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National Aeronautics and 

Space Administration

DATE

NASA STEM

NASA Student Launch ARW 

Rocketry by the Numbers

PRESENTED BY NASA Student Launch

DATE July 24, 2023
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Parachute Selection

Kinetic Energy (KE):

Energy of motion

Each independent section of the launch vehicle will have a 

maximum kinetic energy of 75 ft-lbf at landing. There are 

many forms of KE

Focus on translational motion –motion linearly from point 

A to point B. 

KE is a scalar quantity 

Typical units:

• foot-pounds force (ft-lbf) [English]

• Joules (J = Nm) [SI]

The KE of an object is dependent upon two variables: 

• Mass (m) 

• Speed (V) KKKK =

1

2 mmvv2

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Parachute Selection

Launch vehicle with 3 

Independent tethered sections

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Recall that drag is determined by:

• Velocity

• Air density

• Reference area

• drag coefficient (cd)

Substituting the drag equation, Newton’s 2nd Law becomes:

The equation is reordered to solve for the reference area (S):

Make an initial guess for the rocket’s weight and set your drag coefficient 

to numbers varying from 0.8 to 2.5 and solve for reference area (S). This 

will help you begin to determine a range to shop for parachutes.

Parachute Selection

Drag (D)

Weight (W)

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Perform the calculations again using the specific parachutes reference area and the manufacturer’s calculated drag 

coefficient

(Descent Velocity = 18 ft/s) typically want below 20 ft/s for your landing velocity

For this case, the rocket will require a parachute that has an area of 26 ft2

Your design will continue to mature, and you will need to re-evaluate your parachute selection as you get better 

estimates for your rocket’s weight

Parachute Selection

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....and now some simpler methods

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Parachute Selection

STANDARD 'CHUTES

9" 1-2 OZ.

12" 2-3 OZ.

15" 3-5 OZ.

18" .5-1 LB.

24" 1-1.75 LB.

30" 1.75-3 LB.

36" 3-5 LB.

45" 5-7 LB.

50" 7-9 LB.

58" 9-12 LB.

72" 12-18 LB.

84" 18-24 LB.

96" 20-32 LB.

120" 32-50 LB.

X-TYPE 'CHUTES

10" 2-3 OZ.

18" 4-12 OZ.

24" .75-1 LB.

30" 1-1.75 LB.

36" 1.5-2.5 LB.

42" 2.5-3.5 LB.

48" 3.5-4.5 LB.

54" 4.5-5.5 LB.

60" 5.5-7.5 LB.

70" 7.5-9.5 LB.

80" 9.5-12.5 LB.

90" 12.5-17.5 LB.

Manufacturer Data

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Parachute Selection

Do not assume 

drag coefficient 

ratings are 

accurate on 

vendor websites

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Parachute Selection

Parachute Descent Calculator

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Key Design Requirements

Each independent section of the launch vehicle will have a maximum kinetic energy of 75 ft-lbf at landing. 

Descent time of the launch vehicle will be limited to 90 seconds (apogee to touch down).

Quick tips to ensure you don’t end up in this situation

• Do not design a rocket to meet the upper (lower) end of our allowed constraints.

• Do not fall in love with manufacturer ratings especially for parachute drag coefficients: Test, Test, Test!!!!!!

• Simulation data is good....but Raw flight data is better. “But our simulation said....”

• Descent rate is more important than descent mass: KE = (1/2) * mass * velocity squared

• Don’t build bigger than you need

• Teams almost ALWAYS UNDERESTIMATE mass: Hardware, nuts, bolts, epoxies, threaded rods, u-bolts, eye-bolts, 

parachutes, shock cords

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Stability:

An object is directionally stable if tends to return to its 

original direction in relation to the oncoming medium 

(water, air, etc.) when disturbed away from that 

direction

Also called “weathervaning”

Without stability, a rocket would tumble end over end, 

spin, or orient itself at a high angle of attack and the 

rocket may experience structural failure

A rocket is considered stable if its Center of Gravity 

(CG) is at least one body diameter in front of its 

Center of Pressure (CP).

Stability

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Static Margin:

Or Margin of Stability describes the directional stability of a rocket

Recall: 

• An object is directionally stable if tends to return to its original direction in relation to the oncoming medium 

(water, air, etc.) when disturbed away from that direction and 

• A rocket is considered stable if its Center of Gravity (CG) is at least one body diameter in front of its Center of 

Pressure (CP). 

Generally, it is desirable to have a static margin of 1.5 to 2.0. A rocket is considered over stable if it has a static margin 

of 3.0 or greater. For NASA Student Launch we do require a minimum static stability margin (on the pad) of 2.0 or 

above.

An over stable rocket will lean or “weathervane” further into the wind and not travel as high.

Generally, the CG will move forward as a solid rocket motor burns, causing the rocket to become more stable. 

Stability: Static Margin

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Center of Gravity (CG):

The Center of Gravity of rigid body is the mean location of all 

the masses in a system

The CG can be determined analytically or empirically

The analytical method requires accounting for:

The individual point masses that compose the system 

their location in the system as measured from the tip of a 

rocket’s nose cone

The average of their positions weighted by their masses is the 

location of the center of gravity

Stability: Center of Gravity (CG)

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Center of Pressure (CP):

Aerodynamic forces act on all parts of the rocket. Those aerodynamic forces act through a single 

point called the Center of Pressure (CP). 

CP can be determined by regional influence using algebraic forms of the Barrowman equations 

and accounting for:

• Each primary component’s Normal Force (Cnα)

• Their location in the system as measured from the tip of a rocket’s nose cone

The basic assumptions used to calculate the theoretical CP for a rocket are:

• The angle of attack (α) of the rocket is near zero (less than 100)

• The speed of the rocket is much less than the speed of sound 

• The air flow over the rocket is smooth and does not change rapidly

• The rocket is thin compared to its length (L >> D)

• The nose of the rocket comes smoothly to a point 

• The rocket is an axially symmetrical rigid body 

• The fins are thin flat plates

Stability: Center of Pressure (CP)

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How to “Fix” a Rocket

What happens if you build a rocket, and its stability margin is not safe to fly? Or its thrust to weight ratio is 

not sufficient? 

No, you don’t need to buy/build a new rocket!

• add weight to the front of the rocket. Remember, we need to shift the CG as far in front of the CP as possible 

(minimum one body tube diameter)

• choose a stronger motor

• lengthen the airframe (body tube) by adding a coupler

• lengthen the fins, moving the CP back 

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RockSim

(free trial, otherwise paid license)

Open Rocket 

(Opensource software very similar to 

RockSim)

RocketyPy library via Python

Computer Software to Aid in Rocket Design

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RockSim

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Questions?
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