Introduction and classification

What is Jet Propulsion?¶

Jet propulsion is a method of generating thrust by expelling mass in one direction (a “jet”), which produces a reaction force in the opposite direction. This fundamental principle underlies all rocket and jet engines, from the simple water rocket to the powerful engines that launch spacecraft into orbit.

Thrust and Newton’s Third Law¶

Thrust is the force created due to a change in momentum by ejecting mass from a system. The principle governing thrust is Newton’s Third Law of Motion: every action has an equal and opposite reaction. When a propulsion system expels mass (such as hot gases), it experiences an opposite force that propels the vehicle forward.

Mathematically, thrust can be understood through the conservation of momentum. As mass is expelled at high velocity, the momentum change of the ejected mass equals the momentum change of the vehicle, but in the opposite direction. A common engineering form for rocket thrust that we’ll derive later is

where $\dot{m}$ is the mass flow rate (kg/s) and $V_e$ is the exit velocity of the exhause (m/s), giving the thrust force $T$ (N).

In terms of rocket design, from Equation (1) we see there are two primary ways to increase thrust:

1. maximize the exhaust velocity, $V_e$, or

2. increase the mass flow rate $\dot{m}$.

As we will see later, for most rocket types, $V_e$ comes from a combination of the chemical energy stores in the propellants and the nozzle design, while $\dot{m}$ is mainly a function of the engine/motor size.

With this basic definition of a rocket in mind, how can we compare the performance of different rocket types?

Specific Impulse¶

Specific impulse (Isp) is a fundamental performance metric for rocket engines that measures the efficiency of propellant use. It represents the impulse (change in momentum) per unit mass of propellant consumed:

where $g_0 = 9.8066 \,\text{m}/\text{s}^2$ is the acceleration due to gravity at sea level on Earth.
Specific impulse has units of seconds and can be thought of as how long one kilogram of propellant can produce one newton of thrust.

Higher specific impulse values indicate more efficient engines that can produce more thrust per unit of propellant, allowing for greater vehicle performance or reduced propellant requirements.

A brief history of rocket propulsion¶

From Hero to von Braun.

Ancient origins: Hero of Alexandria (10–70 CE)¶

The earliest known demonstration of reactive thrust comes from Hero of Alexandria, a Greco-Egyptian mathematician and engineer. Hero created the aeolipile (Hero engine), a steam-powered device that demonstrated the principle of jet propulsion.

The aeolipile operated by heating water to generate steam. The high-pressure steam escaped tangentially through nozzles, generating thrust that caused the sphere to rotate. While Hero’s device demonstrated reactive thrust, there was no mathematical explanation for the phenomenon until Newton’s laws of motion were formulated centuries later.

Chinese rockets (10th–13th century CE)¶

The practical development of rocket propulsion began in China during the 10th century with the invention of black-powder rockets and fireworks. These early rockets used gunpowder as the propellant.

By the 13th century, rockets had evolved from entertainment devices to weapons of war. They were reportedly used in battle during the Mongol invasion of China in 1232 CE. These rocket weapons were later described in detail in the Huolongjing (“Fire Drake” or “Fire Dragon Manual”), compiled around 1400 CE.

The technology gradually spread beyond China to Mongolia, the Middle East, India, Korea, and eventually reached Europe, where it would continue to evolve.

Congreve rocket (early 19th century)¶

William Congreve (1772–1827) developed a new generation of rocket artillery for the British military. His designs were inspired by rockets used against the British East India Company in India. The Congreve rocket came in various sizes ranging from 6 to 300 pounds and represented a significant advancement in rocket warfare.

These rockets were deployed extensively during the Napoleonic Wars and the War of 1812. They were reportedly used by both Union and Confederate forces during the American Civil War. The Congreve rocket represented the first systematic European development of military rocket technology.

Jules Verne and science fiction (1878)¶

In 1878, science fiction author Jules Verne published From the Earth to the Moon, which captured the public imagination about space travel. In the novel, Verne used a giant cannon called the Columbiad to fire a manned projectile at the Moon from Florida. The spacecraft carried a crew of three.

While Verne’s vision was prescient in many ways—including the Florida launch location and a three-person crew—the technology to achieve the necessary velocities using a cannon did not exist and would prove impractical due to the extreme accelerations involved.

The Fathers of Modern Rocketry (early 20th century)¶

Three pioneers are credited as the “Fathers of Modern Rocketry” for their theoretical and practical contributions in the early 20th century:

• Konstantin Tsiolkovsky (Russian teacher and mathematician)

• Dr. Robert Goddard (American engineer and professor)

• Hermann Oberth (Austro-Hungarian-born German physicist and engineer)

Additionally, Robert Esnault-Pelterie, a French aircraft designer and spaceflight theorist, made important contributions to nuclear propulsion concepts and interplanetary travel theory.

Konstantin Tsiolkovsky (1857–1935)¶

Tsiolkovsky was the first to advocate for liquid propellant rocket engines in 1903. His most enduring contribution is the rocket equation (also called the Tsiolkovsky rocket equation), which relates the rocket engine exhaust velocity to the change in velocity of the vehicle:

where:

• $\Delta V$ is the change in velocity

• $V_e$ is the exhaust velocity

• $m_0$ is the initial mass

• $m_f$ is the final mass

This equation remains fundamental to rocket propulsion analysis today, and we will derive it.

Dr. Robert Goddard (1882–1945)¶

Dr. Goddard made crucial practical contributions to rocket technology:

• 1914: Filed patents for rocket nozzles, liquid propellant feed systems, and multi-stage rockets

• 1926: Successfully launched the first modern rocket using gasoline and liquid oxygen, establishing the foundation for modern rocket technology

• Applied the de Laval nozzle (converging-diverging nozzle) to rockets, which remains the standard design today

Goddard’s experimental work transformed rocketry from theory to practical engineering.

Hermann Oberth (1894–1989)¶

In 1923, Oberth published The Rocket into Planetary Space, influenced by Jules Verne’s science fiction. He proposed using hydrogen and alcohol as fuels and later conducted experiments with liquid oxygen and gasoline. Oberth’s work helped establish the theoretical foundations for space travel and inspired many future rocket engineers.

Wernher von Braun (1912–1977)¶

Von Braun represents both the technological advancement and the moral complexity of rocket development:

• Designed the V-2 rocket for Nazi Germany during World War II

• Had ambiguous and disputed involvement with the Nazi party and SS

• Oversaw and benefited from slave labor at the Peenemünde rocket factory

• Brought to the United States in Operation Paperclip following WWII

• Built upon Goddard’s earlier rocket work

• Became the chief architect and engineer of the Saturn V heavy-lift launch vehicle for the Apollo moon missions

• Played a major role in NASA’s development and advocated for crewed missions to Mars and STEM/space education outreach

Women in rocket propulsion and spaceflight development¶

While the “Fathers of Modern Rocketry” are well known, numerous women made critical contributions to rocket propulsion and space exploration, often facing significant barriers based on gender and race.

The “Human Computers” at JPL and NASA¶

Teams of women mathematicians, known as “human computers,” performed the complex calculations necessary for rocket trajectory design and mission planning from the 1940s through the 1960s at both NASA’s Jet Propulsion Laboratory and Langley Research Center.

At JPL, Barbara “Barby” Canright calculated trajectories for America’s first satellite, Explorer 1, while Macie Roberts supervised the computing section. These women performed trajectory calculations, propellant performance analysis, and mission planning for early missile and planetary exploration programs.

At NASA Langley, African American women mathematicians worked in the segregated West Area Computing unit, making groundbreaking contributions despite facing both racial and gender discrimination:

Katherine Johnson (1918–2020) calculated trajectories for Alan Shepard’s Freedom 7 mission and John Glenn’s Friendship 7 orbital flight. Glenn specifically requested that Johnson verify the electronic computer’s calculations before his flight. Her work was also crucial for Apollo 11 and the Space Shuttle program. She received the Presidential Medal of Freedom in 2015.

Dorothy Vaughan (1910–2008) became NACA/NASA’s first African American supervisor in 1949. When IBM computers were introduced, she taught herself and her staff FORTRAN, becoming one of the first female FORTRAN programmers, and contributed to the Scout Launch Vehicle Program.

Mary Jackson (1921–2005) became NASA’s first African American female engineer in 1958, analyzing data on air flow, thrust, and drag forces to improve aircraft and spacecraft design.

Christine Darden (1942–) joined Langley in 1967 and became an aerospace engineer specializing in supersonic flight and sonic boom research, eventually becoming the first African American woman promoted to the Senior Executive Service at NASA.

These contributions were documented in Hidden Figures Shetterly, 2016, which was also adapted into a movie in 2016, and all four women were awarded Congressional Gold Medals in 2024.

Engineering leadership in spacecraft and launch systems¶

Mary Sherman Morgan (1921–2004) was an American chemist and engineer who developed Hydyne, a high-performance rocket fuel used in the Jupiter-C launch vehicle. Hydyne enabled the higher performance needed for the Explorer 1 launch (first U.S. satellite) Morgan, 2013.

Margaret Hamilton (b. 1936) led development of Apollo flight software at MIT Instrumentation Lab, including core ideas around software engineering and the fault-tolerant behavior that helped Apollo 11 succeed despite computer overload alarms.

Frances “Poppy” Northcutt (b. 1943) part of the team doing return-to-Earth trajectory calculations and mission operations for Apollo, becoming one of the first women in NASA mission control.

Yvonne Brill (1924-2013) was a pioneering rocket propulsion engineer who fundamentally changed satellite technology. She began her career at Douglas Aircraft in the 1940s working on rocket propellants and engines, believed to be the only woman rocket scientist in the United States at that time. Her most significant contribution was inventing the electrothermal hydrazine thruster (EHT), which increased satellite fuel efficiency by approximately 50%. This innovation became an industry standard, with hundreds of these engines launched into space.

Brill also contributed to propulsion systems for NASA’s TIROS weather satellite, the Nova rockets for Apollo missions, and served as director of NASA’s Space Shuttle Solid Rocket Motor Program (1981-1983). She received the National Medal of Technology and Innovation in 2011.

Takeaways¶

Even “pure propulsion” achievements (new propellants, injectors, turbopumps, nozzles) only matter if the system can navigate, control, and survive the mission environment. Many historical women contributors worked in the “glue” disciplines—computing, GN&C, verification—that make propulsion useful.

Categorization of propulsion systems¶

Air-breathing vs. rocket propulsion¶

Propulsion systems can be fundamentally divided into two categories based on whether they carry their oxidizer or not:

Rocket propulsion¶

• All propellants carried onboard (both fuel and oxidizer, or single monopropellant)

• Propellants are ejected to produce thrust

• Can operate both in and out of the atmosphere (including in vacuum)

• Thrust and exhaust velocity are independent of flight speed

• Examples: liquid rocket engines, solid rocket motors

Air-breathing propulsion¶

• Only carries fuel onboard; obtains oxidizer from atmospheric air

• The majority of thrust comes from acceleration of air, combined with high mass flow rate

• The air is “free” from the atmosphere, reducing the mass that must be carried

• Exhaust velocity and flight speed are connected

• Cannot operate outside the atmosphere

• Examples: turbojets, turbofans, ramjets

Advantages and disadvantages¶

Air-breathing propulsion:

• ✓ Advantages: Much higher fuel efficiency for atmospheric flight and higher specific impulse; reduced propellant mass

• ✗ Disadvantages: Cannot operate in vacuum; performance depends on atmospheric conditions (thrust drops with increasing altitude); limited to lower speeds (except for ramjets/scramjets)

Rocket propulsion:

• ✓ Advantages: Can operate anywhere (atmosphere or vacuum); performance independent of flight speed; can achieve very high velocities

• ✗ Disadvantages: Must carry both fuel and oxidizer, resulting in lower mass efficiency and lower specific impulse; requires large propellant tanks

Types of rocket propulsion¶

Rocket propulsion systems can be categorized into four main types:

1. Chemical (liquid, solid, hybrid)

2. Cold gas

3. Nuclear (thermal, electric)

4. Electric (electrothermal, electrostatic/ion)

Chemical rocket propulsion¶

Chemical rockets use chemical reactions in one or more propellants to produce high temperatures in the thrust/combustion chamber. A converging-diverging nozzle then converts the thermal energy (i.e., enthalpy) into high kinetic energy, which is exhausted to produce thrust.

Chemical rockets are subdivided into three main categories:

Liquid propellant engines¶

Liquid rocket engines store propellants as liquids in tanks and feed them into a combustion/thrust chamber where chemical energy is released. The hot gases produced in the thrust chamber are then accelerated through a supersonic nozzle.

Bipropellant systems use separate fuel and oxidizer (e.g., liquid oxygen (LOX) and kerosene, or LOX and liquid hydrogen). The two propellants are injected into the combustion chamber where they react.

Monopropellant systems use a single liquid propellant that decomposes into hot gases when passed over a catalyst. Hydrazine is a common monopropellant.

Advantages:

• Thrust can be controlled and throttled

• Can be shut down and restarted

• High specific impulse (300–460 seconds for bipropellants)

• Suitable for large launch vehicles

Disadvantages:

• Complex feed systems with pumps and valves

• Requires propellant handling and storage systems, particularly challenging for cryogenics

• More expensive and complex than solid motors

Solid rocket motors¶

Solid rocket motors combine propellant storage, feed system, and thrust chamber into a single case. The fuel and oxidizer are mixed together into a solid grain that is cast or molded into the motor case.

Once ignited, the highly reactive mixture burns until the propellant is completely exhausted. The burn rate and thrust profile are determined by the grain geometry and propellant composition.

Advantages:

• Simple design with few moving parts

• High reliability

• Long storage life

• Immediate readiness (no fueling required)

• High thrust for launch applications

Disadvantages:

• Cannot be throttled or shut down once ignited

• Lower specific impulse (150–350 seconds) compared to liquid bipropellants

• Structural integrity concerns with large grain castings

• Safety concerns with large quantities of propellant

Hybrid propellant systems¶

Hybrid rocket systems combine the best features of liquid and solid rockets. The typical configuration uses a solid fuel grain stored in the thrust chamber, with a feed system that supplies liquid or gaseous oxidizer. The oxidizer flows over the solid fuel, causing it to gasify and react, producing hot gases.

Advantages:

• Safer than solid or liquid systems (oxidizer and fuel stored separately)

• Can be throttled and shut down (by controlling oxidizer flow)

• Simpler than liquid bipropellant systems

• Better performance than solid motors

Disadvantages:

• More complex than solid motors

• Fuel regression rate can be difficult to predict

• Lower performance than liquid bipropellants

• Limited flight heritage / demonstrations

Cold gas propulsion¶

Cold gas systems use stored high-pressure gas as the working fluid. Common gases include air, nitrogen, and helium. The gas is exhausted through a nozzle to produce thrust. These are often used for thrusters, with applications including low thrust maneuvers and attitude control.

Advantages:

• Very simple and reliable

• No combustion or cooling issues

• Low cost

• Ideal for low-thrust maneuvers and attitude control

Disadvantages:

• Requires heavy, high-pressure tanks

• Low performance (Isp: 60–250 seconds)

• Limited total impulse capability

Warm gas systems heat the gas before expansion to achieve higher performance, though this adds complexity.

Nuclear propulsion¶

Nuclear propulsion uses nuclear reactions as the energy source rather than chemical reactions.

Nuclear thermal propulsion¶

Nuclear thermal rockets operate similarly to liquid propellant engines, but nuclear fission supplies heat to a working fluid (typically hydrogen) instead of chemical combustion. The working fluid is heated to very high temperatures by passing through a nuclear reactor core, then expanded through a nozzle.

Performance: Very high specific impulse (800–1,000 seconds), approximately double that of chemical rockets.

Nuclear electric propulsion¶

Nuclear electric systems use a nuclear powerplant to produce electricity, which then powers an electric rocket propulsion system.

Advantages:

• Very high specific impulse

• High efficiency for deep space missions

• Large total impulse capability

Disadvantages:

• High system complexity and mass

• Nuclear safety concerns

• Regulatory and political challenges

• Radiation shielding requirements

Electric propulsion¶

Electric propulsion systems use electricity to add energy to the propellant. These systems offer very high specific impulse but relatively low thrust magnitude.

Electrothermal systems¶

Electrothermal thrusters (resistojets and arcjets) heat the propellant electrically, then expand it through a nozzle. Working fluids include hydrogen, ammonia, and helium. Used for satellites since the 1970s.

Electrostatic/ion propulsion¶

Ion propulsion systems ionize the working fluid (typically xenon) and then use electric fields to accelerate the electrically charged heavy ions to very high velocities.

Advantages:

• Very high specific impulse (500–10,000 seconds)

• Excellent for long-duration missions

• High propellant efficiency

Disadvantages:

• Very low thrust (0.0005–20 N)

• Requires significant electrical power

• Long firing times needed to achieve velocity changes

• Not suitable for launch or high-acceleration maneuvers

Performance and typical applications¶

The following table summarizes the performance characteristics and typical applications for various propulsion technologies:

Application insights¶

• Launch vehicles require very high thrust, typically provided by liquid bipropellant or solid rocket motors

• Orbit insertion requires moderate to high thrust and good efficiency, suited to liquid or solid systems

• Orbit maintenance (station-keeping) can use low-thrust, high-efficiency systems like electric or monopropellant

• Attitude control requires precise, small thrust levels, typically from cold gas or monopropellant systems

The choice of propulsion system depends on mission requirements, including required thrust level, total velocity change, mission duration, and available power.

Key takeaways¶

• Thrust comes from momentum change by expelling mass (Newton’s 3rd Law).

• Rockets are self-contained (carry fuel + oxidizer), enabling operation in space; air-breathers trade that for atmospheric intake and coupling to flight speed.

• Rocket propulsion spans a wide design space (chemical, cold gas, nuclear, electric) with major tradeoffs between thrust, specific impulse, complexity, and mission fit.