Space X rocket

This activity allows students to analyze the controlled descent program of a reusable rocket. It develops the ability to interpret kinematic data and understand aerospace engineering strategies.

On December 21, 2015, SpaceX made history by successfully landing the first stage of a Falcon 9 rocket vertically after launching a payload into orbit. This feat, once considered science fiction, has since become routine, fundamentally changing the economics of spaceflight. The landing sequence is a masterclass in controlled kinematics: the 70-meter-tall booster, falling at several hundred meters per second, must decelerate to exactly zero velocity at exactly the right altitude (ground level) using precisely timed engine burns. Too little braking and the rocket crashes; too much and it hovers then tips over, wasting fuel. SpaceX solves this problem with a suicide burn strategy: the engines ignite at the last possible moment and decelerate the rocket at maximum thrust, reaching zero velocity just as it touches down. Using FizziQ's kinematic analysis module, students can analyze a landing video to reconstruct the velocity and acceleration profiles and understand the engineering brilliance behind this programmed descent.

Learning objectives:

The student uses the FizziQ Kinematics module to analyze the descent movement of a Falcon 9 rocket from a video. After calibrating the scale using the actual size of the rocket, the student performs precise pointing of the positions then analyzes the speed and position graphs to determine the braking strategy programmed by SpaceX and evaluate its effectiveness.

Level:

High school

FizziQ

Author:

Duration (minutes) :

35

What students will do :

- Analyze the descent and landing of a Falcon 9 rocket using video-based kinematic tracking
- Determine the velocity and acceleration profiles during the landing sequence
- Identify the distinct phases of the descent: atmospheric entry, main braking burn, and final landing burn
- Understand the concept of a suicide burn and why it minimizes fuel consumption
- Connect kinematic analysis to real aerospace engineering challenges

Scientific concepts:

- Movement at controlled speed
- Space propulsion
- Kinematic analysis
- Back-drive braking
- Position and speed

Sensors:

- Camera (video recording for kinematic analysis)
- FizziQ Kinematics module (frame-by-frame position tracking)

What is required:

- Smartphone or tablet with the FizziQ application
- Falcon 9 rocket landing video available via FizziQ map link
- Information on the size of a Falcon 9 rocket (70 meters)
- FizziQ experience notebook

Experimental procedure:

Open FizziQ and navigate to the Kinematics module. Load the Falcon 9 landing video from the FizziQ map link or video library.
Set the scale using the known height of the Falcon 9 first stage: approximately 70 meters (including legs).
Define the origin at the landing pad with the y-axis pointing upward.
Track the base of the rocket frame by frame through the descent sequence. Start from the highest visible point.
Collect as many data points as possible, especially during the final 10 seconds before landing when changes are most dramatic.
Plot the altitude versus time graph. It should show a steep descent that sharply levels off just before touchdown.
Calculate the velocity at each time step from the position differences. Plot velocity versus time.
Identify the braking phases: the velocity should decrease in distinct stages, with sharp changes when engines ignite or shut down.
Calculate the deceleration during the main braking phase. Compare with the acceleration of gravity (9.81 m/s²).
Note that the deceleration must exceed g for the rocket to slow down (the net deceleration is a_thrust - g).
Estimate the velocity at engine ignition and the time from ignition to touchdown. Verify that these are consistent with a constant-deceleration model.
Discuss: why does SpaceX use a last-second suicide burn rather than a gradual, gentle descent? What are the advantages in terms of fuel efficiency?

Expected results:

The Falcon 9 first stage descends at high speed (100-300 m/s) before the main braking burn, which produces a deceleration of 20-40 m/s² (2-4g). The final landing burn brings the velocity from about 20-30 m/s to zero in the last 5-10 seconds. The altitude-time graph shows a characteristic hockey-stick shape: nearly linear (constant velocity) during free descent, then sharply curving as the engines fire. The velocity-time graph shows distinct phases with abrupt transitions. Pointing accuracy in the video analysis is limited by the rocket's distance from the camera, typically giving velocity precision of ±5-10 m/s. Students should observe that the deceleration during the landing burn must be significantly greater than g to overcome both gravity and the existing downward velocity.

Scientific questions:

- Why must the rocket's deceleration exceed g during the landing burn?
- What is a suicide burn, and why is it more fuel-efficient than a gradual descent?
- What would happen if the engine ignited one second too late? One second too early?
- How does SpaceX control the rocket's attitude (orientation) during descent?
- What role do the grid fins play during the atmospheric descent phase?
- How does the mass of the rocket change during the landing burn, and how does this affect the deceleration?

Scientific explanations:

The controlled vertical landing of a Falcon 9 rocket first stage represents a major technological feat for SpaceX. This process involves precise control of trajectory and speed to minimize fuel consumption while ensuring a smooth landing.

Kinematic analysis generally reveals a descent profile in several phases: 1) A high-speed atmospheric reentry phase, with the use of aerodic grids to stabilize the rocket; 2) A main braking phase with ignition of 3 of the 9 Merlin motors; 3) A final phase at constant or slightly decreasing speed. It is this last phase which is particularly visible in the video.

The final descent speed is typically maintained around 5-8 m/s until the final seconds, where further deceleration reduces the impact speed to around 2 m/s. This strategy of controlled speed rather than continuous deceleration has several advantages: it allows better predictability of the trajectory, reduces the risk of engine flameout at low thrust, and minimizes fuel consumption.

On the velocity graph, this results in a plateau rather than a continuous decrease, and on the position graph, a straight line of constant slope rather than a parabolic curve. FizziQ's kinematics tool makes it possible to precisely quantify these phases and appreciate the ingenuity of the landing program.

This technique has revolutionized the space sector by making it possible to reuse launchers, thus considerably reducing the cost of putting them into orbit.

Extension activities:

Frequently asked questions:

Q: The rocket is very far from the camera, making it hard to track precisely. How can I improve?
R: Use the rocket's known height (70 m) as a scale reference in each frame. Focus on tracking a specific feature (like the engine nozzle or the top of the rocket) consistently across frames.

Q: The velocity values seem erratic. Is the analysis meaningful?
R: At long distances, small pointing errors translate to large velocity uncertainties. Use longer time intervals between position measurements to smooth out the noise. Focus on the overall velocity trend rather than frame-to-frame values.

Q: Why does the landing video sometimes show the rocket disappearing behind exhaust plumes?
R: The engine exhaust creates a dense cloud of gas and water vapor that can obscure the rocket during the most critical final seconds. This is a limitation of video analysis for this experiment.

Q: How much fuel is used during the landing burn?
R: The landing burn typically uses about 5-10% of the first stage's fuel capacity. The single-engine suicide burn is specifically designed to minimize this fuel usage while still achieving a safe landing velocity.