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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
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
• 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
• Enter all the constants they describe facts
• 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
• 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
• 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