Application of Work, Energy, Force & Power on the Saturn V Rocket

Divya Mohan - GF202214698 - https://orcid.org/0000-0002-6578-1384

CSE Cybersecurity, Faculty of Engineering, Shoolini University

Engineering Physics (FSU030)

Dr. Pawan Kumar

October 11, 2022.

# Abstract

Mechanics is the core of all mechanical physics. There are four fundamental elements of mechanics namely Work, Force, Power, and Energy. This assignment briefly discusses the application of basic mechanics on the Saturn V Rocket which reached the Moon on July 16, 1969, under the command of Neil Armstong during the Apollo 11 mission. When the rocket lifts off the thrust is applied to it. During this process work is done as the energy is transferred in the displaced direction at an angle because of the thrust. Energy is stored in the form of potential and chemical energy. The rate of change of this potential and chemical energy to the kinetic rate of the rocket is called Power.

And there can be no other perfect example of it than the Saturn V SLS (Space Launch System). Rockets are a marvel of mechanical physics. In today’s ever-changing world where SpaceX’s self-landing rockets have been introduced, there are no limits to the imaginations and contributions of humanity. This space age all goes back to 1969 when the first most powerful rocket to be built was Saturn V. No other launch vehicle in history can claim accomplishments on the level of the Saturn V. The Saturn V rocket was a technological wonder. When it was designed in 1969, Saturn V was more extensive and more powerful than anything ever created. And until the recent introduction of SpaceX’s Starship, no design could match it for nearly 50 years, even after it retired in 1973.

Keywords: Mechanics, Work, Force, Power, Energy, Apollo 11

Application of Work, Energy, Force & Power on the Saturn V Rocket

The Saturn V is still a modern wonder. Be it the five Rocketdyne F-1 main stage engines - where each produced one and a half million pounds of thrust, equating to 32 million horsepower, and burned 6,000 pounds of rocket grade kerosene and liquid oxygen every second; which was used by Saturn V to ascend to the altitude of 38 miles, or, be it the lunar module’s Ascent Engine - built by Bell Aerosystems Company that produced 3,500 pounds of thrust to come back to the parking orbit from Mare Tranquillitatis where Apollo 11 had landed. Nothing compares to the mighty Saturn V. When these five F1 engines ignited at lift-off, the Saturn V pummeled the Earth with 3.4 million kg of thrust – equivalent to 160 million horsepower.

Figure: An Ascent Engine |
Figure: An Rocketdyne F1 Engine |

If we want to apply mechanics efficiently to the rockets then, according to Robert H. Gaudy, the most efficient way to operate a rocket is to increase its exhaust velocity as it accelerates. When this increase is done properly, the final kinetic energy of the rocket is maximized. It is shown that the resulting “perfect rocket” is far simpler to analyze than the traditional constant-thrust rocket.

Mechanics is a branch of physical science that deals with energy and forces and their effect on bodies. The four fundamental elements of mechanics which we will discuss as the application of the Saturn V rocket are Work, Energy, Force, and Power. Let us discuss these four Fundamental Elements of Mechanics.

# Fundamental Elements of Mechanics and its applications

## Force

Force is a description of an interaction that is either External, Internal, or Reactive that causes a change in an object's motion. It can also be represented by the symbol F.

F = ma

where F = force, m = mass, and a = acceleration.

### Application of Force on the rocket

Force is applied in the form of thrust in the rocket. During the Apollo 11 mission, the Saturn V rocket’s first stage carried 770,000 liters of kerosene fuel and 1.2 million liters of liquid oxygen needed for combustion.

Upon liftoff, the first stage’s five F-1 rocket engines ignited and produced 7.5 million pounds of thrust.

Resultant force = thrust – weight

Or, Resultant force = 7.5 million – 2.8 million kilograms

Or, Resultant force = 4.7 million newtons.

Acceleration = resultant force ÷ mass

Or, Acceleration = 4.7 million ÷ 2.8 million kilograms

Or, Acceleration = 1.67 m/s2.

Figure: Rocket Thrust (NASA)

## Work

Work is a measure of energy transfer that occurs when an object is moved over a distance by an external force at least part of which is applied in the direction of the displacement.

W = fd cos θ

where w = work, f = force, d = displacement, cos θ = angle between force and displacement.

### Application of Work on the rocket

In terms of rocket science, work is a measure of energy transferred when the rocket moves at an angle over a distance by the thrust applied to it from its engine which is applied in the direction of the displacement. Since the rocket is moving at an angle from an initial point to a final point, work is done. In our world, a rocket translates, or changes location, from one point to another. And a rocket can rotate, or change its attitude. In general, the motion of a rocket involves both translation and rotation.

Figure: Rocket Translation (NASA)

## Energy

Energy is the capacity for doing work. It may exist in potential, kinetic, thermal, electrical, chemical, or other various forms.

P.E. = mgh

Where PE = Potential Energy, m = mass, g = gravitational force, h = height.

K.E. = ½ mv2

Where KE = Kinetic Energy, m = mass, v = velocity.

### Application of Energy on the rocket

Energy of the rocket is the capacity for doing work. It may exist in potential, kinetic, thermal, electrical, chemical, or other various forms. When the rocket is standing stationary, potential energy is stored. Upon ignition of the first stage, chemical energy is converted to thermal and kinetic energy. When the rocket starts moving, it starts gaining kinetic energy. When the rocket finished all the 3 stages, it circled earth at 38946 kilometers an hour on the trajectory to the Moon.

### Energy analysis on a modern small-scale rocket

An energy analysis shows that a modern rocket system with as low as tens of kg of fuel can be sufficient to deliver a 10g payload into orbit given a sufficiently low mass autonomous rocket flight control system.

## Power

Power is a measure of the rate at which work is done or similarly, at which energy is transferred.

P = W / t

Where P = Power, W = Work done, t = time.

### Application of Power on the rocket

In the Saturn V rocket, Chemical and Potential energy is getting converted to kinetic energy. The power of the rocket is a measure of the rate at which this energy is getting transferred or changed. Therefore in Saturn V, the rate of change of energy stored in the compressed chemical form from oxygen, kerosene, and hydrogen to the exhaust nozzle of engines and the energy produced by their exhaust causes the rocket to move in the opposite direction of thrust where the potential energy of these chemicals is changing to kinetic energy in the form of moving body.

# Results

The four fundamental elements of mechanics namely Work, Force, Power, and Energy are applied to and discussed in a practical real-world application, in this case, a Saturn V Rocket. The future of an SLS may depend on fully autonomous landing systems but the space age began when Saturn V was inducted into the World and achieved the feat of landing on the moon in 1969 inspiring many generations of that time and many more yet to come. We can conclude that the Saturn V has served as the technological marvel of mechanics in the field of SLS to date.

# References

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Kehl, F., Mehta, A. M., & Pister, K. S. (2015). An attitude controller for small scale rockets. Springer Tracts in Advanced Robotics, 201–214. https://doi.org/10.1007/978-3-319-07488-7_14

Bryan, W. (2013, March 20). We have liftoff: Apollo rocket engines pulled from ocean floor. NPR. Retrieved October 10, 2022, from https://www.npr.org/sections/thetwo-way/2013/03/20/174834978/we-have-liftoff-apollo-rocket-engines-reportedly-pulled-from-ocean-floor

US Patent 3,699,772, Elverum Jr., Gerard W., "Liquid propellant rocket engine coaxial injector", issued 1968-01-08

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