Verification methods — analysis, test, inspection, demonstration: Foundations

3.6.28 · D1 · Physics › Spacecraft Structures & Systems Engineering › Verification methods — analysis, test, inspection, demonstra

Yeh page assume karta hai ki tum kuch nahi jaante. Hum har word, symbol, aur picture ko ek-ek karke banate hain jo parent note ne rely kiya tha, taaki jab tum stress formulas ya vibration margins ke baare mein padho, koi bhi symbol anjana na lage.

Level 0 — Maths se pehle ke words

Picture (figure s01): ek gate jisme fixed opening hai daayein taraf khadi hai, uska gap laal rang mein allowed range ke roop mein mark kiya gaya hai. Baayein taraf ek neela box jis par "hardware" likha hai uss ki taraf slide kar raha hai, aur ek hara arrow jis par "verification = check it fits" likha hai poore kaam ko dikhata hai — yeh prove karna ki box launch day se pehle fit hota hai. Yeh promises kahaan se aate hain, uske liye Requirements Development dekhein.

Figure — Verification methods — analysis, test, inspection, demonstration

Level 1 — Numbers, symbols aur unki pictures

Parent note ka har formula inhi atoms se bana hai. Hum har ek ko define karte hain aur draw karte hain.

Topic ko iska kyun zaroorat hai: launch ke dauran rocket tezi se accelerate karta hai, isliye har bolt ek force $F = m (n g)$ feel karta hai — woh force woh hai jo use tod sakti hai. Yeh single equation poore structural-analysis section ka seed hai.

Level 2 — Bending beam ki geometry

Parent ke stress formula ko beam ki ek picture chahiye. Yeh lo.

Figure s02 mein ek neeli cantilever bar draw ki gayi hai jo baayein taraf ek gray wall mein clamp hai. Ek laal arrow jis par $F = mn g$ likha hai, door daayein end par neeche ki taraf kheench raha hai. Bar ke middle se guzarti hui green dashed line neutral axis hai (abhi neeche define ki gayi hai). Bar ke neeche ek double-headed arrow length $L$ mark karta hai; ek chhota inset cut-end cross-section dikhata hai jisme width $b$ , height $h$ , aur outer-edge distance $c = h /2$ green mid-line se upar measure ki gayi hai.

Level 3 — Stress, area moment, aur integral sign

Bilkul isi tarah ki deeper structural modelling Finite Element Analysis mein hai.

Level 4 — Margin, safe-gap number

Figure s03 is idea ke liye ek number line hai: middle mein ek black tick "applied = yield, MoS = 0 (edge)" mark karta hai. Baayein taraf green band (low applied stress) par "MoS > 0 SAFE" likha hai; daayein taraf red band (high applied stress) par "MoS < 0 FAILS" likha hai. Line ko left-to-right padhne par dikhta hai ki jaise load badhta hai margin zero ho jaata hai aur phir negative ho jaata hai.

Woh gap kitna bada hona chahiye iska philosophy Margin Philosophy mein hai.

Level 5 — Heat, rates, aur $\frac{d T}{d t}$ symbol

Thermal example ko symbols ki ek nayi family chahiye.

Common mistake

$Q_{in}$ aur $Q_{out}$ ke liye sign convention Equation is tarah likhi gayi hai ki $Q_{in}$ aur $Q_{out}$ dono positive magnitudes ke roop mein bookkeep hote hain, aur $Q_{out}$ ke aage minus sign accounting karta hai. Ek trap: heat jis direction temperature difference point karta hai usi direction mein flow karta hai. Agar "hot" wall actually battery se thandi hai, toh jo tumne $Q_{rad,in}$ label kiya woh physically bahar flow karta hai — uski value negative ho jaati hai aur woh silently ek outflow ban jaata hai. Safe habit: har term ko temperature difference ka signed function likho (e.g. $Q = G (T_{other} - T_{b})$ ) taaki sign khud apna khayal rakhe, iss ki bajay ki pehle se "in" vs "out" decide karo. Yeh Thermal Math Modeling mein matter karta hai jis moment ek node apne neighbours se ya toh garm ya thanda ho sakta hai.

Yeh Thermal Math Modeling ka seed hai.

Level 6 — Test levels ke liye statistics

Formula Independent variations ko combine karna (aur iske peeche ka assumption)

Do independent random spreads (manufacturing $\pm 10%$ , environment $\pm 10%$ ) is tarah combine hote hain: $σ_{total} = σ_{mfg}^{2} + σ_{env}^{2} = 0. 1^{2} + 0. 1^{2} \approx 0.141$ Square-then-root kyun, sirf add kyun nahi? Independent wobbles partly cancel ho jaate hain; directly add karne par over-count hota hai. Independent sources ke variances ( $σ^{2}$ ) add hote hain; isliye standard deviations Pythagorean style mein combine hote hain. Assumptions — aur woh kahan break hote hain: yeh rule chahiye (1) sources independent hon (ek doosre ko drive nahi karta), aur (2) roughly Gaussian (bell-shaped) spreads hon, taaki "3σ ≈ 99.7%" hold kare. Agar dono effects correlated hain (e.g. garmi part ko kamzor bhi karti hai aur load bhi badhati hai), toh variance addition under-counts karta hai aur tumhe covariance bhi add karni padti hai. Agar spread bell-shaped nahi hai (fat tails, hard limits), toh "3σ = 99.7%" figure trustworthy nahi rehta.

Formula "3-sigma" kyun, aur industry

$1.25$ kyun accept karti hai $\approx 99.7%$ possible units cover karne ke liye, mean + $3 σ$ ka aim karo: $1.0 + 3 (0.141) \approx 1.42$ Toh "honest" 3σ qualification factor lagbhag $1.42$ hai. Industry commonly $1.25$ use karti hai. Full 3σ coverage se kam accept karne ka rationale:

$10%$ inputs already conservative worst-cases hain, isliye true spread usually assumed se chhota hota hai — upar se full 3σ stack karna double-counts pessimism.
Doosre safeguards tail pakad lete hain: har flight unit ki acceptance testing, plus design margins of safety (Level 4), already weak units screen out kar lete hain, isliye qualification ko poora burden nahi uthana padta.
Cost aur over-test risk: $1.42 \times$ par testing khud aise failures induce kar sakti hai jo flight mein kabhi nahi hote (over-test), aur g ka har extra fraction mahanga hai. $1.25$ woh long-standing balance point hai.

Vibration Testing aur Acceptance Testing dekhein.

Prerequisite map

Aage, har proof ek Traceability Matrix ko feed karta hai, models Model Validation pass karne chahiye, aur har change Configuration Management se track hota hai.

Equipment checklist

Har ek reveal karo aur check karo ki tum iska answer cold de sako.

Launch ke dauran

F = ma

hume kya compute karne deta hai?

Har part par force,

F = m (n g)

, quasi-static acceleration se.

Quasi-static load kya hai?

Ek steady acceleration jo extra gravity jaisi lagti hai — ek constant pretend-weight, vibration nahi.

Requirement ke teen parts kya hain?

Ek quantity, ek limit, aur ek condition (kab hold karna chahiye).

Neutral axis kya hai?

Bending beam mein woh line jo na stretch hoti hai na squash;

y

usi se measure hota hai.

Stress

y

ke saath linearly kyun vary karta hai?

Fibres

y

ke proportion mein stretch hote hain, aur stress stretch ke proportional hai (Hooke), isliye

σ (y) = k y

Second moment of area

y^{2}

use kyun karta hai?

Door material dono zyada stretch hota hai aur longer lever bhi hai, do distance effects multiply hokar distance-squared banta hai.

Rectangle ke liye

I

kya hai?

I = b h^{3} /12

Final launch stress formula do.

σ = \frac{6 m n g L}{b h ^{2}}

Downward load ke liye, kaun se fibres tension mein hain?

Top fibres (positive

σ

); bottom fibres compression mein hain.

Margin of Safety se design kab safe hai?

Jab

MoS = σ_{y} / σ_{applied} - 1 > 0

ho.

\frac{d T}{d t} = 0

physically kya matlab rakhta hai?

Energy in, energy out ke barabar hai; temperature steady hai.

Heat terms ko honest rakhne wala sign convention kya hai?

Har ek ko

Q = G (T_{other} - T_{b})

likho taaki sign automatically temperature difference follow kare.

Do independent

\pm 10%

spreads kaise combine hote hain, aur kis assumption par?

0. 1^{2} + 0. 1^{2} \approx 0.14

, independence aur roughly Gaussian spreads assume karke.

1.42 \times

3σ value ki jagah

1.25 \times

kyun accept karte hain?

Inputs already conservative hain, acceptance tests aur margins tail pakad lete hain, aur over-test/cost

1.42

ke against argue karte hain.

Mass requirement kaun sa method prove karta hai?

Inspection (tum use weighing karte ho) — test nahi.