3.5.44 · D1Thrust vector control — single-gimbal, dual-gimbal; TVC angl
Ek rocket steer karta hai apna engine tilt karke — taaki push seedha rocket ke balance point se guzarne ke bajay thoda alag direction mein jaye — aur yeh off-centre push poore vehicle ko ghuma deti hai. Is page par jo kuch bhi hai woh tumhe ek sentence padhne ke liye hai: ek badi thrust T δ ℓ M = ℓ T δ
Yeh Thrust Vector Control ka prerequisite page hai. Hum yahan har letter, arrow, aur word build karenge jo parent note mein use hoti hai — starting karte hain un cheezoon se jo ek 12-saal ka bachcha bhi jaanta hai: pushes, arrows, aur spanner ghoomana.
Kisi bhi physics se pehle, humein vector ka idea chahiye.
Vector ek arrow hai. Isme do cheezein hoti hain: ek length (kitna bada) aur ek direction (kis taraf point karta hai). Hum ise paper par ek actual arrow ki tarah draw karte hain.
Rocket ke engine ki push ek vector hai. Uski length hai kitni zyada engine push karta hai; uski direction hai kis taraf push point karti hai. TVC us direction ko change karne ki kala hai, length ko lagbhag same rakhte hue.
Intuition Hum "vector" ki parwah kyun karte hainPoora topic is baat par hinge karta hai ki ek arrow ko do chhote arrows mein tod sako: ek part jo tumhe aage push kare aur ek part jo tumhe sideways dhakele. Yeh split tab tak nahi kar sakte jab tak yeh accept nahi karte ki arrow ek aisi cheez hai jisme size aur direction dono hain.
Ek arrow jo diagonally point karta hai, usse hamesha kitna right aur kitna upar jaata hai — in do numbers se describe kiya ja sakta hai. Yeh do numbers uske components hain.
Kisi vector ke components do perpendicular directions par uske saaye hote hain. Agar arrow jhukta hai, toh ek saaya rocket ki length ke saath (axial) point karta hai aur doosra sideways (transverse).
Figure dekhein: diagonal cyan arrow tilted thrust hai. Seedha neeche aur across ek line daalo — amber pieces axial part hain (aage push karta hai) aur transverse part (steer karta hai). Poori steering story yeh hai: tilting karne se forward part ka thoda hissa sideways part ban jaata hai.
Yeh measure karne ke liye ki "kitna" tilt karte hain, humein ek angle chahiye.
Angle do directions ke beech ghoomne ki miqdar hai, degrees mein (ek poora circle 36 0 ∘ radians mein (ek poora circle 2 π δ
Jab hum arrow ko δ right triangle banate hain (ek triangle jisme ek square corner ho).
Intuition Right triangle kyun aata haiAxial aur transverse directions perpendicular hain — woh square corner hi right angle hai . Tilted thrust sloped side hai (sabse lambi side, hypotenuse ). Yahan se trigonometry enter hoti hai.
Humein ek rule chahiye jo angle δ trigonometry hai, aur do tools hain sin cos
Intuition Yeh tools kyun, aur koi nahi?Hum jawaab chahte hain: "agar ek fixed-length arrow ko δ Yeh bilkul wahi sawaal hai jiska jawaab dene ke liye cos sin
Do facts jo tum baar baar use karoge:
Aakhri do sentences "steering is cheap" ka raaz hain, aur yeh sirf zero ke paas in do curves ki shapes se aata hai — dekhein Small-Angle Approximation .
Radian ek aisa angle measure hai jisme ek poora turn 2 π ≈ 6.283 π /180
Intuition Near-zero trickJab δ radians mein measured , toh sloped side aur sideways shadow lagbhag equal hote hain, isliye sin δ ≈ δ cos δ ≈ 1 − 2 δ 2 Small-Angle Approximation .
Hum ise yahan re-derive nahi karenge; bas itna trust karna hai ki δ ≤ 8 ∘ 1%
Thrust T newtons , N mein measured) hai jo engine pichhli taraf mass phenk kar banata hai. Uski size kahan se aati hai, yeh dekhein Rocket Thrust Equation mein. Steering ke liye, hum T vector ki tarah treat karte hain jisme fixed length hoti hai jise hum rotate kar sakte hain.
Key mindset jo parent note maangta hai: TVC is arrow ko rotate karta hai, ise lambaata nahi. Engine hamesha same strength T
Definition Center of massCenter of mass woh single point hai jahan rocket balance karta hai — woh point jo aisa move karta hai jaise saari mass isme squeeze ho gayi ho. Iss point se guzarti push rocket ko slide karaati hai; iss point se chuki push use spin karaati hai.
CoM aage drift karta hai jaise fuel jalta hai — yeh Center of Mass Migration hai, aur yeh neeche ka lever length badal deta hai.
Ab payoff. Ek force jo balance point se chook jaati hai woh ek turning effort create karti hai.
Moment arm ℓ
Torque M Torque and Moment Arm ka saara raaz hai.
Intuition Torque kyun, aur sirf sideways part kyun?Thrust ka forward part balance point se guzarta hai — ek spanner jo apne handle ke seedha neeche push ki jaaye woh kuch nahi ghoomata. Sirf sideways part (T sin δ sin
Definition Moment of inertiaMoment of inertia I I
Intuition Loop close karnaTilt δ ⇒ T sin δ ⇒ M = ℓ T sin δ ⇒ ω ˙ = M / I Attitude Control Autopilot is chain ko ulta run karta hai: woh decide karta hai ki use kaunsa ω ˙ δ
Vector = arrow with size and direction
Components = axial and sideways shadows
Angle delta = tilt amount
Sine and cosine = shadow lengths
Small-angle sin delta approx delta
Thrust T = engine push vector
Center of mass = balance point
Moment arm l = CoM to gimbal
Torque M = l times sideways force
Newton rotation M = I omega-dot
Moment of inertia I = spin stubbornness
Right side cover karo aur khud test karo.
Vector kya hota hai? Ek arrow jisme length aur direction hoti hai.
Ek tilted thrust ke components kya hote hain? Uska axial shadow (forward) aur uska transverse shadow (sideways).
Kaun sa trig function tilted push ka forward part deta hai? Cosine, T cos δ
Kaun sa trig function sideways (steering) part deta hai? Sine, T sin δ
Gimbal ke liye sin δ ≈ δ Tilt sirf kuch degrees (radians) ka hota hai, jahan sine curve lagbhag ek seedhi line hoti hai.
Center of mass kya hota hai? Balance point; isse guzarti force slide karaati hai, isse chuki force spin karaati hai.
Moment arm ℓ CoM se us jagah ki doori jahan steering force kaam karti hai (spanner ki length).
Torque M Turning effort = sideways force × M = ℓ T sin δ
Sirf sideways thrust hi torque kyun banata hai? Forward part CoM se guzarta hai aur uska moment arm zero hota hai.
Moment of inertia I Rotational stubbornness — spin rate change karne ka resistance.
Which law links torque to angular acceleration? M = I ω ˙ F = ma
