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There's A Reason It's Called Rocket Science

Scott Neuman

An Atlas missile is launched from Cape Canaveral, Fla., in October 1964. Cape Canaveral has been the site of numerous launch failures as the United States developed missile and rocket technology. Fox Photos/Getty Images hide caption

An Atlas missile is launched from Cape Canaveral, Fla., in October 1964. Cape Canaveral has been the site of numerous launch failures as the United States developed missile and rocket technology.

North Korea this week quite literally demonstrated an old truism, with the world as an anxious witness. It turns out that reaching space is, as the saying goes, as tough as rocket science.

The much hyped launch of the Unha-3 rocket, which North Korea said was meant to place a satellite into orbit to celebrate the centenary of the country's "Great Leader" Kim Il Sung, apparently failed Friday shortly after launch. It was the fourth time North Korea had tried and failed to do it, adding to the growing worldwide history of failed rocket launches.

So why is missile and rocket technology so difficult to get right?

Failure Is Always An Option

Jim Walsh, a research associate at the Massachusetts Institute of Technology's Security Studies Program, says the first thing to consider is that lots of things can go wrong.

"A rocket is an extremely complex device. There are millions of pieces and therefore millions of opportunities to make errors — to make errors in calculations, to make errors in construction," Walsh says.

One of the biggest technical challenges to getting a satellite into orbit — or a long-range missile to its target — is "getting the staging right, so that the separation and ignition occurs at the right time and in such a way that it doesn't change the rocket's trajectory," says Greg Thielmann, a senior fellow at the Washington, D.C.-based Arms Control Association.

The more stages, the greater the difficulty. Like most satellite launch vehicles, the Unha-3 is a three-stage vehicle.

"It's not just that adding a second stage just makes it doubly difficult or that adding three stages makes it three times as difficult," says Walsh. "It goes beyond that. You're trying to integrate those stages and, in this case, carry a payload into orbit. So, it's substantially more challenging and that's why you have so many failures."

And in rocket science, failure is always an option, says Walsh. He points out that while the capability to launch either a spacecraft or a warhead is substantially the same, producing a nuclear bomb such as the one North Korea successfully tested in 2006 "turns out to be far easier to do than to develop a three-stage rocket that can carry it halfway around the world."

A Shallow Talent Pool

For Pyongyang, the talent pool for engineers and rocket scientists is shallow. While some of that expertise exists elsewhere, it takes thousands of qualified individuals, Walsh says.

"Think NASA in the 1960s. It had lots of failures along with lots of successes, but NASA had lots of cash and tens of thousands of employees as well as hundreds of thousands of industrial and university contractors," he says.

What you really need to launch satellites is people who have had experience — and lots of it — at getting things wrong, says Guy Ben-Ari, deputy director and senior fellow with the Defense-Industrial Initiatives Group at the Center for Strategic and International Studies.

"It's not enough to have access to the published papers, the plans and the documents," he says. "You really need to have a talent pool that has experience working on these issues."

There's another complexity that may be more important than the complicated inner workings of a rocket. It has less to do with technology than it does culture, says Ben-Ari.

"How do you structure an organization with so many working parts that need to come together for a common goal? How do you incentivize the right amount of risk-taking, how do you manage knowledge and information-sharing among different parts of the organization? That's not easy," he says.

Even in the United States, those hundreds of thousands of individuals worked together under the NASA rubric that eventually sent men to the moon. In North Korea, a society in which the individual consequences of failure could be quite severe, creating a workable management structure could be supremely difficult, says Walsh.

"In a society like North Korea, people are risk-averse and extremely cautious. That's probably not the best culture for a huge, technical endeavor like this," he says. "When mistakes happen, they may not get corrected out of fear."

The evidence that North Korea's rocket program may suffer from disorganization goes beyond the obvious string of failures, says the Arms Control Association's Thielmann.

"We can see evidence that they are digressing from a well-managed program," he says.

Practice (At Failure) Makes Perfect

Each of the four failed launches involved a different staging configuration, he says.

"Testing is everything in a rocket program, and you can't control the variables that way," Thielmann says. "The more you change things around, the less likely you are to get usable results."

If North Korea is going to successfully weaponize its nuclear arsenal so it has the capability to rain warheads on the West, it's going to take a lot more work, Thielmann says.

"That means they are going to need a warhead that is small enough and can survive the immense vibration of re-entry and they are going to need the telemetry to test it," he says.

Thomas Donnelly, a defense and security expert at the American Enterprise Institute, acknowledges that North Korea's rocket program faces some steep obstacles. At its core, ballistic missile technology is still rocket science — but it's getting easier, he said.

"As it was for us, the engineering challenges are difficult," he says. "But you're not inventing new science here. You just need the resources to do this repeatedly. This is definitely a case of practice makes perfect."

Sooner or later, North Korea will have rockets that work, he warns.

"Relying on them to fail is not a great plan. They are trodding a path that many nations have trod before," he says.

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Demystifying Rocket Science: Just How Difficult Is It?

Space travel and rocket science have an aura of complexity and mystique in popular culture. The phrase “it’s not rocket science” is often thrown about to imply that a concept is relatively simple or straightforward. But exactly how difficult is the real science behind rockets?

In short: Extremely. Rocket science requires an intricate blend of advanced physics, mathematics, aerospace engineering, and computer science. If you’re curious to learn more about the demanding fields and complex concepts that real-world rocket scientists tackle, read on for a comprehensive overview.

Understanding Advanced Physics Concepts

When it comes to rocket science, understanding advanced physics concepts is crucial. These concepts form the foundation of the field and are essential for designing and launching successful rockets. Let’s delve into some of the key concepts that are integral to rocket science.

Newton’s Laws of Motion

One of the fundamental principles in rocket science is Newton’s Laws of Motion. These laws explain how objects move and interact with each other. The three laws state that an object will remain at rest or continue to move in a straight line unless acted upon by an external force, the rate of change of momentum of an object is directly proportional to the force applied to it, and for every action, there is an equal and opposite reaction.

These laws are fundamental to understanding the forces involved in rocket propulsion and trajectory calculations.

Thermodynamics

Thermodynamics is another crucial concept in rocket science. It deals with the study of heat transfer and energy conversion. Rockets rely on the principles of thermodynamics to convert chemical energy from propellants into the kinetic energy needed for propulsion.

Understanding thermodynamics allows engineers to optimize rocket engines for maximum efficiency and performance.

Propulsion is at the heart of rocket science. It involves the study of how rockets generate thrust to overcome gravitational forces and achieve escape velocity. Rocket engines work by expelling high-velocity exhaust gases in the opposite direction, according to Newton’s third law of motion.

The design and efficiency of propulsion systems play a critical role in determining a rocket’s performance and payload capacity.

Aerodynamics

Aerodynamics is the study of how objects move through the air or any fluid. In rocket science, it is vital to understand the aerodynamic forces acting on a rocket during its ascent and re-entry. Factors such as drag, lift, and stability need to be carefully considered to ensure the rocket can maneuver effectively and withstand the extreme conditions it encounters during its flight.

Astrophysics

Astrophysics plays a significant role in rocket science, particularly in the exploration of space. It involves the study of celestial objects, their properties, and the physical processes that occur in the universe.

Understanding astrophysics helps scientists and engineers navigate the challenges of space travel, such as gravitational forces, radiation, and the behavior of celestial bodies.

By gaining a solid understanding of these advanced physics concepts, researchers and engineers can continue to push the boundaries of rocket science and explore the vast expanse of space. If you’re interested in learning more about rocket science and its various concepts, you can visit reputable websites like NASA or SpaceX for further information and resources.

Applying Complex Mathematics

When it comes to rocket science, one cannot underestimate the importance of complex mathematics. The field of aerospace engineering heavily relies on mathematical principles to design and analyze the behavior of rockets.

This article will explore some of the key areas of mathematics used in rocket science.

Calculus plays a fundamental role in understanding the motion of rockets. By utilizing calculus, engineers can determine the velocity, acceleration, and trajectory of a rocket at any given point in time.

This helps in predicting the path that a rocket will take and enables engineers to make necessary adjustments to ensure a successful launch. Calculus is also used in optimizing fuel consumption and maximizing the efficiency of rocket engines.

Differential Equations

Differential equations are another essential tool in rocket science. They describe the relationship between the rate of change of a variable and the variables themselves. Rocket engineers use differential equations to model the behavior of various factors such as airflow, pressure, and thrust.

By solving these equations, engineers can analyze and predict how different parameters will affect the performance of a rocket.

Linear Algebra

Linear algebra is extensively used in rocket science for a variety of purposes. It is employed in solving systems of linear equations, which are commonly encountered in rocket design and optimization. Linear algebra also helps in analyzing the stability and control of rockets by representing their motion as linear transformations.

Additionally, it plays a crucial role in the field of guidance, navigation, and control systems.

Probability and Statistics

Probability and statistics are vital in assessing the reliability and safety of rocket systems. Engineers use statistical analysis to evaluate the likelihood of failures and accidents, allowing them to design robust systems that can withstand unforeseen events.

Probability theory is employed in estimating the probability of successful missions and calculating the risk associated with different launch scenarios.

Understanding and applying these complex mathematical concepts is not an easy task. It requires a strong foundation in mathematics and a deep understanding of the principles underlying rocket science. However, with the advancements in computational tools and simulation techniques, engineers are now able to tackle complex mathematical problems more efficiently than ever before.

For further information on the role of mathematics in rocket science, you can visit NASA’s official website or refer to scientific journals such as the Aerospace Science and Technology journal.

Key Principles of Aerospace Engineering

Structural design.

The field of aerospace engineering encompasses the design and construction of various structures used in aerospace technology. In particular, structural design in aerospace engineering focuses on creating robust and lightweight structures that can withstand the extreme conditions experienced during space travel.

Engineers in this field utilize advanced computer-aided design (CAD) software to develop and analyze the structural integrity of components such as airframes, wings, and fuselages. They also consider factors like aerodynamics, material properties, and load distribution to ensure optimal performance and safety.

Materials Science

Materials science plays a vital role in aerospace engineering as it involves the study and development of materials with specific properties required for space exploration. Engineers in this field work on finding materials that are lightweight, yet strong enough to withstand the stresses and temperature variations encountered in space.

They also consider factors like thermal conductivity, corrosion resistance, and radiation shielding capabilities. Advanced materials such as carbon composites, titanium alloys, and ceramic matrix composites are commonly used in aerospace applications due to their exceptional properties.

Propulsion Systems

Propulsion systems are at the heart of aerospace engineering, as they are responsible for generating the necessary thrust to propel a spacecraft or aircraft. These systems involve the study and design of engines, rockets, and thrusters that enable vehicles to overcome the Earth’s gravitational pull and achieve high speeds.

Engineers in this field focus on optimizing fuel efficiency, minimizing emissions, and enhancing thrust performance. They utilize concepts from thermodynamics, fluid mechanics, and combustion science to develop innovative propulsion systems that can withstand the harsh conditions of space.

Control Systems

Control systems are crucial for maintaining stability, maneuverability, and guidance of aerospace vehicles. Engineers in this field design and implement control algorithms and systems that regulate the movement and orientation of spacecraft or aircraft.

These systems utilize sensors, actuators, and feedback mechanisms to monitor and adjust various parameters such as altitude, speed, and attitude. Control systems in aerospace engineering rely on advanced technologies like inertial navigation systems, autopilots, and fly-by-wire systems to ensure precise control and safe operation of vehicles.

Spacecraft Design

Spacecraft design encompasses the overall architecture, layout, and integration of various systems required for space missions. Engineers in this field collaborate with experts from different disciplines to develop spacecraft that can fulfill specific objectives, such as satellite deployment, human space exploration, or interplanetary missions.

They consider factors like payload capacity, power requirements, communication systems, and life support systems to design efficient and reliable spacecraft. The design process involves extensive analysis, simulations, and testing to ensure the spacecraft’s functionality and safety in the challenging environment of space.

Leveraging Cutting-Edge Computer Science

When it comes to rocket science, leveraging cutting-edge computer science plays a crucial role in various aspects of the field. From modeling and simulation to software development, data analysis, and even machine learning and AI, computer science has revolutionized the way we approach and understand the complexities of rocket science.

Modeling and Simulation

One of the key areas where computer science has had a significant impact in rocket science is through modeling and simulation. By utilizing advanced algorithms and computational techniques, scientists and engineers can create accurate virtual models of rockets and their surrounding environments.

These models allow them to predict and analyze the behavior of rockets under different conditions, enabling them to optimize designs, identify potential issues, and make informed decisions before physical testing even begins.

This not only saves time and resources but also enhances the overall safety and efficiency of rocket launches.

Software Development

Software development is another critical aspect of leveraging computer science in rocket science. Rocket systems are highly complex and require sophisticated software to control various operations such as navigation, propulsion, and communication.

Computer scientists work closely with engineers to develop robust and reliable software solutions that can handle the demanding requirements of space missions. From real-time data processing to fault tolerance and error handling, these software systems are designed to ensure the smooth and successful execution of rocket launches.

Data Analysis

With the advancement of technology, rocket science has become increasingly data-driven. Massive amounts of data are collected during rocket launches, including telemetry data, sensor readings, and environmental data.

Computer scientists play a crucial role in analyzing this data to extract valuable insights and improve the performance of future missions. Through sophisticated algorithms and statistical techniques, they can identify patterns, anomalies, and trends that may be crucial for enhancing rocket design, optimizing trajectories, and mitigating risks.

Machine Learning and AI

Machine learning and artificial intelligence (AI) have also found their way into the realm of rocket science. These technologies have the potential to revolutionize various aspects of the field, from autonomous navigation and decision-making to predictive maintenance and anomaly detection.

By training algorithms on vast amounts of historical data, scientists and engineers can develop intelligent systems that can learn from past experiences and make informed decisions in real-time. This not only enhances the overall performance and reliability of rockets but also opens up new possibilities for space exploration and discovery.

Challenges at Every Stage

When it comes to rocket science, there are numerous challenges that engineers and scientists face at every stage of the process. From designing the rocket to testing it, from manufacturing limitations to budget and time constraints, and even the possibility of failures and disasters, the journey of building a rocket is no easy feat.

Design Process and Testing

The design process of a rocket involves intricate calculations, simulations, and careful considerations of various factors such as aerodynamics, materials used, and payload requirements. Engineers need to ensure that the design is both efficient and safe, as any flaws in the design can have catastrophic consequences.

Extensive testing is conducted to validate the design and ensure that it meets the required standards for performance and safety. The process involves testing various components, propulsion systems, and even full-scale prototypes, all of which require meticulous attention to detail and precision.

Manufacturing Limitations

Manufacturing a rocket involves complex processes and materials that are often limited in terms of availability and capability. The materials used need to withstand extreme temperatures, pressures, and forces, making the manufacturing process highly specialized and challenging.

Additionally, the scale of manufacturing for rockets is relatively low compared to other industries, which can lead to limited resources and specialized expertise. Overcoming these limitations requires innovative approaches and collaboration with various industries and research institutions.

Budget and Time Constraints

Building a rocket is a costly endeavor that requires significant financial resources. The development, testing, and manufacturing processes all require substantial investments. Furthermore, the timeline for building a rocket is often constrained by various factors such as funding availability, project deadlines, and launch windows.

Meeting these budget and time constraints can be a daunting task, requiring careful planning, prioritization, and efficient resource management.

Failures and Disasters

Failures and disasters are an unfortunate reality in rocket science. Despite meticulous planning and testing, there is always a risk of something going wrong. One of the most well-known examples is the Challenger disaster in 1986, which resulted in the loss of seven crew members.

Such incidents highlight the importance of continuous improvement, rigorous safety protocols, and thorough investigations to prevent similar tragedies from occurring in the future.

Contrary to popular belief, real-world rocket science requires mastery of several highly complex STEM fields. The level of scientific depth, mathematical precision, engineering expertise, and problem-solving ability needed is immense.

While the challenges are great, the intricacy and multifaceted nature of rocket science is what makes it such a rewarding and fascinating field for those passionate about the cosmos and advanced technology.

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Rockets educator guide.

Grade Levels

Grades K-4, Grades 5-8, Grades 9-12

Engineering Design, History, Mathematics, Physical Science, Technology, Scientists and Inventors, Timelines, Geometry, Measurement and Data Analysis, Trigonometry, Forces and Motion, Physics, Rocketry

Educator Guides, Lesson Plans / Activities

Few classroom topics generate as much excitement as rockets. The scientific, technological, engineering and mathematical foundations of rocketry provide exciting classroom opportunities for authentic hands-on, minds-on experimentation. The activities and lesson plans contained in this educator guide emphasize hands-on science, prediction, data collection and interpretation, teamwork, and problem solving. The guide also contains background information about the history of rockets and basic rocket science. The rocket activities in this guide support national curriculum standards for science, mathematics and technology.

The guide contains new and updated lessons and activities from the original Rockets Educator Guide.

Introductory Pages A Pictorial History of Rockets What Comes Next How Rockets Work Applying Newton’s Laws Rocket Activities Pop Can Hero Engine 3…2…1…PUFF! Heavy Lifting Newton Car Rocket Races Pop! Rocket Launcher Directions Pop! Rockets Foam Rocket Launch Altitude Tracker Water Rocket Launcher Directions Water Rocket Construction Project X-51

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Rocket Physics

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Classical mechanics.

Hardcore training for the aspiring physicist.

• Ahmed Khalefa
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Rocket physics plays a crucial role in the modern world. From launching satellites into orbit to testing Intercontinental Ballistic Missiles (ICBMs), principles of rocket mechanics have innumerable applications. The history of rockets goes back to the first century Chinese who used rockets as fireworks to ward off bad spirits, and since then rockets have evolved tremendously. The principles behind rocket propulsion describe a fundamental kind of motion, and to understand it, we need to be familiar with Newton's laws of motion.

What are rockets?

Velocity of a rocket as a function of mass, impulse of a rocket, parts of a rocket, structural and payload system of a rocket, guidance and propulsion system of a rocket.

A rocket is a cylindrical projectile that can be propelled to a great height or distance by the combustion of its contents, used typically as a firework or signal, and used for scientific purposes as an engine to carry payloads including satellites.

The propulsion of a rocket is achieved by ejecting fuel at very high velocities opposite to the desired direction of motion. This propulsion is governed by Newton's third law, which states as follows:

Newton's Third Law Every action has an equal and opposite reaction. That is, if a particular amount of force is applied on an object in a given direction, the object in return will exert the same amount of force in the opposite direction.

This clip from the cop drama "Brooklyn 99" shows the operation of a fire extinguisher-propelled roller chair cart, which operates by the same principles that govern rocket motion. Extinguisher fluid is ejected out the back at high velocity, which gives the roller chair cart significant momentum in the opposite direction.

Up to this point, we have come to understand how rockets fly in concept. Let us now derive the central equation for the motion of a thrust-propelled rocket. The calculations that govern rocket motion are somewhat complicated, so let us proceed from the basics.

The motion of a rocket is essentially an effect of the conservation of momentum. That is, for a given isolated system, the total momentum will remain constant. Thus, if the main part of the rocket gains any speed in a given direction, it can only come from ejecting fuel with some velocity in the opposite direction. This movement occurs such that the gain in momentum by the rocket is balanced perfectly by the momentum imparted to the fuel that is ejected.

The simplest way to analyze the motion is to consider a rocket in the moment before, and after, the release of a packet of fuel of mass \(\Delta m\). For simplicity, we consider the frame of an observer who travels with the initial velocity of the rocket.

Prior to combusting the fuel and ejecting it, the whole rocket is cruising along with constant momentum \(M\vec{V}_\text{ship}\).

To boost the rocket velocity, a packet of fuel of mass \(\Delta m\) (boxed in black in the diagram below) is combusted and ejected backward with velocity \(\vec{u}\) relative to the rocket, which reduces the rocket mass by \(\Delta m\), and increases the rocket velocity by an amount \(\Delta \vec{v}_\text{ship}\).

This is the situation illustrated in the diagram below:

Because there is no outside force acting on the system (with the system taken to be the rocket and its fuel), the change in total momentum must be zero. If we subtract the total momentum before the combustion from the total momentum after combustion, we have

\[\begin{align} 0 &= \Delta p \\ &= p_t - p_0 \\ &= \Delta m \left(\vec{V}_\text{ship} - \vec{u}\right) + \left(\vec{V}_\text{ship} + \Delta \vec{v}_\text{ship} \right) \left(M - \Delta m\right) - \vec{V}_\text{ship} M \\ &= \vec{V}_\text{ship} \left(\Delta m - \Delta m\right) - \vec{u}\Delta m + M \Delta \vec{v}_\text{ship} + \vec{V}_\text{ship}\left(M - M\right) \\ &= -\vec{u} \Delta m + M \Delta \vec{v}_\text{ship}, \end{align} \]

which yields the following relationship between the changes in mass and velocity:

\[\vec{u}\Delta m = M \Delta \vec{v}_\text{ship}.\]

Why could we neglect the \(\Delta \vec{v}_\text{ship} \Delta m\) term in the calculation above?

If we rearrange this equation, and take the limit where the \(\Delta\)s become infinitesimal quantities \((\Delta m \rightarrow dm \), and \(\Delta \vec{v}_\text{ship} \rightarrow dv), \) we have

\[\frac{dm}{M} = u^{-1}dv.\]

Finally, we have \(dm = -dM\) (the change in mass of the rocket is equal to minus the mass of the infinitesimal fuel packet), so our relation becomes

\[-\frac{dM}{M} = u^{-1}dv.\]

This says that as our rocket gets lighter and lighter, it needs to eject less and less fuel to get a velocity boost of the same magnitude. Unfortunately, this only works up to a point, when our rocket runs out of fuel entirely and reaches \(v_\text{max}\).

We can integrate this relation from the beginning of fuel combustion to the end, to get the velocity as a function of the current mass of the rocket:

\[ \begin{align} u^{-1}\int_{v_0}^{v_f}dv &= -\int_{M_0}^{M_t} \frac{dM}{M} \\ v_f &= v_0 + u\ln \frac{M_0}{M_t} . \end{align} \]

This shows that the velocity of the rocket ship is a pure function of the mass of fuel that's been ejected up until the current time. It doesn't matter how quickly or slowly the mass was lost, simply the total amount that's been combusted by the current time.

Velocity of a rocket in space as a function of fuel combusted

Carry out the calculation for \(v_t\) as a function of \(M_t\) in the case that the rocket is not in free-space, but is fighting a vertical gravitational field of strength \(g\). Is \(v_t\) still a state function of \(M_t,\) or is \(v_t\) now dependent on the history of fuel usage encoded in \(M_t?\)

Two long barges are moving in the same direction in still water, one with a speed of 10 km/h and the other with a speed of 20 km/h. While they are passing each other, coal is shoveled from the slower to the faster one at a rate of 1000 kg/min.

How much additional force must be provided by the driving engines of (a) the faster barge and (b) the slower barge if neither is to change speed?

Assume that the shoveling is always perfectly sideways and that the frictional forces between the barges and the water do not depend on the masses of the barges. Choose the answer that equals the sum of answers to (a) and (b).

Problem credit: Fundamentals of Physics Extended, 9th Edition

Escape velocity of a rocket: This is the minimum velocity required by the rocket to escape the gravitational attraction of the Earth and escape into the space. The kinetic energy of the rocket at a certain height \(h\) is given by the following equation which can help us derive an expression for the escape velocity: \[\dfrac12mv^2=\dfrac{GMm}R-\dfrac{GMm}{R+h}.\] From the physics point of view, a rocket on a launchpad is a stored form of energy. It needs to use this energy to attain a velocity greater than the escape velocity of the earth, where the escape velocity can be calculated as follows: \[\dfrac12mV_e^2=\dfrac{GM_em}{R_e}\implies V_e^2=\dfrac{2GM_e}{R_e}\implies V_e=\sqrt{\dfrac{2GM_e}{R_e}} \approx 11.2km/s.\]

Impulse is defined as a force acting on an object over time, which in the absence of opposing forces, changes the momentum of the object. As such, it is the best performance class indicator of a rocket, rather than takeoff thrust, mass, or "power". The total impulse of a rocket burning its propellant is given by:

\[ I = \int F dt.\]

When the thrust is fixed, it is simply: \(I= F t\). The total impulse of a multi-stage rocket is the sum of the impulses of the individual stages.

Let's now get to know the basic outer features of a rocket. According to NASA , there are four major systems in a rocket:

• structural system
• payload system
• guidance system
• propulsion system.

These four most basic components make up a very complex rocket.

The structural system of a rocket is like an outer skeleton which includes all of the parts which make up the frame of the rocket, i.e. the cylindrical body, the control fins, and the fairings.

The function of the structural system is to minimize the amount of aerodynamic drag created during the flight. The shape of the rocket, hence, plays an important role and so does the structure. But the most important thing to be noted is that the system is to made up of light weight materials which are strong enough to withstand the flight. To solve this problem, alloys of light weight but strong materials such as titanium or aluminium are used.

Recently, the metals have been replaced by the carbon fiber materials, but except for the outer spacecraft bulkhead itself. Bulkheads are still made from titanium, aluminum or other conventional metals and alloys because of the tremendous thermal and pressure demands.

The performance of the rocket depends directly on the weight of the structure. The distribution of the structural weight also affects the center of gravity of the rocket which, in turn, affects the stability and control of the rocket.

Payload system is the most important part of the rocket, which carries the subjected satellite, telescopes, missiles or humans etc. to the required destination safely . Safety is the most important aspect of this system, so it must carry the object without any damages.

You can see the payload Aquarius/SAC-D, safely kept at the top most part of the rocket.

Payloads of the early period were usually fireworks or crackers for fun making. In the World War II era, most of the payloads in the rockets were missiles equipped with self monitoring systems to destroy cities. Nowadays the payloads are mostly satellites, for various scientific purposes.

The guidance system of a rocket includes very sophisticated sensors, on-board computers, radars, and communication equipment. The guidance system has two main roles during the launch of a rocket: to provide stability for the rocket, and to control the rocket during maneuvers.

One component of the guidance system of a simple rocket is the fins, which act as the steering of the rocket. For complex rockets, the guidance system is computer-based or remote control system. Without the guidance system, a rocket during its flight can be subjected to small gusts of wind or thrust instabilities, which can cause it to "wobble" or change its attitude in flight.

A rocket is said to have a stable guidance system if it naturally returns to its flight configuration when it is disturbed from that configuration. A stable guidance system can correct its mistake on its own without human influence.

The propulsion of a rocket includes all of the parts which make up the rocket engine: the tanks pumps, propellants, power head, boosters, and rocket nozzles, etc. The whole purpose of the propulsion system is to produce thrust.

A rocket engine has a combustion chamber where the oxygen and fuel get mixed up and are exploded. This explosion causes a downward thrust, and as discussed earlier, every action has an equal and opposite reaction. The air around the chamber pushes the rocket upward.

Rocket propulsion in space : We know that rockets propel on Earth as they exert the thrust on the air. Because of Newton's third law, the air pushes the rocket forward. Then how does a rocket propel in outer space where there is no air? Think of an explosion inside a sealed box. The explosion, which is basically no more than a very rapid expansion of a compressed gas, pushes the box apart evenly in all directions. Now imagine that the same explosion takes place in a box that is open at the bottom. The explosion pushes against the sides of the box evenly, but the force against the top of the box is not balanced by any force against the bottom because the bottom isn't there to push against. Result : the box flies into the air because of the force of the expanding gas on the top. A rocket engine is essentially that box with a continuous series of explosions going off inside it. Air actually makes rockets less efficient because of the drag it imparts, especially at the speeds a rocket can travel. \(_\square\)

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Articles on Rocket science

Displaying 1 - 20 of 34 articles.

International Space Station: how Nasa plans to destroy it – and the dangers involved

Heather Muir , University of Cambridge

Curious Kids: how exactly does a spaceship get into space?

Chris James , The University of Queensland

James Webb Space Telescope: how our launch of world’s most complex observatory will rest on a nail-biting knife edge

Leigh Fletcher , University of Leicester ; John Pye , University of Leicester , and Piyal Samara-Ratna , University of Leicester

A new era of spaceflight? Promising advances in rocket propulsion

Gareth Dorrian , University of Birmingham and Ian Whittaker , Nottingham Trent University

Mars: Perseverance rover set for nail-biting landing – here’s the rocket science

Andrew Coates , UCL

How to get people from Earth to Mars and safely back again

SpaceX Starship prototype exploded, but it’s still a giant leap towards Mars

Hugh Hunt , University of Cambridge

SpaceX: Crew Dragon is returning to Earth – here’s when to hold your breath

SpaceX astronaut launch: here’s the rocket science

India has it right: nations either aim for the Moon or get left behind in the space economy

Nicholas Borroz , University of Auckland, Waipapa Taumata Rau

Flat-Earther ‘Mad’ Mike Hughes prepares to launch himself to space – here’s how far he’s likely to get

Ian Whittaker , Nottingham Trent University

5 Moon-landing innovations that changed life on Earth

Jean Creighton , University of Wisconsin-Milwaukee

Wandering Earth: rocket scientist explains how we could move our planet

Matteo Ceriotti , University of Glasgow

Europe blasts off to Mercury – here’s the rocket science

David Rothery , The Open University

Method of making oxygen from water in zero gravity raises hope for long-distance space travel

Charles W. Dunnill , Swansea University

3, 2, 1…liftoff! The science of launching rockets from Australia

Ingo Jahn , The University of Queensland

A sports car and a glitter ball are now in space – what does that say about us as humans?

Alice Gorman , Flinders University

Elon Musk is launching a Tesla into space – here’s how SpaceX will do it

Ben Thornber , University of Sydney

Mining the moon for rocket fuel to get us to Mars

Gary Li , University of California, Los Angeles ; Danielle DeLatte , University of Tokyo ; Jerome Gilleron , Georgia Institute of Technology ; Samuel Wald , Massachusetts Institute of Technology (MIT) , and Therese Jones , Pardee RAND Graduate School

2016: the year in space and astronomy

Alan Duffy , Swinburne University of Technology and Rebecca Allen , Swinburne University of Technology

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• International Space Station (ISS)
• Space exploration
• Space travel

Top contributors

Senior Lecturer in Physics, Nottingham Trent University

Professor of Hypersonic Aerodynamics, The University of Queensland

ARC DECRA Fellow, Centre for Hypersonics, School of Mechanical and Mining Engineering, The University of Queensland

Ph.D. Candidate in Mechanical and Aerospace Engineering, University of California, Los Angeles

Post Doctoral Research Fellow in Space Science, University of Birmingham

Postdoctoral Fellow in Aeromechanics, The University of Texas at Austin

PhD candidate in Computational Physics, University of Cambridge

Professor of Engineering Dynamics and Vibration, University of Cambridge

Chair for Space Engineering, UNSW Sydney

Professor of Physics, Deputy Director (Solar System) at the Mullard Space Science Laboratory, UCL

Pro Vice-Chancellor Flagship Initiatives, Swinburne University of Technology

Co Director Space Technology and Industry Institute, Swinburne University of Technology

Senior Lecturer in Space Systems Engineering, University of Glasgow

Senior Lecturer in Energy, Swansea University

Associate Professor in Archaeology and Space Studies, Flinders University

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Essay on Rocket

Students are often asked to write an essay on Rocket in their schools and colleges. And if you’re also looking for the same, we have created 100-word, 250-word, and 500-word essays on the topic.

Let’s take a look…

100 Words Essay on Rocket

What is a rocket.

A rocket is a vehicle that travels into the air at a very high speed. It burns fuel to make hot gas. The gas shoots out from the back and makes the rocket move forward. This is called ‘thrust’. Rockets can go up into space.

Parts of a Rocket

A rocket has many parts. The main parts are the nose cone, the body, and the engine. The nose cone is the top part. The body holds the fuel. The engine burns the fuel and pushes the rocket up.

Types of Rockets

There are many types of rockets. Some are small and some are very big. Some rockets can carry people. These are called manned rockets. Other rockets carry machines into space.

Uses of Rockets

Rockets are used for many things. They can carry satellites into space. These satellites help us with weather reports, TV signals, and GPS. Rockets are also used for space exploration. They can send astronauts to the moon and beyond.

How Rockets Work

Also check:

250 Words Essay on Rocket

A rocket is a vehicle that moves in the sky and space. It uses a special kind of fuel to go up. The fuel burns and pushes the rocket upwards. This is called thrust. Rockets can move very fast, faster than any car or plane.

The Parts of a Rocket

A rocket has many parts. The main part is the body or frame. This is where the fuel and people or things go. The nose is the top part of the rocket. The fins are at the bottom and help the rocket go straight. The engine is where the fuel burns to make the rocket move.

There are different types of rockets. Some are small and used for fun or to study the weather. Others are big and can carry people or things into space. Space rockets are very powerful and can go very far.

Rockets are used for many things. They can carry people to space to learn more about it. They can also carry satellites. Satellites help us with things like weather reports, TV signals, and GPS. Rockets can also be used for exploring other planets and the moon.

Rockets and Science

In conclusion, rockets are amazing vehicles. They help us explore space and learn more about our world. They are a great example of how science and technology can help us do amazing things.

500 Words Essay on Rocket

A rocket is a vehicle that travels into the sky, and even beyond into space. It is designed to move fast and far. It does this by burning fuel. The burning fuel creates a force called thrust that pushes the rocket upward. This is based on a principle called Newton’s third law of motion, which says that for every action, there is an equal and opposite reaction. When the fuel burns and pushes out of the rocket’s engines, the force of this action pushes the rocket in the opposite direction.

There are many types of rockets. Some are small and used for scientific research. Others are large and used to send things into space. There are also rockets used for military purposes. Some rockets, like the Space Shuttle, are reusable. This means they can go to space, come back, and then go to space again. Other rockets, like the ones that send satellites into space, are not reusable. They are used once and then their parts fall back to Earth.

History of Rockets

The idea of rockets has been around for a long time. The ancient Greeks had a simple type of rocket, and in the 13th century, the Chinese used rockets in warfare. But modern rockets started in the 20th century. A man named Robert H. Goddard is often called the father of modern rocketry. He built and launched the world’s first liquid-fueled rocket in 1926. Since then, rockets have been used to explore space, to study the Earth, and for communication.

The Importance of Rockets

In conclusion, rockets are a fascinating subject. They are complex machines that have been developed over many years. They have a wide range of uses, from scientific research to space exploration. And they continue to be an important part of our world, helping us learn more about the universe we live in.

If you’re looking for more, here are essays on other interesting topics:

Apart from these, you can look at all the essays by clicking here .

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Movie Reviews

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The high school hero of "Rocket Science" stutters, but all high school kids stutter. It's just that most of them don't do it with their voices. They stutter in the way they don't know how to present themselves, what to say next, how to talk their way out of embarrassment, when to make an approach to someone they have a crush on or how to perform in class when everybody's looking at them. It's just that Hal Hefner ( Reece Daniel Thompson ) does it out loud.

That's why he seems to be an odd choice when Ginny Ryerson ( Anna Kendrick ) talks him into joining the school debate team. The movie opens when she loses her regular debate partner, Ben Wekselbaum ( Nicholas D'Agosto ). His meltdown is spectacular. In the middle of a debate, he is effortlessly speeding along at a zillion words a second (I learn debaters call this "spreading") when suddenly he freezes. His mind goes blank and he can't think of a single thing to say. Who can't identify with that?

Ben drops off the team and starts beating himself up psychologically, and that's when Ginny recruits Hal. She has reasons of her own, which are revealed in the fullness of time, but oddly enough, they're not the reasons we're expecting. "Rocket Science" is not a formula high school movie, is not about formula kids and is funny in a way that you laugh but it still kinda hurts.

The movie's director, Jeffrey Blitz , must have learned a lot about overachieving kids and their occasional breakdowns while directing his first film, the suspenseful, Oscar-nominated documentary " Spellbound " (2002) about the National Spelling Bee. He learned other things, too, like how when adolescent boys of a certain age think about anything but sex, it's a distraction.

Hal has too many hangups to develop much of a love life, but the kid who lives next door to Ginny obsesses on her, spies on her, steals her brassiere, and in general makes himself miserable. Meanwhile, does Ginny like Hal, does she feel sorry for him or is she playing a cruel trick?

Hal has problems beside Ginny. His dad ( Denis O'Hare ) walks out of his marriage one day, after saying farewell to Hal and his older brother Earl ( Vincent Piazza ) in the kind of speech a man might make before leaving for a better job. Then his mom (Lisbeth Bartlett) starts dating a nice Korean judge ( Aaron Yoo ), although she lacks certain intra-ethnic instincts. "Is this some kind of an exotic Korean dish?" she asks. "Because it has a strange odor." The judge smiles. "It's tuna casserole."

The movie is not a slick repackaging of visual cliches from Teen Vogue (that one was "Bratz") but instead seems to be in a plausible high school filled with students who act and look about the right age, even though they're a little older. The movie was shot in Baltimore, doubling for "Plainsboro High School" in New Jersey, and even spells Plainsboro correctly throughout, unlike "Carry Nation High School" in "Bratz," which couldn't even spell its title. (This just in: "Carry" is an acceptable spelling for Ms. Nation's first name, but "Bratz" is of course a short form of "Bratwurst.")

Hold on. I'm drifting back toward my review of "Spellbound." The thing about "Rocket Science" is that its behavior, even its villainy, is within plausible margins. Ginny is a hateful "popular girl," but she isn't hateful beyond all reason. Hal's mother's new boyfriend is not a stereotyped interloper, but a nice guy who would be an improvement. And a lot of the laughs come in understated asides that reveal character.

The leads, Thompson and Kendrick ("Camp"), are early in what promise to be considerable careers. Kendrick can make you like her even when you shouldn't, and Thompson fine-tunes the pathos of his dilemma to slip comedy into moments that could be deadly.

I suspect a lot of high school students will recognize elements of real life in the movie (that's why it's rated R, to protect them from themselves), and that the movie will build a following. It may gross as little as " Welcome To The Dollhouse " or as much as " Clueless ," but whichever it does, it's in the same league.

Roger Ebert

Roger Ebert was the film critic of the Chicago Sun-Times from 1967 until his death in 2013. In 1975, he won the Pulitzer Prize for distinguished criticism.

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Film credits.

Rocket Science (2007)

Rated R for profanity and sexual themes

101 minutes

Anna Kendrick as Ginny Ryerson

Denis O'Hare as Doyle Hefner

Reece Daniel Thompson as Hal Hefner

Nicholas D'Agosto as Ben

Vincent Piazza as Earl Hefner

Written and directed by

• Jeffrey Blitz

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Classroom Activity

Simple rocket science.

Video of a rocket launch

Plastic milkshake straw

10 long party balloons

Clear cellophane tape

6-8 meters of nylon monofilament fishing line (any size)

Spring clothespin or binder clip

Rocket figure , colored and cut out

3 pieces of chart paper

Journal or sheet of paper (1 per student)

(Optional) Balloon hand pump

(Optional) Camera

• Set up the experiment in an area where students can all gather around and see clearly but stand back far enough to not interfere with the balloon travel.
• Prior to class, cut out (and color, if desired) the rocket figure.

NASA uses rockets to launch satellites and probes into space. NASA rockets are powered by burning solid, liquid or gas rocket fuel.

Long before the development of modern rockets, Sir Isaac Newton described the principles of rocket science in three laws of motion.

A simplified explanation of his third law of motion helps young students understand how rockets work. This law states that every action has an equal and opposite reaction.

When a rocket expels fuel or propellant out of its engine, the rocket moves in the opposite direction. The rocket pushes the propellant out, and the propellant then pushes the rocket. The propellant comes out of the engine. This is the action. The rocket lifts off the launch pad in the opposite direction. This is the reaction. In this activity, the rocket is a balloon propelled by air.

Launch of the GRACE-FO spacecraft on May 22, 2018. | Watch on YouTube

• Show students a video of a rocket launch. Note the direction that the rocket moves. Note where the engines are and where the flames or fire comes out.
• Ask students if they know how a rocket works. Explain to them that they will be conducting a simple demonstration or science experiment to show how a rocket lifts off the launch pad. Students, just like the astronauts in space and scientists on Earth, will conduct an experiment to gather information.

Image credit: NASA/JPL-Caltech | + Expand image

• Thread the fishing line through the straw, then attach each end of the line to the back of two classroom chairs. Pull the chairs apart to stretch the line tightly.
• Inflate a balloon and keep it tightly closed using fingers, a clothespin or a binder clip while carefully taping the balloon to the straw.
• Slide the balloon-straw assembly to the middle of the fishing line span.
• Show students the position of the balloon on the fishing line. Explain to the class that, in this experiment, an adult will release air from the balloon and students will predict what will happen.
• Introduce the word “hypothesis,” if appropriate. Show the class the word written on a piece of chart paper. For scientists, a hypothesis is a reasonable or good guess about what they think will happen in an experiment.
• Discuss the direction the air will move when it is released from the balloon. The balloon will also begin to move. Based on their prior experiences, ask the students to make a good guess about the direction the balloon will travel when air is released. Ask the class to verbalize their hypotheses, or guesses, about the movement of the balloon. Have students point with their fingers to indicate the direction in which they think the rocket will travel.
• Write the hypothesis developed by the class on the chart paper.
• When discussing the direction of movement, encourage the class to use the word “opposite.” Introduce or review the concept of opposites.
• To help students remember the correct sequence of events in the experiment, write directions or draw pictures to represent the steps on chart paper. Display the directions in the classroom.
• Ask students which way, based on their hypotheses, we should tape the rocket figure to the balloon. If necessary, remind students that the nose cone of the rocket points in the direction the rocket will travel. Use cellophane tape to attach the rocket figure to the balloon.
• Prepare to launch, or release, the air from the balloon. Just like a rocket launch, practice a countdown, “10,9,8,7,6,5 ... ,” before the air is released.
• Carefully remove fingers, clothespin or binder clip from the balloon and release the air. The balloon will travel in the opposite direction from which the air escaped.
• Ask students if their guesses or hypotheses were correct.
• Explain to students that scientists must repeat an experiment many times. Repetition of an experiment ensures that the results are accurate. Like scientists, the class must repeat the experiment with the balloon to determine that the results are always the same.
• Let students choose a reasonable number of times to repeat the experiment. Scientists need to have many repetitions to increase the reliability of their results.
• Before repeating the experiment, tell the class that scientists need a method to record the results from experiments.
• Ask the class to devise a simple way to record information or data from the experiment. For example, if the experiment repeats five times, ask students to write the numerals 1 to 5 on an individual sheet of paper or in a journal.
• Have students observe the experiment being performed a number of. Have students draw an arrow next to the numeral to indicate the direction the balloon traveled each time. Be sure students are only on one side of the rocket so arrow directions are consistent. Data collection could also be a class activity.
• Be ready to repeat the experiment the number of times suggested by the class. If necessary, use a new balloon blown up by an adult. When attaching the balloon to the straw, be certain that the open end of the balloon is always facing the same direction. Remember to practice a countdown. Collect data from the experiment.
• As the experiment repeats, let students participate by holding the balloon closed and releasing the air. Remind the class to observe the balloon’s movement and to record the data.
• Allow students to compare their data. Ask students if they can learn something or draw a conclusion from this information.
• If appropriate, introduce the word “conclusion.” Write the word "conclusion" on chart paper. A conclusion is a statement of the results from the experiment. Ask the class what they learned from the experiment. Write their conclusion on the paper. For example, the conclusion could be, “When the air was released from the balloon, the balloon moved in the opposite direction.”
• Discuss whether the original hypothesis or guess was correct. Have students verbalize why they think the balloon traveled in the opposite direction.
• Explain to students why the movement of the balloon is like a real rocket’s movement. If appropriate, introduce Newton’s third law of motion. In a rocket, propellant escapes from the bottom of the rocket. In the balloon experiment, air escapes from the end of the balloon. The balloon moves due to the escaping air providing a “push” to the balloon the same way a rocket lifts off due to the escaping propellant providing a “push” to the rocket. Also like a rocket, the balloon travels in the opposite direction of the escaping air.
• Display the chart paper with the hypothesis, the chart paper with the conclusion, and the data collection sheets in the room. If a camera is available, add pictures of the students conducting the experiment to the display.
• Observe students as they answer questions about the experiment.
• Have students draw a picture of the experiment in their journals or on a piece of paper. Ask them to explain their drawing and explain the relationship between the balloon’s movement and the released air.
• Ask students to describe how a rocket works.
• Challenge students to apply what they learned in this experiment. Repeat the experiment with one change. When attaching a balloon to the straw, reverse the placement of the open end of the balloon. If the open end was to the left, place it to the right. Ask students to form a hypothesis about the movement of the balloon when the air releases. Conduct the experiment. Repeat if necessary. Discuss whether the hypothesis was correct. Talk about the similarities and differences in this experiment and the original experiment. Ask the students if the balloon, in both experiments, moved in the opposite direction from the release of the air. Discuss how students applied what they learned or their conclusion from the first experiment to a new situation.
• Repeat the experiment with another variation. Change the position of the fishing line. Attach one end to the ceiling. Place the straw on the line and stretch the line tightly. Attach the balloon. Attach the other end of the line to a chair or object in the room. Repeat the experiment. Ask students to apply what they learned to a new situation.
• In a journal or on a sheet of paper, or as a group exercise with the teacher writing on chart paper, ask students to list the steps needed to conduct the experiment. Discuss the importance of completing the steps in the right order. Encourage the use of ordinal numbers, such as first, second and third in students’ descriptions.
• Have students use directional words to describe the movement in the balloon experiment or a rocket launch. Discuss words such as up and down, left and right, and forward and backward. Introduce or review the concept of words that are opposites. Have students generate a list of words that are opposites.
• Locate books that feature pictures and drawings of rocket launches. Encourage students to look at the depictions of rocket launches and think about what they now know about how a rocket works. Ask students to look at the pictures and note the direction in which the rockets move.

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Rocket Physics, the Hard Way: The Tyranny of the Rocket Equation

• by Jess Sia
• January 7, 2021 June 5, 2024

“Rocket science is tough, and rockets have a way of failing.” – Sally Ride , NASA astronaut

To go to Mars, we need rocket science. But why is rocket science so hard?

In this series, Rocket Physics, the Hard Way , we will learn the basic science and engineering behind rocket propulsion and interplanetary travel. Knowledge of high school physics, algebra, and basic calculus is useful, but not required. Mathematics will be kept to an absolute minimum, and more in-depth resources will be provided at the end for those who want to dig deeper. This will not be a rigorous technical series; rather, it will focus on demystifying the science and engineering needed to put things and people on Mars.

Before we begin, make sure you have a good grasp of Newton’s Laws of Motion. Here’s a refresher from TED-Ed if you need it:

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Why Rockets are Hard

All propulsion systems – jet engines, rockets, automobiles, and even walking – rely on Newton’s Third Law: For every action, there is an equal and opposite reaction. If one pushes on an object, the object pushes back. A jet engine or a propeller pushes on the air around it to propel an aircraft forward, while our feet push off the ground. However, rockets are in a class of their own, because they must operate in the vacuum of space. With nothing in the environment to push against, they must bring their own mass to propel themselves.

Consider an extremely simple toy model of a rocket. It stores two units of fuel in its tanks, shown in red:

Then, it ejects one unit of fuel at a high speed (the exhaust velocity) causing the rocket and the remaining unit of fuel to gain a little velocity. If we wanted the rocket to go even faster, we could simply load on more fuel so that we have more to eject.

Here’s the problem: Each unit of fuel has to accelerate not only the mass of the rocket, but also the mass of the remaining fuel!

This means that the more fuel one carries, the less effective each unit is at providing the rocket with momentum – it’s a problem of diminishing returns. As a result, if more momentum needs to be imparted to the payload, the proportionate mass of fuel required increases exponentially. Using integral calculus to model this problem of the rocket accelerating as its mass diminishes gives us the Rocket Equation. First derived by Russian rocket scientist Konstantin Tsiolkovsky in 1897, it is the most important governing equation for rocket design, because it determines the vehicle’s ability to perform a mission.

To further prepare us for an exploration of rocket physics, let’s introduce some important quantities and measures.

ΔV (delta-V)

We measure the difficulty of each particular rocket maneuver using a quantity called delta-V. In science and engineering, the Greek letter Δ (delta) symbolizes change – delta-V is the amount of velocity change that a rocket’s engines need to supply to perform the maneuver. 

Imagine a SpaceX Starship in low Earth orbit. As it orbits the Earth, it is travelling at approximately 7.8 km/s (about 28,000 km/h) relative to the planet. Unlike an aircraft, it does not need to keep its engines firing continuously to maintain this enormous velocity, because nothing is stopping it – there is no air resistance in space 1 .

However, to send it on a 250-day trajectory to Mars, we need to add about 3.7 km/s to its velocity. This is the trans-Mars injection maneuver. To do this, we fire the engines until the spacecraft has reached 11.5 km/s relative to the Earth.

Accordingly, we say that the delta-V of the trans-Mars injection maneuver is 3.7 km/s. However, 250 days is a long time to wait – this is the lowest-energy transfer we can use. We could get to Mars faster if we wanted to, but we would need to travel at a greater velocity. That means we would need more delta-V, which means that we would need more fuel – exponentially more fuel.

To determine if a spacecraft can perform a mission, we tally the delta-V of all the maneuvers it will need to perform and compare that with how much delta-V the spacecraft can supply. We can reduce the amount of delta-V – and hence, fuel – required with clever tricks such as:

• Using gravity assists to steal some momentum from planets and moons.
• Using planetary atmospheres to brake on arrival, so that the engines aren’t needed to slow down.
• Using the quirks of the Solar System’s gravity field to get extremely slow, but low-cost trajectories .

After the engines shut down, the Starship is on its way to Mars. Unlike what bad science-fiction films may suggest, it will not need to fire its engines to keep moving due to the lack of air resistance, with the exception of small burns for course corrections. As a result, spacecraft usually 2 spend the majority of their missions with the engines off.

Exhaust velocity

A rocket engine’s efficiency is measured by its exhaust velocity , or how fast the exhaust is going when it leaves the nozzle. Everything else held equal, a rocket with a high exhaust velocity will gain more momentum from each unit of fuel than a rocket with a low exhaust velocity, because the recoil from ejecting a unit of fuel is stronger. This reduces the mass of fuel required, because it’s used more effectively.

Exhaust velocity depends on both the fuel used and the engine. Energetic fuels with a low molecular mass – like burning hydrogen and oxygen – will have better exhaust velocities. But engines can also be optimized to extract as much momentum as possible from the fuel through techniques like high combustion chamber pressures and large nozzles.

An alternative (and more commonly used) efficiency measure to exhaust velocity is specific impulse or Isp. It is measured in seconds, and is simply the amount of time that burning one kilogram of fuel can produce one kilogram of thrust – generally, higher is better. For example, the Space Shuttle Main engines had an Isp of 452 seconds in a vacuum. The SpaceX Merlin engines (used on the Falcon 9 family) have an Isp of 311 seconds in a vacuum. The reasons SpaceX’s engines have a lower performance despite using newer technology are complicated and will be covered in future installments.

The final important concept is that of mass ratio . This is how we quantify how much fuel a spacecraft needs. A spacecraft has a wet mass – its gross mass, full of fuel – and a dry mass – its empty mass, with dry tanks. The mass ratio is simply the ratio of wet mass to dry mass. The higher the mass ratio, the greater the fraction of the spacecraft’s wet mass is fuel. The greater the delta-V required, the greater the mass ratio required, and the more difficult the rocket will be to engineer.

Virgin Galactic’s SpaceShipOne has a mass ratio of about 3, which means it’s two-thirds fuel by mass at the beginning of the mission. Note that SpaceShipOne is merely a suborbital rocket – it follows a ballistic trajectory that briefly enters space before falling back to Earth, somewhat resembling an artillery shell’s flight.

On the other hand, the orbital spacecraft have much higher mass ratios. The Space Shuttle had a mass ratio of 16, making it almost 94% fuel by mass at launch. The mass of everything that wasn’t fuel: its structure, engines, avionics, life support systems, control systems – and oh yes, don’t forget the crew and the payload – had to fit within the remaining 6%. The only reason it could get away with such a high mass ratio at launch is because it leveraged staging.

By jettisoning its spent booster rockets during ascent (and afterwards, the spent external fuel tank), it didn’t have to drag as much dead weight all the way into orbit.

The Saturn V had even more demanding requirements – it had to deliver the Apollo spacecraft and lunar lander to the Moon. This gave it a monstrous mass ratio of 23, again possible only by staging. While nothing in the laws of physics limits a rocket’s mass ratio, having a much higher mass ratio than 20-30 pushes the limits of modern aerospace engineering, driving up costs for little additional payload capacity.

This is why rockets use exotic, exorbitantly expensive high-strength materials and have razor-thin margins for error. This is also why orbital rockets are enormous fuel tanks with a cluster of engines and a tiny payload or crew compartment attached. Everything needs to be as lightweight as possible to maximize the amount of payload that can be carried into orbit. In the case of the Saturn V, each extra kilogram of payload would demand an additional twenty-three kilograms of fuel for the mission.

This is the so-called Tyranny of the Rocket Equation.

Staging is one way to cheat it – all current orbital rockets resort to staging, even the planned Starship Super Heavy. Another cheat is to design engines that use atmospheric oxygen during ascent, reducing the mass of on-board oxidizer that needs to be carried. An example is the Skylon spaceplane , which is designed to reach orbit with a mass ratio of merely 6. Unfortunately, the Skylon and other air-breathing spacecraft like it are still in the early stages of development.

And finally, without further ado, here is the Rocket Equation itself, the second hardest part of rocket engineering (the hardest part being funding, of course):

While the meaning of the above equation may not be immediately clear, these are the important takeaways:

• Increasing the engine’s exhaust velocity increases the rocket’s delta-V capability (i.e. the rocket can do harder missions if it has better engines/fuel.)
• Increasing the rocket’s mass ratio also increases its delta-V capability (i.e. the rocket can do harder missions if a greater fraction of its mass is fuel.)
• Increasing the mass ratio causes exponentially diminishing returns in delta-V (i.e. adding more fuel will only help you so much.)

And that is why rocket science is hard. If you can remember only one thing about rocket physics, remember the Tyranny of the Rocket Equation.

In the installments to follow, we will use the concepts of delta-V, exhaust velocity, mass ratio, and the Rocket Equation to learn how to plan a mission to Mars. If you’re up to the challenge, stay tuned.

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Footnotes and further reading

1 Actually, even in high orbit around the Earth, there is still some atmosphere, but it’s extremely thin. Air resistance is just so weak at such high altitudes that it only matters over long periods of time. The International Space Station’s orbit needs to be periodically boosted because of this tiny amount of air resistance. For details, read: Orbital Decay

2 Spacecraft spend the majority of their time with the engines off if they have high-thrust engines, which means they perform short, intense maneuvers. Spacecraft using weaker engines like ion engines have to fire their engines for a very long period of time (days, months, or even years) to get anywhere. Learn how we might generate the fuel for missions back to Earth from Mars in our ISRU series

The derivation of the rocket equation: https://www.grc.nasa.gov/www/k-12/rocket/rktpow.html

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Rocket engineering is hard, but rocket science is simple.

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As a physicist I would like to point out that rocket science is pretty simple: basic Newtonian equations will do. Even if one will add relativistic effects (as is done in GPS systems) this is physics that can be understood and applied by any high school graduate. On the other hand, rocket engineering, i.e., building rockets and especially their engines, is still an art, cf. e.g., recent problems NASA had with SLS engines.

Competing interests: No competing interests

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Papers were sprawled on my desk. Books were stacked two feet high. I was sitting in my cubicle, hunched over old lectures, trying to learn the jargon of rocket science. My eyes squinted at the tiny text as I stumbled through the abstruse vocabulary. Hydrazine, MEOP, PED delta pressures, annealed material properties...those terms were all Greek to me.

It was my first week of work at Boeing. I was busy learning about propulsion and satellites systems. Every time I found something I was unsure of, I would rush over to my mentor and ask him to explain the concept. Drawing on the little whiteboard in his office, he practically exhausted the entire spectrum of propulsion. The obscure terms that once seemed so foreign to me soon became a part of my everyday vocabulary.

As the days passed, I began to interview various scientists for my research project. I asked Mr. Dave Bronson, a metallurgical engineer, about tensile testing of titanium. I chatted with Dr. Jeffrey Hollender, an attitude control scientist, about the buckling and burst pressures during launch. I also talked with Dr. Ray Kushida about the theory behind fracture mechanics.

During the eight weeks, I was also able to gain hands-on experience. Wearing a smock and a pair of...

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NASA Thinks This Radical Mars Rocket Could Revolutionize Space Travel

NASA has invested $725,000 in a new rocket system that could solve one of the major obstacles standing in our way of sending humans to Mars : travel time.

With current technology, a round-trip to the red planet would take almost two years. For astronauts, spending that much time in spaceflight comes with big health risks.

They'd be exposed to high levels of solar and cosmic radiation , the harmful effects of zero-gravity, and a long period of isolation.

Space radiation is arguably the biggest threat. Astronauts who spend just six months in space are exposed to roughly the same amount of radiation as 1,000 chest X-rays, and this puts them at risk for cancer , nervous system damage, bone loss, and heart disease, according to NASA.

The best way to reduce radiation exposure and other harmful health effects is to shorten the length of the trip, Troy Howe, president of Howe Industries, told Business Insider.

That's why he's teamed up with NASA to develop the Pulsed Plasma Rocket (PPR): a new rocket system that could shorten a round-trip to Mars to just two months.

This technology "holds the potential to revolutionize space exploration," NASA wrote in a statement , and could one day take humans even further than Mars.

How a rocket could get us to Mars and back in 2 months

The PPR is a propulsion system that uses pulses of superheated plasma to generate a lot of thrust very efficiently. It's currently in phase two of development, funded by the NASA Innovative Advanced Concepts (NIAC) Program.

This phase two study is scheduled to begin this month, and is focused on optimizing the engine design, performing proof-of-concept experiments, and designing a PPR-powered, shielded spaceship for human missions to Mars .

The big advantage of the PPR is that it can make a spacecraft go really, really fast. It has both a high thrust and high specific impulse. Specific impulse is how quickly a rocket engine generates thrust, and thrust is the force that moves the spacecraft along.

The PPR generates 10,000 newtons of thrust at a specific impulse of 5,000 seconds. That means a PPR-equipped spacecraft carrying four to six passengers could travel roughly 100,000 miles per hour, Howe told BI over email.

A spacecraft flying that fast would eventually have to slow down to reach its destination. Howe said the company has accounted for the additional energy and propellant this would require to land on Mars.

Even after phase two is complete, it will still be about a couple of decades before the PPR is ready to blast astronauts off to the red planet.

But once it's available for spaceflight, Howe hopes that this technology will significantly expand the range of human space exploration , perhaps even aiding missions to Pluto one day.

"You can pretty much achieve anything you want in the solar system once we get this technology running in 20 years," he said.

This article was originally published by Business Insider .

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• Physics Concept Questions And Answers

Rocket Science Questions

Rocket science has uncountable applications, from launching satellites to testing ballistic missiles. The propulsion of rockets is based on a fundamental kind of motion, and one needs to be familiar with Newton’s Laws of Motion to understand it.

Important Questions on Rocket Science

1) In a gravity-free, drag-free environment, what is the nature of the trajectory of rockets?

a) Straight-line path, one-dimensional

b) Curved path, three-dimensional

c) Straight-line path, three-dimensional

d) Curved path, two-dimensional

Correct Option: (a)

Explanation: Since the only force acting on the rocket is its thrust, and it acts in the flight direction, a straight-line, one-dimensional acceleration path is followed in such conditions. The flight path will become curved under the influence of gravity.

2) In an ideal chemical rocket engine, which among the following is not a feature of the combustion chamber?

a) Higher transient time

b) Higher temperature

c) Higher velocity of flow

d) Low pressure

Explanation: In an ideal chemical rocket engine, the transient time is very low to confirm that the flow and related procedures are stable and remain constant at all times. Also, an ideal chemical rocket engine has a high temperature, high pressure, and low flow velocity.

3) What will be the estimated amount of energy loss due to the transfer of heat to the walls of the rocket for a typical real rocket engine?

Correct Option: (d)

Explanation: Due to the transfer of heat to the walls, the energy loss is generally less than 1% and rarely may go up to 2% of the total energy. Due to this reason, the effects of heat transfer can be ignored in real rockets.

4) The effective propellant fraction can be reduced by which of the following factors?

a) Increase in temperature at the inlet of the nozzle

b) Favourable nozzle area ratio

c) Lower chamber pressure

d) Higher system inert mass

Explanation: The ratio of the mass of propellants to the initial mass of the system is known as the effective propellant fraction. Therefore, the total initial mass(m o ) will increase if inert mass(m f ) increases.

5) For single-stage vehicles, gravitation free and drag-free space flight, what should be the practical value of the mass ratio that is (Initial mass/inert mass)?

Explanation: Spherical shape of the rocket is desirable in a single-stage rocket vehicles system. Even though it may not be the easiest to manufacture, it can help to minimise weights and lateral loads. Therefore, single-stage rocket vehicles can have a mass ratio up to about 20.

6) For multistage vehicles, gravitation free and drag-free space flight, what should be the practical value of the mass ratio that is (Initial mass/inert mass)?

Explanation: In multistage vehicles, the rocket is split into many segments in which each of the sections is a separate propulsive system, and in this case, it can have mass ratios that exceed 200.

7) For orbital adjustments, the rocket engines used are also named as _____.

a) Propulsion boost system

b) Secondary propulsion system

c) Strap-on motors

d) Auxiliary rockets

Explanation: Auxiliary rockets also help in the purpose of attitude control manoeuvring apart from orbital adjustments. Auxiliary rockets are also named as reaction control systems.

8) How many thrusters are required for the application of clean torques in three directions?

Correct Option: (c)

Explanation: To generate clean torques in the three orthogonal directions, 12 thrusters are required. Roll, pitch and yaw thrusters are also included with control valves.

9) What should be the nature of the working substance for an ideal rocket?

a) Anisotropic

b) Amphoteric

c) Homogeneous

d) Heterogenous

Explanation: Homogeneous means that the configuration and character of the substance are uniform throughout. Hence, the working substance and chemical products should be homogeneous.

10) Which is the correct statement for an ideal rocket among the following?

a) The boundary layer cannot be neglected, and all frictional effects are not present.

b) Shock waves are allowable

c) Propellant flow is constant and steady

d) The extension of the working fluid is stable, but the flow is not necessarily uniform

Explanation: Propellant flow is considered to be constant and steady in an ideal rocket. Along with the possible cut-offs in flow, such as shock waves, all types of boundary layers and frictional effects are neglected in such vehicles. The expansion of the working fluid is uniform as well as steady.

Practice Questions

1) How does rocket fuel burn in space without oxygen?

2) What is rocket propulsion?

3) What are the fuels used in rockets?

4) What is rocket science?

5) What is thrust?

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Jeff Bezos, Amazon CEO, abandoned PPT in 2012. His presentation replacement = ET method for doing meetings:

Elizabeth Lane Lawley, a professor visiting Microsoft, comments on "the culture of the deck."

There are many things I've been delighted and impressed by during the nearly five months I've now spent at Microsoft. However, there have also been a few things that i've found extraordinarily disheartening. One of the latter has been the organizatational dependence on "the deck" (that is, Powerpoint files) as the standard mechanism for conveying nearly all information. Tonight I was reading through one of the blogs I've recently added to my aggregator, the most-excellent Presentation Zen (by Garr Reynolds), and I came across a post entitled " The sound of one room napping ." It included this wonderful passage, which sums up beautifully what I've been trying to say to the people around me at Microsoft: Attempting to have slides serve both as projected visuals and as stand-alone handouts makes for bad visuals and bad documentation. Yet, this is a typical, acceptable approach. PowerPoint (or Keynote) is a tool for displaying visual information, information that helps you tell your story, make your case, or prove your point. PowerPoint is a terrible tool for making written documents, that's what word processors are for. Why don't conference organizers request that speakers instead send a written document that covers the main points of their presentation with appropriate detail and depth? A Word or PDF document that is written in a concise and readable fashion with a bibliography and links to even more detail, for those who are interested, would be far more effective. When I get back home from the conference, do organizers really think I'm going to "read" pages full of PowerPoint slides? One does not read a printout of someone's two-month old PowerPoint slides, one guesses, decodes, and attempts to glean meaning from the series of low-resolution titles, bullets, charts, and clipart. At least they do that for a while...until they give up. With a written document, however, there is no reason for shallowness or ambiguity (assuming one writes well). To be different and effective, use a well-written, detailed document for your handout and well-designed, simple, intelligent graphics for your visuals. Now that would be atypical.

I wish there was some way to make this (and Tufte's The Cognitive Style of Powerpoint , and Atkinson's Beyond Bullet Points ) required reading for every Microsoft employee.

Here is a link to William Harwood's excellent account of shuttle risks in the upcoming flight, scheduled for this Saturday, context for my comments that follow.

About 18 months ago in Houston I reviewed the shuttle Probability Risk Assessment (PRA) material for NASA. PRA works with a list of possible threats, estimates their probablilities and expected losses, and then seeks to assist decision-making for shuttle risk-reduction.

After the PRA group presented their results, I had two major suggestions:

(1) They should prepare a detailed summary matrix (on, of course, 11" by 17" paper), ordering the risks and providing, in a comments column, relevant background for each estimate. Let that intense matrix, backed up by similar more-detailed 11" by 17" arrays of risk estimates, be the main presentation device and analytical tool for making decisions. This was designed to replace their chippy and twiddly PP slides, which made a hash of their good technical work and made it difficult to assess the overall risk context. (2) The PRA assessments did not take into account a major risk factor in both the Challenger and Columbia accidents: on-ground intellectual failures in engineering analysis. In the case of the Challenger, the analytic process on the day before the accident was seriously deficient, in the sense that--in hindsight to be sure--the Challenger would not have been launched on that very cold day (which compromised the O-rings and caused the accident) if smarter engineering analysis and better decision-making had taken place. In the case of the Columbia, better analysis and decision-making during the flight might have yielded rescue efforts to try to save the crew, which was endangered by damage to the Columbia suffered at launch. I suggested to the PRA group that on-ground analytic problems contributed to something like 1.3 of the 2.0 accidents in the 113 flights. But there was no risk assessment of such in the PRA; that is, about 65% of the directly observed empirical risk in the 113 flights was not accounted for by the PRA model. The shuttle itself was considerably less risky than what was happening on the ground in decision-making about the shuttle.

At the meeting, I also handed out Richard Feynman's famous discussion of shuttle risks, which Feynman prepared as a part of the Challenger investigation in 1987.

The analysis for the upcoming launch of the Discovery in July 2006, as the link above indicates, was an intense evaluation of risks and trade-offs.

On the basis of reading some of the public documentation (and no direct knowledge) for the upcoming flight in the last few weeks, I think that NASA has made a reasonable and well-informed decision for the upcoming flight. It was also a contested decision. I would vote for the launch. The on-ground factors that contributed to 1.3 shuttle losses appear to be mitigated by the thorough analysis for this flight. The current risk number is a cloudy 1 in 100, which is risky but has been acceptable in the past. The cloudy contributions to risk are the recent changes in the foam, which turns Discovery into something of an experiment.

John Schwartz, New Scrutiny for Every Speck on the Shuttle , New York Times, 11 July 2006 Is the space shuttle Discovery safe to re-enter the atmosphere on its way to landing next Monday? Determining that it is, as the National Aeronautics and Space Administration did on Sunday, is an arduous process. Even though engineers and analysts say there is really no choice for an agency still climbing back from a horrendous re-entry accident -- the loss of the shuttle Columbia and its crew of seven on a bright February morning in 2003 -- the level of detail can sometimes seem absurd. Blame the tools that have been developed since the Columbia disaster. They give such stunningly clear and detailed images of the shuttle from orbit that there are endless new problems to worry about. On Sunday, mission managers announced results of their close look at every suspicious mark and irregularity on the shuttle surface, including stiff bits of cloth called gap fillers that were poking out of the underbelly, as well as loosened patches on insulating blankets. Before the Columbia, such problems would have probably not been noticed. Now, each becomes a potentially troubling issue, to be dealt with one by one by one by one. On Sunday, the sixth day of the 13-day flight, Steve Poulos, the orbiter projects office manager, said every item had finally been checked off.

. . . many breast cancers found by mammography screening have excellent prognosis not just because of early detection, but also because many of the cancers are relatively benign, requiring minimal therapy. from Sandra Y. Moody-Ayers, MD; Carolyn K. Wells, MPH; Alvan R. Feinstein, MD, MS, "Benign" Tumors and "Early Detection" in Mammography-Screened Patients of a Natural Cohort With Breast Cancer, Arch Intern Med. 2000; 160: 1109-1115.

There was an interview with Steve Balmer , Microsoft CEO, in the Sunday New York Times. When asked what it's like to be in a meeting run by Steve Balmer he says that he decided that what he calls the "long and winding road" meeting style of a few years ago at Microsoft isn't productive. He says that for most meetings, he now gets the materials in advance and he reads them. For the meeting he comes in and says "I've got the following four questions. Please don't present the deck."

Incredible!

"One of the first things [Steve] Jobs did during the product review process was ban PowerPoints. `I hate the way people use slide presentations instead of thinking,' Jobs later recalled. `People would confront a problem by creating a presentation. I wanted them to engage, to has things out at the table, rather than show a bunch of slides. People who know what they're talking about don't need PowerPoint.'"

-- Walter Isaacson, Steve Jobs (New York: Simon & Schuster, 2011), 337.

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Chinese space firm unintentionally launches its new rocket, space pioneer had been prepping the vehicle for its debut launch later this summer..

Eric Berger - Jul 1, 2024 12:52 pm UTC

One of the most promising Chinese space startups, Space Pioneer, experienced a serious anomaly this weekend while testing the first stage of its Tianlong-3 rocket near the city of Gongyi.

The rocket was undergoing a static fire test of the stage, in which a vehicle is clamped to a test stand while its engines are ignited, when the booster broke free. According to a statement from the company , the rocket was not sufficiently clamped down and blasted off from the test stand "due to a structural failure."

Video of the accidental ascent showed the rocket rising several hundred meters into the sky before it crashed explosively into a mountain 1.5 km away from the test site. (See various angles of the accident here , on the social media site X, or on Weibo .) The statement from Space Pioneer sought to downplay the incident, saying it had implemented safety measures before the test, and there were no casualties as a result of the accident. "The test site is far away from the urban area of ​​Gongyi," the company said.

This is not entirely true, however. Located in the Henan province in eastern China, alongside the Yellow River, Gongyi has a population of about 800,000 people. The test stand is only about 5 km away from the city's downtown and less than a kilometer from a smaller village.

Such accidents are rare in the launch industry but not unprecedented. Typically, during a static fire test, the mass of propellant on board a vehicle combined with strong clamps hold a rocket down. However, in 1952, a US Viking rocket broke loose of its moorings at White Sands Missile Range in New Mexico. It crashed 6 km downrange of the launch site without casualties.

How big of a setback?

It is unclear how big of a setback this will be for Space Pioneer, a quasi-private company founded in 2019. A little more than a year ago, Space Pioneer became the first Chinese company to reach orbit with a liquid-fueled rocket. It did so, impressively, on the first attempt of its small Tianlong-2 rocket. This was a notable achievement, but the rocket's engines were provided by a Chinese state-operated firm, the Academy of Aerospace Liquid Propulsion Technology, rather than the private company.

For the larger Tianlong-3 rocket, Space Pioneer says it is manufacturing its own kerosene-fueled engines, known as TH-12. (They appear to have performed as expected this weekend.) Nine of these engines will power the Tianlong-3 rocket, which is intended to have a thrust of 17 tons to low-Earth orbit. The rocket's design and the planned reuse of its first stage mimic the Falcon 9 rocket developed by SpaceX.

Space Pioneer had been prepping the vehicle for its debut launch later this summer or fall—and first-stage static-fire tests are indicative of a rocket's final testing phase before liftoff. The company's statement did not set a new timeline for a launch attempt but said it would complete the fault analysis "as soon as possible."

China has the most vibrant commercial space industry in the world after the United States. Nearly a decade ago, the country's leadership committed to sharing state-owned technology with companies that raised private funding, seeking to emulate the commercial success of SpaceX and other US companies.

Today, there are dozens of Chinese firms developing rockets, satellites, and other spaceflight products. Space Pioneer has been among the most promising, having raised more than $400 million since its inception five years ago.

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Teen’s model rocket sticks a SpaceX-inspired vertical landing

By Andrew Paul

Posted on Jul 10, 2024 2:51 PM EDT

It took SpaceX years to successfully pull off the first vertical landing for its reusable Falcon 9 rocket. Since then, model rocket designers have attempted to recreate the feat—with Joe Barnard’s BPS.space accomplishing the milestone in 2022 after 7 years of work. The latest model to achieve a vertical landing, however, comes from a high schooler.

In a video uploaded to YouTube on July 5 under his company’s account, JRD Propulsion , Kapoor describes first setting out in August 2021 to design a model rocket capable of handling a propulsive landing. Three years of “development, testing, and many failures” later, it all reportedly came together on May 25 after four previous launch tries. 

Unlike Barnard’s iteration, Aryan Kapoor’s rocket is also an original design instead of a scale replica of a SpaceX. As Hackaday notes, Kapoor’s model relies on a stack of two solid-propellant motors—one for liftoff and one for its descent and soft landing. One of the most striking aspects of Kapoor’s rocket is its overall design, which ditches stability fins for thrust-vector controls using a 3D-printed gimbal mount. The inclusion of two servo motors allows the stack to pivot plus and minus 7 degrees in two directions. All of this is then controlled through a custom computer array, inertial measurement unit, and barometric altimeter. In his video, Kapoor says creating the thousands of lines of software code proved to be “by far” the most complicated step during his multiyear trials and errors.

[Related: SpaceX’s Starship may mess up the moon’s surface .]

After a successful liftoff, the altimeter lets the rocket’s computer know when to eject the first propellant and switch over to the second motor for its controlled descent. To stick the landing, Kapoor attached much longer legs than a standard model—with some creative adaptations. Each leg is rigged with a repurposed syringe and rubber bands that serve as shock absorbers, enabling the rocket to further dampen its landing.

Interestingly, Kapoor’s rocket nailed its first successful landing even in spite of some internal issues. During its ascent, the system failed to eject its first spent propellant stack, which added unintended extra weight during the controlled descent. This caused the model’s springy legs to bounce it slightly back upward after first touching down, technically meaning it landed upright not once—but twice.

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