Interactive Orbital Space Launcher Simulator: Delta-V and Launch Efficiency

Orbital Space Launcher Simulator

Developed By: Ir. MD Nursyazwi

Instructions on How To Use

This simulator allows you to compare the performance of a space launcher when initiated from two distinct locations on Earth: the Equator and the North Pole. The simulation models the fundamental physics principles that influence launch efficiency, namely the rotational velocity of the Earth.

Follow these steps to conduct a simulation:

• Enter the primary physical parameters of your hypothetical launcher in the "Data Input" section below, or use the preset buttons.
• Click the "Run Simulation" button to initiate the calculations and graphical representation.
• Observe the four graphical simulations, two for each launch type.
• Review the calculated payload capacity and fuel consumption in the Data Output section below.

Data Input

1. Total Rocket Mass (Wet Mass, in kilograms):

2. Total Fuel Mass Available (in kilograms):

3. Target Orbital Velocity (V_Target, in meters per second):

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4. Engine Performance (Specific Impulse, I_sp in seconds):

5. Trajectory/Gravity Loss (V_{Loss, Gravity} in m/s):

6. Aerodynamic Drag Loss (V_{Loss, Aero} in m/s):

Graphical Simulation

Equatorial Launch (Top-Down)

Polar Launch (Top-Down)

Equatorial Launch (Side View)

Polar Launch (Side View)

The graphical simulations now provide a comprehensive comparison of launch trajectories and the influence of Earth's rotation.

• Equatorial Launch (Top-Down): The launch is shown starting from the edge of the globe. The rocket's curved path demonstrates how the Earth's eastward spin contributes significantly to the rocket's final velocity, providing a substantial velocity bonus.
• Polar Launch (Top-Down): The launch is shown starting from the center (North Pole). The rocket's path is nearly straight, visually representing that it gains zero velocity from the Earth's rotation, as rotational speed is zero at the poles.
• Equatorial Launch (Side View): This view shows the rocket's trajectory as it performs a vertical climb followed by a gravity turn to gradually enter a stable, horizontal orbit. Crucially, a label now indicates the +465 m/s free velocity gained from the Earth's spin.
• Polar Launch (Side View): This view also shows the typical ascent trajectory, but a label confirms the rocket receives +0 m/s free velocity, highlighting the higher fuel requirement.

The top-down views illustrate the rotational speed advantage, while the side views show the typical ascent profile required to fight gravity and reach orbit, with the side-view labels clarifying the speed boost difference.

Data Output

Enter parameters or select a preset and click Run Simulation.

Mission Rectification Required

The Equatorial launch scenario failed to reach orbit. The following changes are proposed to achieve a successful mission:

Equatorial Launch Results

Polar Launch Results

Graphs and Charts

Science Explanations

The Principle of Delta-V (Change in Velocity)

In orbital mechanics, Delta-V is the total change in speed and direction required for a rocket to achieve a specific maneuver, such as reaching orbit. It is the primary metric because it directly dictates the amount of propellant required.

Delta V_{Ideal, Total} = V_Target + V_{Loss, Gravity} + V_{Loss, Aero}

Where:

• V_Target: The speed needed for a stable orbit (e.g., 7800 m/s for Low Earth Orbit).
• V_{Loss, Gravity}: The speed lost due to the constant downward pull of gravity during the climb. This is minimized by performing a "gravity turn" rather than climbing straight up. (Typically around 1500 - 2500 m/s).
• V_{Loss, Aero}: The speed lost due to friction with the atmosphere (aerodynamic drag). This is minimized by launching in a low-density area. (Typically around 500 m/s).

This Delta V_{Ideal, Total} is then adjusted by the rotational speed of the Earth:

• Equatorial Launch (Eastward): The rotational velocity is approximately 465 m/s, reducing the engine's work:
  Delta V_{Required, Eq} = Delta V_{Ideal, Total} - 465 m/s
• Polar Launch: The rotational velocity is 0 m/s, meaning the full Delta V must be generated by the engines:
  Delta V_{Required, Pol} = Delta V_{Ideal, Total}

The Tsiolkovsky Rocket Equation: Quantifying Efficiency

The Tsiolkovsky Rocket Equation defines the exponential relationship between the required Delta V and the amount of fuel needed. Engine Performance (Specific Impulse, I_sp) is the key input here.

Required Fuel Mass = Total Mass × [ 1 - e ^ ( -Delta V / (I_sp × g₀) ) ]

(Where 'e' is Euler's number and g₀ is standard gravity)

Where:

• Delta V: The required change in velocity (m/s).
• I_sp: The Specific Impulse of the engine (a measure of engine efficiency, in seconds). A higher I_sp means less fuel is required for the same Delta V.
• g₀: Standard gravity (approximately 9.81 m/s²).
• Initial Mass: The total mass of the rocket before launch.
• e: Euler's number (base of the natural logarithm).

Since the Delta V required for an Equatorial launch is smaller, the amount of fuel calculated by the Tsiolkovsky equation is also smaller. The fuel mass saved can then be converted directly into extra payload capacity, making equatorial launch sites significantly more efficient for placing mass into orbit.

Scripture and Authority in Space Exploration

Surah Ar-Rahman 55:33 (Authority and Power)

This verse presents a profound challenge regarding the exploration of the cosmos, connecting the physical ability to traverse space with the concept of authority or power.

يَا مَعْشَرَ الْجِنِّ وَالْإِنسِ إِنِ اسْتَطَعْتُمْ أَن تَنفُذُوا مِنْ أَقْطَارِ السَّمَاوَاتِ وَالْأَرْضِ فَانفُذُوا لَا تَنفُذُونَ إِلَّا بِسُلْطَانٍ

Translation

"O company of jinn and mankind, if you are able to pass beyond the regions of the heavens and the earth, then pass. You will not pass except by [a] sultan (power/authority)."

Explanation of "Sultan" (سُلْطَانٍ)

The key term in this verse is Sultan (سُلْطَانٍ), which is often translated as authority, power, or proof. In the context of traversing the regions (أَقْطَارِ) of the heavens and the earth, scholars interpret this word as encompassing several interconnected meanings:

• Scientific Authority/Knowledge: This is the interpretation most relevant to modern rocketry. It refers to the knowledge, technology, and means—the verifiable scientific proof—required to overcome natural barriers like gravity and atmospheric drag. To traverse the vastness of space, mankind requires highly sophisticated Delta-V calculations, high-performance engines (I_sp), and the technological capability to build and launch rockets, which are all forms of this scientific authority.
• Divine Authority/Permission: This suggests that any power or ability granted to creation ultimately originates from the Creator. Mankind's eventual success in reaching space is, therefore, tied to a form of permission or enablement by God.
• Political/Societal Authority: This suggests that any power or ability granted to creation ultimately originates from the Creator. Mankind's eventual success in reaching space is, therefore, tied to a form of permission or enablement by God.

The verse thus stands as both a challenge and a statement: the physical barrier to leaving Earth is immense, and overcoming it requires immense authority in the form of deep scientific knowledge and technological power.

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Surah Al-Anbiya 21:16 (Purposeful Creation)

This verse introduces the concept of intentionality and seriousness in the cosmos, contrasting the intricate precision required for space travel with the idea of creation as a casual act. It serves as a challenge and an invitation to mankind to explore the cosmos.

وَمَا خَلَقْنَا ٱلسَّمَآءَ وَٱلْأَرْضَ وَمَا بَيْنَهُمَا لَٰعِبِينَ

Translation

"And We did not create the heaven and earth and that between them in play." (Saheeh International)

Explanation

The term "in play" (لَٰعِبِينَ - lā'ibīn) suggests frivolity or lack of purpose. This verse challenges mankind to travel outside the Earth (similar to the preceding verse 55:33) and witness the cosmos firsthand. When explorers utilize the laws of physics to traverse the universe, they confirm that creation operates according to absolute, precise, and serious laws, not by chance or amusement.

The success of space travel—relying on exact calculations like Delta-V and I_sp—is a testament to this purposeful creation. The meticulous engineering required to escape Earth's gravity directly reflects the miraculous precision of the cosmic order established by the Creator, which demands respect and rigorous scientific authority to navigate.

References

This simulator is based on simplified physics models for illustrative purposes. For a comprehensive understanding of orbital mechanics and rocketry, consult the following resources:

• NASA and ESA educational materials on spaceflight.
• Principles of Rocketry and Propulsion by various academic authors.
• Orbital Mechanics for Engineering Students by Howard D. Curtis.

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