During the Cold War, the United States investigated the possibility of using the space domain for weapons, by having a satellite in orbit carrying long tungsten rods, which could deorbit and impact the Earth with a high velocity, thereby causing damage. The United States Air Force even tested orbital bombardment, but little information can be found about those tests. In literature, this concept is often considered to be a superweapon, capable of striking anywhere in the world at short notice, and as a suitable alternative to small nuclear ‘bunker busters’. However, this claim is not supported by scientific research.
At present, the military uses of the space domain are primarily communications and Intelligence, Surveillance and Reconnaissance (ISR). However, in this work, the concept of orbital bombardment and its present feasibility will be investigated. When studying this concept, it is good to bear in mind that laws also apply to space. In 1966, at the peak of the Space Race, the Soviet Union and the United States agreed on an Outer Space Treaty, by the United Nations (UN), which states the following (UN Outer Space Treaty of 1966; Article IV 1966):
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Evidently, this treaty created boundary conditions for weapons that are allowed in orbit. Incidentally, placing nuclear warheads in ballistic missiles does not constitute a violation, because they fly suborbital trajectories instead of orbits. A kinetic orbital bombardment system consists of a satellite in orbit around the Earth with a bus of multiple heavy metal (tungsten or depleted uranium) rods. These rods can be deorbited, and their kinetic energy upon impact can destroy targets on Earth (Watts 2005). The great advantage of such a weapon system is the rapid response time and, with a suitable constellation, every target on Earth can be hit. Another advantage is that it is not a ‘doomsday weapon’, the use of which would have catastrophic effects, and as such it would not violate the Outer Space Treaty. This weapon system can be used in both small conflicts and larger conflicts, because the projectile does not have an explosive warhead, and thus little collateral damage is expected from these weapons. The US Air Force explored this idea from 1978 to 1988, including at least one flight test from Vandenberg Air Force Base (AFB) to Kwajalein Atoll, using a suborbital trajectory (Watts 2005). Very few technical details are known, but the program was reportedly terminated because ‘Air Force fighter generals were not interested in a non-nuclear global weapon’ (Watts 2005).
However, the Air Force’s 2003 Transformation Flight Plan included plans for orbiting weapons, including hypervelocity rod bundles, called ‘Rods from God’. According to Johnson-Freese (2017), the idea was not new or even original. The science fiction writer Pournelle (1974) conceived it while working at Boeing in the 1950s. He called it ‘Thor’. Pournelle (1974) was well-aware of the (strategic) importance of orbit around Earth, which is reflected by a conversation with the well-known science fiction writer Robert A. Heinlein (Pournelle 1974):
As far as is known,
In this orienting work on kinetic orbital bombardment, we have studied the most essential features of both the projectile trajectory from orbit and the expected target penetration, including the seismic effects. For this reason, it was inevitable to make simplifications. For instance, the impact model is a 1D semi-hydrodynamic model. It is used to calculate the penetration depth. However, the overall model includes oblique impact and projectile ricochet to allow for a realistic evaluation of the concept. Seismic effects have been estimated to demonstrate that these are much smaller than for a weapon of mass destruction, and they are thus restricted to the direct vicinity of the target.
The structure of this paper is as follows. First, the relevant theory is discussed, i.e. for calculating the flight trajectories, target penetration, seismic effects of kinetic impact, and material properties of the targets and projectiles. After this theory is discussed, the results from the study are presented. The flight trajectories of the projectiles are calculated using a computer. To calculate the projectile penetration, the Tate-Alekseevskii (TA) model is simulated. Finally, flight trajectories and target penetration simulations are combined, including oblique impacts and ricochets. This is followed by a discussion and conclusions.
The present exploratory research aims to better understand the capabilities of the space weapon by qualitatively and quantitatively mapping the influence of different parameters involved. This is done using computer simulations. The flight parameters, i.e. altitude, projectile length (
Material properties are another vital aspect of this study, as a projectile would penetrate deeper into a softer material than in a harder material, e.g. concrete instead of armour. These properties are used in the penetration modelling. As stated above, the primary targets are urban structures such as airfields, tall buildings and missile silos. Most such structures are made of concrete or steel. Hence, those will be the main material used for this study. In the study, it is assumed that a perpendicular impact with respect to the Earth’s surface is optimal for penetrating the target.
To calculate a trajectory, the initial conditions must be determined first. They serve as a starting point for the re-entry simulation. The focus of this study is orbital re-entry, where a satellite in orbit around Earth manoeuvres the projectile so that it falls towards Earth’s surface. This scenario is shown in Figure 1. In order for the projectile to hit a target on the Earth’s surface, it needs to manoeuvre and enter the atmosphere and go through orbital re-entry. The orbital velocity,
In order to induce this change in velocity the projectile needs to be equipped with a retro-rocket that thrusts the projectile in the opposite direction of the flight direction. This manoeuvre burns propellant, which has to be carried by the satellite. To estimate the amount of propellant necessary for the manoeuvre, the Tsiolkovsky rocket equation is used:
Figure 2 displays a diagram of the re-entering projectile, with orange arrows representing the velocity vector and blue arrows portraying the forces acting on the projectile.
The re-entry model used includes aerodynamic drag. Once the initial conditions are acquired, they are put into the re-entry simulation, which is bound by several assumptions:
The scenario is two-dimensional. The Earth is modelled as a perfect sphere with gravity pointing down to the centre of the coordinate system; gravity is altitude dependent. Earth rotation is not included. The effect of wind is neglected. The atmosphere is modelled using the International Standard Atmosphere, see e.g. Anderson (2016). The rod experiences aerodynamic drag, The projectile is symmetric and the angle of attack of the projectile is effectively zero, and thus it generates no lift.
The latter point can be understood as follows. To keep the projectile stable during flight, it would have to be fin-stabilised. Tailfins ensure that, if the projectile were to gain an angle of attack, the aerodynamic force moment on the tail counteracts this motion, thus stabilising its flight and limiting the angle of attack. Furthermore, the projectile is assumed to be unguided during the atmospheric flight.
When the projectile travels at a hypersonic velocity, through the atmosphere, the air molecules ionise and a plasma forms around the projectile. This plasma blocks Electromagnetic (EM)-transmission (Bond 1958), which is essential for communication. This means that no external input can be given to navigate the projectile. Another way to guide the projectile to its target is to use a seeker head, but building a seeker capable of withstanding the high temperature may not be feasible. Finally, flight control would be problematic, since, if the angle of attack were to become too large, the force moment on the projectile might cause it to break up in flight.
The equations of motion for the subsequent suborbital trajectory are given by Hankey (1988).
The parameters
The drag coefficient of the projectile depends on its shape and the Mach number. As no information about actual orbital projectiles is available, we have to make some assumptions about the projectile. Elbasheer (2014) proposed a length of 6.1 m and a diameter of 0.3 m with a length over diameter (
Assuming the projectile has a flechette-like shape, a close resemblance can be found in the XM110 projectile with an
By simulating two trajectories, with one assuming fully turbulent flow and the other considering both types of flow, the difference can be observed. To best visualise the effect, a trajectory with a long flight path through the atmosphere is chosen. Thus, the projectile experiences the longest time under the influence of aerodynamic drag. Normally the flow transitions at the critical velocity. This transition means that there is a grey area where it could be either turbulent or laminar. Furthermore, an initial altitude of 400 km and a projectile with
The resulting trajectory, flight velocity and pitch can be seen in Figures 4a, 4b and 4c, respectively. As all three figures show, a minor difference can be seen for the different methods. The impact velocity deviates 2.72%, the pitch deviates 4.70%, the flight time deviates 0.28% and the range deviates 0.32%. This is included in the model, although the effect is small.
To describe the projectile penetration into concrete and steel a semi-hydrodynamic model was chosen, i.e. the 1D-model of Tate and Alekseevksii. Of course, this 1D-model is less advanced than, for instance, models based on cavity expansion theory. However, it is a classical model that ought to be capable of adequately estimating the penetration depth of long rod projectiles in steel and concrete. The characteristic equation of Tate and Alekseevskii (see e.g. Alekseevskii 1966; Tate 1969; Hohler and Stilp 1990; Walker 2021) is a modified Bernoulli equation:
Eqs (7a–c) are representative of the Tate and Alekseevksii model. These equations are integrated to obtain the penetration depth (
Evidently, the Tate–Alekseevskii model has limitations, for projectile impacts are 3D-phenomena. However, the penetration depth is for our purpose the most important parameter, and it can be described using the 1D-model. Moreover, the (finite) speed of sound in the material is not considered, see e.g. Walker (2021). The longitudinal speed of sound in metals is typically 5–6 km/s. As long as the projectile velocity is smaller than the speed of sound in the material, the effect can be considered to be negligible. For further limitations of the model, see e.g. Bavdekar et al. (2017, 2019).
As said, material properties are a vital aspect of this study, as a projectile penetrates deeper into softer materials. The primary targets we consider are urban structures such as airfields, tall buildings and missile silos. Most such structures are made of concrete or steel. Hence, it is on these materials that this study will be focused. Table 1 shows different materials with their respective density (
Overview of relevant material properties.
Material | |||
---|---|---|---|
7 ksi Concrete [HJC] | 2,440 | 48 | |
SAC5 Concrete [N et al.] | 2,299 | 37.9 | |
WSMR-5 3/4 Concrete [SYG] | 2,299 | 44.8 | |
3.7 ksi Concrete [SYG] | 1,990 | 25.5 | |
Concrete [VLK] | 2,300 | 51 | |
Limestone [VLK] [WHP] | 2,300–2,320 | 58–63 | |
Sandstone [B et al.] | 2,000–2,040 | 16–30 | |
Steel [T] | 7,850 | - | 3.45–5.18 |
Data sources are – for concrete: Butler, Nielsen, Dropek & Butters (1977); Holmquist, Johnson & Cook (1993); Warren, Hanchak & Poormon (2004); Noble, Kokko, Darnell, Dunn, Hagler & Leininger (2005); Stokes, Yarrington & Glenn (2005); Vahedi, Latifi & Khosravi (2008); and for steel: Tate (1986).
This table is inspired by the work of Flis (2016).
For the impact simulations, the upper and lower bounds of the concrete properties are used. This gives the best indication for the minimum and maximum expected values for penetration depth. Not only are the properties of the target material important but also those of the projectile. The tungsten alloy rod has a density of
Overview of material properties with dynamic penetration parameters.
Material | ||||
---|---|---|---|---|
Concrete (lower boundary) [SYG] | 1,990 | 25.5 | 362 | - |
Concrete (upper boundary) [VLK] | 2,300 | 51 | 495 | - |
Steel (lower boundary) [T] | 7,850 | - | 3,450 | - |
Steel (upper boundary) [T] | 7,850 | - | 5,180 | - |
Tungsten alloy [T] | 17,000 | - | - | 1,930 |
Sources are given in the caption of Table 1.
To calculate the dynamic strength of concrete from the unconfined compressive strength,
So, to calculate dynamic strength, only a value of the compressive strength is necessary. The equation of Frew et al. (1998) is based on experimental data and valid for concrete with unconfined compressive strengths between 13.5 MPa and 97 MPa.
Granular materials such as soil or sand are not treated in this paper. These materials are also characterised by their grain size and have a very low target strength. Of course, penetration depths for long rods are expected to be higher than for both concrete and steel.
For realistic projectile impact simulations, both oblique impact and the possibility of ricochet have to be considered. First, we will treat ricochet. When the impact angle is too high with respect to the normal of the surface, the projectile skips off the surface. This is called ricochet. It is a complex projectile target interaction, but Tate (1979) developed a simplified model to calculate the critical ricochet angle
Penetration models, such as the TA-model, implicitly assume perpendicular impact. However, usually, the projectile will hit the target with an oblique impact angle. Since the velocity vector is in the same direction as the body axis of the projectile, the penetration depth can be calculated by simply correcting for the impact angle:
When a rod impacts the ground, a small fraction of the kinetic energy is transferred into seismic energy. This fraction is known as the seismic efficiency
First, impact simulations were conducted for steel and concrete targets (without the flight model). The vital difference between these materials is that for concrete, the dynamic penetration resistance is smaller than the dynamic penetration strength of tungsten (
In Figure 7, the normalised penetration depth,
The full simulation considers the influence of the impact angles and impact velocity. Figure 8 shows the flight time of the trajectory. In this figure a significant difference can be distinguished in flight time. The higher flight altitudes result in longer flight times, obviously because the projectile travels along a longer path for a higher altitude than for lower altitude.
The resulting penetration depth is shown in Figure 9. The figure shows that the initial orbital altitude does not have a significant influence on the penetration depth. At a first glance, it may seem remarkable that for projectiles with a length of more than roughly 1 m, the penetration depth is less than the length of the projectile. However, this is a consequence of the relatively shallow impact. The orbital altitude has only a small influence on the impact parameters because the initial orbital velocity
These impacts are shallow due to the Δ
Different trajectories for deorbiting the projectiles are possible, resulting in steeper impacts, but at the cost of a higher Δ
Earthquakes can cause significant damage to urban structures. To calculate the possible earthquake magnitudes caused by projectile impact, the magnitudes are calculated for different projectile lengths from an altitude of 400 km, using a minimal Δ
Figure 12 shows a maximum magnitude of 2.5 on the Richter scale. According to the US geological survey (USGS 2010) more than 1.3 million earthquakes of this magnitude happen annually, and damage occurs above a magnitude of 4 or 5 (USGS 2022), meaning that the seismic effects caused by high velocity impacts are insignificant compared to the penetration effects.
The Δ
In spaceflight, the mass of the payload is an indication for the price to bring such a payload into an orbit. In Figure 14, the payload mass for a 4″, a 1 m and a 6.1 m projectile is presented. For a minimum Δ
There are two alternative methods to deliver a payload to its target, other than the orbital bombardment that we consider in this work. It can also be dropped from a bomber or launched using an ICBM. In a comparison of the kinetic orbital bombardment system with a suborbital trajectory, the range of both trajectories has been matched. For the suborbital trajectory, we chose a burnout velocity of 6,750 m/s and a launch elevation of 30°, which are typical values for an ICBM. These parameters result in a range of approximately 6,700 km, depending on the projectile length. To match this range of the suborbital flight, the re-entry uses 435.49 m/s of Δ
For these flight trajectories, the impact velocity and impact angle can be seen in Table 3, for projectile lengths between 0.1016 m (i.e. 4″) and 6.1 m. For the impact angle, 0° is horizontal. For the impact velocity, the lower boundary corresponds to the shorter projectile and the higher boundary corresponds to the longer projectile. For the impact angle, the opposite is true.
Flight parameters for different delivery methods (the range of the results is associated with the effect of the projectile length).
Method | Impact velocity [m/s] | Impact angle [°] |
---|---|---|
Re-entry | 240–6,600 | 5–60 |
Bomber | 250–600 | 63–80 |
Suborbital flight | 1,215–6,325 | 35–36 |
The penetration depth
From these results, it is apparent that an orbital bombardment system is, in principle, less effective than using a conventional method. For steel targets, launching the projectiles with an ICBM gives a better performance and for concrete targets, using a bomber shows better performance. This is not unprecedented. The US used so-called ‘Lazy Dog’ kinetic projectiles dropped by aircraft in the Korean and Vietnam Wars, see e.g. Karmes (2014). More recently, in the prelude to the 2003 invasion of Iraq, the US used concrete-filled laser guided bombs, to limit collateral damage (Copp 2003a, 2003b). An obvious downside of using a bomber is that it has to fly to its destination to deliver the payload and is more susceptible to intercepts.
In the present research, projectile penetration and seismic effects of kinetic orbital bombardment systems are studied. Also, the question of whether these systems are feasible has been examined, and an analysis conducted concerning identification of the improvements that would move these systems closer to operational application.
Two different groups of materials were simulated, the first being concrete and the second being steel. Figure 7 shows that the concrete and steel targets show different behaviour. For concrete targets, an optimum impact velocity can be found, which is roughly 1400 m/s, depending on type of concrete. For steel, the optimum impact velocity is the highest achievable impact velocity because the penetration depth converges to a limit as the impact velocity increases.
The flight simulations demonstrate that changing the orbital height for a minimum Δ
Combining the impact simulation and the re-entry simulations shows that a bottleneck of this concept is the impact angle (
The shallow angle is a result of the choice of using a Hohmann transfer to 15 km. At this height the projectile will be captured by the atmosphere. Applying a much larger Δ
The calculations show that the impact of a tungsten alloy rod with a length of 8 m and a 0.4 m diameter results in an earthquake with a seismic magnitude of only 2.5 on the Richter scale. Approximately 1.3 million of such earthquakes happen every year, indicating that the seismic effect is insignificant. An earthquake with a magnitude of 2.5 is generally not felt and only recorded by seismic centres. This clearly shows that kinetic bombardment is not a WMD.
Moreover, alternative delivery methods show better performance for both steel and concrete targets. If a bomber would drop the same projectile from 15 km altitude, the projectile would penetrate 2.5 m. For steel targets, a 1 m projectile would penetrate 0.2 m, and using an ICBM, the same projectile would penetrate 1 m. Both these are methods in relation to which a significant amount of experience has already been accumulated, and it is thus apparent that a kinetic orbital bombardment system cannot be considered a serious alternative. The flight time might appear to be a clear advantage. A bomber would need to fly to its targets, be vulnerable and deliver the payload. An ICBM has a flight time of roughly 30 min, whereas an orbital bombardment system has a flight time ranging from 5 min to 15 min. However, this is solely the flight time of the projectile, and thus excluding the time required for an orbital bombardment satellite to fly or manoeuvre to suitable initial conditions for launching the projectile.
Two adjustments would make the concept more feasible. The first adjustment is to use a hypersonic drag device to decelerate the projectile. Even though this reduces the impact velocity, it results in better penetration performance because the impact angle is steeper. Depending on the ability to increase the drag, the penetration depth can be increased. If the drag can be increased by a factor 10, the best penetration would be provided by a tungsten projectile with a length of 5 m and a diameter of 0.25 m, with a penetration depth of 18 m. The second adjustment is to accept a very high price. By doing so, heavy projectiles with a significant amount of propellant can be brought into orbit, resulting in a large Δ
Further important topics for operational application that were not explicitly included in this study are the accuracy of the weapon system and the number of satellites necessary to be able to cover the entirety of the Earth’s surface. Since the projectile itself is unable to manoeuvre, it would be difficult to accurately hit a target. This also applies to re-entry vehicles of ICBMs, but they typically carry nuclear warheads, such that accuracy is less important. Since the damage of a kinetic orbital bombardment system is essentially caused by penetration, the damage radius of the projectile is very small. It is therefore crucial that the system be very accurate. This requires some form of guidance and flight control, and it may not be possible to achieve this at the relevant velocities. Conventionally armed ballistic missiles, with a considerably smaller damage radius than that of a nuclear warhead, have a similar issue. Some do have guided re-entry vehicles with fins for flight control, to improve their accuracy, but these operate at much smaller velocities. The other topic is, as mentioned, the number of satellites needed to achieve an adequate coverage of the Earth’s surface. The weapon system should be able to strike any place on Earth in a short time. For this purpose, a large constellation of satellites is necessary. Furthermore, to ensure a short response time, the vehicle that deorbits the rod should also carry propellant for out-of-plane manoeuvres, as well as for a larger Δ
Little quantitative information about the different kinetic orbital bombardment systems that have been considered is available and we have used simplified models. For instance, the Δ