Reaction control system — thruster selection, plume impingement limits: Question bank

3.5.46 · D5 · Physics › Guidance, Navigation & Control (GNC) › Reaction control system — thruster selection, plume impingem

Neeche jo vocabulary assume ki gayi hai — thruster, wrench $w = [F; τ]$ , allocation matrix $B$ , couple, keep-out cone — yeh sab parent note mein define hain. Agar koi symbol yahan unfamiliar lage, toh woh tumhara cue hai ki answer dene se pehle parent note dobara padho.

True or false — justify karo

Ek single offset thruster pure torque produce karta hai.

False. Yeh torque

r \times F

aur net force

F \hat{u}

dono produce karta hai, isliye ship drift bhi karta hai; torque-only couple banane ke liye ek opposing thruster chahiye.

Har thruster fire karna control authority maximize karta hai.

False. Authority net wrench

w = B f

ke baare mein hai; extra jets aksar unwanted force add karte hain ya torque cancel kar dete hain, isliye useful net shrink ho sakta hai chahe

\sum F_{i}

badhe.

Jo thruster ka force line center of mass se guzre woh koi torque nahi deta.

True. Tab

r ∥ \hat{u}

hota hai, isliye

r \times \hat{u} = 0

; yeh pure translation thruster hai.

Negative on-time command karke thruster ka push reverse kiya ja sakta hai.

False. Thrust one-sided hota hai,

F_{i} \geq 0

— ek jet sirf push kar sakta hai. Opposite direction ke liye ek alag, opposite-mounted thruster fire karna padta hai.

Surface se distance aadha karne par plume pressure double ho jaata hai.

False. Pressure

1/ d^{2}

ke hisaab se girta hai, isliye

d

aadha karne par pressure chaar guna ho jaata hai — kareeb jaane par danger tezi se badhta hai.

On-axis surface (

θ = 0

) hamesha kisi bhi given distance ke liye sabse harsh plume dekhta hai.

True. Shape function

f (θ) = cos^{k} θ

θ = 0

par peak karta hai jahan

f = 1

; har off-axis angle par

f < 1

milta hai, isliye on-axis worst case hai.

Plume impingement constraint ek hard on/off rule hai, optimize karne layak kuch nahi.

Partly false. Yeh hard keep-out ke roop mein enforce hoti hai (jo thrusters limits violate karein unhe inhibit karo), lekin baaki selection phir bhi allowed jets par minimum-propellant optimization hai.

Couple banane wale do thrusters zero net force produce karte hain.

True. Equal, opposite forces cancel ho jaate hain (

\sum F_{i} \hat{u}_{i} = 0

) jabki unke torques add hote hain, isliye bina drift ke pure rotation milti hai.

Plume force tumhare apne maneuver par disturbance torque ki tarah act kar sakta hai.

True. Ek offset surface (koi panel, ship ki apni belly) par impingement ek lever arm par force apply karta hai, jis se torque produce hota hai jo commanded wrench se ladhta hai ya use corrupt karta hai.

Tighter plume (bada

k

) off-axis nearby surfaces ke liye zyada forgiving hota hai.

Off-axis sense mein True. Bada

k

cos^{k} θ

ko angle ke saath tezi se drop karta hai, isliye off-axis surfaces ko kam pressure milta hai — lekin on-axis peak (

f (0) = 1

) unchanged rehta hai, isliye seedha aage kuch bhi safe nahi hota.

Error pakdo

N > 6

thrusters hona matlab allocation problem ka koi solution nahi."

Error. Zyada thrusters DOFs se zyada hone par solution non-unique ho jaata hai (bahut se

f

same

w

dete hain), isliye hum optimize karte hain — yeh over-determined-free hai, unsolvable nahi. Dekho Control Allocation & Pseudo-inverse.

"Torque equals force times mount distance, hamesha

∣ r ∣ F

Error. Torque

r \times F

hai, jiska magnitude

∣ r ∣ F sin ϕ

hai jahan

ϕ

lever arm aur force ke beech ka angle hai. Sirf lever arm ka perpendicular component matter karta hai; radial thrust zero deta hai. Dekho Cross Product & Rigid-Body Torque.

"Vacuum mein hone ki wajah se plume nozzle exit par gayab ho jaata hai."

Error. Vacuum mein exhaust under-expanded hota hai, isliye woh ek widening cone mein fan out karta rehta hai — yeh zyada spread hota hai, kam nahi, aur door surfaces tak pahunchta hai.

\sum F_{i}

minimize karna nonlinear hai kyunki thrust mein exhaust velocity squared involve hoti hai."

Error. Fixed

I_{s p}

ke liye, force aur propellant mass-rate dono on-time/throttle ke saath linearly scale karte hain, isliye objective aur constraints linear hain — yeh ek linear program hai.

"Agar ek thruster inhibit ho jaaye, toh commanded wrench simply achieve nahi ho sakta."

Error. Redundancy usually doosre thrusters (jaise off-axis pairs) ko same

w

reproduce karne deti hai, bas propellant penalty ke saath — over-actuated cluster ka yahi point hai.

"Heat flux aur pressure impingement ek hi keep-out limit dete hain."

Error. Yeh alag constraints hain (

\overset{q}{˙} \leq \overset{q}{˙}_{m a x}

aur

P \leq P_{m a x}

); ek geometry ek pass kar sakti hai aur doosra fail, isliye dono check karne zaroori hain. Dekho Rarefied Gas Dynamics / Plume Modeling.

"Gimballed engine hamesha fixed-thruster cluster se behtar hoga."

Error. Gimbals heavy, slow, aur single point of failure hote hain. Fixed cluster redundant hai, fast on/off hai, aur jets combine karke kisi bhi axis ke baare mein torque de sakta hai.

Why questions

RCS thrusters opposing directions mein kyun hone chahiye?

Kyunki thrust one-sided hota hai (

F_{i} \geq 0

) — tum jet reverse nahi kar sakte, isliye opposite direction mein push karne ka ek hi tarika hai ki doosra thruster opposite taraf mount karo.

Torque term mein cross product kyun aata hai?

Torque lever-arm-times-force hai, aur cross product

r \times F

automatically perpendicular leverage extract karta hai aur rotation axis deta hai — exactly wahi jo "kisi point ke baare mein twist" ka matlab hai. Dekho Attitude Dynamics — Euler's Equations.

Plume density

1/ d

ki jagah

1/ d^{2}

kyun girta hai?

Mass expanding spherical shells se conserved rehta hai; har shell ki surface area

d^{2}

ke hisaab se badhti hai, isliye same flux us area par spread hokar

1/ d^{2}

ke hisaab se patlaa hota hai.

Docking ke dauran plume impingement specially critical kyun hoti hai?

Target vehicle sirf couple of metres aage ho sakta hai, jahan

1/ d^{2}

pressure large banata hai aur jahan on-axis forward thruster seedha uski taraf point karta hai, isliye limits aasani se violate hoti hain. Dekho Rendezvous and Docking.

Thruster inhibit karne par kabhi kabhi extra propellant kyun lagta hai?

Optimizer apna most efficient combination khota hai aur wrench ko ek kam-aligned subset se reproduce karna padta hai, isliye same

w

hit karne ke liye zyada total thrust (fuel) burn hota hai — safety efficiency se upar hai.

Shape function mein

cos^{k} θ

axis par peak ke saath kyun use hota hai?

Gas centerline ke saath sabse dense hoti hai aur cone edge ki taraf patli hoti hai;

cos^{k} θ

us fall-off ko capture karta hai, aur

k

tune karta hai ki plume kitna tightly collimated hai.

Total thrust

\sum F_{i}

control authority ka poor measure kyun hai?

Kyunki torques aur forces add ya cancel ho sakte hain; do bade jets opposition mein

\sum F_{i}

mein bahut contribute karte hain lekin sirf couple (ya kuch nahi) produce karte hain, isliye sirf net wrench

B f

matter karta hai.

Edge cases

Agar thruster ka mount position exactly CoM par ho (

r = 0

), toh kitna torque milta hai?

Zero, kyunki

τ = r \times F = 0

— yeh pure translation thruster hai chahe kisi bhi direction mein point kare.

Jab surface plume cone ke bilkul edge tak jaaye (

θ \to 9 0^{\circ}

) toh

f (θ)

ka kya hoga?

cos^{k} (9 0^{\circ}) = 0

, isliye modeled impingement zero ho jaata hai — cone axis region ke bahar ki surfaces essentially us jet se safe hain.

d \to \infty

hone par impingement pressure kya hoga?

Yeh

1/ d^{2}

ki tarah zero ki taraf jaata hai; door hardware safe hai, isliye keep-out cones ki finite range

d_{KO}

hoti hai.

Agar commanded wrench ko pure torque chahiye, toh selection mein kya extra constraint aata hai?

Net-force-zero condition

\sum F_{i} \hat{u}_{i} = 0

, jo ek couple force karta hai taaki body bina translate kiye rotate kare.

Agar do opposite-mounted thrusters same direction mein fire karein instead of opposite?

Unke forces add ho jaate hain (net translation) aur unke torques cancel hone lagte hain — couple ka opposite, matlab drift with little or no rotation.

Kya impingement force kabhi maneuver mein help kar sakti hai instead of hurt?

Principle mein uski direction command ke saath align ho sakti hai, lekin yeh unmodeled aur geometry-dependent hai, isliye control design isse bound karne ke liye disturbance treat karta hai, exploit karne ke liye resource nahi.

Agar target clear karne wale saare thrusters inhibit ho jaayein, toh LP kya return karta hai?

Infeasibility — koi

f \geq 0

constraints ke under

B f = w_{cmd}

satisfy nahi karta, signal karta hai ki maneuver re-plan karna hoga (alag geometry, timing, ya attitude).

Recall Ek-line self-test

Kya "zyada authority ke liye zyada thrusters fire karo" kabhi correct hai? ::: Nahi — authority net wrench $B f$ hai; jets add karne se torque cancel ho sakta hai ya unwanted force aa sakta hai, isliye sahi subset full set se behtar hai.