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

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0 50 100 150 200 250 300 350 400 450 500

Time (sec)

Velo

city (

m/s

)

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

• Relating these variables makes a spreadsheet model possible

Thrust SP

mF I

t

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.