Exercises — Requirements — SMART (Specific, Measurable, Achievable, Relevant, Testable)

• Specific
• Measurable
• Achievable
• Relevant
• Testable

Memory hook: "Say My Awesome Rocket's Tested."

• (a) Measurable — "reasonably efficient" mein koi number nahi, koi units nahi, koi operator nahi.
• (b) Achievable — Tsiolkovsky Rocket Equation chemical propulsion se us dry mass par $50\text{km/s}$ forbid karta hai (parent note mein mass ratio $\approx 83000$ dikhaya gaya hai).
• (c) Testable (aur Relevant) — "look nice" ka koi pass/fail criterion nahi hai aur ye kisi mission objective se trace nahi hota.

• S ✅ — exact item naam karta hai ("bus structure").
• M ✅ — number (150), unit (kg), operator ($\le$).
• A — plausible hai, lekin confirm karne ke liye Mass Budget chahiye hoga. Sirf sentence se judge nahi kar sakte.
• R — mission objective chahiye confirm karne ke liye; yahan nahi diya gaya.
• T ✅ — inspection se verify ho sakta hai (weighing se naap lo).

Toh ye clearly S, M, T satisfy karta hai; A aur R ke liye external context chahiye.

"The solar array shall generate $\ge 2.5\text{kW}\pm 5\%$ electrical power at end-of-life (15 years), when oriented normal to sunlight at $1\text{AU}$, across a temperature range of $-100^{\circ }\text{C}$ to $+120^{\circ }\text{C}$."

Jo cheezein humne add ki unki checklist:

• S: "solar array … electrical power" (scope).
• M: $2.5\text{kW}$, $\pm 5\%$, operator $\ge$.
• A: power-budget analysis par chhodo.
• R: implicitly mission ki power need se trace hota hai.
• T: solar simulator ke under test se verifiable hai.

Tsiolkovsky Rocket Equation use karo: $\Delta v=I_{sp}{g}_0\ln \left(\frac{m_0}{m_f}\right)$

• WHAT/WHY the equation: ye exhaust speed aur mass ratio ko velocity change se jodne wala ek hi relation hai — "kya chemistry ye $\Delta v$ deliver kar sakti hai?" ka direct test.
• Exhaust speed: $v_e=I_{sp}{g}_0=230\times 9.81=2256.3\text{m/s}$.
• Wet mass $m_0=50+10=60\text{kg}$; dry mass $m_f=10\text{kg}$; ratio $=6$.
• $\Delta v=2256.3\times \ln 6=2256.3\times 1.7918=4043\text{m/s}$.

$4043\text{m/s}\gg 500\text{m/s}$, toh requirement Achievable hai bade margin ke saath. ✅

• (a) Inspection — coordinate-measuring machine se measure karo.
• (b) Analysis — full-scale reentry test karna impractical hai, toh thermal model use karo.
• (c) Demonstration — end-to-end operational scenario chalao.
• (d) Test — solar simulator ke under real output measure karo.

Chaar-method framework ke liye Verification and Validation dekho.

• S ✅ — item ("reaction wheel assembly"), axes ("each axis") aur quantities sab named hain.
• M ✅ — torque $\ge 0.1\text{N⋅m}$, momentum $\ge 10\text{N⋅m⋅s}$, dono units aur operators ke saath.
• A — flight-qualified wheels ke liye plausible hai (Technology Readiness Levels (TRL) $\ge 6$ check karo); sentence se derivable nahi lekin obviously violate nahi hua.
• R — ek pointing/slew objective tak trace chahiye. Nahi diya gaya → Requirements Traceability Matrix ke liye flag karo.
• T ✅ — "verified by test" plus measurable quantities ek clear pass/fail deta hai.

Verdict: S, M, T par strong hai. Ise airtight banane ke liye ek trace (R) aur ek TRL note (A) add karo.

Ek valid chain (parent ke ice-mass example se match karta hua):

• Mission objective: "Observe Earth's ice-sheet mass balance to $\pm 10\text{Gt/year}$."
• ↓ System requirement: "Maintain radial altitude knowledge to $\pm 5\text{m}$ ($3\sigma$)."
• ↓ Subsystem requirement: upar wali $\pm 3\text{m}$ GPS requirement.

Ye Relevance kaise prove karta hai: gravity-field (ice-mass) recovery ke liye precise orbit knowledge chahiye; orbit knowledge ke liye precise position fixes chahiye. GPS requirement hatao aur chain toot jaati hai — mission apna objective fail kar deta hai. Jo requirement kisi se trace nahi hoti use cut kiya ja sakta hai, aur yahi Relevance ka test hai.

Kyun fail karta hai: "designed to" ek process requirement hai (ye engineers ko batata hai koi activity perform karo), na ki ek performance requirement (product ko kya achieve karna chahiye). Tum test nahi kar sakte ki kisine kuch "design to" kiya ya nahi — ye Testable fail karta hai aur Measurable par bhi vague hai.

Rewrite:

"The structure shall survive quasi-static launch loads of $\ge 8g$ axial and $\ge 4g$ lateral, verified by analysis and by qualification test to $1.25\times$ design limit load."

Ab ye ek outcome constrain karta hai numbers ke saath, factor of safety ke saath, aur verification method ke saath — flow mein ye kahan baithta hai iske liye Systems Engineering V-Model dekho.

Step 1 — Tsiolkovsky ko mass ratio ke liye invert karo (WHAT/WHY): hum $\Delta v$ jaante hain aur propellant chahiye, toh rocket equation ko $m_0/m_f$ ke liye solve karo. $\frac{m_0}{m_f}=\exp \left(\frac{\Delta v}{I_{sp}{g}_0}\right)$

• $I_{sp}{g}_0=200\times 9.81=1962\text{m/s}$.
• Exponent $=120/1962=0.06116$.
• Ratio $=e^{0.06116}=1.06307$.

Step 2 — propellant solve karo. $m_f=8\text{kg}$ ke saath: $m_0=1.06307\times 8=8.5046\text{kg},m_p=m_0-m_f=0.5046\text{kg}.$

Step 3 — SMART requirement likho (margin ke liye round up karo):

"The propulsion subsystem shall provide $\Delta v\ge 120\text{m/s}$ using the cold-gas thruster ($I_{sp}\ge 200\text{s}$) with propellant mass $\ge 0.55\text{kg}$ aur dry mass $\le 8\text{kg}$, verified by analysis (rocket-equation) and thruster-firing test."

Minimum propellant $\approx 0.50\text{kg}$; hum $0.55\text{kg}$ spec karte hain taaki $\sim 10\%$ margin rahe.

• Method: Test (momentum integral ke liye supporting Analysis ke saath).
• Setup: Wheel ek rigid stand par mount kiya gaya, calibrated torque sensor ($\pm 0.001\text{N⋅m}$) aur angular encoder ke saath; ambient temperature, vacuum recommended.
• Procedure: Wheel ko $0$ se max RPM tak command karo; torque vs. time log karo; measured inertia $I$ aur top speed $\omega$ se stored momentum $L=I\omega$ compute karo.
• Acceptance: measured torque $\ge 0.1\text{N⋅m}$ sustained $\ge 10\text{s}$ aur $L\ge 10\text{N⋅m⋅s}$. Results ko Requirements Traceability Matrix aur Verification and Validation records mein fold karo.

Angular momentum $L=I\omega$ (WHY: momentum storage hai hi $I\omega$ — wo quantity jo ek wheel baad mein spacecraft par dump karne ke liye bank karta hai). $L=0.02\times 500=10.0\text{N⋅m⋅s}.$ Ye requirement exactly meet karta hai ($L=10$). ⚠️ Zero margin ke saath, ek real spec $\ge 10$ with margin demand karni chahiye (jaise design to $\omega =550\text{rad/s}$ jisse $L=11$ mile). Requirement "exactly" meet karna ek schedule risk hai — koi bhi manufacturing loss tumhe neeche gira dega.

Mission objective: "Image coastal erosion at ground sample distance $\le 1\text{m}$ from $500\text{km}$ altitude."

↓ System requirement (poori imaging chain ko point karta hai — pointing stability taaki ground pixel smear na ho):

"The spacecraft shall maintain attitude pointing stability $\le 0.5\text{m}$ ground smear over one integration time (i.e. angular rate $\le 1\times 10^{-4}\text{rad/s}$), verified by analysis and hardware-in-loop test."

↓ Subsystem requirement (wo actuator jo stability deliver karta hai):

"The reaction wheel assembly shall provide control torque $\ge 0.1\text{N⋅m}$ about each axis with momentum storage $\ge 10\text{N⋅m⋅s}$, verified by test."

Interface: camera-to-bus mechanical, electrical, aur data boundary ko ek Interface Control Document (ICD) mein freeze karna zaroori hai. Poori chain Requirements Traceability Matrix mein rehti hai; har level Systems Engineering V-Model ke hisaab se verify hota hai.

WHY this geometry: ek chhota pointing rate $\dot{\theta }$ line-of-sight ko ground par sweep karta hai; us sweep ki ground velocity range $h$ par $v_{\text{gnd}}=h\dot{\theta }$ hai (arc-length $=$ radius $\times$ angle). Smear wo velocity hai baar shutter kitna der khula hai.

• Ground sweep rate: $v_{\text{gnd}}=h\dot{\theta }=500000\text{m}\times 10^{-4}\text{rad/s}=50\text{m/s}$.
• Integration par smear: $s=v_{\text{gnd}}t=50\times 0.010=0.5\text{m}$.

Smear $=0.5\text{m}$, bilkul budget ke barabar — toh is integration time par rate spec binding limit hai. (L4.3 jaisi wahi zero-margin warning: practice mein $\dot{\theta }$ tighten karo ya $t$ chhota karo.)

• Momentum: $L=I\omega =0.02\times 500=10.0\text{N⋅m⋅s}$ per wheel → $\ge 10$ meet karta hai (zero margin).
• Mass: $4\times 2.0\text{kg}=8.0\text{kg}>6\text{kg}$ budget → $2\text{kg}$ se fail karta hai.

Conflict: dono requirements jaise likhi hain inconsistent hain. Options, preference ke order mein:

1. Mass Budget ko $8\text{kg}$ tak negotiate karo agar mission margins allow karein.
2. 3 wheels par jaao (no redundancy) — lekin Failure Modes and Effects Analysis (FMEA) ek single-point failure flag karega.
3. Higher spin rate wale lighter wheels select karo (mass aur $I$ shrink karte hue $L$ rakhne ke liye $\omega$ raise karo).

Lesson: individual requirements har ek SMART ho sakti hain phir bhi collectively infeasible ho sakti hain. Traceability aur budgets isi cross-coupling ko hardware cut hone se pehle surface karne ke liye hain.