In this unit, you will be predicting the performance of a model rocket that you will build using common materials (no "store-bought versions" allowed). In order to make your predictions, you will first use the average motor thrust for a simple model. Then for more precise modeling of the rocket's trajectory you will use the thrust (force) data from a classroom static test fire of the motor. You will transfer the data to Vernier's Graphical Analysis, utilize basic force, mass, velocity and acceleration formulas to simulate your rocket's performance. You will compare your results with computer modeling programs, wRASP, and Stella. You will then launch a model rocket, collecting actual performance data. At the conclusion of the activity, you will compare the rocket's simulated performance to its actual performance and account for any differences.

Begin by building your model rocket according to the instructions given under the side bar tool "Experiments".

Part I: Hand Calculations of Predicted Rocket Performance

Use the student Worksheet S1 to record the following calculations 

Force:  F = ma

Using Newton's 2^nd Law, SF=ma. 

The forces acting on the rocket are:

• Thrust (+4.76 N for the C5-3 motor)
• Weight (mass of the rocket in kilograms*gravity)
• Drag (F_drag= 0.5 * Cd * r * A * V² )  Cd is the coefficient of drag, r (rho) is the air density, A is the cross-sectional area of the rocket at its widest point, the nose cone 

A very smooth rocket may have a drag coefficient of 0.6. An average number would be closer to 0.8. Initially, a value of 0.8 is arbitrarily assigned for Cd. There are no units on the drag coefficient just as there are no units on the coefficient of friction.

Air density changes according to weather conditions but at our elevation it is very nearly 1.0 kg/m³.  The units here are the important part of the calculation.

A must be expressed in square meters for the units to work out in the equation.

V is the velocity squared and makes a huge difference in the outcome of this equation.  

The units become ( kg *  m²  *  m² )   /  (m³   *  s ²  )  = Newton's

Determine the mass of your rocket in kilograms for this calculation.

The C5-3 motor burns for 2.1 seconds, giving a maximum velocity of about 40 m/s. 

To get a quick idea of your rocket's flight path using the TI-83+SE, click this link to the TI instruction page.

If TI-Interactive is available, try this link to a model using parametric equations to show the rocket's trajectory. TI Interactive

Part II: Graphical Analysis of Predicted Rocket Performance

You will be using the Estes C5-3 engine for launching your egg from a rocket in an area of about the size of a football field. Static firing of the engine allows for the calculation of force (thrust). The engine is clamped into a stand and held so it pushes on a Vernier 50 N force gauge. The set up looks something like this:

The teacher will demonstrate the static firing, and you will record the data to input into Vernier's Graphical Analysis program.

Here is the graph obtained from a Vernier 50N Force probe set up to a CBL /TI-83 calculator with the PHYSICS program. The data was collected as 0.05 seconds and 60 samples for a 3 second graph.

Graphs are fundamental to understanding the change in any quantity over time. You will be producing several graphs and you should print out each of the graphs you generate.  Using Vernier's Software Graphical Analysis program on the computer, enter the values obtained from the previous hand calculations as (constant) values of acceleration into the first column as a function of time for 2.1 seconds (see Graph Analysis Screen). Click on Data, fill column, and set the time column to values of 0 to 15 sec in 0.1 sec intervals.   Then for the first 2.1 seconds enter the acceleration by copy and pasting whatever value you obtained in the hand calculations.   After the first 2.1 seconds (end of thrust), the acceleration drops to -9.8 m/s/s.   This is the only information you need to input the velocity and then the height will be calculated from the acceleration.  

Once the acceleration values are entered, take the area under the curve of each acceleration graph by creating a new data column under the calculated function of the program. In the "Data" box, click on "New Column" and then "Calculated". Rename the new column "Velocity" and put in the units (ms). Open the "Other Functions" box, choose "Integral". Then in "column", click on acceleration, Go back and click on the word acceleration. Turn on velocity by clicking the box and turn off acceleration in the same manner.

To determine the distance traveled (height), repeat the steps above, labeling the new column as "Height", and taking the integral of the velocity column. Here is what your graphs should look like:

Part III: VCP Determination of drag coefficient and center of pressure

Using your model rocket, and the VCP program provided by your teacher, you will now calculate the actual coefficient of drag and center of pressure. The VCP program will allow you to play some "what if" games with changing the dimensions of your rocket for greater performance. If, after performing the calculations you would like to make modifications to your rocket, you may do so. Print out your final VCP analysis.

At this point, you should begin completing Worksheet S2

Part IV: wRASP computation of Predicted Rocket Performance

You now have all the raw data necessary to simulate your rocket's performance. Using the wRASP program provided by your teacher, you will predict your rocket's maximum altitude (apogee) based on the coefficient of drag computed in VCP. This modeling program will simulate the rocket launch. Print out your wRASP analysis.

Once you have completed the wRASP simulation, compare the results with that obtained using another modeling program, Stella. The Stella simulation can be performed using the side toolbar "Run the Model"

It is now time to launch your rocket!

Part V: wRASP Computation of Actual Rocket Performance

Now it is time to assess your rocket's performance. Using the actual altitude of your rocket (obtained from triangulating the inclinometer readings taken by your assistants), you will backtrack the actual coefficient of drag. You will then compare this value to the computed coefficient of drag obtained in Part III.

Run wRASP as you did in Part IV, only this time you will use the observed apogee for the maximum altitude value. All other values remain the same. wRASP will then compute the true coefficient of drag. Print out the wRASP performance data and graph, complete Worksheet S2 and then consider the value of rocketry models versus modeling using the guidelines presented in Worksheet S3.