Water Rockets

        In this project, water rockets will be used for testing. Water rockets are filled with water and compressed air. Thrust is created when the water is released. Air enters the rocket as water is expelled. This lowers air pressure inside the rocket, and as a result lowers the mass flow rate of water through the nozzle and therefore the thrust. Weight and thrust constantly change during the powered portion of the rocket’s flight. 

When all of the water is expelled, there is still a difference of pressure inside the rocket and outside the rocket (ambient). This creates a small amount of thrust. When the two pressures equal each other, the thrust stops and the rocket begins its coasting ascent. It is eventually slowed by weight and drag and reaches its apogee (maximum altitude). It then begins to fall back down. The ideal flight path of a water rocket would be straight up and down. However, water rockets often turn into the wind. The effects of the aerodynamic forces lead to a parabolic arc trajectory. 

NERVA

       The NERVA, Nuclear Engine for Rocket Vehicle Application, system was developed by the National Aeronautics and Space Administration during the Space Race. The NERVA engine was planned as a third stage for the Saturn rocket, used in the Apollo lunar missions, which would allow it to carry larger payloads into space. The NERVA rocket engine fit the requirements for a manned Mars mission. At the time it was developed, NERVA was more powerful than any chemical engine. 

Nuclear thermal rockets work by heating liquid hydrogen to a very high temperature using a nuclear reactor, which then expands and accelerates through the nozzle to create thrust. The reactor is powered by nuclear fission (the splitting of an atom). Nuclear rockets have a specific impulse two to three times that of chemical rockets. 

NASA initiated nuclear rocket research in 1955. The program was given major emphasis in the 1960’s in the Rover/NERVA program. This program involved two government agencies: NASA (National Aeronautics and Space Administration) and the AEC (Atomic Energy Commission). In an effort to not separate the development of the engine and the reactor, a joint program was created. It was managed by the SNPO (Space Nuclear Propulsion Offics), which was led by both representatives from NASA and the AEC. 

Principal research for the project was conducted by the Los Alamos National Laboratory. In 1961, engine development for NERVA began. The contractors were Aerojet and Westinghouse. The priorities for the engine were safety and reliability (considered more important than weight and performance), an emphasis on engine components (specifically the propellant feed system, nozzle, and engine control system), and facilities for engine assembly and tests. Most research was directed towards graphite reactor technology with a hydrogen coolant, however two alternatives, both with a higher risk and benefits, were also given attention: metal reactors and liquid and gas core reactors. 

Mission planning for this technology centered around lunar exploration and a manned mission to Mars. The latest model was the NRX/XE. Other models included, Phoebus, KIWI, and Peewee.

Testing of the NERVA engine began in 1966. After many successful tests, the SNPO certified that the NRX/XE nuclear thermal rocket engine fit the requirements for a manned Mars mission. Such a mission was planned for 1978. However, even though the NERVA engine was a success, Congress judged that a manned mission to Mars would continue the expensive Space Race for decades. So, along with most of the space program, NERVA funding was cut by the Nixon administration before a manned Mars mission could take place. 

NERVA could be used for multiple missions. It can be stored in space for up to three years. It has 45,000 megawatts of thermal power, 250,000 pounds of thrust, 850 seconds of specific impulse, and a 5,500 degree Fahrenheit exhaust temperature. The technology, which could still be used today, costs about 1.5 billion dollars. 

The Space Shuttle

Rocket Propulsion

A rocket engine consists of a nozzle, combustion chamber, and injector. The combustion chamber is where the burning of the propellant takes place. It has high pressure and temperature. The chamber must be strong enough to withstand immense pressure and long enough  to ensure complete combustion. The nozzle accelerates the hot gases created in the combustion chamber. This converts chemical-thermal energy to kinetic energy. The highest performing nozzles are bell-shaped. The injector is very important for rocket performance. It injects propellant, closes the chamber, and other tasks involved with combustion and cooling. 

       Combustion is a chemical reaction known as oxidation. Throughout the process, mass remains the same because of the Law of Conservation of Mass. Mixture ratio is the ratio of the flow rate of oxidizer to the flow rate of fuel. An optimum mixture ratio typically leads to a higher specific impulse. The combustion process causes the separation of molecules into simpler constituents (dissociation). High chamber temperature and pressure and low exhaust gas weight results in high ejection velocity and thrust.

Some heat from the combustion chamber is transferred to the chamber walls. The most common cooling method is regenerative cooling, where coolant flows over the back of the chamber and is discharged into the injector and used as propellant. 

        Solid, liquid, and nuclear rockets are all chemical rockets.

  In solid rockets, “fuel and oxidizer are mixed together into a solid propellant which is packed into a cylinder” (Solid Rocket Engine). The combustion chamber is a hole through the cylinder. Combustion of the fuel takes place on the propellant’s surface. This creates a flame front, which burns into the propellant. This process creates copious amounts of exhaust, high temperature, and great pressure. Their geometry determines surface area and burn pattern. The exhaust accelerates through the nozzle and creates thrust.

          Unlike turbine engines and propellers, which rely on the atmosphere for oxygen, rockets work in a vacuum (such as space). This is because the oxidizer is mixed with the propellant.

In liquid rockets, fuel and oxidizer are stored in the engine. Then, they are both pumped into the combustion chamber, where they are mixed and burned. The exhaust flows through the nozzle and creates thrust. The amount of thrust depends on “the mass flow rate through the engine, the exit velocity of the exhaust, and the pressure at the nozzle exit” (Liquid Rocket Engine). These variables are all dependent on the nozzle design. Liquid rockets can also create thrust in a vacuum because oxidizer is carried on board. 

Newton's Laws of Motion

  In the year 1686, at the age of twenty three, Isaac Newton presented his three laws of motion in the “Principalia Mathematica Philosophae Naturalis.” These three laws can be used the explain the motion of a rocket. The first law is known as the law of inertia and the second law relates force to mass and acceleration. The third law explains actions and reactions, which create the thrust that accelerates the rocket.

Newton’s first law states that “Every object persists in its state of rest or uniform motion in a straight line unless it is compelled to change that state by forces impressed upon it.” This is known as inertia. If all external forces cancel each other out (a net force of zero), the object will maintain a constant velocity. If this velocity is zero, the object will stay at rest. If it is greater that zero, the object will maintain its velocity and travel in a straight line. 

If an external force is applied, the velocity will change. Velocity, the speed of an object in a certain direction, is a vector quantity. A vector quantity has both magnitude and direction. Therefore, a change in velocity can involve magnitude, direction, or a combination of both.

One application of Newton’s first law of motion is to the flight of a rocket. When the rocket is sitting on its fins, its weight is balanced by the reaction (from Newton’s third law) of the Earth on the rocket. Because there is no net force and the velocity is zero, the rocket is at constant velocity and would remain at rest indefinitely. When the engine is fired, the rocket does not immediately lift off because the weight is greater than the thrust. As the thrust increases, it eventually equals the force of the rocket’s weight. This creates a net force of zero and the rocket does not lift off. When the force of the thrust is greater than the weight, a net force (thrust-weight), lifts the rocket. As it rises, it encounters another force: aerodynamic drag. Drag opposes motion. Drag increases as the square of velocity. However, with full size rockets, drag eventually decreases as it rises higher into the atmosphere because of the decrease in air density. For the rocket to continue accelerating, the thrust must be greater than weight, which is constantly changing as the fuel is used.

  Newton’s second law of motion states that “A force is equal to the change in momentum per change in time. For constant mass, force equals mass times acceleration."
  For objects with constant mass, the equation is F=ma.  The external force, F, is the combination all four aerodynamic forces. Therefore, and increase in force would create an increase in acceleration. The assumption of constant mass may work for stomp rockets and solid model rockets, but for bottle and full-scale rockets, it is not usable.   
       Newton’s third law states that for every action, there is an equal and opposite reaction. This law is very important for rockets because it explains the generation of thrust by the rocket engine. In a rocket engine, hot exhaust gas is created in the combustion chamber using fuel and an oxidizer. This gas is accelerated through the rocket nozzle. The reaction to this force is thrust . According to newton’s second law, this accelerates the rocket. 
        Even though these fundamental laws were created long ago, they still influence current physics and engineering. All of these laws have more applications that just to rocketry. The laws of inertia, force equals mass times acceleration, and actions and reactions are basic physics principles that influence our entire universe.

What is a force?

A force is an action exerted on an object that may change the object’s state of motion or rest. Force is measured in Newtons. A contact force comes in contact with the object (ex: friction, catching a ball, pulling a string). A field force acts at a distance (ex: electricity, static, gravity, magnetism). Force is a vector quantity. A vector is a physical quantity with both magnitude and direction.  The net force is the vector sum of all forces acting on a body. An external force is a single force that acts on a body. Net force is equivalent to one force that produces the same effects as all the forces acting on the body. 

        The four main aerodynamic forces applied to a rocket are weight, thrust, lift, and drag. Weight is the gravitational force on an object. It pulls the object directly towards the earth from the center of gravity. Thrust is an oppositional force to weight. It propels the rocket through the air. Lift is a force perpendicular to direction of motion. Lift does not have much affect on the flight of a rocket, but it is what propels an airplane. Drag is a force that opposes motion. It decreases with altitude. 

Introduction - Problem and Hypothesis

          From the first Chinese ingenuities to the epoch of the Space Age, the rocket has, both literally and symbolically, taken the world to great heights. There are many different types and utilizations of rockets. The first rockets, invented in 1232 by the Chinese, were used as fireworks (and later as weapons). Rockets have been used to launch satellites, telescopes, and astronauts into space. They have incited national competitions as well as global unity. Behind the flight of a rocket is a baroque field of physics and engineering. In this study, I will examine the effects of ambient pressure, internal pressure, and propellant volume on the apogee of a water and compressed air powered rocket.

My hypothesis is that increased air pressure, lower ambient pressure, and greater water volume will lead to increased apogees. An increase in air pressure inside of the rocket will lead to a higher apogee because the greater potential energy will cause a greater force when the rocket is launched. Lower ambient pressure will lead to a higher apogee because, according to the thrust equation , thrust is proportional to  mass flow rate, exit and ambient pressures, and exit area. Therefore, lower ambient pressure will lead to more thrust and higher apogee. Greater water volume will lead to a higher apogee because it will cause a greater full mass (mo). According to the payload mass ratio , a greater value of mf will lead to a greater payload mass ratio . The payload mass ratio is also used in the Tsiolkovsky Rocket Equation. The change in velocity would be increased by a higher mass ratio. Consequently, a greater volume of water will lead to a higher apogee.