Table of Content

# Rockets - A guide

Rockets as we know today are massive machines that can be used to shoot payloads and Teslas into space, although some bad people tend to use them to hurl bombs at one another at supersonic speeds when they disagree, as that is the most mature thing to do. Rockets have fascinated humans since long, past 7 centuries to be exact. Emerging from its development as a weaponry half a millennium ago, rockets are now mostly (NORTH KOREA) used for transportation, communication and space exploration.

It was in 20th century a formal scientific study of rockets was done. In 1903, Konstantin Tsiolkovsky formulated the famous rocket equation which pretty much tells us that almost 80% of the mass of rockets has to be propellant (fuel), simply because gravity is a bitch, and the rest includes the structure, engines and the payload. Rockets are incredibly complex machines that require huge amount of manpower and money to build and building one touches on all areas of engineering be it Material Science, Civil, Mechanical, Electronics, Computer Science or Aerospace. Most rockets today are one-offs i.e you build once, launch your payload into a desired orbit/trajectory, forget about that expensive rocket you built and start building all over again. The first stages (modern rockets consist of multiple stages) generally end up in the ocean following a parabolic flight path and upper stages of rockets are still either intentionally de-orbited if they have enough fuel left for de-orbiting maneuver or are left in orbit for their orbit to decay due to atmospheric drag after which they generally burn up during reentry. If you think about it, these one-off rockets are really expensive.

In 1960, Philip Bono proposed the VTVL (vertical-takeoff-vertical-landing) reusable concept that would transport passengers to any point in the world in 45 minutes and significantly reduce the cost of space travel. Such proposals were in large ignored by the scientific community. Moreover, NASA backed the more conservative semi-reusable VTHL (vertical-takeoff-horizontal-landing) Space Shuttles. These semi-reusable Space Shuttles which were envisaged to cut down the cost of space travel, on the contrary, were much more expensive than one-off rockets. The Space Shuttle program was retired by the NASA in 2011. It was in 21st century thanks to private ventures ( like SpaceX and Blue Origin ) and advancements particularly in Material Science and Control Systems VTVL have finally become a reality. Although SpaceX has successfully reused the first stage boosters of the Falcon9 vFT on numerous occasions these boosters need to be refurbished and the second stage is still discarded, full and rapid re-usability is what SpaceX aims to achieve in this decade.

Surely rockets are the coolest machines out there. Frequent PSLV, GSLV launches by ISRO, Falcon upgrades at SpaceX, Missile tests and Space Voyages have been keeping the buzz of rockets on the beat. If you have ever wondered, How did man ever begin to use them as launch vehicles? How these massive things work? How are they evolving? What engines power up a rocket so that they can defy gravity? This short introduction to rockets is for you spaceman.

## A brief history

Back in the 13’th century, the Chinese started using rockets as fire arrows by burning the gunpowder (fuel) pasted to the stem. These fire arrows were used for entertainment and not as weapons when they were first invented. The fire arrow rockets were then adopted as a choice of weaponry. Also, there are apocryphal accounts of a daring although a less successful Chinese astronaut of the Ming Dynasty, Wan hu, who supposedly used a chair strapped with forty-seven rockets to launch himself into space, the chair hypothetically exploded killing Wan hu. Rockets were used extensively in warfares by people all over the globe. Conrad Haas, in the middle of 16th century, formulated logs on how these weapons can be used as vehicles. He wrote how instead of merely using gunpowder to shoot rockets, one can use fuel mixtures and build multistage rockets. If only his work was seen. In the eighteenth century, Tipu Sultan developed and used iron-cased rockets for wars. This technology was later adopted by the British to develop Congreve rockets.

Modern Rocket Technology only came into existence when Konstantin Tsiolkovsky formulated theories on rocket propulsion. He came up with the famous rocket equation in 1903 which helps us calculate the maximum $\Delta{v}$ a rocket can achieve given initial and final mass (once all the fuel is used up) ratio and the exhaust velocity of gases from the nozzle of the rocket engine - an important parameter in to determine if a particular rocket can perform a certain maneuver. The ideal rocket equation, which ignores the affect of atmospheric drag and lift is:

$\Delta{v} = v_e \ln{\frac {m_0} {m_f}}$

Where:
$\Delta{v}$ is the maximum change of velocity of the vehicle.
$v_e$ is the effective exhaust velocity.
$m_0$ is the initial total mass, including the propellant.
$m_f$ is the final total mass, without the propellant.
$\ln$ is the natural logarithmic function.

Robert Goddard conducted serious analysis on rockets. He formulated theories about ignition of propellants and exhaust nozzles. On 16 th March 1926, he launched the world’s first rocket- a conventional rocket engine attached to a supersonic nozzle that would cool the hot exhaust gases and produce high thrust with greater efficiency. Rockets technology developed to be popular during the II world war.

After the II world war, rockets were used as launch vehicles for Space Exploration. Rockets as weaponries are still prevalent in the modern world as Missiles.

## Principle of Operation

Rockets accelerate by expelling part of their mass i.e. the propellant with high speed through a nozzle and moves forward due to conservation of momentum. Hence, they are called non-air-breathing engines, in contrast to jet engines you often see on commercial airliners, that use a turbine to works on the most simple principle of is a device that propels itself forward by emitting hot gases in a direction opposite to its direction of acceleration.

Rockets function according to Newton’s third law of motion: Every action has an equal and opposite reaction. To support this, let me tell you that rockets enclose high-pressure gases and when these gases are let out, the rocket moves forward. The motion of the exhaust gases is the action and the forward thrust of the rocket in the direction opposite to the stream of gases is the equal and opposite reaction.

For the rocket to lift off the ground, the mass of the rocket must be much lesser than the thrust produced i.e TWR(Thrust to weight ratio) must be greater than 1. Rockets on an average weigh about 50000 Kg. Evolution of rocket technology proves that it is possible to achieve a large amount of thrust that is required to propel the rocket forward and keep it going. Also, it is possible to escape the earth’s gravity through greater hypersonic speeds. Efficient design and propulsion optimization have helped the folks achieve heights in rocket science.

## Design

Given in the figure below, is a sketch simple single stage rocket.

A single stage rocket like the one shown in the figure above generally consists of 3 major components:

• A propellant tank: to store the fuel and the oxidizer (because rockets, unlike the jet engines, do not breathe air and oxidizers help burn the fuel).
• A Rocket Engine that facilitates ignition of the propellant and exhausts burnt gases to the atmosphere, thereby producing thrust.
• A Payload: that serves the mission of the flight. For instance, when they have to place a satellite in the orbit, the satellite is the payload. Components like fins, extra engines, boosters, and wheels are often added to rockets in order to optimize flight. Multistage rockets are used when it comes to breaking the gravity barrier (escape velocity). This is done by adding extra stages filled with propellants to the existing stages.

When a stage fuel is emptied, it detaches itself from the rocket, thereby reducing mass, making the rocket lighters. The combustion keeps going due to the burning of the succeeding stage.

## Rocket Engines

Rocket engines are non-airbreathing engines that use propellants for producing exhaust gases which accelerate the vehicle forward. Why do you think that rockets can operate in space? It’s because they carry their own oxidants and unlike the jet engines, they do not rely on the air outside for compression and combustion.

### The Thermal Rocket Engine:

Thermal rocket engines, like conventional engines, convert heat energy generated by the fuel to Kinetic Energy that helps the rocket propel forward. A thermal rocket engine comprises of: Combustion chamber: It contains two separate compartments for fuel and oxidant in the case of liquid propellants but one compartment for solid propellants since the fuel and oxidants are in a solid state. Exhaust nozzle: Under ignition of the propellants, the hot gases formed are expanded in the nozzle. They are thus, ejected out with high velocity, accelerating the rocket in the forward direction.

Thrust Coefficient and characteristic Velocity:

Thrust Coefficient Cf = F/(AP) Where, F = Thrust Force A= Nozzle Throat Area P = Pressure Characteristic Velocity C* = (pAt/m.) Where, p = Chamber Pressure At= Throat Area m.=mass flow rate Thrust coefficient and characteristic velocity are the parameters used to determine the efficiency of the rocket engine. Thrust coefficient determines the nozzle efficiency whereas the characteristic velocity is a measure of the combustion chamber efficiency.

### Liquid Propellant Rocket Engines:

These rockets as mentioned earlier, contain separate chambers for propellants and oxidants. When high-pressure gas is pumped into the tank, the propellants are forced into the combustion chamber. The performance of the engine is determined by thrust coefficient and characteristic velocity. Thrust coefficient is solely determined by the properties of the nozzle but the characteristic velocity depends on the choice of propellants. Technically, the thrust depends on the square root of Combustion temperature. Given below is the list of combustion temperature and exhaust velocity for various propellants:

Tc is the combustion temperature and Ve the exhaust velocity. Their values have been tabulated for combinations of different fuels and Liquid Oxygen (LOX) -Oxidizer. According to the table, fuel with hydrogen and beryllium are taken in the ratio 49:51 gives highest exhaust velocity whereas it shows the lowest combustion temperature. Methane appears to be ideal in terms of optimal exhaust velocity and combustion temperature.

Given above is a picture of a liquid Oxygen and methane driven rocket engine, Aerojet weighing 100-lbf taken during a test at NASA Liquid Propellant engines are said to deliver low thrust due to low flow rates at high pressure which is why they are limited to the upper stages of the vehicle.

### Solid Propellant Rockets Engines:

A solid Propellant rocket functions the same way the liquid propellant rocket does. The only difference is the kind of propellant used and the way it is ignited. The fuel and oxidizers are in the form of a solid block, which in the fuel terminology is called, the grain. The hot gases are produced when the grains are burnt.

The exhaust velocity is not that high but the absence of separate tanks, pumping devices and pipelines can reduce the mass to a greater extent thereby increasing the thrust. Solid propellants are storage-friendly, safe and no external pressure source is required to pump them into the chamber. The main drawback is that they cannot be controlled once ignited.

### Electric Propulsion:

Thermal rockets produce enough thrust and achieve exhaust velocities as high as 4 km/s. But when it comes to achieving higher power and increasing the exhaust velocity beyond 4 km/s, Electric Propulsion is preferable.

Electric propulsion can be achieved by applying electric energy to the propellant from an external source. When this is done, the propellant burns faster than when it is burnt during thermal propulsion, thus overcoming its ignition temperature earlier. This method is also proved to generate higher exhaust velocity. Remember Electromagnetism? Where Magnetic Field is used to generate electricity? Well, the propellants are made to disassociate into ions and a magnetic field is used to accelerate them to really great speeds. This, in addition to the velocity generated earlier increases the total exhaust velocity enabling the launch vehicle to achieve greater speeds. Common power sources: Batteries, solar cells, power from nuclear generators. The major disadvantage of this propulsion system is the increase in the overall structural mass due to electric power generators.

### Nuclear Propulsion:

In nuclear propulsion (thermal), liquid hydrogen is usually taken as a working fluid, heated in a reactor and then expanded through the nozzle. This kind of propulsion system is said to achieve really high velocities.

Although various theories have been proposed for nuclear, electric and reusable propulsion systems, conventional engine propulsion is still in use. Electric Rockets haven’t been used for launches because of their low thrust on earth surface. They have been used by the Soviet Union in Spacecraft Propulsion Systems. Nuclear thermal rocket theory is just a proposal as no launch has ever taken place since NERVA was tested in 1967. 100% reusable launch vehicles are yet to be invented. In this space advancement era, research and progress in Rocket propulsion can help man reach out to the stars.

1. Reference, wikipedia

2. Reference, wikipedi

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