Visual walkthrough — Spacecraft bus — structure, power, thermal, ADCS, C&DH, comms, propulsion

3.6.21 · D2 · Physics › Spacecraft Structures & Systems Engineering › Spacecraft bus — structure, power, thermal, ADCS, C&DH, comm

Yeh deep dive Spacecraft Bus — Structure, Power, Thermal, ADCS, C&DH, Comms, Propulsion ka hissa hai. Hum parent note ke "Energy Balance in Orbit" formula se gehre jaate hain — hum har symbol ko kama ke laate hain.

Step 1 — "Power" kya hai, aur orbit do hisson mein kyun banti hai?

KYA HAI. Low Earth Orbit (LEO) mein ek satellite lagbhag dedh ghante mein planet ka chakkar lagata hai. Us loop ke kuch hisse mein use sunlight milti hai; baaki mein woh Earth ki shadow se guzarta hai.

KYUN do hisson mein baanto. Solar panels tabhi power banate hain jab unhe Sun dikhe. Isliye orbit ke dono hisson ka character fundamentally alag hota hai, aur energy ko alag alag track karna padta hai.

PICTURE. Neeche ka circle ek orbit hai. Peela arc sunlit phase hai (duration $T_{\text{sun}}$); gray arc eclipse phase hai (duration $T_{\text{eclipse}}$). Dono milke ek poori orbit banate hain, $T_{\text{orbit}}$.

$T_{\text{orbit}}=\underset{\text{panels see Sun}}{\underbrace{T_{\text{sun}}}}+\underset{\text{in shadow}}{\underbrace{T_{\text{eclipse}}}}$

• $T_{\text{orbit}}$ — ek poora loop karne mein lagta waqt (seconds ya minutes).
• $T_{\text{sun}}$ — panels kitni der roshan rehte hain.
• $T_{\text{eclipse}}$ — satellite kitni der andheron mein rehta hai.

Step 2 — Load kabhi sota nahi

KYA HAI. Hum ek flat line kheenchte hain: load har second orbit mein usi $P_{\text{load}}$ watts ki maang karta hai.

KYUN important hai. Eclipse ke dauran koi sunlight nahi hoti, phir bhi load apne watts maangta rehta hai. Uss maang ka sirf ek hi possible source hota hai: battery. Toh panel sirf din mein load ko feed nahi kar raha — usne battery ko pehle se charge karna tha taaki poori eclipse cover ho sake.

PICTURE. Orange line constant load hai. Peela bar (daylight) panel ka output hai; notice karo yeh load se upar jaata hai — woh surplus hi battery charge karta hai. Gray region (eclipse) mein panel kuch nahi deta, aur sirf battery orange line ko carry karti hai.

• $P_{\text{load}}$ — constant demand, dono hisson mein maujood.
• $P_{\text{SA}}$ — solar-array output, sirf daylight mein present (yahi hum solve kar rahe hain).

Step 3 — Eclipse deficit: darkness kitni energy ki cost karta hai

KYA HAI. Woh energy calculate karo jo battery ko eclipse ke dauran supply karni padti hai. Energy = power × time, toh:

$E_{\text{need}}=P_{\text{load}}\times T_{\text{eclipse}}$

• $E_{\text{need}}$ — energy (joules) jo battery ko andheron mein deliver karni hai.
• $P_{\text{load}}$ — constant watts jo kheenche ja rahe hain.
• $T_{\text{eclipse}}$ — darkness kitni der chalti hai.

KYUN. Yeh woh karza hai jo daylight ne pehle hi chuka diya hoga. Yeh ek seedha rectangle hai: height = load, width = eclipse duration. Area = energy.

PICTURE. Neeche ka shaded gray rectangle bilkul yahi energy hai — woh "hole" jo battery ko bharna hai.

Step 4 — Batteries leaky buckets hain: efficiency ka entry

KYA HAI. Hum raw energies ko in leaks ke liye correct karte hain.

KYUN yeh do hain, aur divide vs. multiply kyun?

• Charging: hum $E_{\text{charge}}$ daalte hain, lekin sirf $E_{\text{charge}}\cdot {\eta }_{\text{charge}}$ hi store hoti hai. Hum 1 se chhote number se multiply karte hain → kam bachta hai.
• Discharging: load ko $E_{\text{need}}$ chahiye, lekin battery ko zyada dena padta hai apni khud ki losses cover karne ke liye: $E_{\text{need}}/{\eta }_{\text{discharge}}$. Hum 1 se chhote number se divide karte hain → requirement badhti hai.

PICTURE. Ek funnel diagram: andar daali gayi energy shrink hoti hai (charge loss); doosri taraf maangi gayi energy aur bada draw force karti hai (discharge loss). Dono leaks panel ka kaam mushkil banate hain.

$\text{stored}=E_{\text{charge}}{\eta }_{\text{charge}},\text{must draw}=\frac{E_{\text{need}}}{{\eta }_{\text{discharge}}}$

Step 5 — Daylight surplus: battery actually kya charge karta hai

KYA HAI. Daylight mein panel $P_{\text{SA}}$ banata hai, load $P_{\text{load}}$ khaata hai, aur bacha hua battery charge karta hai:

$P_{\text{charge}}=P_{\text{SA}}-P_{\text{load}}$

• $P_{\text{charge}}$ — surplus watts battery mein ja rahe hain.
• $P_{\text{SA}}$ — solar-array output (unknown).
• $P_{\text{load}}$ — wahi constant demand jaise hamesha.

Sunlit duration ke dauran yeh surplus energy $P_{\text{charge}}\cdot T_{\text{sun}}$ deliver karta hai, jisme se sirf ${\eta }_{\text{charge}}$ battery mein survive karta hai.

KYUN. Yeh ledger ka supply side hai — woh energy jo hum Sun ke rehte jama kar paate hain.

PICTURE. Lamba peela bar minus orange load line ek green surplus band chhodta hai. Uska area (times $T_{\text{sun}}$) woh energy hai jo hum bachaa rahe hain.

Step 6 — Ledger balance karo: stored = withdrawn

KYA HAI. Battery ke kabhi khaali na hone ke liye, daylight mein successfully store ki gayi energy eclipse mein withdraw ki gayi energy ke barabar honi chahiye:

$\underset{\text{banked in daylight}}{\underbrace{P_{\text{charge}}{T}_{\text{sun}}{\eta }_{\text{charge}}}}=\underset{\text{withdrawn in eclipse}}{\underbrace{\frac{P_{\text{load}}{T}_{\text{eclipse}}}{{\eta }_{\text{discharge}}}}}$

KYUN yeh equality. Agar left side badi hoti, battery har orbit ke baad pehle se fuller hoti — panel waste. Agar chhoti hoti, toh har orbit mein thodi drain hoti aur eventually mar jaati. Steady state = exact balance. Yeh derivation ka dil hai.

PICTURE. Do-pan balance scale: ek pan par green "banked" area, doosre par gray "withdrawn" area, barabar.

Ab $P_{\text{charge}}=P_{\text{SA}}-P_{\text{load}}$ substitute karo aur $P_{\text{SA}}$ ke liye solve karo:

$(P_{\text{SA}}-P_{\text{load}})T_{\text{sun}}{\eta }_{\text{charge}}=\frac{P_{\text{load}}{T}_{\text{eclipse}}}{{\eta }_{\text{discharge}}}$

Divide karo, $P_{\text{load}}$ wapas add karo, aur factor out karo:

$\boxed{P_{\text{SA}}=P_{\text{load}}\left(1+\frac{T_{\text{eclipse}}}{T_{\text{sun}}{\eta }_{\text{charge}}{\eta }_{\text{discharge}}}\right)}$

Term by term padho:

• Leading $P_{\text{load}}$: panel ko kam se kam running load cover karna hi hai.
• $1$: woh daytime load khud.
• Fraction: panel ka extra hissa jo battery refill karne ke liye bhi chahiye.
• $T_{\text{eclipse}}/T_{\text{sun}}$: zyada lamba andhera ya chhota ujala → bada extra.
• ${\eta }_{\text{charge}}{\eta }_{\text{discharge}}$ denominator mein: leaky batteries → bada extra.

Step 7 — Edge aur degenerate cases (reader ko koi unseen scenario na mile)

Case A — Koi eclipse nahi ($T_{\text{eclipse}}=0$). Permanent sunlight mein satellite (jaise dawn-dusk Sun-synchronous orbit). Fraction gayab ho jaata hai: $P_{\text{SA}}=P_{\text{load}}(1+0)=P_{\text{load}}.$ Samajh mein aata hai: koi andhera prepare karne ke liye nahi, toh panel bas load match karta hai.

Case B — Perfect battery (${\eta }_{\text{charge}}={\eta }_{\text{discharge}}=1$). $P_{\text{SA}}=P_{\text{load}}\left(1+\frac{T_{\text{eclipse}}}{T_{\text{sun}}}\right).$ Panel enlargement purely din/raat ka time ratio hai — sabse clean possible case.

Case C — Sunlight practically zero ($T_{\text{sun}}\to 0$). Denominator $\to 0$ ho jaata hai, toh $P_{\text{SA}}\to \infty$. Physically sahi: lagbhag koi light nahi, toh koi finite panel enough energy bank nahi kar sakta. Yeh designers ko warn karta hai ki bahut chhote sunlit arcs ek hard limit hain.

PICTURE. Enlargement factor $(1+\frac{T_{\text{eclipse}}}{T_{\text{sun}}{\eta }_c{\eta }_d})$ ka ek single plot vs. $T_{\text{sun}}$, dikhata hai ki lamba daylight hone par yeh 1 ki taraf flatten hota hai aur jaise daylight shrink hoti hai uda jaata hai — teeno cases marked hain.

Step 8 — Worked number (parent ka LEO example, dobara trace kiya)

Khud check karo:

Ek picture mein poori summary

Ek hi graph par poori kahani: ek lamba peela daylight bar flat orange load se upar jaata hai; green surplus (${\eta }_{\text{charge}}$ se shrink karke bank ki gayi) exactly gray eclipse deficit ($1/{\eta }_{\text{discharge}}$ se badi hui) ko fill karta hai. Un do areas ko balance karo aur boxed formula nikal aata hai.