Terminal landing — propulsive descent, suicide burn: Foundations

3.4.26 · D1 · Physics › Rocket Flight Mechanics › Terminal landing — propulsive descent, suicide burn

Suicide-burn formula $h_{b u r n} = \frac{v ^{2}}{2 ( a _{T} - g )}$ pe trust karne se pehle, isme har letter ka koi aisa matlab hona chahiye jo tum picture kar sako. Yeh page har symbol ko kuch nahi se build karta hai, uss order mein jisme woh ek doosre pe depend karte hain. Koi bhi cheez draw kiye bina use nahi ki jaati.

0. Stage: ek vertical number line

Sab kuch ek hi upar–neeche ki line pe hota hai. Pehle hume yeh agree karna hoga ki positive direction kaun si hai, warna baad ke har sign ek guess ban jaata hai.

Figure — Terminal landing — propulsive descent, suicide burn

Kyun zaroori hai: rocket neeche girta hai lekin thrust upar deta hai. Agar ek fixed positive direction nahi hogi, toh "add" aur "subtract" ka koi matlab nahi. Figure dekho: orange arrow (fall) aur teal arrow (thrust) opposite directions mein point karte hain — sign convention hi woh cheez hai jo unhe $+$ aur $-$ se combine karne deti hai.

1. Altitude $h$ — kitna upar

Picture: rocket aur floor ke beech ka vertical gap. Topic ko kyun chahiye: poora maneuver "height remaining" aur "height needed to stop" ke beech ki race hai. $h$ height remaining hai.

2. Velocity $v$ — kitna fast, aur kaunsi direction mein

Picture: motion arrow ki length; lamba arrow = fast. Arrow descent ke dauran neeche point karta hai.

Speed aur velocity ka poora toolkit dekhne ke liye Kinematics — Equations of Motion dekho.

3. Acceleration $a$ — velocity kitni fast change hoti hai

Picture: agar velocity motion arrow ki length hai, toh acceleration yeh hai ki woh arrow clock ki har tick pe kitni tezi se bhadh ya ghad raha hai.

4. Gravity $g$ — hamesha on rehne wala downward pull

Picture: rocket se hamesha judi ek invisible downward arrow, engine on ho ya off — length same rehti hai.

Topic ko kyun chahiye: yahi villain hai. Gravity brake lagane ke dauran bhi downward speed add karta rehta hai, toh engine ko gravity plus fall ko beat karna hota hai. Yahi wajah hai ki formula mein $a_{T} - g$ hai, sirf $a_{T}$ nahi.

5. Thrust $F$ aur thrust acceleration $a_{T}$

Picture: figure mein teal upward arrow, gravity ko oppose karta hua. Mass se divide kyun? Ek given push ek halke rocket ko bhaari se zyada fast move karta hai — yeh Newton's second law hai, $a = F / m$ . $F$ kahan se aata hai, yeh jaanne ke liye Thrust and Specific Impulse dekho.

6. Mass $m$ — kitna stuff hai

Topic ko kyun chahiye: $m$ $a_{T} = F / m$ ke andar aata hai. Jaise fuel jalta hai, $m$ ghatta hai, toh steady thrust ke saath burn ke through $a_{T}$ badhta jaata hai. Parent ka constant- $m$ formula ek pehla estimate hai; exact kahani Tsiolkovsky Rocket Equation mein hai.

7. Net acceleration $a_{n e t}$ — actual braking

Picture: upar ke figure mein, $a_{n e t}$ teal thrust arrow ki bacha hua length hai, gravity ke orange arrow ke uss ka kuch hissa cancel karne ke baad.

Teeno cases jo har reader ko dekhne chahiye:

$a_{T} > g$ → net arrow upar point karta hai → tum decelerate ho → landing possible. ✓
$a_{T} = g$ → arrows cancel → net zero → tum constant speed se girate raho → crash.
$a_{T} < g$ → net arrow neeche point karta hai → tum aur tez hote jao → hopeless.

8. Kinematic tool $v^{2} = v_{i}^{2} + 2 a d$

Yahi tool kyun, koi aur kyun nahi? Hum speed aur distance ko time ki parwah kiye bina relate karna chahte hain (hum nahi poochhte "rukne mein kitne seconds lagte hain," hum poochhte hain "rukne ke liye kitni height chahiye"). Yeh woh ek equation of motion hai jisme $t$ nahi hai, toh yeh exactly hamaara sawaal answer karta hai. Poori derivation Kinematics — Equations of Motion mein hai.

Yahan apply kiya: falling speed $v$ pe braking start karo, $h_{b u r n}$ height par $v_{f} = 0$ pahunchna chahte ho, braking acceleration $a_{n e t}$ ke saath: $0 = v^{2} - 2 a_{n e t} h_{b u r n} \Rightarrow h_{b u r n} = \frac{v ^{2}}{2 ( a _{T} - g )}$

$v^{2}$ ki wajah se fall speed double karne par zaroorat ki jagah chaar guna ho jaati hai.

9. Square root: drop height se fall speed

Picture: upar se drop karo → zyada tez hit karo. Square root bas $v^{2} = 2 g H$ ko ulta padhna hai ("kaun si speed $2 g H$ tak square hoti hai?"). Yeh hume kisi bhi point par falling speed predict karne deta hai, jo seedha $h_{b u r n} (v)$ mein jaata hai.

Foundations topic ko kaise feed karte hain

Isse neeche se upar padho: sign line → quantities → net acceleration → no-time kinematics → ignition altitude → parent topic ka suicide burn.

Equipment checklist

Right side cover karo aur khud test karo. Agar koi bhi jawab fuzzy lage, toh main note se pehle woh section dobara padho.

Humne positive direction kaun si choose ki?

Up is positive, down is negative, ground is zero.

h

ka kya matlab hai aur uski unit kya hai?

Ground se height, metres mein; "height remaining."

Speed aur velocity mein kya fark hai?

Speed yeh hai ki kitna fast; velocity speed hai direction sign ke saath — girna negative hai.

Acceleration kya measure karta hai aur uski unit?

Velocity har second mein kitna change hoti hai,

m/s^{2}

mein.

g

kya hai aur kya yeh kabhi band hota hai?

Downward gravitational acceleration (

\approx 10

Earth pe,

1.6

Moon pe); yeh kabhi band nahi hota.

a_{T} = F / m

kyun hai?

Newton's second law — ek given push

F

mass

m

F / m

se accelerate karta hai.

a_{n e t} = a_{T} - g

kyun hota hai?

Burn ke dauran gravity abhi bhi kheenchti hai, toh sirf weight se upar wala thrust tumhe decelerate karta hai.

Landing work karne ke liye

a_{T}

aur

g

mein kya condition honi chahiye?

a_{T} > g

, taaki net acceleration upar point kare.

Kaun si kinematic equation speed aur distance ko time ke bina relate karti hai, aur use kyun use karte hain?

v_{f}^{2} = v_{i}^{2} + 2 a d

; hume time-to-stop nahi, height-to-stop chahiye.

Rest se height

H

girane par fall speed?

v = 2 g H

Connections

Parent: suicide burn
Kinematics — Equations of Motion — jahan se $v^{2} = 2 a d$ aur $v = 2 g H$ aate hain
Thrust and Specific Impulse — jahan se $a_{T} = F / m$ aata hai
Tsiolkovsky Rocket Equation — kya hota hai jab $m$ change hota hai