SPARROW

stem.nasa.gov

National Aeronautics and 

Space Administration

DATE

NASA STEM

NASA Student Launch ARW 

Propulsion Systems

PRESNTED BY NASA Student Launch

DATE July 24, 2023
SPARROW

stem.nasa.gov

Impulse is the work done by the propellant

Typically measured in units of Newton-seconds

The impulse parameter is used to categorize 

different classes of rocket motors in hobby 

rocketry

Impulse can be calculated for both variable and 

constant thrust rocket motors

The Thrust (T) and Total Impulse (I) equations 

above work for both liquid and solid rocket 

motor

SLI teams are limited to motors with a 

maximum impulse of 2,560 Ns

Total Impulse

Thrust curves can be downloaded from Thrustcurve.org and imported into RockSim or Open Rocket.

Practical Example of Impulse

• I = T∆t

• Exact Impulse is derived by integrating the Thrust Curve over the time interval of interest.

• Impulse can be estimated by I = Tavg * burn time 

• I = (1790N)*(4.5sec) = 8055 Ns (8088 Ns is advertised by vendor)

2
SPARROW

3 stem.nasa.gov
SPARROW

stem.nasa.gov

Black Powder Motors

Charcoal, potassium nitrate, sulfur

Always come in paper casings

Pros

• Cheaper

• Ready to fly out of the box

• BP is very flammable, so ignition is

consistent

Cons

• Lower energy density (not as much bang

for your buck)

• Propellant can crack easier causing

uneven pressurization leading to burst

casings and/or rockets

• Limited in sizes (typically smaller motors)

• Larger motors require hazmat shipping

Black Powder vs. Composite

Composite Motors

Mixture of ingredients; fuel and oxidizer

Can be single use or reload

Pros

• Higher energy density

• Rubbery material so more resistant to

cracking

• Available in nearly all diameters and

impulse classes

• Optional flame colors

Cons

• More expensive

• Can be difficult to light

4
SPARROW

stem.nasa.gov

Inorganic Oxidizers

• Most common is Ammonium Perchlorate (AP)

• Toxic chlorine gas in exhaust

Fuels

• Common metals used as fuel: powdered Aluminum, Magnesium, Barium, Strontium, Titanium

• Causes exhaust smoke (varying colors)

Binders

• Serves dual purpose as fuel and binder

• Common binders are HTPB, PBAN

Contain small amounts of chemical additives to improve physical properties

• Burn rate, smooth burning, casting characteristics, structural properties, absorb moisture during storage

Composite Propellant

SL teams are limited to Ammonium Perchlorate (AP) motors.

5
SPARROW

stem.nasa.gov

A rocket exceeds the definition of a model rocket under NFPA 

1122 and becomes a high-powered rocket under NFPA 1127 if 

it:

• Uses a motor with more than 160 Newton-seconds of total 

impulse (and ‘H’ motor or larger) or motors that all 

together exceed 320 Newton-seconds

• Uses a motor with more than 80 Newtons average thrust 

(see rocket motor coding)

• Exceeds 62.5 grams of propellant

• Weighs more than 1,500 grams including motor(s)

• Includes any airframe parts of ductile metal

Definitions of HPRs

6
SPARROW

stem.nasa.gov

HPR motors approved for sale in the United States are 

stamped with a two-part code that gives some basic 

information about the motor’s power and behavior:

• A letter specifying the impulse class ("H“)

• Number specifying the average thrust ("225")

HPR motors cannot be purchased over the counter

Special storage, handling, and shipping procedures are 

required. (overseen by Team Mentor)

Rocket Motor Classifications

The SLI team maximum Impulse limit of 2,560 Ns 

translates to a K or lower motor.

7
SPARROW

stem.nasa.gov

The exam is twenty-five (25) questions

The exam consists of a master question bank available 

(with answers) for study

The exam will be distributed to NAR Sections and 

Certification Team members meeting the minimum 

requirements

The exam will be administered by Section Officers and 

JrHPP Certification Team members who are L1 or higher

The exam will be taken and passed prior to the 

certification flight

The exam may be re-taken immediately in case of a 

failure but may only be taken twice in a seven-day period

The exam will comply with any other details and 

processes as with the L2 exam

Junior L1 Rocketry Certification

1. Launch rockets containing multiple motors with a 

total installed impulse of 320.01 Newton-seconds 

to 640 Newton-seconds, or

2. Launch rockets containing a single motor with a 

total installed impulse of 160.01 Newton-seconds 

to 640 Newton-seconds, or

3. Launch rockets that weigh more than 53 ounces 

(1500 grams), or

4. Launch rockets powered by motors not classified 

as model rocket motors per NFPA 1122, e.g.: 

• Average thrust in excess of 80.0 Newtons

• Containing in excess of 125 grams of 

propellant and are limited to only H and I 

motors

National Association of Rocketry 

8
SPARROW

stem.nasa.gov

Student Launch requires use of commercially 

certified motors

Certifying Agencies:

• National Association of Rocketry (NAR)

• Tripoli Rocketry Association (TRA)

• Canadian Association of Rocketry 

(CAR) Motors are occasionally decertified – make sure you are 

using a recent list.

Commercially Certified Motors 

TARC also requires the use of certified motors.

9
SPARROW

stem.nasa.gov

Some of the more popular solid rocket motor manufacturers are 

• Cesaroni Technology Inc. (CTI), Aerotech (AT)

Wide variety in all different impulse and thrust ranges

Reloadable solid rocket motor systems are composed 

• A reusable motor case 

• A reload kit

Commercially Certified Motors

Reloads have 4 standard parts:

• Fuel grains

• Nozzle

• Liner

• O-rings

Cases have 3 standard parts:

• the case

• forward closure

• An aft closure

The motor list in RockSim is neither complete nor always up to date.

10
SPARROW

stem.nasa.gov

Single Use

• Cannot screw up assembly

• Cheaper initial setup, as there is no casing to purchase

• More expensive in the long-run. If you’ll be launching 

mid-power more than 3 times, it’s a better investment 

to get a reload system.

• No casing to replace if you lose your rocket

• Available with both black powder and composite 

propellants.

• Most (with a few exceptions on high power varieties) 

don't require age 18+

• No age requirement for low and mid power SU motors

• No control on delay times (with a few exceptions on 

high power varieties) -- Delays are pre-set, so you need 

to purchase the correct delay.

• Expensive to ship in larger diameters or lengths due to 

HAZMAT requirements (check motor info to see if 

required).

Single Use vs. Reloadable Motors

Reloadable Motors

• Cheaper propellant means lower cost-per-flight. You 

typically save $6-10 per flight.

• Requires casing purchase, so there is a higher initial 

investment. That investment is paid off by cheaper 

propellants.

• Larger variety of options, particularly in more 

powerful motors

• Assembly required, with Aerotech having more steps 

than Cesaroni

• Precise control over delay times (except if it's 

plugged).

• More difficult to find at hobby shops, often require a 

special order or online purchase.

• Age of 18+ verification required (due to access to 

propellant itself)

11
SPARROW

stem.nasa.gov

Aerotech vs. Cesaroni

Aerotech Cesaroni

12
SPARROW

stem.nasa.gov

Aerotech

• Readily available. Typically takes less time to receive 

than Cesaroni motors. Lead time can be up to 6 

weeks.

• All 38mm and larger motors require HAZMAT 

shipping

• You can use up to 3 casing spacers (one more than 

Cesaroni) to reduce the number of casings you need 

for a full arsenal.

• Getting the casing and closures can be more 

expensive than Cesaroni, but you have several 

options for forward and aft closures depending on 

your needs. 

Cesaroni

• Canadian based company so when vendors run 

out the lead time on restock can be very lengthy.

• Since Cesaroni propellant kits come mostly preassembled, you just need to adjust the delay, then 

slide the propellant into the Cesaroni casing. 

• Since the propellant kits are contained in an 

enclosed plastic sheath, you just need to slide that 

out, take a quick paper towel wipe to the casing 

and you’re ready to load up for your next launch.

13
SPARROW

stem.nasa.gov

Aerotech

• Assembly and cleaning of the motors are more time 

consuming. Since Aerotech motors ship piecemeal, it 

can help with shipping costs in some cases, but 

requires careful assembly before use. open-ended 

sheath around the propellant slugs makes residue 

buildup more likely.

• Aerotech offers a few high-power single-use motors. 

This means that there is no expensive casing to 

purchase and potentially lose. While they are 

currently only available in 38mm diameter.

Cesaroni

• All Cesaroni motors are required to ship via 

HAZMAT (average $50 shipping cost), so it’s best 

to order as many as you can at once since the fee 

is per shipped box, not per motor. 

• There are often 7, 8, 9, or more motors that will 

work in each casing, depending on what you like.

• You can use up to two spacers in each casing, so 

you only need the 3-grain and 6-grain casings to 

get the most out of your Cesaroni collection.

14
SPARROW 15 stem.nasa.gov
SPARROW

stem.nasa.gov

A rocket motor must produce enough thrust to overcome the force of gravity

• A rocket motor, at a minimum, must produce enough mechanical energy to achieve a Thrust to Weight Ratio of just 

over 1.0

• The Space Shuttle had a thrust to weight ratio of 1.5 as it left the launch pad

• Nearly 90% of the Space Shuttle was propellant and that ratio would quickly rise as fuel was consumed

For model rocketry, the rule of thumb for thrust to weight is 5:1, as it helps to ensure dynamic stability as soon as 

rocket becomes a free-flyer

• That means that the rocket motor must produce 5 times the force of the weight of your rocket

• The NAR legal minimum is 3:1, however SL requires 5:1.

Thrust to Weight 

SL requires a minimum thrust to weight ratio of 5:1

16
SPARROW

stem.nasa.gov

Thrust Curves

Obtained experimentally for solid rocket motors by:

• Placing the motor on a test stand

• Igniting the propellant

• Recording thrust as a function of time

Total Impulse is most accurately determined by 

calculating the area under the curve

Average thrust is calculated as the total impulse 

divided by the burn time

Burn time is generally considered the time when thrust 

drops below 5% of the maximum thrust

A thrust curve can show whether a motor is:

• Neutral – does not vary more than 10%

• Regressive – Decreasing thrust/surface area

• Progressive – Increasing thrust/surface area

Thrust varies directly with the surface area of propellant 

being combusted

Initial Thrust is vitally important for establishing a rocket’s 

dynamic stability

17
SPARROW

stem.nasa.gov

Thrust Curves

Regressive Progressive Neutral

18
SPARROW

stem.nasa.gov

Questions?
SPARROW

stem.nasa.gov
SPARROW

stem.nasa.gov

Backup Slides

(For those looking more into theory and mathematics of 

propulsion systems)

21
SPARROW

stem.nasa.gov

Solid vs. Liquid Propulsion

Solid Propulsion

Fuel and oxidizer are premixed

Efficiency: 200 – 300 sec ISP

Single use

Compact size, moderate cost: great for throw-away 

stages

Major failures are managed by minimal safe 

distances

Liquid Propulsion

Fuel and oxidizer stored separately

Efficiency: 250 – 450 sec ISP

Can be restarted

Requires tanks, valves

Failures are catastrophic

SL teams are limited to commercial solid motors

22
SPARROW

stem.nasa.gov

Propulsion Theory

Propulsion Systems

Store propellants

Move propellants into a combustion chamber

Burn propellants to raise their energy and pressure 

Expand the combustion gases through a converging-diverging nozzle to achieve high 

exit velocities

Newton’s Laws

1st Law: “Law of Inertia”

• Objects in motion/rest will remain in that state until acted on by an outside force. 

2nd Law: “Law of Momentum” 

• Resultant Force of an object is proportional to the object’s change in momentum

3rd Law: “Law of Action/Reaction”

• Two bodies interact with equal and opposite force

23
SPARROW

stem.nasa.gov

Newton’s Laws and Rocketry

Linear momentum = objects mass x objects velocity. 

Force is equal to the change in momentum per change in time. By 

rearranging we get the below equation

Impulse-momentum theorem. From the equation, we see that the impulse equals the average net 

external force multiplied by the time this force acts. It is equal to the change in momentum.

Fnet = net external Force

∆p = change in momentum

∆t = change in time

By taking the change in each side of the first equation we get this. 

Recall from calculus that 

Assuming we have a constant mass, we can re-write our equation

Thus, 

24
SPARROW

stem.nasa.gov

Newton’s Laws and Rocketry

Recall Newton’s third law, “Two bodies react with equal and opposite force, or 

Worth noting the forces don’t “cancel” because they are acting on 

different objects. We can take the derivative of each side and end up with 

By using p = m*v we replace m1v1 with p1 and similar logic for p2 we end up with

Thus, 

25
SPARROW

stem.nasa.gov

Ideal Rocket Equation

m*v = -v*dm + dm*ve + m*v + m*dv + dm*v + dm*dv, now canceling of terms we’re left with

-ve*dm = m*dv calculus allows us to separate into and then integrate to 1

mm

dd = − 1

vvee

dd

�

mmii

mmff dd

mm

= −1

vvee

�

vvii

vvff

dd By solving this we get ln mmff − ln mmii = −1

vvee

∆v

∆vviiii iiii= vvee[ln mmii − ln mmff = vvee ∗ llll

mmii

mmff

∆vv aaaaaa = ∆vviiii iiii − ∆vTTTTTT − ∆vvDDDD DD − ∆vv

**Note ∆vTTTTTT, ∆vvDDDD DD, ∆vv are dependent on your angle of attack**

Assuming no other external forces

26
SPARROW

stem.nasa.gov

Rocket Thrust Equation and Specific Impulse

TT = mm ∗ vvee + ppee − pp0 ∗ AAee

Assume (fully expanded flow) 

TT = mm ∗ vvee

Specific Impulse Isp=

TT

mm∗ 0

Or TT = mm ∗ gg0 ∗ IIssss

mm ∗ vvee = mm ∗ gg0 ∗ IIssss vvee = gg0 ∗ IIssss

∆vviiii iiii= vvee[ln mmii − ln mmff = vvee ∗ llll

mmii

mmff

∆vviiii iiii= gg0 ∗ IIssss ∗ llll

mmii

mmff

MMMM =

mmii

mmff

= ee � ∆vv

0∗IIssss

mmff = mmii ∗ ee

− � ∆vv

0∗IIssss

Momentum exchange between exhaust & vehicle

All these variables depend on the design of the nozzle

Thrust is generated by a rocket engine through

the reaction of accelerating a mass of gas.

27
SPARROW

stem.nasa.gov

Ideal Rocket Equation

m*v = -(dm)(v-ve) + (m+dm)(v+dv) or m*v = -v*dm + dm*ve + m*v + m*dv + dm*v + dm*dv

28
SPARROW

stem.nasa.gov

Mass Equations

mmii = mmiiii + mmPP/ + mm pp

mmff = mmii − mm pp

MMMM =

mmii

mmff

= ee � ∆vv

0∗IIssss =

mmiiii + mmPP/ + mm pp

mmiiii + mmPP/

ffiiii =

mmiiii

mmiiii + mm pp

mmiiii =

ffiiii ∗ mm pp

1 − ffiiii

ff pp = 1 − ffiiii

mm pp =

mmPP/ (MMMM − 1)(1 − ffiiii )

1 − ffiiii ∗ MMMM

29
SPARROW

stem.nasa.gov

Basic Flavors of Propulsion

Liquid Propellant

• Both fuel and oxidizer are separately stored liquids

• Mechanically complex, expensive, not generally used by amateurs

• Examples: LH2/LOX, kerosene/LOX, alcohol/H2O2, NTO/MMH

• Applicability: Earth Surface and Outer Space

Solid Propellant

• Both fuel and oxidizer are mixed as a solid mass.

• Examples: black powder, ammonium perchlorate propellant

• Applicability: Earth Surface and Outer Space

Hybrid

• Solid fuel, liquid oxidizer

• Examples: plastic/NO2, HTPB/O2, HTPB/NO2, Paraffin/O2

• Applicability: Earth Surface and Outer Space

30
SPARROW

stem.nasa.gov

Basic Flavors of Propulsion

Monopropellant

• Catalyzes a propellant to generate hot, high- pressure

• Examples: hydrazine, H2O2

• Applicability: Outer Space mostly

Electric

Electrical ions generate thrust

Very low thrust, very high efficiency

Applicability: Outer Space only

31
SPARROW

stem.nasa.gov

Specific Impulse

• Isp is a measure of efficiency for rockets, as mpg is to 

automobiles

• Measure of the work (thrust) per unit mass of propellant, 

measured in seconds

• shows the tie between engine parameters and propulsion 

thermodynamic parameters like exit velocity

• The rocket weight will define the required value of thrust

• HPR solid rocket motors generally have an Isp between 170 

sec and 220 sec

• It gives us an easy way to "size" an engine during preliminary 

analysis

Propellant Combination Specific Impulse Isp

Lox/Kerosene (RP-1, 

Falcon)

300s

Methane/Lox (Starship) 

(1/4 cost)

380s

Lox/H2 450s

Li-F (1950’s) 542s

NERVA (Nuclear Engine 

ended in 1970s

850s

Isp=

TT

mm∗ 0

32
SPARROW

stem.nasa.gov

Solid Rocket Motors

Typical space exploration applications of SRMs include:

• Launch vehicle booster

• Kick stages for geosynchronous and interplanetary spacecraft

• Breaking motors for interplanetary spacecraft

Every solid rocket motor has:

• Nozzle

• Combustion chamber

• Solid propellant 

• Igniter

SRMs are extensively used where:

• Total impulse requirement is known accurately in advance 

• Where no restart is required 

There are two types of solid rocket motors that you will see in sport rocketry:

• Black powder motors 

• Composite propellant motors

33