Forces on a rocket in flight — thrust, aerodynamic (normal, axial), gravity: Question bank

3.4.3 · D5 · Physics › Rocket Flight Mechanics › Forces on a rocket in flight — thrust, aerodynamic (normal,

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Figure — Forces on a rocket in flight — thrust, aerodynamic (normal, axial), gravity

Intuition Equations of motion mein exactly yahi terms kyun hain (picture)

Figure s02 dekhein, body-vs-wind axes. Velocity direction (ise tangential bolein) aur perpendicular direction (ise normal-to-path bolein) do rulers hain. Har force ko unpar project karein:

Thrust body ke along point karta hai, $v$ se $α$ se tilt hua, toh yeh $T cos α$ (forward) aur $T sin α$ (turning) ki tarah project hota hai.
Drag $D$ by definition $v$ ke opposite hai, toh yeh purely tangential ruler par $- D$ ke roop mein baithta hai; lift $L$ $v$ ke perpendicular hai, toh yeh purely normal ruler par $+ L$ ke roop mein baithta hai.
Weight $m g$ neeche point karta hai; $γ$ se tilt karne par $m g sin γ$ forward motion ko oppose karta hai aur $m g cos γ$ path ko bend karta hai.

Tangential projections jodne par (jo speed change karte hain) $m d v / d t = T cos α - D - m g sin γ$ milta hai. Normal projections jodne par (jo direction change karte hain, aur path ke turning ki rate $v d γ / d t$ hai) $m v d γ / d t = T sin α + L - m g cos γ$ milta hai. Har term bas ek arrow ki shadow ek ruler par hai.

True or false — justify karein

True or false: Thrust flight ke har instant par exactly

\overset{m}{˙} v_{e}

hota hai.

False — sirf tab jab nozzle perfectly pressure-matched ho (

p_{e} = p_{a}

). Generally

T = \overset{m}{˙} v_{e} + (p_{e} - p_{a}) A_{e}

; pressure term nonzero hai sivaay ek special altitude ke.

True or false: Ek rocket engine vacuum mein sea level se zyada thrust produce karta hai.

True — jab

p_{a} \to 0

toh pressure term

(p_{e} - p_{a}) A_{e}

apni maximum value

p_{e} A_{e}

tak badhta hai, toh wohi

\overset{m}{˙} v_{e}

sabse bade possible pressure bonus se top up hota hai.

True or false: Normal force

N

equals lift

L

False generally —

N = L cos α - D sin α

. Ye sirf

α = 0

par coincide karte hain, kyunki tab body axes aur wind axes aligned hote hain.

True or false: Agar angle of attack zero hai, toh normal force zero hai.

Essentially true —

α = 0

par,

N = L cos 0 - D sin 0 = L

, aur ek symmetric rocket

α = 0

par koi lift generate nahi karta, toh

N \approx 0

. Koi bhi residual asymmetry se aata hai, flow angle se nahi.

True or false: Aap poori burn mein

F = ma

mein launch mass

m_{0}

use kar sakte hain.

False — mass propellant nikalne ke saath girti hai, toh instantaneous

m (t) = m_{0} - \overset{m}{˙} t

use karein; acceleration burnout ke paas exactly isliye surge karta hai kyunki

m

shrink ho gayi hai.

True or false: Gravity hamesha rocket ko slow karti hai.

False — sirf along-path component

m g sin γ

slow karta hai; across-path component

m g cos γ

sirf trajectory bend karta hai (yeh gravity turn hai), aur agar rocket dive kare toh gravity speed bhi badhati hai.

True or false: Axial force

A

hamesha bas drag hota hai.

False —

A = D cos α + L sin α

. Jab body tilted hoti hai, lift ka kuch hissa body ke along bhi press karta hai, toh

A > D

jab bhi

α \neq = 0

aur

L > 0

True or false: Thrust aur axial force body ke along opposite directions mein point karte hain.

True — thrust naak ko body axis ke along forward drive karta hai jabki axial force (drag-jaisa) usi motion ko resist karta hai, toh ye tangential equation mein subtract karte hain (

T cos α - D

True or false: Aerodynamic force mein

\frac{1}{2} ρ v^{2}

nature ka ek fundamental constant hai.

False — yeh dynamic pressure

q

hai, ek convention jo speed aur air density ko isolate karta hai taaki shape ki poori personality coefficient

C

mein reh sake;

\frac{1}{2}

sirf bookkeeping hai.

Error dhundhein

Error: "Kyunki

F = ma

exact hai, aur

m

current mass hai, rocket ka acceleration simply

T / m

hai — kuch aur matter nahi karta."

Yeh drag aur gravity ko ignore karta hai. Sahi along-path law hai

m d v / d t = T cos α - D - m g sin γ

; sirf deep vacuum mein

α = 0

ke saath

a

T / m

ke paas jaata hai.

Error: "Sea level par pressure term hamesha thrust mein add karta hai, toh pad par

T > \overset{m}{˙} v_{e}

Zaruri nahi — agar exit over-expanded hai (

p_{e} < p_{a}

), toh

(p_{e} - p_{a}) A_{e} < 0

aur pressure term subtract karta hai,

T < \overset{m}{˙} v_{e}

deta hai (parent ka Example 1 dekhein: 529.5 kN < 560 kN).

Error: "Lift 'upar' hai, toh poori lift body ke across normal force ban jaati hai."

Ek tilted body lift ko axes ke beech split karti hai:

N = L cos α

sirf woh part rakhta hai jo body ke perpendicular hai, jabki

L sin α

axial direction mein leak ho jaata hai. Wind-axis ka 'upar' body-axis ka 'across' nahi hai.

Error: "Rocket jahan naak point karti hai wahan fly karta hai, toh

α

hamesha zero hota hai."

Naak body axis ke along point karti hai, lekin rocket

v

ke along move karta hai; jab bhi ye disagree karte hain (gusts, pitch-over, gravity turn) tab ek real

α \neq = 0

hota hai, jo exactly normal force create karta hai.

Error: "Hum aerodynamics ko axial aur normal mein isliye split karte hain kyunki yeh mathematically lift aur drag jaisa hi hai, bas rename kiya hua."

Ye ek rotation se related hain, rename se nahi. Body axes choose karne ka reason physical hai: fins, skin, aur structural loads body ke along aur across act karte hain, toh

A

aur

N

batate hain ki airframe ko kya survive karna hai.

Error: "Thrust velocity vector ke along point karta hai."

Thrust body axis ke along point karta hai,

v

ke nahi. Jab

α \neq = 0

tab sirf

T cos α

forward speed mein madad karta hai jabki

T sin α

flight path ko turn karta hai (normal equation mein

+ T sin α

term).

Why questions

Hum aerodynamic force ko lift aur drag ki jagah axial aur normal mein kyun resolve karte hain?

Kyunki rocket ek slender arrow hai aur uski structure apne body ke along aur across loads feel karti hai; body axes un forces ko directly visible banate hain jo airframe ko carry karne padte hain — aur pitching moments bhi.

Wohi engine climb karte waqt zyada strong kyun hota jaata hai?

Ambient pressure

p_{a}

altitude ke saath giraata hai, toh pressure term

(p_{e} - p_{a}) A_{e}

badhta hai; momentum part

\overset{m}{˙} v_{e}

barely change hota hai, toh total

T

apni vacuum maximum ki taraf badhta hai.

Tangential equation mein thrust par

cos α

kyun hai lekin normal equation mein

sin α

kyun hai?

Body axis

v

α

se tilt hai, toh along-body thrust ko flight direction par project karne par

T cos α

milta hai, aur perpendicular direction par project karne par

T sin α

milta hai — pure vector resolution (figure s02 dekhein).

Force

ρ v

ki jagah

ρ v^{2}

ke roop mein kyun scale karta hai?

Force = air ko momentum dena per second

\approx (mass/time) \times (velocity) \approx (ρ v S) \times v = ρ v^{2} S

; ek

v

count karta hai ki aap per second kitni air hit karte hain, doosra woh speed hai jo aap use dete hain.

Rockets seedha upar climb karne ki jagah pehle pitch over kyun karte hain?

Seedha upar jaane ka matlab

γ = 9 0^{\circ}

hai aur poora weight

m g sin γ = m g

motion ko oppose karta hai — maximum gravity loss; tilting karne se

sin γ

reduce hota hai aur orbit ke liye zaruri horizontal speed build up hoti hai (gravity turn logic).

Hume ek ki jagah do equations of motion kyun chahiye?

Velocity ek vector hai: yeh magnitude mein change ho sakti hai (

d v / d t

equation) aur direction mein bhi (

v d γ / d t

equation). Ek scalar law ek saath speed-up aur turn dono describe nahi kar sakta.

Edge cases

Edge case: Exactly us altitude par thrust kya hota hai jahan

p_{e} = p_{a}

Pressure term vanish ho jaata hai aur

T = \overset{m}{˙} v_{e}

precisely — yeh pressure-matched altitude wahi hai jahan nozzle optimally expanded hai, us nozzle ke liye thrust efficiency ka peak.

Edge case: Launch ke waqt aerodynamic forces ka kya hota hai, jab

v = 0

ho?

Dynamic pressure

q = \frac{1}{2} ρ v^{2} = 0

, toh

A

aur

N

dono vanish ho jaate hain; lift-off par sirf thrust aur gravity act karte hain, aur

α

ka concept momentarily undefined hai kyunki

v

ki koi direction nahi hai.

Edge case: Jab rocket atmosphere chhod raha hota hai (

ρ \to 0

) toh aerodynamic forces ka kya hota hai?

q \to 0

toh

A, N, L, D

sab zero ho jaate hain; sirf thrust aur gravity rehte hain, aur thrust apni vacuum value tak pahunch jaata hai — vehicle ab purely ek variable-mass body hai free space mein.

Edge case: Negative angle of attack (

α < 0

) — normal force ka kya hota hai?

Flow ab body ke doosri side press karta hai, toh

N

sign reverse kar leta hai:

α < 0

ke saath ek symmetric body

L < 0

deta hai, isliye

N = L cos α - D sin α < 0

, body ke across opposite taraf push karta hai. Magnitude same behave karta hai, sirf direction flip hoti hai.

Edge case: Negative angle of attack (

α < 0

) — kya axial force phir bhi drag se zyada hota hai?

Zaruri nahi —

A = D cos α + L sin α

, aur

α < 0

ke saath

sin α < 0

bhi hai aur (ek symmetric body ke liye)

L < 0

bhi, toh unka product positive hai aur

A

phir bhi badh sakta hai; lekin sign bookkeeping matter karti hai, toh hamesha magnitude ki jagah signed

α

plug in karein.

Edge case:

γ = 9 0^{\circ}

par vertically climb karta rocket — across-path gravity term kya hai?

m g cos γ = m g cos 9 0^{\circ} = 0

, toh gravity koi turning nahi karti; trajectory tab tak bend nahi ho sakta jab tak

γ

9 0^{\circ}

se neeche na gire, isliye turn shuru karne ke liye ek initial nudge ki zarurat hoti hai.

Edge case: Agar ek gust suddenly

α

ko bada kar de, toh structural load mein kya dominate karta hai?

Normal force

N = q S C_{N} (α)

badhta hai (uska coefficient

C_{N}

α

ke saath climb karta hai), body ke across hard press karta hai — yeh max-Q ke paas stability aur airframe bending ke liye danger zone hai.

Edge case: Bahut high Mach number par, kya

C_{A}

aur

C_{N}

low speed par same hote hain?

Nahi — coefficients Mach number par bhi depend karte hain (compressibility, shock waves), toh [[Drag Coefficient and Mach Number|

C_{A}

aur

C_{N}

speed ke saath change karte hain]], sirf

α

ke saath nahi.

Edge case:

α = 0

lekin

γ = 0

(level flight) — equations ka kya hota hai?

α = 0

ke saath: tangential

m d v / d t = T - D

(

sin 0 = 0

hone se path ke along koi gravity nahi), aur normal

m v d γ / d t = L - m g

— gravity ab poori tarah lift ko oppose karti hai kyunki path horizontal hai.

Recall Har trap ki one-line summary

Symbols rulers par rehte hain: $A, N$ body par, $D, L$ wind par, $T$ body ke along, $g$ Earth ki taraf. Upar har galti ya toh galat ruler use karna hai, ya koi term ( $p$ -thrust, drag, gravity) bhool jaana, ya yeh bhool jaana ki $m$ shrink karti hai, ya yeh bhool jaana ki $α$ nonzero aur negative bhi ho sakta hai.