Activity 4.2.5 – Maximum Velocity and
Acceleration
Introduction
Velocity is a vector quantity as opposed to scalar quantities; vectors have both
magnitude and direction. For example, + 10 miles/hour could indicate that a rocket is
(ascending) traveling upward, parallel to the launch pad at 10 miles/hour; where -10
miles/hour could indicate that the rocket is descending at a rate of 10 miles/hour.
Acceleration is a vector quantity. Accelerating or “speeding up” by convention is a
positive quantity, whereas decelerating or “slowing down” is a negative quantity.
This method is a theoretical calculation that ignores drag. Therefore, the calculations
will not be entirely accurate (will differ than actual results depending on various
experimental conditions) but should give a good indication of the velocity of the
rocket.
In this activity the equations have been simplified so the emphasis is on working with
simple equations to determine velocity rather than using complicated mathematics.
You will calculate the velocity of rockets that you and your team members have
launched in previous activities and answer questions related to various model rocket
engines and rocket performance. Even though mathematical calculations are
required, the emphasis is on applying the formulas rather than developing a deep
understanding of each formula. Engineers often use mathematical formulas from
physics and tables of specifications to calculate values that describe physical
phenomena.
Equipment





Scientific Calculator (optional)
Computer
Excel spreadsheet program
Max Calc Excel file
Engine Specs Excel file
Procedure
In this activity, you will calculate the maximum velocity and maximum acceleration a
model rocket will obtain during a launch using various size model rocket engines.
The maximum velocity of a model rocket occurs at the moment just before the rocket
engine’s propellant “burns out.” After the propellant is exhausted, the rocket
Project Lead The Way, Inc.
Copyright 2010
AE – Unit 4 – Lesson 4.2 – Activity 4.2.5 – Maximum Velocity and Acceleration – Page 1
continues to travel upward due to momentum (the coast phase); however, gravity is
gradually slowing the rocket during its vertical assent. Eventually the force of gravity
will return the rocket to earth. Smoke that is coming from the model engine during
the coast phase is the tracking smoke; it is not smoke from burning propellant.
Use the following formulas and the table of Model Rocket Engine Specifications
found in Activity 4.2.5 Rocket Engine Specs.xls, which is used to calculate the
maximum velocity and maximum acceleration of the flight of an Alpha model rocket
with an A8-3 engine. This is the rocket and engine type that was flown earlier.
Maximum Velocity
Maximum Velocity  (
V (
Thrust Avg
Weight Avg
1)(gravity)(time)
TAvg
1)gt
W Avg
V = Maximum velocity of the rocket
TAvg = Average thrust of the rocket engine
WAvg =
Average weight of the rocket before launch and at the moment when the
propellant is exhausted
g = acceleration of gravity (32 ft./sec.2) or (9.8 m/s2)
t = thrust duration of the engine
The thrust duration of the engine can be obtained from the table of Model Rocket
Engine Specifications. However, the average thrust of the rocket engine and the
average weight of the rocket before launch and at the moment the propellant is
exhausted must be calculated using the table of Model Rocket Engine
Specifications and the weight of the rocket.
Average Thrust, TAvg
To calculate the average thrust of the rocket engine, TAvg., use the Model Rocket
Engine Specifications and the following equation.
TAvg 
Total Im pulse 16 oz.
x
Thrust Duration 1 lb.
This equation calculates the average thrust of the rocket engine and converts the
thrust from ounces (oz.) to pounds (lb.).

Average Weight, WAvg
To calculate the average weight of the rocket before launch and at the moment
when the propellant is exhausted, use the following equation, the weight of the
rocket, and the Model Rocket Engine Specifications.
Project Lead The Way, Inc.
Copyright 2010
AE – Unit 4 – Lesson 4.2 – Activity 4.2.5 – Maximum Velocity and Acceleration – Page 2
rocket weight and engine weight prior toliftoff  weight of rocket at moment when propellant isexhased
2
rocket weight and engine weight prior toliftoff  (weight of rocket and engine  propellant weight)
W Avg. 
2
W Avg. 

Maximum Acceleration
The acceleration of the rocket expressed in terms of the number of “g”s a rocket
experiences is given by the following equation. (Note the acceleration equation is
one of the factors in the maximum velocity equation above.)
Acceleration  a  (
TAvg
1)
W Avg
Calculations can be made in either English units or metric units. Remember to show
units of measure inyour calculations.
In order to change parameters and to answer questions that require numerous
routine calculations, engineers look for short cuts to save time. Using a spreadsheet
program allows an inquirer to change conditions and view results instantaneously to
answer questions.
1. Open the Excel spreadsheet file, Max Calc, to calculate the maximum velocity in
feet/second and miles/hour and to calculate the g force of the maximum
acceleration. For example, you will learn that if the velocity of the rocket is 3g,
then the acceleration is three times as strong as gravity.
2. The rocket’s weight and required engine specifications can be found in the Excel
spreadsheet file, Engine Specs. Use the spreadsheet to calculate the maximum
velocity and acceleration for the Alpha model rocket with an A8-3 engine and
compare the results with your calculations from Step 1. Note: The calculations
made with a calculator and with a spreadsheet maybe slightly different due to
rounding.
3. The following five engines are recommended for use with the Alpha model
rocket: 1/2A6-2, A8-5, B4-4, B6-4, and C6-5. Use the spreadsheets Max Calc
and Engine Specs, and the table of Model Rocket Engine Specifications to
calculate the maximum velocity and maximum acceleration of the Alpha rocket
for each of the five engines.
4. Compare maximum velocity and acceleration data for the five engines.
Project Lead The Way, Inc.
Copyright 2010
AE – Unit 4 – Lesson 4.2 – Activity 4.2.5 – Maximum Velocity and Acceleration – Page 3
5. Which engine provides the maximum velocity?
6. Which engine provides the maximum acceleration?
7. Does the engine that has the maximum velocity also have the maximum
acceleration? If yes, give evidence. If no, provide an explanation.
8. The B8-5 engine is not recommended for use in the Alpha model rocket.
Calculate the maximum velocity and maximum acceleration for the Alpha model
rocket if a B8-5 engine were used.
9. Compare the results from the B8-5 engine and the engines that are
recommended.
10. Provide reasons why the B8-5 engine is not recommended for use in the Alpha
rocket.
11. Now go back and use your data to calculate your maximum velocity and
acceleration for each launch of your rocket. (If you have not yet measured the
mass - do so! Fill out the table below (add more columns if necessary.
Launch #
Maximum Velocity
Maximum Acceleration
1
2
3
Project Lead The Way, Inc.
Copyright 2010
AE – Unit 4 – Lesson 4.2 – Activity 4.2.5 – Maximum Velocity and Acceleration – Page 4
Conclusion
1. Print your spreadsheet data and compare your data with other groups.
2. Write a short summary of your results and implications for future model rocket
flights.
3. Do you think your calculated values for velocity and acceleration are correct?
Why or why not?
4. Why do you feel that model rocket manufactures state that no live payload
should be used on a model rocket? Comment on this advisory using your data on
velocity and acceleration. Be prepared to discuss results with the class.
5. Since the data generated by the spreadsheet neglects drag, are the calculations
for maximum height and maximum velocity too large or too small? Explain your
reasoning.
Project Lead The Way, Inc.
Copyright 2010
AE – Unit 4 – Lesson 4.2 – Activity 4.2.5 – Maximum Velocity and Acceleration – Page 5