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

3.4.3 · Physics › Rocket Flight Mechanics

Intuition Badi picture

Ek rocket flight mein basically ek body hai jo $F = m a$ follow karta hai — lekin ek twist ke saath: yeh peeche mass phenkta hai aur iska mass time ke saath change hota hai. Kisi bhi instant par, exactly teen families of external forces iske upar act karti hain:

Thrust $T$ — engine ka push (ejected gas ke momentum + pressure se).
Aerodynamic force — axial (drag-jaisi, body ke along) aur normal (lift-jaisi, body ke across) mein split hoti hai.
Gravity $W = m g$ — hamesha Earth ke centre ki taraf.

WHY aerodynamics ko axial + normal mein split karein instead of lift + drag? Kyunki ek rocket ek patla arrow hai jo ek angle of attack $α$ par fly karta hai. Iska skin, fins aur nose force ko naturally body-ke-along aur body-ke-across "feel" karte hain. Body axes mein resolve karne se structural loads aur moments clearly dikhte hain.

1. Forces kya hain? (WHAT)

Angle of attack $α$ woh angle hai jo body axis aur velocity vector ke beech hota hai. Yahi KEY hai jo "wind axes" (lift $L$ , drag $D$ ) ko "body axes" (normal $N$ , axial $A$ ) se connect karta hai.

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

2. First principles se thrust derive karna (HOW & WHY)

Momentum se shuru karte hain. Time $d t$ mein rocket mass $d m_{p} = \overset{m}{˙} d t$ ko exhaust velocity $v_{e}$ par eject karta hai (rocket ke relative). (rocket + ejected gas) system ke liye momentum conservation, koi external forces nahin:

$m d v = v_{e} d m_{p} \Rightarrow m \frac{d v}{d t} = momentum thrust \overset{m}{˙} v_{e}$

Ab pressure term add karte hain. Gases area $A_{e}$ ke through pressure $p_{e}$ par nikalta hai; ambient $p_{a}$ hai. Exit plane par net pressure force $(p_{e} - p_{a}) A_{e}$ hai. Isliye:

Effective exhaust velocity $c$ define karo taaki poori cheez compact ho jaye: $T = \overset{m}{˙} c, c = v_{e} + \frac{( p _{e} - p _{a} ) A _{e}}{m ˙}$

3. Aerodynamic split derive karna (HOW)

Hawa ek resultant aerodynamic force produce karta hai. Wind axes mein hum iske components ko drag $D$ ( $v$ ke opposite) aur lift $L$ ( $v$ ke perpendicular) kehte hain. Lekin rocket body $v$ ke relative $α$ se tilt hai. Wind axes se body axes mein angle $α$ se rotate karne par:

A N = D cos α + L sin α (axial, body ke along) = L cos α - D sin α (normal, body ke across)

4. Motion ka full equation (sab kuch jodke)

5. Worked examples

6. Common mistakes

7. Active recall

Recall Feynman: ek 12-saal ke bachche ko samjhao

Imagine karo tum ek skateboard par ho aur ek fire extinguisher pakde ho. Usse peeche spray karo aur tum aage shoot karte ho — yahi thrust hai. Ab extinguisher spray karte waqt halka hota jaata hai, toh tum aur tezi se speed up karte ho — yahi changing mass hai. Jaise tum jaate ho hawa tumpe do taraf push karti hai: sidha tumhare chest par peeche (axial, drag jaisa) aur sideways agar tum isme lean karo (normal, lift jaisa). Aur Earth hamesha tumhe neeche khenchti hai (gravity). Ye saare pushes add karo aur tum exactly jaanoge tum kahan jaoge.

Flashcards

Ek rocket in flight par teen families of external forces kya hain?

Thrust, aerodynamic (axial + normal), aur gravity.

Full thrust equation likho aur har term ka naam batao.

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

— momentum thrust plus pressure thrust.

Altitude badhne se thrust kyun badhta hai?

Kyunki

p_{a}

girta hai, toh pressure term

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

badhta hai.

Lift/drag ko axial force mein convert karo.

A = D cos α + L sin α

Lift/drag ko normal force mein convert karo.

N = L cos α - D sin α

Axial force aur drag kab equal hote hain?

Sirf zero angle of attack par,

α = 0

Tangential equation of motion kya hai?

m d v / d t = T cos α - D - m g sin γ

Normal (turning) equation of motion kya hai?

m v d γ / d t = T sin α + L - m g cos γ

Dynamic pressure

q

kya hai?

q = \frac{1}{2} ρ v^{2}

; aerodynamic forces

q S C

ke saath scale hoti hain.

F = ma

mein instantaneous mass kyun use karni chahiye?

Rocket propellant kho deta hai, toh

m (t) = m_{0} - \overset{m}{˙} t

burn ke dauran decrease hoti hai.

Connections

Tsiolkovsky Rocket Equation — thrust integrate karke $Δ v$ nikalta hai.
Angle of Attack and Stability — jahan $N$ act karta hai woh pitching moment set karta hai.
Gravity Turn Trajectory — $m g cos γ$ term rocket ko steer karta hai.
Drag Coefficient and Mach Number — $C_{A}, C_{D}$ supply karta hai.
Variable Mass Systems — thrust ke peeche momentum derivation.
Nozzle Expansion and Pressure Matching — $(p_{e} - p_{a}) A_{e}$ term explain karta hai.