Level 1 — RecognitionRocket Flight Mechanics

Rocket Flight Mechanics

⏱ 20 minutes30 marksprintable — key stays hidden on paper

Difficulty: Level 1 (Recognition — MCQ, matching, true/false with justification) Time limit: 20 minutes Total marks: 30

Section A — Multiple Choice (1 mark each) [10 marks]

Choose the single best answer.

Q1. The Earth-Centered Inertial (ECI) frame is best characterized by:

(a) It rotates with the Earth's surface
(b) Its axes are fixed relative to the stars (non-rotating)
(c) Its origin is at the launch pad
(d) Its z-axis points North-Down

Q2. The ballistic coefficient for reentry is defined as:

(a) $\beta = C_D A / m$
(b) $\beta = m / (C_D A)$
(c) $\beta = \tfrac{1}{2}\rho v^2$
(d) $\beta = m C_D / A$

Q3. Maximum dynamic pressure (Max-Q) is given by the expression:

(a) $q = \rho v$
(b) $q = \tfrac{1}{2}\rho v^2$
(c) $q = m g h$
(d) $q = C_D A v$

Q4. The static margin of a finned rocket is expressed (in calibers) as:

(a) $(X_{CG} - X_{CP})/d$
(b) $(X_{CP} - X_{CG})/d$
(c) $X_{CP} \cdot X_{CG}/d$
(d) $(X_{CP} + X_{CG})/d$

Q5. During a gravity-turn trajectory, the aerodynamic angle of attack is ideally kept at:

(a) 90°
(b) 45°
(c) 0°
(d) Constantly increasing

Q6. Euler's equations in 6DOF modeling describe:

(a) Translational motion of the center of mass
(b) Rotational motion about the body axes
(c) Aerodynamic heating rate
(d) Propellant mass flow

Q7. A "suicide burn" refers to:

(a) An early staging failure
(b) A single, precisely-timed propulsive braking burn ending at touchdown
(c) Deliberate destruction of the vehicle
(d) Uncontrolled tumbling on reentry

Q8. Communications blackout during reentry is caused by:

(a) Antenna melting
(b) An ionized plasma sheath around the vehicle
(c) Loss of battery power
(d) Doppler shift only

Q9. Aerocapture differs from aerobraking in that aerocapture:

(a) Uses a single deep atmospheric pass to enter orbit
(b) Takes many months of gradual orbit lowering
(c) Requires no atmosphere
(d) Only works for landing

Q10. PICA and SLA are examples of:

(a) Metallic tiles
(b) Ablative thermal protection materials
(c) Guidance algorithms
(d) Coordinate frames

Section B — Matching (1 mark each) [8 marks]

Match each term in Column A with its correct description in Column B. Write the letter.

#	Column A		Column B
Q11	ECEF frame	A	Force acting along the rocket's longitudinal axis
Q12	Axial force ( $C_A$ )	B	Rotates with Earth; used for ground position
Q13	Barrowman equations	C	Reinforced Carbon-Carbon, used on wing leading edges
Q14	RCC	D	Estimate center of pressure for finned rockets
Q15	Direction cosine matrix	E	Restoring rotation of rocket into the wind
Q16	Weather-cocking	F	Transforms vectors between reference frames
Q17	Stagnation heat flux	G	Represents CG, inertia tensor evolution
Q18	Mass properties	H	Chapman equation, peak at stagnation point

Section C — True/False with Justification (2 marks each: 1 T/F + 1 justification) [12 marks]

State whether True or False and give a one-line justification.

Q19. A rocket with its center of pressure ahead of (nose-side of) its center of gravity is statically stable.

Q20. As propellant is depleted during flight, the rocket's mass, CG location, and inertia tensor all change with time.

Q21. Increasing the ballistic coefficient $\beta$ causes a reentry vehicle to decelerate higher in the atmosphere.

Q22. A thrust vector misalignment or gimbal angle produces a torque about the vehicle's center of gravity.

Q23. Fairing separation is typically performed at high dynamic pressure, deep in the dense atmosphere.

Q24. In an ideal gravity turn, the pitch-over of the trajectory is driven by gravity rather than by aerodynamic side forces.

Answer keyMark scheme & solutions

Section A — MCQ (1 mark each)

Q1 — (b). ECI axes are fixed relative to inertial space (stars) and do not rotate with Earth; this is why Newton's laws apply directly. (1)

Q2 — (b). $\beta = m/(C_D A)$ ; higher mass per unit drag area penetrates deeper. (1)

Q3 — (b). Dynamic pressure $q=\tfrac12\rho v^2$ . (1)

Q4 — (b). Static margin $=(X_{CP}-X_{CG})/d$ ; positive when CP is aft of CG. (1)

Q5 — (c). Gravity turn holds $\alpha=0$ so aerodynamic loads/steering losses are minimized. (1)

Q6 — (b). Euler's equations govern rotational dynamics; Newton's govern translation. (1)

Q7 — (b). Suicide (hoverslam) burn: single late braking burn timed so velocity reaches zero at ground. (1)

Q8 — (b). Ionized plasma sheath absorbs/reflects RF, causing blackout. (1)

Q9 — (a). Aerocapture = single pass to capture into orbit; aerobraking = many passes. (1)

Q10 — (b). PICA and SLA are ablative TPS materials. (1)

Section B — Matching (1 mark each)

Q	Answer
Q11 ECEF	B
Q12 Axial force $C_A$	A
Q13 Barrowman	D
Q14 RCC	C
Q15 DCM	F
Q16 Weather-cocking	E
Q17 Stagnation heat flux	H
Q18 Mass properties	G

(1 mark each, total 8)

Section C — True/False with Justification (2 marks each)

Q19 — FALSE (1). Justification (1): Static stability requires CP behind (aft of) CG so aerodynamic force creates a restoring moment; CP ahead of CG is unstable.

Q20 — TRUE (1). Justification (1): Burning propellant reduces mass and shifts CG (usually forward), and changes the inertia tensor components with time. (1)

Q21 — FALSE (1). Justification (1): Higher $\beta=m/(C_DA)$ means the vehicle is "heavier" per drag area, penetrates deeper, and decelerates lower in the atmosphere. (1)

Q22 — TRUE (1). Justification (1): A thrust line offset/gimbal from the CG gives a moment arm, producing a control (or disturbance) torque about the CG. (1)

Q23 — FALSE (1). Justification (1): Fairings are jettisoned once dynamic pressure/aerothermal heating are low enough (high altitude) to protect the payload; separating at high-Q would damage it. (1)

Q24 — TRUE (1). Justification (1): In a gravity turn $\alpha=0$ , so gravity's component normal to velocity pitches the trajectory over, not aerodynamic forces. (1)

[
  {"claim":"Dynamic pressure q for rho=1.0, v=300 equals 45000 Pa", "code":"rho=1.0; v=300; q=Rational(1,2)*rho*v**2; result = (q==45000)"},
  {"claim":"Ballistic coefficient beta = m/(Cd*A): m=1000,Cd=0.5,A=4 gives 500", "code":"m=1000; Cd=Rational(1,2); A=4; beta=m/(Cd*A); result = (beta==500)"},
  {"claim":"Static margin (Xcp-Xcg)/d with Xcp=1.2, Xcg=1.0, d=0.1 equals 2 calibers", "code":"Xcp=Rational(12,10); Xcg=1; d=Rational(1,10); sm=(Xcp-Xcg)/d; result = (sm==2)"},
  {"claim":"Positive static margin requires Xcp aft of Xcg (Xcp>Xcg)", "code":"Xcp=1.2; Xcg=1.0; result = ((Xcp-Xcg)>0)"}
]