hai, isliye ek kilogram dry mass ke upar extra

(e^{Δ V / v_{e}} - 1)

kg propellant cost hota hai; pure propellant add karne par sirf woh ek kilogram cost hota hai.

Error dhundho

SE1. "CBE mein pehle se component margins hain, isliye MEV = CBE."

Galat — CBE (Current Best Estimate) mein koi margin nahi hota; MEV (Maximum Expected Value) CBE plus component-level margins hota hai (figure s04). Dono sirf us impossible case mein equal hote hain jab uncertainty zero ho.

SE2. "Hamare paas 300 kg margin hai, toh chalte hain woh bhaari camera fit karte hain jo hum chaahte the."

Galat — margin unknown growth ke khilaf insurance hai, spending account nahi. Historically zyaatar spacecraft grow karte hain, aur features par margin jalane se kuch nahi bachta jab structure ya harness heavy aa jaye.

SE3. "Ek burn

Δ V

add karta hai, isliye burn ke baad mass

m_{i} e^{Δ V / v_{e}}

hai."

Galat direction — burn mass reduce karta hai, isliye

m_{f} = m_{i} / e^{Δ V / v_{e}}

hota hai. Multiply karne se ship grow ho jaati; halka final mass denominator mein hota hai.

SE4. "Dry mass 50 kg badh gaya lekin

Δ V

unchanged hai, isliye propellant unaffected hai."

Galat —

Δ V

fixed hone par mass ratio fixed hota hai, isliye extra dry mass proportionally zyada propellant force karta hai:

Δ m_{prop} = Δ m_{dry} (e^{Δ V / v_{e}} - 1)

. Penalty sirf tab invisible hoti hai jab

Δ V \approx 0

SE5. "Payload mission hai, isliye ise dry-mass budget mein nahi hona chahiye."

Galat — payload vehicle ka permanent, non-consumable part hai aur squarely dry mass ke andar hai. Yeh kabhi "spend" nahi hota, isliye kabhi wet mass nahi ho sakta.

SE6. "125 kg add karne ke baad margin percentage same raha, kyunki reserve abhi bhi bacha hai."

Galat — margin current mass ka ek fraction hai; growth reserve consume bhi karta hai aur base bhi badhata hai, isliye percentage raw reserve se zyada tezi se girta hai (jaise 25% se ~13% tak, figure s04).

SE7. "

v_{e} = I_{s p}

directly use karna theek hai."

Galat — specific impulse

I_{s p}

seconds mein hota hai; rocket equation se pehle exhaust velocity

v_{e} = I_{s p} g_{0}

m/s mein paane ke liye

g_{0} = 9.81 m/s^{2}

se multiply karna zaroori hai.

SE8. "Structural mass fraction sirf structure mass over wet mass hai."

Galat — structural mass fraction inert/structural mass ko total se compare karta hai aur ek consistent base use karna zaroori hai; standard forms hain

σ = m_{structure} / (m_{structure} + m_{prop})

m_{dry} / m_{wet}

. Casually numerator aur denominator mein dry aur wet mix karne se ek meaningless number milta hai.

Why questions

WHY1. Ek kilogram dry-mass growth kai kilograms propellant kyun cost karta hai?

Kyunki us kilogram ko poore mission

Δ V

mein accelerate karna padta hai, aur use carry karne ke liye fuel chahiye, jiske liye aur fuel chahiye — exponential

e^{Δ V / v_{e}} - 1

(figure s03) is compounding ko capture karta hai.

WHY2. High-

Δ V

missions jaise interplanetary transfers mein propellant penalty kyun explode karta hai?

Penalty

e^{Δ V / v_{e}} - 1

Δ V / v_{e}

ke saath exponentially grow karta hai; bada mission

Δ V

(ya chhota

v_{e}

) exponent ko tezi se upar push karta hai (figure s03), isliye margins exactly wahan sabse zyada matter karte hain jahan missions sabse mushkil hote hain.

WHY3. Engineers carefully estimate karne ki jagah mass margin kyun carry karte hain?

Kyunki kai masses genuinely unknown hote hain jab tak hardware exist nahi karta — coating thickness, harness routing, weld beads, late requirements — aur ~70% spacecraft grow karte hain, isliye margin woh buffer hai jo ek grow hoti design ko uske budget ke andar rakhta hai.

WHY4. Sirf launch par wet mass track karne ki jagah time ke saath kyun track karte hain?

Kyunki rocket equation aur thrust-to-weight ratio instantaneous mass use karte hain; maneuver planning aur remaining ΔV dono is par depend karte hain ki abhi kitna propellant bacha hai.

WHY5. Ek chhoti navigation error mass budget ke through ek lost mission mein kyun badal sakti hai?

Off-nominal burn extra propellant spend karta hai, baad ke corrections ya orbit insertion ke liye reserve shrink karta hai; agar woh residual khatam ho jaaye (jaise Mars Climate Orbiter cautionary tale mein) toh vehicle recover nahi kar sakta.

WHY6. Mass ko idhar udhar move karne se design kyun change hoti hai jab total mass unchanged hai?

Kyunki layout center of mass aur inertia ko affect karta hai; ek balanced total phir bhi attitude control ya thruster torque authority ko tod sakta hai agar mass distribution shift ho jaaye.

WHY7. Program reviews ke through deliberately margin kyun draw down kiya jaata hai?

Kyunki har review estimates ko measurements se replace karta hai, uncertainty retire karta hai; V-model margin ko design par ~20% se flight par ~5% tak shrink karne ke liye schedule karta hai jab knowledge badhti hai (figure s04, right panel).

Edge cases

EC1. Dry mass per kg propellant penalty kya hoti hai jab

Δ V \to 0

Yeh zero ho jaati hai:

e^{0} - 1 = 0

. Koi maneuver na hone par, extra dry mass ko extra propellant cost nahi hota — ise sirf launch karna padta hai, baad mein accelerate nahi karna (figure s03 ka left edge).

EC2. Required propellant ka kya hota hai jab

v_{e} \to \infty

(ek perfect, near-infinite-

I_{s p}

engine)?

Exponent

Δ V / v_{e} \to 0

isliye

e^{Δ V / v_{e}} \to 1

, aur

m_{prop} \to 0

— ek ideal high-

I_{s p}

engine ko almost koi propellant nahi chahiye, isliye low thrust hone ke bawajood electric propulsion itna prized hai.

EC3. Opposite limit

v_{e} \to 0

(almost-stationary exhaust) mein kya hota hai?

Exponent

Δ V / v_{e} \to \infty

, isliye

e^{Δ V / v_{e}} \to \infty

aur

m_{wet} \to \infty

— ek almost stationary exhaust kisi bhi real

Δ V

ke liye infinite propellant maangta hai, EC2 ka exact mirror aur reason ki slow exhaust engines bade maneuvers ke liye useless hain.

EC4. Kya "zero margin" budget kabhi acceptable hota hai?

Sirf fully measured flight hardware ke liye jahan har mass known hai; usse pehle, zero margin ka matlab hai pehla surprise budget blow kar deta hai, isliye design ke dauran yeh essentially reckless hai.

EC5. Negative remaining margin kya signal karta hai?

Current best estimate already allowed mass exceed kar chuka hai — design over budget hai aur ise fly karne se pehle payload descope karna hoga,

Δ V

cut karna hoga, ya launcher upgrade karna hoga.

EC6. Agar dry mass

\pm 50

kg uncertain hai ek Mars transfer par (penalty factor

\approx 6.4

), toh kitni propellant uncertainty implied hai?

Lagbhag

\pm 320

kg propellant, kyunki dry mass ka har uncertain kilogram

e^{Δ V / v_{e}} - 1 \approx 6.4

ke through propagate hota hai — uncertainty amplified hoti hai, sirf carry nahi hoti.

EC7. Kya wet mass kabhi dry mass se kam ho sakta hai?

Nahi — wet mass dry mass plus non-negative consumables hota hai, isliye

m_{wet} \geq m_{dry}

hamesha, equality sirf tab jab consumables khatam ho jaayein.

Recall Do-line self-test

Dry mass ke per kg propellant penalty ::: $e^{Δ V / v_{e}} - 1$ , jo $Δ V = 0$ par zero hoti hai aur mission difficulty ke saath exponentially badhti hai. CBE vs MEV ::: CBE no-margin sum hai; MEV CBE plus component margins hai — jab tak uncertainty exist karti hai tab tak dono kabhi equal nahi hote.