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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 (equal and opposite).
• The force resulting from the expulsion of
combustion products is the thrust that moves
the rocket upward.
• Momentum is conserved in rocketry.
Free body diagram
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 the thrust force
overcomes the downward force of weight (mg).
• As the rocket moves upwards, mass (water) is
ejected so weight gets smaller.
• Increasing speed/velocity increases drag force.
• When fuel runs out, drag force and the weight of
the (empty) rocket slows it down to zero velocity
before it falls back to the ground.
We will use IF functions in Excel to account for
the following changes in behavior in the forces.
Thrust remains constant until fuel runs
out and then it equals zero.
Weight decreases steadily until fuel runs out
and then it remains the mass of the rocket
plus any payload.
Drag force (downwards) increases as
velocity increases and then drag force
changes directions to upward when the
rocket falls back down toward the ground.
Sample of velocity vs. time
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
Why is Specific Impulse important?
Lots of Data Points
• If small time intervals are used the
acceleration of the rocket can be
assumed to be constant for that small
interval.
• If this is true Newton’s 2nd Law and
Equations of Motion (Kinematic
Equations) can be used to model the
motion of the rocket.