3.3.43 · D5 · HinglishRocket Propulsion
Question bank — FEEP, MEMS thrusters — micro-propulsion
3.3.43 · D5· Physics › Rocket Propulsion › FEEP, MEMS thrusters — micro-propulsion
Shuru karne se pehle, parent topic note ke do load-bearing formulas yaad karo:
- Ek accelerated ion ki exhaust speed: — voltage yeh control karta hai.
- Poore beam ki thrust: — beam current isse scale karta hai.
Un do knobs — aur — ko mentally alag rakho. Niche ke zyaadatar traps inhe confuse karne se aate hain.
Do aur real-world limits jinhe parent note sirf hint karta hai — figures study karo, phir traps use karo:
- Knudsen number (mean free path channel size se divide karke): micro-scale par bada ho sakta hai, toh gas ek smooth continuum ki tarah behave karna band kar deti hai aur transitional ya free-molecule (rarefied) flow mein enter karti hai — nozzle equations upar quietly break down ho jaate hain.
- Child–Langmuir (space-charge) limit: beam ka apna charge peeche wale ions ko repel karta hai, isliye maximum current jo tum pull kar sakte ho woh voltage aur geometry se cap hoti hai — aur fully free knobs nahi hain.
- Beam divergence: real ions ek straight line ki jagah ek cone ke along nikalta hai, isliye har ion ki velocity ka sirf axial component useful thrust produce karta hai — yeh loss ek divergence half-angle se capture hota hai.
True or false — justify karo
FEEP beam ka har ion same speed se nikalta hai regardless of ion mass, jab tak voltage fixed hai.
False — , toh fixed ke liye zyada heavy ek slower exit speed deta hai; sirf energy per charge fixed hai, speed nahi.
Fixed accelerating voltage ke liye, heavier ion lower specific impulse deta hai lekin beam current ke per amp zyada thrust deta hai.
True — (lower ), phir bhi , toh current ka har ampere zyada push karta hai. Yeh ek genuine trade-off hai, koi flaw nahi.
Beam current double karne se thrust double hoti hai lekin exhaust speed unchanged rehti hai.
True — ko linearly multiply karta hai lekin mein kabhi appear nahi karta; zyada ions per second, har ek phir bhi same speed par.
Accelerating voltage double karne se exhaust speed double ho jaati hai.
False — , toh double karne se sirf se multiply hoti hai, se nahi.
Zyada specific impulse ka matlab hamesha CubeSat ke liye "better" thruster hai.
False — high propellant bachata hai lekin usually matlab hai tiny thrust aur high voltage; "better" is baat par depend karta hai ki mission ko fine attitude control chahiye, fast maneuvers chahiye, ya fuel economy chahiye.
Taylor cone tabhi banta hai jab electric field surface tension ko balance karne ke liye kaafi strong ho.
True — us threshold ke niche surface tension surface ko rounded rakhti hai; exactly wahan sharp cone appear hota hai jahan outward electrostatic pressure ki inward pull ke barabar hoti hai.
MEMS nozzle ko chhota banana same expansion efficiency rakhta hai kyunki ideal-gas formula mein koi length scale nahi hai.
False — ideal formula size-blind hai, lekin real micro-nozzles mein small Reynolds number (viscous losses) aur large Knudsen number (rarefaction) hota hai, isliye wall friction aur free-molecule effects dominate karte hain aur efficiency drop hoti hai.
Ek FEEP thruster, principle mein, purely electrical power par chal sakta hai jisme small ke liye essentially koi propellant nahi chahiye.
Spirit mein True — kyunki aur m/s, kuch m/s ka sub-gram propellant chahta hai; lekin yeh kabhi zero nahi hota — momentum ke liye ejected mass hamesha chahiye.
Tum beam current ko freely raise kar sakte ho sirf emitter voltage badhake.
False — Child–Langmuir space-charge limit extractable current ko ek given voltage aur geometry ke liye cap karti hai; pehle se flight mein ions baad wale ions ko repel karte hain, isliye ko arbitrarily high nahi push kar sakte.
FEEP ion beam ki saari kinetic energy forward thrust mein convert ho jaati hai.
False — ions ek divergence cone ke along nikalta hai, isliye sirf har ion ki axial velocity component spacecraft ko push karta hai; off-axis part waste hota hai, effective thrust coefficient kam karta hai.
Error dhundo
"FEEP se zyada thrust lene ke liye, sirf voltage raise karo — thrust ke saath linearly badhti hai."
Galat scaling — , toh thrust sirf voltage ke square root ki tarah badhti hai; raise karna linear knob hai.
"Kyunki hai, thrust maximize karne ke liye sabse heavy ion choose karna chahiye."
Half-right, half-wrong — heavy ions thrust-per-amp zaroor raise karte hain, lekin (isliye aur fuel economy) ko crater kar dete hain. Yeh choice ek balance hai, "heaviest wins" nahi.
"Reynolds number MEMS thruster mein large hota hai kyunki gas bahut fast move karti hai."
Error — tiny channel length ke saath bhi shrink karta hai; chota win karta hai, isliye high speed ke bawajood small hota hai, viscosity ko dominant banata hai.
"Continuum nozzle equations micro-scale par bilkul theek apply hoti hain jab tak gas move kar rahi hai."
Error — jab Knudsen number large ho jaata hai, gas rarefied (transitional ya free-molecule) hoti hai, aur exhaust formula ke peeche wala continuum assumption fail ho jaata hai.
"Thrust hai, aur beam current hai, isliye hai."
Error — charge per second hai, mass per second nahi. Mass flow hai, jo deta hai.
"Cold-gas MEMS thruster ki thrust sirf hai; pressure term hamesha negligible hai."
Error — poora expression hai, jahan exit pressure hai, ambient pressure hai, exit area hai. Jab under- ya over-expanded ho, ya vacuum mein jahan ho, pressure term automatically zero nahi hota.
"Kyunki energy conservation ke roop mein hai, saari electrical energy useful thrust ban jaati hai."
Error — energy conservation speed set karta hai, lekin useful thrust beam divergence (off-axis ions), non-ionized neutrals, aur current losses se bhi lose hoti hai; real efficiency ideal se neeche hoti hai.
"FEEP ko sirf kuch volts chahiye kyunki hum tiny ions push kar rahe hain."
Error — se m/s reach karne ke liye kilovolt-level chahiye; small mass required voltage ko small nahi banata.
"Kyunki aur independent knobs hain, main koi bhi voltage aur koi bhi current choose kar sakta hoon."
Error — Child–Langmuir limit unhe couple karta hai: ek fixed geometry ke liye space-charge-limited current sirf ki tarah badhti hai, isliye maximum ek baar choose hone ke baad set ho jaata hai.
Why questions
Chhote satellites deliberately micro-newton thrust kyun choose karte hain zyada powerful thrusters ki jagah?
Unhe precision chahiye (attitude arc-seconds tak) aur fuel economy chahiye, brute force nahi; ek firehose har tiny correction overshoot kar dega aur scarce propellant drain kar dega.
FEEP itna fine, tunable thrust resolution kyun deta hai?
Thrust beam current se set hoti hai, jise electronically nanoamps tak dial kiya ja sakta hai, isliye ko fractions of a micro-newton tak trim kiya ja sakta hai.
High exhaust velocity ka matlab almost koi propellant consume nahi hota, aisa kyun?
Rocket equation deta hai small ke liye; denominator mein ek bada required propellant mass ko near nothing tak shrink kar deta hai.
FEEP mein liquid metal ek smooth blob ki tarah rehne ki jagah cone mein organize kyun ho jaata hai?
Outward electrostatic pressure inward surface-tension pull ko sirf ek specific cone geometry ke along balance karta hai, isliye surface Taylor cone self-select karti hai.
FEEP thruster mein aur thrust control karne ke liye voltage aur current ko semi-independently kyun tune kiya ja sakta hai?
Voltage exhaust speed (isliye ) set karta hai jabki current yeh set karta hai ki kitne ions per second nikalt hain (isliye thrust) — lekin Child–Langmuir limit har voltage par available current ko cap karti hai, isliye independence total nahi hai.
FEEP mein caesium ya indium use kyun kiya jaata hai bahut light ion ki jagah?
Heavy ions per charge zyada momentum carry karte hain, per amp zyada thrust aur steadier low-thrust control dete hain, jabki kilovolt voltages par phir bhi high reach karte hain.
Enthalpy-to-kinetic-energy picture MEMS cold-gas exhaust formula kyun explain karta hai?
Gas ki stored thermal (pressure–temperature) energy nozzle mein directed motion mein convert hoti hai; bracket (jahan specific-heat ratio hai) exactly woh fraction hai jo enthalpy release hoti hai jab gas chamber pressure se exit pressure tak girti hai.
Beam divergence real FEEP thrust ko ideal se neeche kyun reduce karta hai?
Kyunki thrust ek vector hai: har ion ki velocity ka sirf axial ke saath wala component spacecraft ko aage push karta hai, isliye nonzero divergence half-angle ka matlab hai off-axis components cancel ho jaate hain aur waste ho jaate hain.
Edge cases
Agar beam current zero ho jaaye jabki voltage high rahe toh FEEP thrust ka kya hoga?
Thrust vanish ho jaati hai — jab ; field phir bhi exist kar sakta hai, lekin koi ion na nikle toh koi reaction force nahi hogi.
Accelerating voltage zero ho toh exhaust speed kya hogi?
Zero — ; koi potential drop nahi hoga toh ions koi kinetic energy gain nahi karte aur usefully expel nahi hote.
Under-expanded nozzle () ke liye, pressure term kaunsa sign contribute karta hai?
Positive — exit pressure ambient se zyada hai, isliye term thrust mein add karta hai; flow mein abhi bhi pressure "bacha hua" tha jise aur expand kiya ja sakta tha.
Over-expanded nozzle () ke liye, pressure term kaunsa sign contribute karta hai?
Negative — ambient pressure exit pressure se zyada hai, isliye term thrust se subtract karta hai; gas bahut zyada expand ho gayi aur bahar wali pressure exit plane par peeche push karti hai.
Space ke deep vacuum mein MEMS thrust pressure term kya ban jaata hai?
Ambient pressure hone par, term ban jaata hai, ke upar residual exit pressure se ek positive bonus contribution.
Jab , kya propellant-fraction formula blow up hoti hai ya simplify hoti hai?
Simplify hoti hai — tiny ke liye, give karta hai , ek small, well-behaved amount, divergence nahi.
Bahut large channel (large ) ki limit mein, MEMS viscous- aur rarefaction-loss problems ka kya hoga?
Dono fade ho jaate hain — bada raise karta hai (kam viscous drag) aur lower karta hai (continuum flow wapas aa jaati hai), isliye yeh loss inherently ek micro-scale penalty hai.
Real FEEP thruster mein accelerating voltage ko kitna high push kar sakte ho uski limit kya hai?
Practical breakdown, insulation, aur power-supply limits ko cap karte hain; (aur ) ko unbounded raise nahi kar sakte kyunki arcing aur available spacecraft power intervene karte hain.
Jab FEEP beam ka divergence half-angle zero ki taraf shrink hota hai, toh useful thrust ka kya hota hai?
Yeh ideal approach karta hai — ek perfectly collimated (zero-divergence) beam koi off-axis velocity waste nahi karta, isliye thrust coefficient approach karta hai.
Recall Two-knob summary — bina dekhe bata sako?
Kaun sa knob set karta hai aur kaun sa thrust? ::: Voltage exhaust speed set karta hai aur isliye ; beam current thrust set karta hai — lekin Child–Langmuir maximum ko se couple karta hai. MEMS micro-nozzle mein small aur large kyun hota hai? ::: Tiny length scale shrink karta hai (viscosity rule karti hai) aur inflate karta hai (gas rarefy hoti hai), dono efficiency hurt karte hain.