Impulse of a Rocket Engine – Area Under a Force Curve

December 11, 2014

Thrust curves for model rocket engines are a great way to explore impulse. While every student has everyday experiences with impulses, they are less familiar with the mathematical concept and resulting units of N’s. Analyzing force curves using real data gives students the opportunity to visualize and connect the abstract concept to an image they can more easily interpret. By selecting regions of force data and seeing the area under the curve, students gain an immediate interpretation of impulse.

Model rocket engines have a characteristic Force vs. Time curve. Lift-off is achieved with an initial large force for a short duration. As the propellant continues to burn, the next region of the force curve will show a constant force for a period of time until the propellant is exhausted. The force then drops to zero as the delay charge is burning, which provides a coasting phase for the trajectory. Finally, if there is an ejection charge for the parachute, the ejection charge will ignite.

B6-4 Thrust Profile

With a Force Sensor (PS-2104) and Rocket Engine Test Bracket (ME-6617), a model rocket engine can be measured directly.

Model engine rocket

This PASCO Capstone™ file is a video sync of a model rocket engine and collected force data. Pressing play in the replay control in Capstone will replay the data collection and video. (Requires PASCO Capstone software. Download your free 60-day trial.)

Capstone screen shot

By adjusting the “Data Highlighter” tool and selecting different regions of data, impulse can be measured directly from the graph with the “Area Under the Curve” tool in Capstone.

Data Highlighter tool Data Highlighter Tool

Area Under a Curve tool Area Under the Curve Tool

Compare the initial impulse on launch to the impulse over the range where the force is constant. What is the total impulse from the engine? Measuring the mass of the engine before and after allows your students to apply their physics knowledge to some theoretical questions.

Using the average mass of the engine, what would the velocity of the engine be if it were allowed to launch? If the impulse was instantaneous, how high would the rocket go (ignoring air drag)? Using the average thrust, what is the maximum acceleration of the rocket engine?