Aerospace Engineering Analysis: China's Fractional Orbital Bombardment System (FOBS) test (2024)

Table of Contents:

• Overview

• Background

  • Ballistic Trajectory

  • Fractional Orbit Bombardment System Trajectory

  • Soviet FOBS System

  • China: FOBS Enters the 21st

  • Hypersonic Glide Vehicle

  • Hypersonic Glide Vehicle Trajectory

  • Implications

• Assumptions and Caveats:

• Calculations

  • TLDR

  • Assumptions about calculations

  • Calculations and estimations

• Conclusion

• References

Overview:

In 2021, China launched and tested what was labeled a “Fractional Orbital Bombardment System”, or FOBS, according to the Financial Times.

However, while the FOBS weapon system had origins with the Soviet Union during the Cold War, China’s 2021 test incorporated updates that foreshadowed a weapon that could be the most challenging type of hypersonic weapon to intercept.

In this edition of The Engineer’s Perspective, we will go over the Fractional Orbit Bombardment System, how China modified this Cold War era weapon to create something that is potentially more dangerous, and using open source equations, attempt a basic modeling of this new hypersonic weapon’s behavior.

Background:

We go into the a bit of missile defense terms and history, explaining some background of:

1. Types of missile trajectories

2. Where FOBS belongs in all this

   See Also

   SOLVED: a) ¿Cuáles son las similitudes y diferencias entre los orbitales 1 s y 2 s para el átomo de hidrógeno? b) ¿En qué sentido el orbital 2 p tiene carácter direccional? Compare las características "direccionales" de los orbitales px y dx^2-y^2. (Es de

3. And how China upgraded the FOBS system for the 21st century

Ballistic Trajectory

All Ballistic missiles, whether used by the United States, Russia, China, etc. have a single unifying characteristic: All leave the Atmosphere and briefly enter space before descending back to earth under the pull of gravity. An example of a ballistic missile trajectory is shown below:

Fractional Orbital Bombardment System Trajectory:

A FOBS weapon system, unlike a ballistic trajectory, enters an orbit around the planet, de-orbiting through a retro-grade engine burn and reenter the atmosphere just before reaching its target, only then entering a ballistic trajectory:

The Soviet FOBS System

The Fractional Orbital Bombardment System (FOBS) was initially developed by the Soviet Union as a nuclear weapon delivery system in the 1960s around the time of Sputnik. According to Wikipedia, “ It was one of the first Soviet efforts to use space o deliver nuclear weapons.” Furthemore “The Success of the Soviet Vostok program, which sent a human into orbit, and then landed at a pre-designated location, made [The FOBS-style] weapon seem more feasible.”

The advantages of the FOBS System versus that of the United States Ballistic Missile were that systems launched in this manner, unlike ballistic missiles, could essentially fly over and past traditional missile defense systems, or could even coming in the opposite direction of where traditional missile threats would be expected to come from.

China: FOBS enters the 21st Century

China utilized a Chang Zheng, or “Long March” Rocket:

However, China’s FOBS test differed from the Soviet system by utilizing a Hypersonic Glide Vehicle for a warhead instead of a traditional reentry vehicle:

Hypersonic Glide Vehicle:

A Hypersonic Glide Vehicle is a warhead designed to glide through the upper reaches of the atmosphere at speeds greater than Mach 5. Unlike other types of warheads however, Hypersonic Glide Vehicles exhibit greater range of movement than any other type of Hypersonic Weapon, even ballistic missile warheads. This high level of maneuverability results in a warhead that is more difficult to defeat than other types of warheads.

Hypersonic Glide Vehicle Trajectory

The Hypersonic Glide Vehicle reenters the atmosphere at a lower altitude when compared to an ICBM, allowing it to maneuver around and below the detection systems of current missile defenses. This trajectory allows for the re-entry vehicle to move laterally as well as change altitude in order to attack its target, adding a dimension of difficulty for missile defense systems.

Implications:

The major implications from China’s modification of the FOBS delivery system are three-fold:

1. Utilizing a method of delivery like FOBS enables a missile to be sent into an orbital trajectory in the opposite direction of where an enemy’s defenses are.

2. However, combining the FOBS method with a Hypersonic Glide Vehicle, which is more maneuverable than any other hypersonic re-entry vehicle after entering the atmosphere, enables the weapon to maneuver out of range or around, or even below air defenses.

3. The resulting system’s two methods of maneuverability built into it results in a completely new system that maximizes the opportunities to strike, but minimizes the ability of the system to be defeated.

Assumptions and Caveats

The assumptions I made for this basic-level model are the following:

• The Rocket was estimated to have flown 40,000km at over 100 minutes

• Low Earth Orbit is normally around 300km, or 186 miles

• The assumed altitude for the FOBS system is below this, at approximately 100km to 200km according to Quest magazine

• Mach 1 = 700 mph

• The circumference of the earth is approximately 40,000 km, or 25,000 miles

• Relevant altitudes traversed by a Hypersonic Glide Vehicle is between 30km-100km

Calculation and Caveats:

TLDR:

• China’s HGV Flew approximately 29,655km in LEO orbit before de-orbiting, and gliding through the atmosphere for 11,356 km/7040 miles at an average speed of Mach 21 or 6.67km/s

• Assuming:

  • Calculated LEO Orbital speed is 7.78km/s or Mach 25, meaning the Hypersonic Glide Vehicle would need to drop below Mach 25 to exit orbit and re-enter the atmosphere.

  • Open-source information indicates the Hypersonic Glide Vehicle flew 40,000 km prior to impacting in China, for a total of over 100 minutes.

  • Staying with approximately 100 minutes for the overall flight, the speed of the Hypersonic Glide Vehicle for most of this 40,000 km flight was 24,000 km/h, or 14,814 mph; approximately Mach 21 if Mach 1 is 700mph, which is in line with the calculated orbit speed from above.

Calculation of orbital speed

Orbital speed is the speed at which satellites are moving to remain in orbit over the earth. when in a Low Earth Orbit of between the 160-300km I have bounded for this model. We are assuming that the HGV stayed in Low Earth Orbit.

We can utilize the classic satellite kinematic orbital velocity calculation to estimate this speed.

Where:

g = universal gravitational constant of 6.67*10 to the -11.

Mcentral = Mass of the central body; in this case, earth at 5.97 *10 to the 24 kg

radius = radius of the earth, which is 6.378 *10 to the 6th meters

For our calculations we will use the radius of the earth (6,371km, and add the additional 200km):

The result is approximately 7.8 km/s a second, or around Mach 25, meaning that a Hypersonic Glide Vehicle will need to travel slower than 7.8km/s or Mach 25 in order to return back to earth, otherwise, at 7.78km/s and above at LEO altitude, the system will enter orbit.

Deriving the average speed the Hypersonic Glide Vehicle is moving

Open sources indicate the Glider traveled approximately 40,000km at over 100 minutes.

1. Going with that we can divide 40,000km by 100 minutes to approximate the amount of miles the glider traveled every 60 seconds, and then multiply that by 60 to derive how many km/h the system was moving:

2. We can then work with 24,000km/h and convert it to mph and convert that into Mach:

   \(24000 \ km/h *.62 = 14880 mph; \frac{14480 mph}{700} = Mach \ 21.26\)

The result is we find out that the Hypersonic Glide Vehicle is traveling at around Mach 21, which is what we had predicted as a speed below Mach 25 that the system will need to be traveling at.

Calculation for Glide distance:

Taken from Hypersonic Boost Glide Weapons, we will utilize the following Equation to estimate the glide distance of the Chinese HGV test:

With the above equation, we will also assume a Lift to Drag ratio L/D of 2.6

As we know Ve, we can calculate Vi then from the 24,000km/h, and convert it to km/s:

Filling in the blanks then with the equation, we get the following numbers:

And then we input them all into the equation altogether:

Assuming the Hypersonic Glide Vehicle has a Lift-to-Drag ratio of 2.6, and that the glider’s initial speed was 6.67 km/s, the Chinese rocket traveled 28,664km, or 17,759 miles while outside of the atmosphere prior to de-orbiting, with the hypersonic glide vehicle then then traveling 11,536 km, or ~7040 miles on the final leg of its journey before impacting in China.

Conclusion:

The Fractional Orbital Bombardment system that China tested in 2021 was a harbinger of the capabilities that near-pear future competitors of the United States could exhibit. The original FOBS weapon system provided the potential of evading traditional missile defense systems by sending a weapon system from the opposite direction that the system is facing.

However, by taking the FOBS weapon system from the Cold War and modifying it to include a Hypersonic Glide Vehicle, the most maneuverable of reentry vehicles. China updated the FOBS system for the 21st century.

Based on the information given, the previous assumptions listed, combined with the open-source calculations, China launched a rocket that traveled approximately 28,664 km or 17,759 miles in Low Earth Orbit before releasing a Hypersonic Glide Vehicle warhead, which then traveled 11,536km, or 7040 miles before impacting in China.

The implication from these calculations indicates that the combination of the two systems creates an intercontinental weapon system without the vulnerabilities that older ballistic missiles present: A weapon that can evade missile defense systems while providing the ability to come from any direction.

References:

• The Financial Times: China tests new space capability with hypersonic missile

• Wikipedia: Long March 2C

• Wikipedia: Fractional Orbital Bombardment System

• Quest: The History of Spaceflight Quarterly - The Soviet Fractional Orbiting Bombardment System (FOBS) A Short Technical History

• Military and Security Developments Involving The People's Republic of China 2022

• Hypersonic Boost Glide Weapons

• Wikipedia: Ballistic Missile

• Astronautix: Long March 2C (Chang Zeng) Burn Time and Mass Specifications

• Analysis of optimal initial glide conditions for hypersonic glide vehicles