Transcript Rocket Science Lab PPT

Rocket Science
Modeling the motion of a small
rocket using a spreadsheet.
Introduction to Rockets
• A rocket is basically a fuel can with a hole
in it that is set on fire such that the
products are expelled to power its motion
– Newton’s 3rd Law equates the force of the rocket on
the exhaust to the force of the exhaust on the rocket.
• The force resulting from the expulsion of
combustion products is the thrust that
moves the rocket forward. Momentum is
conserved in rocketry.
Forces
• Weight (mg) depends on rocket mass.
• Drag (Fd) depends on cross sectional
area, drag coefficient and velocity.
• Thrust (T) depends on the fuel flow rate
and ejection velocity from the nozzle
Motion of a Rocket
• The rocket begins to move as thrust
overcomes weight
• As it moves, mass is ejected so weight
gets smaller. Speed increases increasing
drag force.
• When fuel runs out, drag force and the
weight of the empty rocket slows it down
to a stop before it falls back to the ground
We will use IF functions to account for the
following changes in behavior in the forces.
Thrust remains constant until fuel
runs out and then it equals 0
Weight decreases steadily until fuel runs out and then it
reamains the mass of the rocket and payload.
Drag force increases as velocity increases and
then changes directions when the rocket falls back
down toward the ground.
Rocket Motion
300
250
Velocity (m/s)
200
150
100
50
0
0
50
100
150
200
250
-50
-100
Time (sec)
300
350
400
450
500
Burning Fuel
• The fuel type and engine type will
determine the thrust.
• Specific Impulse: A fuel property that is
measured as time or as the ratio of the
mass flow rate of the fuel to the thrust of
the rocket.
– Time: If the initial weight of the rocket is equal
to the thrust.
– Multiply this time by g and get the ratio of
Thrust to mass flow rate…this is used in the
lab.
Why is Specific Impulse important?
• It gives us the thrust for a given rate
of fuel consumption
• OR it gives us the fuel consumption
for a given thrust
FThrust  I SP
m
t
• Relating these variables makes a
spreadsheet model possible
Lots of Data Points
• If small time intervals are used the
acceleration of the rocket can be assumed
to be constant.
• If this is true Newton’s 2nd Law and
Equations of Motion can be used to model
the motion of the rocket.