Rocket Performance
Thrust
Weight
Total Mass
Drag
Gravity
Fins
Impulse Class
Body
Nose
Burn Time
Shape
Number
Shape
Size
Length
Developed by Kyle Voge for the
Texas Tech T-STEM Center © 2007
Diameter
Material
Length
Thrust
Impulse Class
I 
 F  dt
Burn Time
• “Thrust” refers to the force that a motor produces during flight
• For simpler but less accurate simulations, assume constant thrust
• For more complicated but more accurate simulations, determine
force profile, I.e. force as a function of time F(t)
• The thrust given by a specific motor depends on the impulse class
of the motor and the amount of time it burns• You could have a motor burn:
• Relatively weakly for a longer time
• Relatively strongly for a shorter time
• THIS MAKES A BIG DIFFERENCE!
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Impulse Class
•Motors are classified by impulse- though not technically
accurate, you could think of this as the amount of power a
motor can generate.
•Impulse = force x time
•Think of this as “man-hours” on a job
•J motors put out between 640 and 1280 N*s of impulse
•That’s:
•640 Newtons for 1 second or
•1 Newton for 640 seconds or
•Some combination thereof
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Burn Time
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Burn Time
• The amount of impulse a motor generates is indicated by the letter- but the letter
alone tells you nothing about how long the motor will fire.
• The motor manufacturer will provide data on the specifications of each motor.
For example- HyperTek makes a J331 motor.
•The burn time is 3.2 seconds
•The “331” refers to average thrust (in Newtons)
•Therefore the total impulse = 331N*3.2s = 1059.2N*s
•(This is between 6640 and 1280, so that’s why it’s a “J” motor)
• This is for THAT SPECIFIC MOTOR- each “J” is going to be different.
• The one you want depends on many factors- average thrust, diameter, burn time,
and perhaps most importantly, price.
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Impulse Class
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Weight
Total Mass
Gravity
• The weight of a rocket is one of three principle forces acting
during flight
• Newton’s 2nd Law says F = ma…. In this case, Weight = Mass
times Gravity
• Of course, the total mass of the rocket and the acceleration of
gravity both change during flight- you’ll have to decide how
accurate you want your simulation to be.
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Total Mass
• The total mass of the rocket is just that- all components of the airframe, recovery,
payload, and perhaps the most overlooked component of mass: the motor and
propellant.
• It is difficult to accurately predict the mass of a planned rocket because the exact
amount of glue and epoxy you will use isn’t known.
• Perhaps a good strategy would be to slightly overestimate your mass in your
simulations- you could always add some modeling clay or silly putty later.
• Intuitively one might think that you’d want your rocket to be as light as possible
to maximize altitude.
• This is correct during powered flight… but not during the “coast” phase of flight.
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Gravity
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Gravity
• Near the surface of the Earth, the acceleration of gravity is 9.81 m/s/s.
• As you increase altitude, the acceleration of gravity decreases:
Gm1m2
Fg 
r2
• The effect of this is quite small for low to moderate altitudes- even at 100 miles
above the surface, the acceleration has dropped less than 5% to 9.38 m/s/s
• This is probably going to be the least significant effect to model in the simulationin other words, it probably won’t make much of a difference.
• Again, it all depends on how accurate you want your simulation to be.
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Total Mass
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Drag
Fins
Body
Nose
• Arguably the most significant effect on a rocket’s performance, aerodynamic drag
is a non-conservative force that always acts to oppose the rocket’s motion.
• The general equation for drag depends on area, velocity, fluid density, and the
coefficient of drag:
1
Fd  AV 2C D 
2
• Practical considerations:
• As velocity increases, drag forces increase
• As the surface area of a rocket increases, drag increases
• As the density of air decreases, drag decreases
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Fins
Number
Shape
Size
• Fins increase the surface area of the rocket, and when placed near the rear end,
can help improve stability by moving the CP back.
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Body
Nose
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Number
• More fins = more stability, but also means more mass and more drag
• Another factor to consider is ease of construction- many people have
chosen 4 fins over 3 because 90 degree angles are easier to construct
than 120 degree angles.
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Shape
Size
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Shape
• Fin shape plays an important role in both drag and stability.
• Fin shapes help determine the CP• “Forward-swept” fins won’t move the CP back as far as “Back-swept” shapes
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Number
Size
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Size
• Bigger fins = more stability, but also means more mass and more drag
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Number
Shape
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Body
Length
Diameter
Material
• Body here refers to the tube- not including the nose nor fins.
• Body tube design plays a significant role in both determining stability and in drag
forces.
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Fins
Nose
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Length
•The length of the body tube plays a role in CP and CM
• A longer body can mean more stability, but…
• It also means more drag and more mass.
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Diameter
Material
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Diameter
• The diameter of the body tube GREATLY affects drag.
• A bigger diameter will mean more drag… and because the drag force is
proportional to the AREA of the rocket (which is proportional to the radius
squared)….
• Doubling the diameter doesn’t double the drag force- it QUADRUPLES
it.
•Of course, diameter will be determined by payload- your tube needs to be
big enough to carry what you want.
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Length
Material
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Material
• The material the body tube is made of has significant effects on mass and
cost, but only minor effects on drag.
• You need to choose a material that will be strong enough to resist the
forces it will encounter during flight.
•Usually, stronger materials are heavier, so there is a trade-off between
strength and mass.
• Whichever material you choose, it is important to sand and finish it
smooth to minimize drag effects.
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Length
Diameter
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Nose
Shape
Length
• The nose cone design plays arguably the biggest role in drag effects.
• The main purpose of a nosecone is to decrease the pressure-induced drag of
the rocket as it moves through the air.
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Fins
Body
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Shape
• There are several common nosecone shapes available:
•Ogive
•Parabolic
•Conical
• Each of these shapes has distinct advantages and disadvantages.
• Select the shape based on your goals- breaking Mach, maximizing altitude, etc.
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Length
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Length
• Von Karman’s equations show that maximum efficiency occurs when the
length of the nosecone approaches infinity.
• Of course, there are trade-offs here, too:
• A longer nose will:
• Decrease pressure-induced drag
• Increase mass
• Decrease stability by moving the CP forward
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Shape
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