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It Doesn't Take a Rocket Scientist to Do Rocket Science

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Applied Math Series: Mathematics and Model Rocketry. Applied Math with Mr. Cheek. Introduction ... unit during your problem-solving time about model rocketry ... – PowerPoint PPT presentation

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Title: It Doesn't Take a Rocket Scientist to Do Rocket Science


1
It Doesn't Take a Rocket Scientist to Do Rocket
Science
Applied Math Series Mathematics and Model
Rocketry
  • Brian Cheek
  • Centerville High School

2
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!

3
The Basic Process
  • Well be going through a 10-step unit during your
    problem-solving time about model rocketry
  • And the 10 steps are

4
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

5
The Basic Process
  • Finding acceleration
  • Finding velocity from acceleration
  • Finding altitude from velocity
  • Putting it all together
  • Launching a model rocket!

6
Basic Conceptssetting 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!

7
Basic Conceptssetting up a spreadsheet
  • Heres an example

8
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

9
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

10
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

11
The Three Forces that Act on a Rocket
  • Motor Thrust
  • Gravity (weight)
  • Air Resistance (drag)

12
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

13
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

14
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.

15
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

16
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)

17
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

18
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

19
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

20
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

21
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

22
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

23
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?

24
Unit Conversion
  • To change velocity from m/sec to mph, multiply by
    2.237
  • To change meters to feet, multiply by 3.28
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