Rocket PerformanceRocket Performance

Thrust Weight Drag

Burn TimeImpulse Class

GravityTotal Mass

Fins Body Nose

Shape Size

Length Diameter

Shape Length

Material

Number

Developed by Kyle Voge for theTexas Tech T-STEM Center © 2007

Thrust

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Burn TimeImpulse Class

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• “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!

Impulse Class

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•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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• 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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Weight

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GravityTotal Mass

• 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.

Total Mass

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• 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

HOMETotal Mass

• 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:

• 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 simulation- in 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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Drag

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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:

• 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

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• Fins increase the surface area of the rocket, and when placed near the rear end, can help improve stability by moving the CP back.

Shape SizeNumber

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Number

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• 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

HOMESizeNumber

• 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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Size

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• Bigger fins = more stability, but also means more mass and more drag

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Body

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• 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.

Length Diameter Material

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Length

HOMEDiameter Material

•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

HOMELength Material

• 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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Material

HOMELength Diameter

• 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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Nose

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Shape Length

Fins Body

• 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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Shape

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• 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.

Length

HOMEShape

• 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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