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It Doesn't Take a Rocket Scientist to Do Rocket

Science

Applied Math Series Mathematics and Model

Rocketry

- Brian Cheek
- Centerville High School

Introduction

- Why are we doing this?
- To explore how math can be applied to things that

happen in the real world - To help you understand how to use technology to

make the job easier - To convince you that math can actually be useful

and maybe even fun!

The Basic Process

- Well be going through a 10-step unit during your

problem-solving time about model rocketry - And the 10 steps are

The Basic Process

- Basic concepts setting up a spreadsheet
- The three basic forces that act on a rocket
- Thrust and gravity
- Air resistance
- Newtons 2nd Law of Motion

The Basic Process

- Finding acceleration
- Finding velocity from acceleration
- Finding altitude from velocity
- Putting it all together
- Launching a model rocket!

Basic Concepts setting up a spreadsheet

- Enter all the constants they describe facts

about your rocket, motor, the air, etc. - Set up column titles they are the categories

that youll teach the spread sheet to compute - Set up the time increments well be computing

what a rocket does every tenth of a second!

Basic Concepts setting up a spreadsheet

- Heres an example

Basic Concepts

- Lift-off
- Motor thrust acceleration
- Motor burnout coast phase
- Tracking smoke
- Ejection charge at apogee
- Recovery system deployed
- Rocket slowly descends
- Rocket recovery

Mass

- The problem mass changes during flight - fuel is

burned over time, so the rocket gets lighter - The solution take the average.
- Find mass of pre-launch rocket
- Find mass of rocket when fuel is all burned out
- Add these together, divide by two

Mass (continued)

- Use this average until motor burnout time
- After motor burnout, use the value for the mass

of the rocket when fuel is all burned out

The Three Forces that Act on a Rocket

- Motor Thrust
- Gravity (weight)
- Air Resistance (drag)

The Three Forces that Act on a Rocket

- Motor Thrust
- Thrust how hard the rocket motor is pushing

the rocket upward - Measured in Newtons
- One pound 4.45 N
- We read average thrust right off the outside of

the motor

The Three Forces that Act on a Rocket

- Gravity (weight)
- Force with which gravity pulls you down depends

on your mass - However, gravity causes all falling objects to

accelerate at the same rate - This rate is called the Gravitational Constant

-9.81

The Three Forces that Act on a Rocket

- Air resistance (drag)
- Drag how hard the air is pushing against you,

trying to slow you down - Depends on your size, shape, how fast you are

going, and how dense the air is.

Thrust

- Read from the motor casing
- In our example, C6-5, the 6 gives the average

thrust of the motor - This motor pushes the rocket upward with a force

of 6 Newtons - Enter a 6 in all the cells in the Thrust

column until motor burnout - Enter a 0 in the rest of the Thrust column

Gravity

- The force with which gravity pulls on an object

is given by the equation - F mg
- m the mass of the rocket (kg)
- g acceleration caused by gravity (-9.81 m/sec2)

Air Resistance (Drag)

- We get to steal a formula figured out by

experts in fluid mechanics - The formula is
- Drag 0.5?CdAV2
- ? Air density 1.2 kg/m3
- A Cross-sectional area of rocket
- V velocity

Total Net Force

- We have computed the forces due to
- Thrust
- Gravity
- Drag
- The sum of those forces is the Total Net Force on

the rocket

Newtons 2nd Law

- Newtons second law states that sum of all forces

acting on an object is equal to the product of

its mass and its acceleration, i.e. - F ma
- Since we know F and m, we can easily compute a

Computing Acceleration

- Acceleration describes how much an objects

velocity changes each second - Simply take the computed force acting on the

rocket and divide it by the computed mass of the

rocket

Computing Velocity

- Velocity describes how much our rockets altitude

changes each second - Current velocity previous velocity plus current

acceleration - Since we are computing the change in altitude

every tenth of a second, we need to multiply

current acceleration by 0.1

Computing Altitude

- Current altitude previous altitude plus current

velocity - Since we are computing the change in altitude

every tenth of a second, we need to multiply

current velocity by 0.1

Youve done it!

- Now you can simply use the spreadsheet to look up

the acceleration, velocity, and altitude - Acceleration is in m/sec2
- Velocity is in m/sec
- Altitude is in meters
- Want to convert these to more familiar units?

Unit Conversion

- To change velocity from m/sec to mph, multiply by

2.237 - To change meters to feet, multiply by 3.28