Defying gravity – How to navigate Unidentified Flying Objects?
Unidentified Flying Objects (UFOs) are rarely treated as serious scientific phenomena, maybe because 98.5% of reported cases turn out to be explicable. Yet, the remainder contains intriguing cases in which reliable observers witnessed flight manoeuvres that seemingly defy gravity and exceed our best technology. This short manuscript, based on the sparse information publicly available, discusses the possibility that moderately charged flying objects could use the Earth’s electromagnetic field to perform these seemingly impossible “stunts”. Can this mysterious aeronautics be explained as a larger-scale version of Millikan’s Oil Drop Experiment?
From Humbug to Harvard
Observations of mysterious unidentified aerial phenomena (UAPs) can have multiple, down-to-Earth origins. The vast majority of the 12,618 cases in Project Blue Book collected by the Air Force between 1947 and 1969 turned out to be weather balloons, atmospheric anomalies, and malfunctions or artefacts in the observing/ recording device. Only 701 objects remained unidentified. Similarly, there are only 18 remarkable UAPs in the recent UAP report focussing on 144 UAPs observed by U.S. Armed Forces personnel from 2004 to 2021 [8]. However, the three examples for which videos were released are sufficient cause for detailed scientific analysis because neither the design of the vessel nor the manoeuvres performed match currently known ones, at least in the U.S.. Whether the technology is of extraterrestrial origin will, among others, be analysed by the Galileo Project, which has just started looking for techno-signatures of alien civilisations on and around Earth, especially UFOs, also called Anomalous Aerial Vehicles. Irrespective of the answer, feasibility studies to explain the reported UFOs based on our laws of physics shed further light on potentially misinterpreted observations, possible origins, and, ultimately, the universality of physics as we know it.
Here, we assume reports and data to be correct within the range of uncertainties and scope of the descriptions given, as the witnesses were experienced pilots and special forces with the necessary knowledge to give trustworthy estimates. First, we will give a brief overview of two confirmed vessel types, disc-shaped and capsular UFOs [3, 4] and argue that these designs are optimised for stable subsonic to potentially hypersonic motion in an atmosphere. Then, we assume that the surface of these vessels can be charged to use the Earth’s electromagnetic field for navigation. For the specifications and estimates given in paper 1 and paper 2 by Knuth et al. [3, 4], we estimate order of magnitude charges and masses of these vessels. We conclude with a summary of all findings, which offers the possibility that these UFOs may be easier to understand than previously thought. Consequently, further research on UFOs is strongly encouraged to reveal more details and characteristics about this very efficient, environmental friendly, and silent means of fast transportation.
“Flying Saucer” Design
UFOs were jokingly called “flying saucers” by the media after the Kenneth Arnold UFO seeing of 1947. Several other people also reported UFOs being disc-shaped soon afterwards. In [3], two disc-shaped UFOs were analysed, a large one with a disc diameter of 210 to 330 meters and a small one with disc diameter of 60 to 90 meters. A second type of UFOs shaped like a Tic-Tac candy is also known by now. In [3], its extensions were estimated to be about 17 meters in length with a diameter of 3 to 4.5 meters in width, being thus much smaller than the disc-type UFOs for which no height was mentioned (and for which the heights are estimated below). Fig. 1 gives a brief summary of the three geometries and their sizes.
Fig. 1 UFO geometries and sizes for the three vessel types considered here. Heights for the large and medium disc are estimated for the same aspect ratio. All UFOs are assumed to be built as a shell of 5 cm thickness with an empty centre.
The mere fact that we observe them having such smooth, highly symmetric shapes implies that stealth is of much less importance than minimising drag forces in the Earth’s atmosphere to enable them to move at high speeds. The designs are thus in contrast to speculations that UFOs controlled the gravitational field in their surroundings to move. Even if they could, amounts of energy required would exceed those that are necessary for the navigation method detailed below due to the weakness of gravity compared to electromagnetism. Besides, calculations show that gravitational wells surrounding an object cannot conceal it fully over a broad range of wavelength bands [9], not offering any advantage for stealth, either.
The UFO types are very hard to recognise from the publicly released infrared video footage [10]. However, the shapes described in [3] and other reports allow for both types to take on a profile from the Haack series, particularly a von-Kármán profile, which minimises drag forces for a given vessel length and diameter, or having a power-law profile with power-law index n = 0.5, which enables manoeuvring for trans- and supersonic motions alike [1]. The shapes also need to be optimised for a hardly detectable sonic boom at the observers’ positions, a reduction of heating, and exposing maximum surface charge to the Earth’s electromagnetic field for navigation. Thus, the actual shape may deviate a bit from the one which only minimises drag forces. Fig. 2 shows a comparison between the von-Kármán and the power-law profile for the upper left quadrant of an axisymmetric vessel profile and for a thickness typical for shieldings of space shuttles. The length of the quadrant L and its maximum radius R are scaled to arbitrary units.
Fig. 2 Upper left quadrant of a normalised von-Kármán profile (black) and power-law profile with power-law index n = 0.5 (right) both with thickness D.
Having more than one UFO type may hint at a fine-tuning for flights in different media and speed ranges: The blunter power-law shape may be better adapted for heat reduction, i. e. for hypersonic speeds, and for reducing drag in subsonic flight, as well as for motion in water. In contrast, the cuspy von-Kármán profile reduces drag in trans- and supersonic speed ranges, but faces aerodynamic heating.
Assuming the surface of the UFO can be charged, materials based on silicon carbide (SiC) are low-weight robust semiconductors with suitable properties. They are highly efficient under extreme thermal conditions in high-voltage fields and even suitable to cool thermal shocks, such that the charged vessels may suffer from less heating than their neutral counterparts. The most common SiC is α-SiC with a density of 3160 kg/m3 [2]. SiC also has a low efficiency to emit blue light.
If the capsular UFOs of 17 m length in [3, 4] have a power-law profile built of 0.05 m thick SiC, their masses lie between 13,490 kg and 26,613 kg, which is lower than the 30,000 kg maximum takeoff weight of a F/A-18 Super Hornet. Fig. 3 shows that, with a von-Kármán profile, the mass only amounts to 6361 kg in this minimalistic estimate. Since no height was given for the disc-shape UFOs, we assume half the aspect ratio as for the smallest possible Tic-Tac-shaped UFO, 0.09, and plot the diameters versus masses for those UFOs for both profile types as well. The sizes of the three largest UFO extensions exceed the 640,000 kg takeoff weight of the Antonov An-225 “Mriya” holding the world record so far.
Fig. 3 UFO masses for these profile specifications for the sizes given in Fig. 1 and 2 and a thickness of D = 0.05 m.
Manoeuvring in Earth’s Electromagnetic Field
Electromagnetic fields play a decisive role in making our planet habitable for us, but are still barely explored and understood [5]. Are they strong enough to explain the aeronautics of the UFOs described in [3, 4], if we assume that the vessels have the characteristics discussed in the previous section? To answer this question in detail, numerical simulations can be performed as soon as more precise constraints on the UFO design is obtained. For now, the ballpark estimates for the UFO geometries and the simplifying assumptions on their aerodynamics made here are sufficient for a proof-of-principle calculation. Without engineering practical techniques, we presuppose that the UFO navigators know the amplitude and direction of the electromagnetic fields on Earth and are able to adjust the charge on the surface of their vessels on time scales corresponding to the switching time of SiC devices. The latter are some tens of nanoseconds, which can explain the seemingly instantaneous starting and stopping of motions. In [3, 4], UFOs kept a distance of several hun- dred meters to observers, such that the electromagnetic field strengths caused by an UFO are constrained by no observable effects on the observers’ electronic devices at minimum distance.
We focus on motion in air as the surrounding medium, but note that, for the motion through water, the salty sea is a good conductor, so that the same mech- anism could provide navigation under water as well. Due to air pollution, clouds, or radioactive processes occurring above land, the most stable conditions to exploit Earth’s global fair-weather electric fields can be found above oceans [7]. To estimate UFO charges, we start by assuming a constant vertical gradient of about 100 V/m in the Earth’s electric field between ground and 1500 m altitude and an exponentially decreasing field at higher altitudes according to E(h) = E0 exp(−h/h0) with E0 = 45 V/m and h0 = 4551 m. Both E-fields are directed downward (see Fig. 2 in [7] for further details on the discontinuity at 1500 m). We also assume a constant field strength B = 50 μT directed upwards. With these prerequisites, we analyse the three maneouvres in [3] as follows. The UFO mass is denoted by M, its charge by Q, the acceleration of gravitation is always g = 9.8 m/s2. Fig. 4 summarises all available fields.
Fig. 4 Summary of global and local electromagnetic fields on Earth.
Hovering
Balancing the gravitational force of an UFO, Fg = Mg, pointing downward by the electrical one, Fe = QE, pointing upward for a negatively charged vessel, hovering is achieved when |Fg| = |Fe|, such that the charge-to-mass-ratio is given by
Q/M = g/|E|
The acceleration of gravity g has a negligible dependence on h, but the electrical field strength E varies strongly with h, such that, for constant UFO mass M, the required charge Q to hover varies. At h = 10, 000 m, E = 5 V/m, such that Q/M = 1.96 C/kg, while at h = 0 m, E = 100 V/m, such that Q/M = 0.098 C/kg. For a Tic-Tac-shaped UFO with power-law profile this implies charges of Q(10, 000 m) = 26, 440 C and Q(0 m) = 1322 C. For a capsular UFO with a von-Kármán profile, the charges reduce to Q(10, 000 m) = 12, 468 C and Q(0 m) = 623 C.
Assuming a diameter of 60 m, height of 11 m, and a von-Kármán profile for the disc-shaped UFO in the Bethune Encounter, hovering in front of the airplane at 3000 m altitude in an E-field of E = 23 V/m requires Q = 202, 806 C. If additional local perturbations of the E-field are included in the calculation, which may be up to 100 kV/m [6], the charge of the latter UFO is reduced to Q = 47 C. This is about the charge carried by five thunderbolts.
Thus, even for the smallest vessels, charges required for hovering in the global fair-weather electric field are so large that UFOs need to keep a large distance in order not to damage airplanes. However, local perturbations in the E-field, like clouds, can increase the E-field strength and thereby reduce the necessary amount of charge by orders of magnitude. Consequently, the distance of closest encounter to a UFO greatly depends on the local strength and configuration of the E-field. While buoyancy due to the air also reduces Q, it is of minor effect because it is proportional to the dynamic viscosity of the atmosphere, which is of the order of 10−5 Ns/m2, and the velocity of the UFO which is close to zero while hovering.
Fig. 5 Hovering: the gravitational force Fg is balanced by the electric part of the Lorentz force Fe and drag Fd is negligibly small due to almost zero velocity.
Horizontal circling
Next, we analyse the potentially circular motion around JAL 1628, in which the largest UFO we consider takes T = 24 s to circle once around the airplane and keeps a distance of r = 12, 000 m. As in [3], we neglect the forward motion and the drag forces as well because the von-Kármán profile should minimise the latter. Then, the B-field strength required to cause this circular motion in the plane of the airplane at h = 10, 000 m, orthogonal to the direction of the Earth’s B-field can be determined. Balancing the centrifugal force, Fc = M(2π/T)2r, with the Lorentz force caused by the magnetic field, FL = Q r(2π/T) |B|, yields
|B| = 2π/T * (Q/M)-1
Inserting the Q/M = 1.96 C/kg that is required to keep h = 10, 000 m constant in the vertical direction, |B| = 0.13 T. This value is about the magnitude of the field strength of a sun spot and four orders of magnitude larger than the global magnetic field of the Earth, such that additional local, perturbing B-fields have to be taken into account if this manoeuvre actually used a magnetic field.
Fig. 6 Horizontal circling around a plane at constant h = 10, 000 m: the magnetic part of the Lorentz force FL is balanced by the centrifugal force Fc, and drag is negligible due to the UFO profile.
Since the JAL 1628 Encounter included two additional UFOs, it may be possible that the missing B-field amplitude was generated by an accompanied flight manoeuvre of the two other charged vessels. While such fine-tuning is possible in principle, the hypothesis that the stronger electric field, caused by the local natural configuration or the two additional UFOs, is used in this flight manoeuvre seems more likely. Assuming the UFO travels the 2r = 24, 000 m in an accelerated rectilinear motion, we can determine the required (horizontal) electrical field that is required to cause this acceleration, a = 4r/(T/2)2, as
|E| = 4r/(T/2)2 * (Q/M)-1
Inserting the values given above, |E| = 170 V/m, now in horizontal direction, which can be easily caused by charges of the order of a few Coulombs at about 10 km distance. Finally, we note that both explanations of the observed flight can be completely expressed in terms of Earth’s gravito-electromagnetic characteristics.
Fig. 7 Horizontal motion due to local electric fields, again with negligible drag.
Swooping
The Nimitz Encounters with swarms of 10 to 20 smallest capsular UFOs include a swooping manoeuvre in which a UFO drops from h = 8535 m to h = 15 m in about t = 0.78 s. If the UFO were falling the entire height ∆h = 8520 m with the constant terminal velocity that is reached as soon as the vertical drag forces balance gravity, this velocity would be vt = ∆h/t = 10, 923 m/s. This value is about 30 times the sound speed and thus unrealistic to reach without any additional acceleration.
Since previous manoeuvres benefitted from local perturbing electric fields, we model the E-field for the descent to be constant for two different field strengths |E1| = 100 V/m and |E2| = 100 kV/m. Due to the downward-pointing natural E-field, a positive charge has to be imposed on the UFO’s surface, contrary to the previous cases. As no detailed acceleration information over time is provided, including velocity-dependent drag forces is difficult. However, any drag force only increases the Q/M-ratio required for this descent, so that neglecting frictional forces yields a lower bound on Q/M. Thus, we can solve for Q/M in the simplified approach that the effective acceleration aeff required to travel ∆h = 1/2aeff t2 is the acceleration of gravitation plus the acceleration downwards due to the E-field
Q/M = (2∆h − gt2)/(t2|E|)
For E1, we obtain Q/M = 280 C/kg, while for E2, Q/M = 0.28 C/kg. Whether this is feasible from the material science viewpoint depends on the maximum charge carrier density possible in a potentially doted SiC semiconductor. While E2 could be caused by ionising radiation from earthquake regions [6], it is also possible that this stunt is enabled by a specific spatial configuration of the entire UFO swarm. Manipulating the natural E-field by several charged vessels has the advantage to make the flights less dependent on external conditions.
In any case, given that aeff = 28, 008 m/s2, we do not assume any carbon-based living being to be inside such UFOs, as this acceleration exceeds those tolerable by humans by several orders of magnitude. Consequently, UFOs are most probably controlled by robots or remotely.
Fig. 8 Swooping from h = 8535 m to h = 15 m when Fd is overcome by Fg and Fe.
Conclusion
As shown here, UFOs are less mysterious than they appear at first glance because their design criteria and potential aeronautics can be based on very down-to-Earth physical principles and theories. Vessel shapes seem to be tuned for small drag, small sonic booms, low heating, and large surface area exposable to the Earth’s electromagnetic field. UFOs may also be optimal for hypersonic flights (beyond Mach 5), which we cannot analyse because our fastest plane, a Lockheed SR-71 Blackbird, has only reached Mach 3.3 so far. Yet, some information may be available for missiles and rockets. Interestingly, stealth does not seem to play a role as design criterion.
There are at least two types of vehicles, multi-purpose small capsular ones that may navigate well through subsonic water environments, as well as travelling hypersonically through the atmosphere, and disc-shaped, larger ones, that may be built as carrier-ships for trans- and supersonic flights over longer time spans. Appropriate materials to build such vehicles are also known, silicon carbide, for instance, fulfils all necessary prerequisites. The masses determined from assuming axisymmetric von-Kármán and power-law profiles of a given length, width, height, and thickness are mostly smaller than known comparable airplane classes, but are idealised lower bounds still subject to large uncertainties. The specifications are sufficient for feasibility estimates, as the latter are based on simplified aerodynamics, too.
As demonstrated by three different flight characteristics of UFOs, hovering, circulating, and swooping, we conclude that the global fair-weather electric field and the Earth’s magnetic field are most likely not sufficient to explain the manoeuvres that have been reported in [3]. But, including local perturbations, an explanation in terms of an electric propulsion mechanism becomes plausible. To support this idea, these perturbations require more detailed research, particularly on the frequency of their occurrence, their stability, and more precise field strength measurements. The ability to arbitrarily charge the surface of the vessels helps to reduce the strong dependency of the possible manoeuvres on the surrounding electromagnetic field configuration. In addition, these UFOs are often observed in groups and swarms, such that it is also possible that additional UFOs enhance and adapt the natural field configuration for specific manoeuvres.
Thus, on the whole, we can conclude that whoever builds these vehicles must be well familiar with conditions prevailing on Earth, which entails the question whether these UFOs come from a similar environment as ours or are fabricated on this very planet. First concrete steps for independent follow-up investigations are being taken in the Galileo Project and NASA will hopefully fund UFO research in the future as well. Most conveniently, a good part of the required research can also be undertaken under the umbrella of environmental studies, which are currently well-supported to prevent a climate crisis.
Further information and reading
- Limina (the upcoming Journal of UAP Studies)
- Galileo Project
- UAPExpedition (webpage of a further data-collecting team)
- Weaponized (enthusiastic and motivating blog about UAPs by J. Corbell and G. Knapp)
- Metabunk (skeptical and critical analysis of reported UAPs by Mick West)
- MUFON (Mutual UFO Network)
- Kevin Knuth's homepage with a lot of resources
References
[1] Chin, S. S.: Missile Configuration Design. McGraw-Hill (1961)
[2] Haynes, W.M.: CRC Handbook of Chemistry and Physics. 92nd Edition. Anticancer Research 32(5) (2012
[3] Knuth, K.H., Powell, R.M., Reali, P.A.: Estimating Flight Characteristics of Anomalous Unidentified Aerial Vehicles. Entropy 21(10) (2019)
[4] Knuth, K.H., Powell, R.M., Reali, P.A.: Estimating Flight Characteristics of Anomalous Unidentified Aerial Vehicles in the 2004 Nimitz Encounter. Proceedings 33(1) (2019)
[5] Koskinen, H., Kilpua, E.: Physics of Earth’s Radiation Belts. Springer (2022). DOI 10.1007/978-3-030-82167-8
[6] Liperovsky, V.A., Meister, C.V., Mikhailin, V.V., Bogdanov, V.V., Umarkhodgaev, P.M., Liperovskaya, E.V.: Electric field and infrared radiation in the troposphere before earthquakes. Natural Hazards and Earth System Sciences 11(12), 3125–3133 (2011). DOI 10.5194/nhess-11-3125-2011
[7] Markson, Ralph: The Global Circuit Intensity: Its Measurement and Variation over the Last 50 Years. Bulletin of the American Meteorological Society 88(2), 223 – 242 (2007). DOI 10.1175/BAMS-88-2-223
[8] Office of the Director of National Intelligence: Preliminary Assessment: Unidentified Aerial Phenomena. https://www.dni.gov/files/ODNI/ documents/assessments/Prelimary-Assessment-UAP-20210625.pdf (2021)
[9] Subedi, S.: Scattering Theory and Geometry. Ph.D. thesis, Miami U. (2022)
[10] United States Department of Defense: Statement by the De- partment of Defense on the Release of Historical Navy Videos. https://www.defense.gov/News/Releases/Release/Article/2165713/ statement-by-the-department-of-defense-on-the-release-of-historical-navy-videos/ (2020)
From Humbug to Harvard
Observations of mysterious unidentified aerial phenomena (UAPs) can have multiple, down-to-Earth origins. The vast majority of the 12,618 cases in Project Blue Book collected by the Air Force between 1947 and 1969 turned out to be weather balloons, atmospheric anomalies, and malfunctions or artefacts in the observing/ recording device. Only 701 objects remained unidentified. Similarly, there are only 18 remarkable UAPs in the recent UAP report focussing on 144 UAPs observed by U.S. Armed Forces personnel from 2004 to 2021 [8]. However, the three examples for which videos were released are sufficient cause for detailed scientific analysis because neither the design of the vessel nor the manoeuvres performed match currently known ones, at least in the U.S.. Whether the technology is of extraterrestrial origin will, among others, be analysed by the Galileo Project, which has just started looking for techno-signatures of alien civilisations on and around Earth, especially UFOs, also called Anomalous Aerial Vehicles. Irrespective of the answer, feasibility studies to explain the reported UFOs based on our laws of physics shed further light on potentially misinterpreted observations, possible origins, and, ultimately, the universality of physics as we know it.
Here, we assume reports and data to be correct within the range of uncertainties and scope of the descriptions given, as the witnesses were experienced pilots and special forces with the necessary knowledge to give trustworthy estimates. First, we will give a brief overview of two confirmed vessel types, disc-shaped and capsular UFOs [3, 4] and argue that these designs are optimised for stable subsonic to potentially hypersonic motion in an atmosphere. Then, we assume that the surface of these vessels can be charged to use the Earth’s electromagnetic field for navigation. For the specifications and estimates given in paper 1 and paper 2 by Knuth et al. [3, 4], we estimate order of magnitude charges and masses of these vessels. We conclude with a summary of all findings, which offers the possibility that these UFOs may be easier to understand than previously thought. Consequently, further research on UFOs is strongly encouraged to reveal more details and characteristics about this very efficient, environmental friendly, and silent means of fast transportation.
“Flying Saucer” Design
UFOs were jokingly called “flying saucers” by the media after the Kenneth Arnold UFO seeing of 1947. Several other people also reported UFOs being disc-shaped soon afterwards. In [3], two disc-shaped UFOs were analysed, a large one with a disc diameter of 210 to 330 meters and a small one with disc diameter of 60 to 90 meters. A second type of UFOs shaped like a Tic-Tac candy is also known by now. In [3], its extensions were estimated to be about 17 meters in length with a diameter of 3 to 4.5 meters in width, being thus much smaller than the disc-type UFOs for which no height was mentioned (and for which the heights are estimated below). Fig. 1 gives a brief summary of the three geometries and their sizes.
Fig. 1 UFO geometries and sizes for the three vessel types considered here. Heights for the large and medium disc are estimated for the same aspect ratio. All UFOs are assumed to be built as a shell of 5 cm thickness with an empty centre.
The mere fact that we observe them having such smooth, highly symmetric shapes implies that stealth is of much less importance than minimising drag forces in the Earth’s atmosphere to enable them to move at high speeds. The designs are thus in contrast to speculations that UFOs controlled the gravitational field in their surroundings to move. Even if they could, amounts of energy required would exceed those that are necessary for the navigation method detailed below due to the weakness of gravity compared to electromagnetism. Besides, calculations show that gravitational wells surrounding an object cannot conceal it fully over a broad range of wavelength bands [9], not offering any advantage for stealth, either.
The UFO types are very hard to recognise from the publicly released infrared video footage [10]. However, the shapes described in [3] and other reports allow for both types to take on a profile from the Haack series, particularly a von-Kármán profile, which minimises drag forces for a given vessel length and diameter, or having a power-law profile with power-law index n = 0.5, which enables manoeuvring for trans- and supersonic motions alike [1]. The shapes also need to be optimised for a hardly detectable sonic boom at the observers’ positions, a reduction of heating, and exposing maximum surface charge to the Earth’s electromagnetic field for navigation. Thus, the actual shape may deviate a bit from the one which only minimises drag forces. Fig. 2 shows a comparison between the von-Kármán and the power-law profile for the upper left quadrant of an axisymmetric vessel profile and for a thickness typical for shieldings of space shuttles. The length of the quadrant L and its maximum radius R are scaled to arbitrary units.
Fig. 2 Upper left quadrant of a normalised von-Kármán profile (black) and power-law profile with power-law index n = 0.5 (right) both with thickness D.
Having more than one UFO type may hint at a fine-tuning for flights in different media and speed ranges: The blunter power-law shape may be better adapted for heat reduction, i. e. for hypersonic speeds, and for reducing drag in subsonic flight, as well as for motion in water. In contrast, the cuspy von-Kármán profile reduces drag in trans- and supersonic speed ranges, but faces aerodynamic heating.
Assuming the surface of the UFO can be charged, materials based on silicon carbide (SiC) are low-weight robust semiconductors with suitable properties. They are highly efficient under extreme thermal conditions in high-voltage fields and even suitable to cool thermal shocks, such that the charged vessels may suffer from less heating than their neutral counterparts. The most common SiC is α-SiC with a density of 3160 kg/m3 [2]. SiC also has a low efficiency to emit blue light.
If the capsular UFOs of 17 m length in [3, 4] have a power-law profile built of 0.05 m thick SiC, their masses lie between 13,490 kg and 26,613 kg, which is lower than the 30,000 kg maximum takeoff weight of a F/A-18 Super Hornet. Fig. 3 shows that, with a von-Kármán profile, the mass only amounts to 6361 kg in this minimalistic estimate. Since no height was given for the disc-shape UFOs, we assume half the aspect ratio as for the smallest possible Tic-Tac-shaped UFO, 0.09, and plot the diameters versus masses for those UFOs for both profile types as well. The sizes of the three largest UFO extensions exceed the 640,000 kg takeoff weight of the Antonov An-225 “Mriya” holding the world record so far.
Fig. 3 UFO masses for these profile specifications for the sizes given in Fig. 1 and 2 and a thickness of D = 0.05 m.
Manoeuvring in Earth’s Electromagnetic Field
Electromagnetic fields play a decisive role in making our planet habitable for us, but are still barely explored and understood [5]. Are they strong enough to explain the aeronautics of the UFOs described in [3, 4], if we assume that the vessels have the characteristics discussed in the previous section? To answer this question in detail, numerical simulations can be performed as soon as more precise constraints on the UFO design is obtained. For now, the ballpark estimates for the UFO geometries and the simplifying assumptions on their aerodynamics made here are sufficient for a proof-of-principle calculation. Without engineering practical techniques, we presuppose that the UFO navigators know the amplitude and direction of the electromagnetic fields on Earth and are able to adjust the charge on the surface of their vessels on time scales corresponding to the switching time of SiC devices. The latter are some tens of nanoseconds, which can explain the seemingly instantaneous starting and stopping of motions. In [3, 4], UFOs kept a distance of several hun- dred meters to observers, such that the electromagnetic field strengths caused by an UFO are constrained by no observable effects on the observers’ electronic devices at minimum distance.
We focus on motion in air as the surrounding medium, but note that, for the motion through water, the salty sea is a good conductor, so that the same mech- anism could provide navigation under water as well. Due to air pollution, clouds, or radioactive processes occurring above land, the most stable conditions to exploit Earth’s global fair-weather electric fields can be found above oceans [7]. To estimate UFO charges, we start by assuming a constant vertical gradient of about 100 V/m in the Earth’s electric field between ground and 1500 m altitude and an exponentially decreasing field at higher altitudes according to E(h) = E0 exp(−h/h0) with E0 = 45 V/m and h0 = 4551 m. Both E-fields are directed downward (see Fig. 2 in [7] for further details on the discontinuity at 1500 m). We also assume a constant field strength B = 50 μT directed upwards. With these prerequisites, we analyse the three maneouvres in [3] as follows. The UFO mass is denoted by M, its charge by Q, the acceleration of gravitation is always g = 9.8 m/s2. Fig. 4 summarises all available fields.
Fig. 4 Summary of global and local electromagnetic fields on Earth.
Hovering
Balancing the gravitational force of an UFO, Fg = Mg, pointing downward by the electrical one, Fe = QE, pointing upward for a negatively charged vessel, hovering is achieved when |Fg| = |Fe|, such that the charge-to-mass-ratio is given by
Q/M = g/|E|
The acceleration of gravity g has a negligible dependence on h, but the electrical field strength E varies strongly with h, such that, for constant UFO mass M, the required charge Q to hover varies. At h = 10, 000 m, E = 5 V/m, such that Q/M = 1.96 C/kg, while at h = 0 m, E = 100 V/m, such that Q/M = 0.098 C/kg. For a Tic-Tac-shaped UFO with power-law profile this implies charges of Q(10, 000 m) = 26, 440 C and Q(0 m) = 1322 C. For a capsular UFO with a von-Kármán profile, the charges reduce to Q(10, 000 m) = 12, 468 C and Q(0 m) = 623 C.
Assuming a diameter of 60 m, height of 11 m, and a von-Kármán profile for the disc-shaped UFO in the Bethune Encounter, hovering in front of the airplane at 3000 m altitude in an E-field of E = 23 V/m requires Q = 202, 806 C. If additional local perturbations of the E-field are included in the calculation, which may be up to 100 kV/m [6], the charge of the latter UFO is reduced to Q = 47 C. This is about the charge carried by five thunderbolts.
Thus, even for the smallest vessels, charges required for hovering in the global fair-weather electric field are so large that UFOs need to keep a large distance in order not to damage airplanes. However, local perturbations in the E-field, like clouds, can increase the E-field strength and thereby reduce the necessary amount of charge by orders of magnitude. Consequently, the distance of closest encounter to a UFO greatly depends on the local strength and configuration of the E-field. While buoyancy due to the air also reduces Q, it is of minor effect because it is proportional to the dynamic viscosity of the atmosphere, which is of the order of 10−5 Ns/m2, and the velocity of the UFO which is close to zero while hovering.
Fig. 5 Hovering: the gravitational force Fg is balanced by the electric part of the Lorentz force Fe and drag Fd is negligibly small due to almost zero velocity.
Horizontal circling
Next, we analyse the potentially circular motion around JAL 1628, in which the largest UFO we consider takes T = 24 s to circle once around the airplane and keeps a distance of r = 12, 000 m. As in [3], we neglect the forward motion and the drag forces as well because the von-Kármán profile should minimise the latter. Then, the B-field strength required to cause this circular motion in the plane of the airplane at h = 10, 000 m, orthogonal to the direction of the Earth’s B-field can be determined. Balancing the centrifugal force, Fc = M(2π/T)2r, with the Lorentz force caused by the magnetic field, FL = Q r(2π/T) |B|, yields
|B| = 2π/T * (Q/M)-1
Inserting the Q/M = 1.96 C/kg that is required to keep h = 10, 000 m constant in the vertical direction, |B| = 0.13 T. This value is about the magnitude of the field strength of a sun spot and four orders of magnitude larger than the global magnetic field of the Earth, such that additional local, perturbing B-fields have to be taken into account if this manoeuvre actually used a magnetic field.
Fig. 6 Horizontal circling around a plane at constant h = 10, 000 m: the magnetic part of the Lorentz force FL is balanced by the centrifugal force Fc, and drag is negligible due to the UFO profile.
Since the JAL 1628 Encounter included two additional UFOs, it may be possible that the missing B-field amplitude was generated by an accompanied flight manoeuvre of the two other charged vessels. While such fine-tuning is possible in principle, the hypothesis that the stronger electric field, caused by the local natural configuration or the two additional UFOs, is used in this flight manoeuvre seems more likely. Assuming the UFO travels the 2r = 24, 000 m in an accelerated rectilinear motion, we can determine the required (horizontal) electrical field that is required to cause this acceleration, a = 4r/(T/2)2, as
|E| = 4r/(T/2)2 * (Q/M)-1
Inserting the values given above, |E| = 170 V/m, now in horizontal direction, which can be easily caused by charges of the order of a few Coulombs at about 10 km distance. Finally, we note that both explanations of the observed flight can be completely expressed in terms of Earth’s gravito-electromagnetic characteristics.
Fig. 7 Horizontal motion due to local electric fields, again with negligible drag.
Swooping
The Nimitz Encounters with swarms of 10 to 20 smallest capsular UFOs include a swooping manoeuvre in which a UFO drops from h = 8535 m to h = 15 m in about t = 0.78 s. If the UFO were falling the entire height ∆h = 8520 m with the constant terminal velocity that is reached as soon as the vertical drag forces balance gravity, this velocity would be vt = ∆h/t = 10, 923 m/s. This value is about 30 times the sound speed and thus unrealistic to reach without any additional acceleration.
Since previous manoeuvres benefitted from local perturbing electric fields, we model the E-field for the descent to be constant for two different field strengths |E1| = 100 V/m and |E2| = 100 kV/m. Due to the downward-pointing natural E-field, a positive charge has to be imposed on the UFO’s surface, contrary to the previous cases. As no detailed acceleration information over time is provided, including velocity-dependent drag forces is difficult. However, any drag force only increases the Q/M-ratio required for this descent, so that neglecting frictional forces yields a lower bound on Q/M. Thus, we can solve for Q/M in the simplified approach that the effective acceleration aeff required to travel ∆h = 1/2aeff t2 is the acceleration of gravitation plus the acceleration downwards due to the E-field
Q/M = (2∆h − gt2)/(t2|E|)
For E1, we obtain Q/M = 280 C/kg, while for E2, Q/M = 0.28 C/kg. Whether this is feasible from the material science viewpoint depends on the maximum charge carrier density possible in a potentially doted SiC semiconductor. While E2 could be caused by ionising radiation from earthquake regions [6], it is also possible that this stunt is enabled by a specific spatial configuration of the entire UFO swarm. Manipulating the natural E-field by several charged vessels has the advantage to make the flights less dependent on external conditions.
In any case, given that aeff = 28, 008 m/s2, we do not assume any carbon-based living being to be inside such UFOs, as this acceleration exceeds those tolerable by humans by several orders of magnitude. Consequently, UFOs are most probably controlled by robots or remotely.
Fig. 8 Swooping from h = 8535 m to h = 15 m when Fd is overcome by Fg and Fe.
Conclusion
As shown here, UFOs are less mysterious than they appear at first glance because their design criteria and potential aeronautics can be based on very down-to-Earth physical principles and theories. Vessel shapes seem to be tuned for small drag, small sonic booms, low heating, and large surface area exposable to the Earth’s electromagnetic field. UFOs may also be optimal for hypersonic flights (beyond Mach 5), which we cannot analyse because our fastest plane, a Lockheed SR-71 Blackbird, has only reached Mach 3.3 so far. Yet, some information may be available for missiles and rockets. Interestingly, stealth does not seem to play a role as design criterion.
There are at least two types of vehicles, multi-purpose small capsular ones that may navigate well through subsonic water environments, as well as travelling hypersonically through the atmosphere, and disc-shaped, larger ones, that may be built as carrier-ships for trans- and supersonic flights over longer time spans. Appropriate materials to build such vehicles are also known, silicon carbide, for instance, fulfils all necessary prerequisites. The masses determined from assuming axisymmetric von-Kármán and power-law profiles of a given length, width, height, and thickness are mostly smaller than known comparable airplane classes, but are idealised lower bounds still subject to large uncertainties. The specifications are sufficient for feasibility estimates, as the latter are based on simplified aerodynamics, too.
As demonstrated by three different flight characteristics of UFOs, hovering, circulating, and swooping, we conclude that the global fair-weather electric field and the Earth’s magnetic field are most likely not sufficient to explain the manoeuvres that have been reported in [3]. But, including local perturbations, an explanation in terms of an electric propulsion mechanism becomes plausible. To support this idea, these perturbations require more detailed research, particularly on the frequency of their occurrence, their stability, and more precise field strength measurements. The ability to arbitrarily charge the surface of the vessels helps to reduce the strong dependency of the possible manoeuvres on the surrounding electromagnetic field configuration. In addition, these UFOs are often observed in groups and swarms, such that it is also possible that additional UFOs enhance and adapt the natural field configuration for specific manoeuvres.
Thus, on the whole, we can conclude that whoever builds these vehicles must be well familiar with conditions prevailing on Earth, which entails the question whether these UFOs come from a similar environment as ours or are fabricated on this very planet. First concrete steps for independent follow-up investigations are being taken in the Galileo Project and NASA will hopefully fund UFO research in the future as well. Most conveniently, a good part of the required research can also be undertaken under the umbrella of environmental studies, which are currently well-supported to prevent a climate crisis.
Further information and reading
- Limina (the upcoming Journal of UAP Studies)
- Galileo Project
- UAPExpedition (webpage of a further data-collecting team)
- Weaponized (enthusiastic and motivating blog about UAPs by J. Corbell and G. Knapp)
- Metabunk (skeptical and critical analysis of reported UAPs by Mick West)
- MUFON (Mutual UFO Network)
- Kevin Knuth's homepage with a lot of resources
References
[1] Chin, S. S.: Missile Configuration Design. McGraw-Hill (1961)
[2] Haynes, W.M.: CRC Handbook of Chemistry and Physics. 92nd Edition. Anticancer Research 32(5) (2012
[3] Knuth, K.H., Powell, R.M., Reali, P.A.: Estimating Flight Characteristics of Anomalous Unidentified Aerial Vehicles. Entropy 21(10) (2019)
[4] Knuth, K.H., Powell, R.M., Reali, P.A.: Estimating Flight Characteristics of Anomalous Unidentified Aerial Vehicles in the 2004 Nimitz Encounter. Proceedings 33(1) (2019)
[5] Koskinen, H., Kilpua, E.: Physics of Earth’s Radiation Belts. Springer (2022). DOI 10.1007/978-3-030-82167-8
[6] Liperovsky, V.A., Meister, C.V., Mikhailin, V.V., Bogdanov, V.V., Umarkhodgaev, P.M., Liperovskaya, E.V.: Electric field and infrared radiation in the troposphere before earthquakes. Natural Hazards and Earth System Sciences 11(12), 3125–3133 (2011). DOI 10.5194/nhess-11-3125-2011
[7] Markson, Ralph: The Global Circuit Intensity: Its Measurement and Variation over the Last 50 Years. Bulletin of the American Meteorological Society 88(2), 223 – 242 (2007). DOI 10.1175/BAMS-88-2-223
[8] Office of the Director of National Intelligence: Preliminary Assessment: Unidentified Aerial Phenomena. https://www.dni.gov/files/ODNI/ documents/assessments/Prelimary-Assessment-UAP-20210625.pdf (2021)
[9] Subedi, S.: Scattering Theory and Geometry. Ph.D. thesis, Miami U. (2022)
[10] United States Department of Defense: Statement by the De- partment of Defense on the Release of Historical Navy Videos. https://www.defense.gov/News/Releases/Release/Article/2165713/ statement-by-the-department-of-defense-on-the-release-of-historical-navy-videos/ (2020)
“Flying Saucer” Design
UFOs were jokingly called “flying saucers” by the media after the Kenneth Arnold UFO seeing of 1947. Several other people also reported UFOs being disc-shaped soon afterwards. In [3], two disc-shaped UFOs were analysed, a large one with a disc diameter of 210 to 330 meters and a small one with disc diameter of 60 to 90 meters. A second type of UFOs shaped like a Tic-Tac candy is also known by now. In [3], its extensions were estimated to be about 17 meters in length with a diameter of 3 to 4.5 meters in width, being thus much smaller than the disc-type UFOs for which no height was mentioned (and for which the heights are estimated below). Fig. 1 gives a brief summary of the three geometries and their sizes.
 |
| Fig. 1 UFO geometries and sizes for the three vessel types considered here. Heights for the large and medium disc are estimated for the same aspect ratio. All UFOs are assumed to be built as a shell of 5 cm thickness with an empty centre. |
The mere fact that we observe them having such smooth, highly symmetric shapes implies that stealth is of much less importance than minimising drag forces in the Earth’s atmosphere to enable them to move at high speeds. The designs are thus in contrast to speculations that UFOs controlled the gravitational field in their surroundings to move. Even if they could, amounts of energy required would exceed those that are necessary for the navigation method detailed below due to the weakness of gravity compared to electromagnetism. Besides, calculations show that gravitational wells surrounding an object cannot conceal it fully over a broad range of wavelength bands [9], not offering any advantage for stealth, either.
The UFO types are very hard to recognise from the publicly released infrared video footage [10]. However, the shapes described in [3] and other reports allow for both types to take on a profile from the Haack series, particularly a von-Kármán profile, which minimises drag forces for a given vessel length and diameter, or having a power-law profile with power-law index n = 0.5, which enables manoeuvring for trans- and supersonic motions alike [1]. The shapes also need to be optimised for a hardly detectable sonic boom at the observers’ positions, a reduction of heating, and exposing maximum surface charge to the Earth’s electromagnetic field for navigation. Thus, the actual shape may deviate a bit from the one which only minimises drag forces. Fig. 2 shows a comparison between the von-Kármán and the power-law profile for the upper left quadrant of an axisymmetric vessel profile and for a thickness typical for shieldings of space shuttles. The length of the quadrant L and its maximum radius R are scaled to arbitrary units.
| Fig. 2 Upper left quadrant of a normalised von-Kármán profile (black) and power-law profile with power-law index n = 0.5 (right) both with thickness D. |
| Having more than one UFO type may hint at a fine-tuning for flights in different media and speed ranges: The blunter power-law shape may be better adapted for heat reduction, i. e. for hypersonic speeds, and for reducing drag in subsonic flight, as well as for motion in water. In contrast, the cuspy von-Kármán profile reduces drag in trans- and supersonic speed ranges, but faces aerodynamic heating. |
Assuming the surface of the UFO can be charged, materials based on silicon carbide (SiC) are low-weight robust semiconductors with suitable properties. They are highly efficient under extreme thermal conditions in high-voltage fields and even suitable to cool thermal shocks, such that the charged vessels may suffer from less heating than their neutral counterparts. The most common SiC is α-SiC with a density of 3160 kg/m3 [2]. SiC also has a low efficiency to emit blue light.
If the capsular UFOs of 17 m length in [3, 4] have a power-law profile built of 0.05 m thick SiC, their masses lie between 13,490 kg and 26,613 kg, which is lower than the 30,000 kg maximum takeoff weight of a F/A-18 Super Hornet. Fig. 3 shows that, with a von-Kármán profile, the mass only amounts to 6361 kg in this minimalistic estimate. Since no height was given for the disc-shape UFOs, we assume half the aspect ratio as for the smallest possible Tic-Tac-shaped UFO, 0.09, and plot the diameters versus masses for those UFOs for both profile types as well. The sizes of the three largest UFO extensions exceed the 640,000 kg takeoff weight of the Antonov An-225 “Mriya” holding the world record so far.
Manoeuvring in Earth’s Electromagnetic Field
Electromagnetic fields play a decisive role in making our planet habitable for us, but are still barely explored and understood [5]. Are they strong enough to explain the aeronautics of the UFOs described in [3, 4], if we assume that the vessels have the characteristics discussed in the previous section? To answer this question in detail, numerical simulations can be performed as soon as more precise constraints on the UFO design is obtained. For now, the ballpark estimates for the UFO geometries and the simplifying assumptions on their aerodynamics made here are sufficient for a proof-of-principle calculation. Without engineering practical techniques, we presuppose that the UFO navigators know the amplitude and direction of the electromagnetic fields on Earth and are able to adjust the charge on the surface of their vessels on time scales corresponding to the switching time of SiC devices. The latter are some tens of nanoseconds, which can explain the seemingly instantaneous starting and stopping of motions. In [3, 4], UFOs kept a distance of several hun- dred meters to observers, such that the electromagnetic field strengths caused by an UFO are constrained by no observable effects on the observers’ electronic devices at minimum distance.
We focus on motion in air as the surrounding medium, but note that, for the motion through water, the salty sea is a good conductor, so that the same mech- anism could provide navigation under water as well. Due to air pollution, clouds, or radioactive processes occurring above land, the most stable conditions to exploit Earth’s global fair-weather electric fields can be found above oceans [7]. To estimate UFO charges, we start by assuming a constant vertical gradient of about 100 V/m in the Earth’s electric field between ground and 1500 m altitude and an exponentially decreasing field at higher altitudes according to E(h) = E0 exp(−h/h0) with E0 = 45 V/m and h0 = 4551 m. Both E-fields are directed downward (see Fig. 2 in [7] for further details on the discontinuity at 1500 m). We also assume a constant field strength B = 50 μT directed upwards. With these prerequisites, we analyse the three maneouvres in [3] as follows. The UFO mass is denoted by M, its charge by Q, the acceleration of gravitation is always g = 9.8 m/s2. Fig. 4 summarises all available fields.
Fig. 4 Summary of global and local electromagnetic fields on Earth.
Hovering
Balancing the gravitational force of an UFO, Fg = Mg, pointing downward by the electrical one, Fe = QE, pointing upward for a negatively charged vessel, hovering is achieved when |Fg| = |Fe|, such that the charge-to-mass-ratio is given by
Q/M = g/|E|
The acceleration of gravity g has a negligible dependence on h, but the electrical field strength E varies strongly with h, such that, for constant UFO mass M, the required charge Q to hover varies. At h = 10, 000 m, E = 5 V/m, such that Q/M = 1.96 C/kg, while at h = 0 m, E = 100 V/m, such that Q/M = 0.098 C/kg. For a Tic-Tac-shaped UFO with power-law profile this implies charges of Q(10, 000 m) = 26, 440 C and Q(0 m) = 1322 C. For a capsular UFO with a von-Kármán profile, the charges reduce to Q(10, 000 m) = 12, 468 C and Q(0 m) = 623 C.
Assuming a diameter of 60 m, height of 11 m, and a von-Kármán profile for the disc-shaped UFO in the Bethune Encounter, hovering in front of the airplane at 3000 m altitude in an E-field of E = 23 V/m requires Q = 202, 806 C. If additional local perturbations of the E-field are included in the calculation, which may be up to 100 kV/m [6], the charge of the latter UFO is reduced to Q = 47 C. This is about the charge carried by five thunderbolts.
Thus, even for the smallest vessels, charges required for hovering in the global fair-weather electric field are so large that UFOs need to keep a large distance in order not to damage airplanes. However, local perturbations in the E-field, like clouds, can increase the E-field strength and thereby reduce the necessary amount of charge by orders of magnitude. Consequently, the distance of closest encounter to a UFO greatly depends on the local strength and configuration of the E-field. While buoyancy due to the air also reduces Q, it is of minor effect because it is proportional to the dynamic viscosity of the atmosphere, which is of the order of 10−5 Ns/m2, and the velocity of the UFO which is close to zero while hovering.
Fig. 5 Hovering: the gravitational force Fg is balanced by the electric part of the Lorentz force Fe and drag Fd is negligibly small due to almost zero velocity.
Horizontal circling
Next, we analyse the potentially circular motion around JAL 1628, in which the largest UFO we consider takes T = 24 s to circle once around the airplane and keeps a distance of r = 12, 000 m. As in [3], we neglect the forward motion and the drag forces as well because the von-Kármán profile should minimise the latter. Then, the B-field strength required to cause this circular motion in the plane of the airplane at h = 10, 000 m, orthogonal to the direction of the Earth’s B-field can be determined. Balancing the centrifugal force, Fc = M(2π/T)2r, with the Lorentz force caused by the magnetic field, FL = Q r(2π/T) |B|, yields
|B| = 2π/T * (Q/M)-1
Inserting the Q/M = 1.96 C/kg that is required to keep h = 10, 000 m constant in the vertical direction, |B| = 0.13 T. This value is about the magnitude of the field strength of a sun spot and four orders of magnitude larger than the global magnetic field of the Earth, such that additional local, perturbing B-fields have to be taken into account if this manoeuvre actually used a magnetic field.
Fig. 6 Horizontal circling around a plane at constant h = 10, 000 m: the magnetic part of the Lorentz force FL is balanced by the centrifugal force Fc, and drag is negligible due to the UFO profile.
Since the JAL 1628 Encounter included two additional UFOs, it may be possible that the missing B-field amplitude was generated by an accompanied flight manoeuvre of the two other charged vessels. While such fine-tuning is possible in principle, the hypothesis that the stronger electric field, caused by the local natural configuration or the two additional UFOs, is used in this flight manoeuvre seems more likely. Assuming the UFO travels the 2r = 24, 000 m in an accelerated rectilinear motion, we can determine the required (horizontal) electrical field that is required to cause this acceleration, a = 4r/(T/2)2, as
|E| = 4r/(T/2)2 * (Q/M)-1
Inserting the values given above, |E| = 170 V/m, now in horizontal direction, which can be easily caused by charges of the order of a few Coulombs at about 10 km distance. Finally, we note that both explanations of the observed flight can be completely expressed in terms of Earth’s gravito-electromagnetic characteristics.
Fig. 7 Horizontal motion due to local electric fields, again with negligible drag.
Swooping
The Nimitz Encounters with swarms of 10 to 20 smallest capsular UFOs include a swooping manoeuvre in which a UFO drops from h = 8535 m to h = 15 m in about t = 0.78 s. If the UFO were falling the entire height ∆h = 8520 m with the constant terminal velocity that is reached as soon as the vertical drag forces balance gravity, this velocity would be vt = ∆h/t = 10, 923 m/s. This value is about 30 times the sound speed and thus unrealistic to reach without any additional acceleration.
Since previous manoeuvres benefitted from local perturbing electric fields, we model the E-field for the descent to be constant for two different field strengths |E1| = 100 V/m and |E2| = 100 kV/m. Due to the downward-pointing natural E-field, a positive charge has to be imposed on the UFO’s surface, contrary to the previous cases. As no detailed acceleration information over time is provided, including velocity-dependent drag forces is difficult. However, any drag force only increases the Q/M-ratio required for this descent, so that neglecting frictional forces yields a lower bound on Q/M. Thus, we can solve for Q/M in the simplified approach that the effective acceleration aeff required to travel ∆h = 1/2aeff t2 is the acceleration of gravitation plus the acceleration downwards due to the E-field
Q/M = (2∆h − gt2)/(t2|E|)
For E1, we obtain Q/M = 280 C/kg, while for E2, Q/M = 0.28 C/kg. Whether this is feasible from the material science viewpoint depends on the maximum charge carrier density possible in a potentially doted SiC semiconductor. While E2 could be caused by ionising radiation from earthquake regions [6], it is also possible that this stunt is enabled by a specific spatial configuration of the entire UFO swarm. Manipulating the natural E-field by several charged vessels has the advantage to make the flights less dependent on external conditions.
In any case, given that aeff = 28, 008 m/s2, we do not assume any carbon-based living being to be inside such UFOs, as this acceleration exceeds those tolerable by humans by several orders of magnitude. Consequently, UFOs are most probably controlled by robots or remotely.
Fig. 8 Swooping from h = 8535 m to h = 15 m when Fd is overcome by Fg and Fe.
Conclusion
As shown here, UFOs are less mysterious than they appear at first glance because their design criteria and potential aeronautics can be based on very down-to-Earth physical principles and theories. Vessel shapes seem to be tuned for small drag, small sonic booms, low heating, and large surface area exposable to the Earth’s electromagnetic field. UFOs may also be optimal for hypersonic flights (beyond Mach 5), which we cannot analyse because our fastest plane, a Lockheed SR-71 Blackbird, has only reached Mach 3.3 so far. Yet, some information may be available for missiles and rockets. Interestingly, stealth does not seem to play a role as design criterion.
There are at least two types of vehicles, multi-purpose small capsular ones that may navigate well through subsonic water environments, as well as travelling hypersonically through the atmosphere, and disc-shaped, larger ones, that may be built as carrier-ships for trans- and supersonic flights over longer time spans. Appropriate materials to build such vehicles are also known, silicon carbide, for instance, fulfils all necessary prerequisites. The masses determined from assuming axisymmetric von-Kármán and power-law profiles of a given length, width, height, and thickness are mostly smaller than known comparable airplane classes, but are idealised lower bounds still subject to large uncertainties. The specifications are sufficient for feasibility estimates, as the latter are based on simplified aerodynamics, too.
As demonstrated by three different flight characteristics of UFOs, hovering, circulating, and swooping, we conclude that the global fair-weather electric field and the Earth’s magnetic field are most likely not sufficient to explain the manoeuvres that have been reported in [3]. But, including local perturbations, an explanation in terms of an electric propulsion mechanism becomes plausible. To support this idea, these perturbations require more detailed research, particularly on the frequency of their occurrence, their stability, and more precise field strength measurements. The ability to arbitrarily charge the surface of the vessels helps to reduce the strong dependency of the possible manoeuvres on the surrounding electromagnetic field configuration. In addition, these UFOs are often observed in groups and swarms, such that it is also possible that additional UFOs enhance and adapt the natural field configuration for specific manoeuvres.
Thus, on the whole, we can conclude that whoever builds these vehicles must be well familiar with conditions prevailing on Earth, which entails the question whether these UFOs come from a similar environment as ours or are fabricated on this very planet. First concrete steps for independent follow-up investigations are being taken in the Galileo Project and NASA will hopefully fund UFO research in the future as well. Most conveniently, a good part of the required research can also be undertaken under the umbrella of environmental studies, which are currently well-supported to prevent a climate crisis.
Further information and reading
- Limina (the upcoming Journal of UAP Studies)
- Galileo Project
- UAPExpedition (webpage of a further data-collecting team)
- Weaponized (enthusiastic and motivating blog about UAPs by J. Corbell and G. Knapp)
- Metabunk (skeptical and critical analysis of reported UAPs by Mick West)
- MUFON (Mutual UFO Network)
- Kevin Knuth's homepage with a lot of resources
References
[1] Chin, S. S.: Missile Configuration Design. McGraw-Hill (1961)
[2] Haynes, W.M.: CRC Handbook of Chemistry and Physics. 92nd Edition. Anticancer Research 32(5) (2012
[3] Knuth, K.H., Powell, R.M., Reali, P.A.: Estimating Flight Characteristics of Anomalous Unidentified Aerial Vehicles. Entropy 21(10) (2019)
[4] Knuth, K.H., Powell, R.M., Reali, P.A.: Estimating Flight Characteristics of Anomalous Unidentified Aerial Vehicles in the 2004 Nimitz Encounter. Proceedings 33(1) (2019)
[5] Koskinen, H., Kilpua, E.: Physics of Earth’s Radiation Belts. Springer (2022). DOI 10.1007/978-3-030-82167-8
[6] Liperovsky, V.A., Meister, C.V., Mikhailin, V.V., Bogdanov, V.V., Umarkhodgaev, P.M., Liperovskaya, E.V.: Electric field and infrared radiation in the troposphere before earthquakes. Natural Hazards and Earth System Sciences 11(12), 3125–3133 (2011). DOI 10.5194/nhess-11-3125-2011
[7] Markson, Ralph: The Global Circuit Intensity: Its Measurement and Variation over the Last 50 Years. Bulletin of the American Meteorological Society 88(2), 223 – 242 (2007). DOI 10.1175/BAMS-88-2-223
[8] Office of the Director of National Intelligence: Preliminary Assessment: Unidentified Aerial Phenomena. https://www.dni.gov/files/ODNI/ documents/assessments/Prelimary-Assessment-UAP-20210625.pdf (2021)
[9] Subedi, S.: Scattering Theory and Geometry. Ph.D. thesis, Miami U. (2022)
[10] United States Department of Defense: Statement by the De- partment of Defense on the Release of Historical Navy Videos. https://www.defense.gov/News/Releases/Release/Article/2165713/ statement-by-the-department-of-defense-on-the-release-of-historical-navy-videos/ (2020)
Manoeuvring in Earth’s Electromagnetic Field
Electromagnetic fields play a decisive role in making our planet habitable for us, but are still barely explored and understood [5]. Are they strong enough to explain the aeronautics of the UFOs described in [3, 4], if we assume that the vessels have the characteristics discussed in the previous section? To answer this question in detail, numerical simulations can be performed as soon as more precise constraints on the UFO design is obtained. For now, the ballpark estimates for the UFO geometries and the simplifying assumptions on their aerodynamics made here are sufficient for a proof-of-principle calculation. Without engineering practical techniques, we presuppose that the UFO navigators know the amplitude and direction of the electromagnetic fields on Earth and are able to adjust the charge on the surface of their vessels on time scales corresponding to the switching time of SiC devices. The latter are some tens of nanoseconds, which can explain the seemingly instantaneous starting and stopping of motions. In [3, 4], UFOs kept a distance of several hun- dred meters to observers, such that the electromagnetic field strengths caused by an UFO are constrained by no observable effects on the observers’ electronic devices at minimum distance.
We focus on motion in air as the surrounding medium, but note that, for the motion through water, the salty sea is a good conductor, so that the same mech- anism could provide navigation under water as well. Due to air pollution, clouds, or radioactive processes occurring above land, the most stable conditions to exploit Earth’s global fair-weather electric fields can be found above oceans [7]. To estimate UFO charges, we start by assuming a constant vertical gradient of about 100 V/m in the Earth’s electric field between ground and 1500 m altitude and an exponentially decreasing field at higher altitudes according to E(h) = E0 exp(−h/h0) with E0 = 45 V/m and h0 = 4551 m. Both E-fields are directed downward (see Fig. 2 in [7] for further details on the discontinuity at 1500 m). We also assume a constant field strength B = 50 μT directed upwards. With these prerequisites, we analyse the three maneouvres in [3] as follows. The UFO mass is denoted by M, its charge by Q, the acceleration of gravitation is always g = 9.8 m/s2. Fig. 4 summarises all available fields.
Hovering
Balancing the gravitational force of an UFO, Fg = Mg, pointing downward by the electrical one, Fe = QE, pointing upward for a negatively charged vessel, hovering is achieved when |Fg| = |Fe|, such that the charge-to-mass-ratio is given by
Q/M = g/|E|
The acceleration of gravity g has a negligible dependence on h, but the electrical field strength E varies strongly with h, such that, for constant UFO mass M, the required charge Q to hover varies. At h = 10, 000 m, E = 5 V/m, such that Q/M = 1.96 C/kg, while at h = 0 m, E = 100 V/m, such that Q/M = 0.098 C/kg. For a Tic-Tac-shaped UFO with power-law profile this implies charges of Q(10, 000 m) = 26, 440 C and Q(0 m) = 1322 C. For a capsular UFO with a von-Kármán profile, the charges reduce to Q(10, 000 m) = 12, 468 C and Q(0 m) = 623 C.
Assuming a diameter of 60 m, height of 11 m, and a von-Kármán profile for the disc-shaped UFO in the Bethune Encounter, hovering in front of the airplane at 3000 m altitude in an E-field of E = 23 V/m requires Q = 202, 806 C. If additional local perturbations of the E-field are included in the calculation, which may be up to 100 kV/m [6], the charge of the latter UFO is reduced to Q = 47 C. This is about the charge carried by five thunderbolts.
Thus, even for the smallest vessels, charges required for hovering in the global fair-weather electric field are so large that UFOs need to keep a large distance in order not to damage airplanes. However, local perturbations in the E-field, like clouds, can increase the E-field strength and thereby reduce the necessary amount of charge by orders of magnitude. Consequently, the distance of closest encounter to a UFO greatly depends on the local strength and configuration of the E-field. While buoyancy due to the air also reduces Q, it is of minor effect because it is proportional to the dynamic viscosity of the atmosphere, which is of the order of 10−5 Ns/m2, and the velocity of the UFO which is close to zero while hovering.
Fig. 5 Hovering: the gravitational force Fg is balanced by the electric part of the Lorentz force Fe and drag Fd is negligibly small due to almost zero velocity.
Horizontal circling
Next, we analyse the potentially circular motion around JAL 1628, in which the largest UFO we consider takes T = 24 s to circle once around the airplane and keeps a distance of r = 12, 000 m. As in [3], we neglect the forward motion and the drag forces as well because the von-Kármán profile should minimise the latter. Then, the B-field strength required to cause this circular motion in the plane of the airplane at h = 10, 000 m, orthogonal to the direction of the Earth’s B-field can be determined. Balancing the centrifugal force, Fc = M(2π/T)2r, with the Lorentz force caused by the magnetic field, FL = Q r(2π/T) |B|, yields
|B| = 2π/T * (Q/M)-1
Inserting the Q/M = 1.96 C/kg that is required to keep h = 10, 000 m constant in the vertical direction, |B| = 0.13 T. This value is about the magnitude of the field strength of a sun spot and four orders of magnitude larger than the global magnetic field of the Earth, such that additional local, perturbing B-fields have to be taken into account if this manoeuvre actually used a magnetic field.
Fig. 6 Horizontal circling around a plane at constant h = 10, 000 m: the magnetic part of the Lorentz force FL is balanced by the centrifugal force Fc, and drag is negligible due to the UFO profile.
Since the JAL 1628 Encounter included two additional UFOs, it may be possible that the missing B-field amplitude was generated by an accompanied flight manoeuvre of the two other charged vessels. While such fine-tuning is possible in principle, the hypothesis that the stronger electric field, caused by the local natural configuration or the two additional UFOs, is used in this flight manoeuvre seems more likely. Assuming the UFO travels the 2r = 24, 000 m in an accelerated rectilinear motion, we can determine the required (horizontal) electrical field that is required to cause this acceleration, a = 4r/(T/2)2, as
|E| = 4r/(T/2)2 * (Q/M)-1
Inserting the values given above, |E| = 170 V/m, now in horizontal direction, which can be easily caused by charges of the order of a few Coulombs at about 10 km distance. Finally, we note that both explanations of the observed flight can be completely expressed in terms of Earth’s gravito-electromagnetic characteristics.
Fig. 7 Horizontal motion due to local electric fields, again with negligible drag.
Swooping
The Nimitz Encounters with swarms of 10 to 20 smallest capsular UFOs include a swooping manoeuvre in which a UFO drops from h = 8535 m to h = 15 m in about t = 0.78 s. If the UFO were falling the entire height ∆h = 8520 m with the constant terminal velocity that is reached as soon as the vertical drag forces balance gravity, this velocity would be vt = ∆h/t = 10, 923 m/s. This value is about 30 times the sound speed and thus unrealistic to reach without any additional acceleration.
Since previous manoeuvres benefitted from local perturbing electric fields, we model the E-field for the descent to be constant for two different field strengths |E1| = 100 V/m and |E2| = 100 kV/m. Due to the downward-pointing natural E-field, a positive charge has to be imposed on the UFO’s surface, contrary to the previous cases. As no detailed acceleration information over time is provided, including velocity-dependent drag forces is difficult. However, any drag force only increases the Q/M-ratio required for this descent, so that neglecting frictional forces yields a lower bound on Q/M. Thus, we can solve for Q/M in the simplified approach that the effective acceleration aeff required to travel ∆h = 1/2aeff t2 is the acceleration of gravitation plus the acceleration downwards due to the E-field
Q/M = (2∆h − gt2)/(t2|E|)
For E1, we obtain Q/M = 280 C/kg, while for E2, Q/M = 0.28 C/kg. Whether this is feasible from the material science viewpoint depends on the maximum charge carrier density possible in a potentially doted SiC semiconductor. While E2 could be caused by ionising radiation from earthquake regions [6], it is also possible that this stunt is enabled by a specific spatial configuration of the entire UFO swarm. Manipulating the natural E-field by several charged vessels has the advantage to make the flights less dependent on external conditions.
In any case, given that aeff = 28, 008 m/s2, we do not assume any carbon-based living being to be inside such UFOs, as this acceleration exceeds those tolerable by humans by several orders of magnitude. Consequently, UFOs are most probably controlled by robots or remotely.
Fig. 8 Swooping from h = 8535 m to h = 15 m when Fd is overcome by Fg and Fe.
Conclusion
As shown here, UFOs are less mysterious than they appear at first glance because their design criteria and potential aeronautics can be based on very down-to-Earth physical principles and theories. Vessel shapes seem to be tuned for small drag, small sonic booms, low heating, and large surface area exposable to the Earth’s electromagnetic field. UFOs may also be optimal for hypersonic flights (beyond Mach 5), which we cannot analyse because our fastest plane, a Lockheed SR-71 Blackbird, has only reached Mach 3.3 so far. Yet, some information may be available for missiles and rockets. Interestingly, stealth does not seem to play a role as design criterion.
There are at least two types of vehicles, multi-purpose small capsular ones that may navigate well through subsonic water environments, as well as travelling hypersonically through the atmosphere, and disc-shaped, larger ones, that may be built as carrier-ships for trans- and supersonic flights over longer time spans. Appropriate materials to build such vehicles are also known, silicon carbide, for instance, fulfils all necessary prerequisites. The masses determined from assuming axisymmetric von-Kármán and power-law profiles of a given length, width, height, and thickness are mostly smaller than known comparable airplane classes, but are idealised lower bounds still subject to large uncertainties. The specifications are sufficient for feasibility estimates, as the latter are based on simplified aerodynamics, too.
As demonstrated by three different flight characteristics of UFOs, hovering, circulating, and swooping, we conclude that the global fair-weather electric field and the Earth’s magnetic field are most likely not sufficient to explain the manoeuvres that have been reported in [3]. But, including local perturbations, an explanation in terms of an electric propulsion mechanism becomes plausible. To support this idea, these perturbations require more detailed research, particularly on the frequency of their occurrence, their stability, and more precise field strength measurements. The ability to arbitrarily charge the surface of the vessels helps to reduce the strong dependency of the possible manoeuvres on the surrounding electromagnetic field configuration. In addition, these UFOs are often observed in groups and swarms, such that it is also possible that additional UFOs enhance and adapt the natural field configuration for specific manoeuvres.
Thus, on the whole, we can conclude that whoever builds these vehicles must be well familiar with conditions prevailing on Earth, which entails the question whether these UFOs come from a similar environment as ours or are fabricated on this very planet. First concrete steps for independent follow-up investigations are being taken in the Galileo Project and NASA will hopefully fund UFO research in the future as well. Most conveniently, a good part of the required research can also be undertaken under the umbrella of environmental studies, which are currently well-supported to prevent a climate crisis.
Further information and reading
- Limina (the upcoming Journal of UAP Studies)
- Galileo Project
- UAPExpedition (webpage of a further data-collecting team)
- Weaponized (enthusiastic and motivating blog about UAPs by J. Corbell and G. Knapp)
- Metabunk (skeptical and critical analysis of reported UAPs by Mick West)
- MUFON (Mutual UFO Network)
- Kevin Knuth's homepage with a lot of resources
References
[1] Chin, S. S.: Missile Configuration Design. McGraw-Hill (1961)
[2] Haynes, W.M.: CRC Handbook of Chemistry and Physics. 92nd Edition. Anticancer Research 32(5) (2012
[3] Knuth, K.H., Powell, R.M., Reali, P.A.: Estimating Flight Characteristics of Anomalous Unidentified Aerial Vehicles. Entropy 21(10) (2019)
[4] Knuth, K.H., Powell, R.M., Reali, P.A.: Estimating Flight Characteristics of Anomalous Unidentified Aerial Vehicles in the 2004 Nimitz Encounter. Proceedings 33(1) (2019)
[5] Koskinen, H., Kilpua, E.: Physics of Earth’s Radiation Belts. Springer (2022). DOI 10.1007/978-3-030-82167-8
[6] Liperovsky, V.A., Meister, C.V., Mikhailin, V.V., Bogdanov, V.V., Umarkhodgaev, P.M., Liperovskaya, E.V.: Electric field and infrared radiation in the troposphere before earthquakes. Natural Hazards and Earth System Sciences 11(12), 3125–3133 (2011). DOI 10.5194/nhess-11-3125-2011
[7] Markson, Ralph: The Global Circuit Intensity: Its Measurement and Variation over the Last 50 Years. Bulletin of the American Meteorological Society 88(2), 223 – 242 (2007). DOI 10.1175/BAMS-88-2-223
[8] Office of the Director of National Intelligence: Preliminary Assessment: Unidentified Aerial Phenomena. https://www.dni.gov/files/ODNI/ documents/assessments/Prelimary-Assessment-UAP-20210625.pdf (2021)
[9] Subedi, S.: Scattering Theory and Geometry. Ph.D. thesis, Miami U. (2022)
[10] United States Department of Defense: Statement by the De- partment of Defense on the Release of Historical Navy Videos. https://www.defense.gov/News/Releases/Release/Article/2165713/ statement-by-the-department-of-defense-on-the-release-of-historical-navy-videos/ (2020)
Hovering
Balancing the gravitational force of an UFO, Fg = Mg, pointing downward by the electrical one, Fe = QE, pointing upward for a negatively charged vessel, hovering is achieved when |Fg| = |Fe|, such that the charge-to-mass-ratio is given by
Q/M = g/|E|
The acceleration of gravity g has a negligible dependence on h, but the electrical field strength E varies strongly with h, such that, for constant UFO mass M, the required charge Q to hover varies. At h = 10, 000 m, E = 5 V/m, such that Q/M = 1.96 C/kg, while at h = 0 m, E = 100 V/m, such that Q/M = 0.098 C/kg. For a Tic-Tac-shaped UFO with power-law profile this implies charges of Q(10, 000 m) = 26, 440 C and Q(0 m) = 1322 C. For a capsular UFO with a von-Kármán profile, the charges reduce to Q(10, 000 m) = 12, 468 C and Q(0 m) = 623 C.
Assuming a diameter of 60 m, height of 11 m, and a von-Kármán profile for the disc-shaped UFO in the Bethune Encounter, hovering in front of the airplane at 3000 m altitude in an E-field of E = 23 V/m requires Q = 202, 806 C. If additional local perturbations of the E-field are included in the calculation, which may be up to 100 kV/m [6], the charge of the latter UFO is reduced to Q = 47 C. This is about the charge carried by five thunderbolts.
Thus, even for the smallest vessels, charges required for hovering in the global fair-weather electric field are so large that UFOs need to keep a large distance in order not to damage airplanes. However, local perturbations in the E-field, like clouds, can increase the E-field strength and thereby reduce the necessary amount of charge by orders of magnitude. Consequently, the distance of closest encounter to a UFO greatly depends on the local strength and configuration of the E-field. While buoyancy due to the air also reduces Q, it is of minor effect because it is proportional to the dynamic viscosity of the atmosphere, which is of the order of 10−5 Ns/m2, and the velocity of the UFO which is close to zero while hovering.
| Fig. 5 Hovering: the gravitational force Fg is balanced by the electric part of the Lorentz force Fe and drag Fd is negligibly small due to almost zero velocity. |
Horizontal circling
Next, we analyse the potentially circular motion around JAL 1628, in which the largest UFO we consider takes T = 24 s to circle once around the airplane and keeps a distance of r = 12, 000 m. As in [3], we neglect the forward motion and the drag forces as well because the von-Kármán profile should minimise the latter. Then, the B-field strength required to cause this circular motion in the plane of the airplane at h = 10, 000 m, orthogonal to the direction of the Earth’s B-field can be determined. Balancing the centrifugal force, Fc = M(2π/T)2r, with the Lorentz force caused by the magnetic field, FL = Q r(2π/T) |B|, yields
|B| = 2π/T * (Q/M)-1
Inserting the Q/M = 1.96 C/kg that is required to keep h = 10, 000 m constant in the vertical direction, |B| = 0.13 T. This value is about the magnitude of the field strength of a sun spot and four orders of magnitude larger than the global magnetic field of the Earth, such that additional local, perturbing B-fields have to be taken into account if this manoeuvre actually used a magnetic field.
Since the JAL 1628 Encounter included two additional UFOs, it may be possible that the missing B-field amplitude was generated by an accompanied flight manoeuvre of the two other charged vessels. While such fine-tuning is possible in principle, the hypothesis that the stronger electric field, caused by the local natural configuration or the two additional UFOs, is used in this flight manoeuvre seems more likely. Assuming the UFO travels the 2r = 24, 000 m in an accelerated rectilinear motion, we can determine the required (horizontal) electrical field that is required to cause this acceleration, a = 4r/(T/2)2, as
|E| = 4r/(T/2)2 * (Q/M)-1
Inserting the values given above, |E| = 170 V/m, now in horizontal direction, which can be easily caused by charges of the order of a few Coulombs at about 10 km distance. Finally, we note that both explanations of the observed flight can be completely expressed in terms of Earth’s gravito-electromagnetic characteristics.
 |
| Fig. 7 Horizontal motion due to local electric fields, again with negligible drag. |
Swooping The Nimitz Encounters with swarms of 10 to 20 smallest capsular UFOs include a swooping manoeuvre in which a UFO drops from h = 8535 m to h = 15 m in about t = 0.78 s. If the UFO were falling the entire height ∆h = 8520 m with the constant terminal velocity that is reached as soon as the vertical drag forces balance gravity, this velocity would be vt = ∆h/t = 10, 923 m/s. This value is about 30 times the sound speed and thus unrealistic to reach without any additional acceleration. Since previous manoeuvres benefitted from local perturbing electric fields, we model the E-field for the descent to be constant for two different field strengths |E1| = 100 V/m and |E2| = 100 kV/m. Due to the downward-pointing natural E-field, a positive charge has to be imposed on the UFO’s surface, contrary to the previous cases. As no detailed acceleration information over time is provided, including velocity-dependent drag forces is difficult. However, any drag force only increases the Q/M-ratio required for this descent, so that neglecting frictional forces yields a lower bound on Q/M. Thus, we can solve for Q/M in the simplified approach that the effective acceleration aeff required to travel ∆h = 1/2aeff t2 is the acceleration of gravitation plus the acceleration downwards due to the E-field |
Q/M = (2∆h − gt2)/(t2|E|)
For E1, we obtain Q/M = 280 C/kg, while for E2, Q/M = 0.28 C/kg. Whether this is feasible from the material science viewpoint depends on the maximum charge carrier density possible in a potentially doted SiC semiconductor. While E2 could be caused by ionising radiation from earthquake regions [6], it is also possible that this stunt is enabled by a specific spatial configuration of the entire UFO swarm. Manipulating the natural E-field by several charged vessels has the advantage to make the flights less dependent on external conditions.
In any case, given that aeff = 28, 008 m/s2, we do not assume any carbon-based living being to be inside such UFOs, as this acceleration exceeds those tolerable by humans by several orders of magnitude. Consequently, UFOs are most probably controlled by robots or remotely.
 |
| Fig. 8 Swooping from h = 8535 m to h = 15 m when Fd is overcome by Fg and Fe. |
Conclusion As shown here, UFOs are less mysterious than they appear at first glance because their design criteria and potential aeronautics can be based on very down-to-Earth physical principles and theories. Vessel shapes seem to be tuned for small drag, small sonic booms, low heating, and large surface area exposable to the Earth’s electromagnetic field. UFOs may also be optimal for hypersonic flights (beyond Mach 5), which we cannot analyse because our fastest plane, a Lockheed SR-71 Blackbird, has only reached Mach 3.3 so far. Yet, some information may be available for missiles and rockets. Interestingly, stealth does not seem to play a role as design criterion. There are at least two types of vehicles, multi-purpose small capsular ones that may navigate well through subsonic water environments, as well as travelling hypersonically through the atmosphere, and disc-shaped, larger ones, that may be built as carrier-ships for trans- and supersonic flights over longer time spans. Appropriate materials to build such vehicles are also known, silicon carbide, for instance, fulfils all necessary prerequisites. The masses determined from assuming axisymmetric von-Kármán and power-law profiles of a given length, width, height, and thickness are mostly smaller than known comparable airplane classes, but are idealised lower bounds still subject to large uncertainties. The specifications are sufficient for feasibility estimates, as the latter are based on simplified aerodynamics, too. As demonstrated by three different flight characteristics of UFOs, hovering, circulating, and swooping, we conclude that the global fair-weather electric field and the Earth’s magnetic field are most likely not sufficient to explain the manoeuvres that have been reported in [3]. But, including local perturbations, an explanation in terms of an electric propulsion mechanism becomes plausible. To support this idea, these perturbations require more detailed research, particularly on the frequency of their occurrence, their stability, and more precise field strength measurements. The ability to arbitrarily charge the surface of the vessels helps to reduce the strong dependency of the possible manoeuvres on the surrounding electromagnetic field configuration. In addition, these UFOs are often observed in groups and swarms, such that it is also possible that additional UFOs enhance and adapt the natural field configuration for specific manoeuvres. Thus, on the whole, we can conclude that whoever builds these vehicles must be well familiar with conditions prevailing on Earth, which entails the question whether these UFOs come from a similar environment as ours or are fabricated on this very planet. First concrete steps for independent follow-up investigations are being taken in the Galileo Project and NASA will hopefully fund UFO research in the future as well. Most conveniently, a good part of the required research can also be undertaken under the umbrella of environmental studies, which are currently well-supported to prevent a climate crisis. Further information and reading
References [1] Chin, S. S.: Missile Configuration Design. McGraw-Hill (1961) [2] Haynes, W.M.: CRC Handbook of Chemistry and Physics. 92nd Edition. Anticancer Research 32(5) (2012 [3] Knuth, K.H., Powell, R.M., Reali, P.A.: Estimating Flight Characteristics of Anomalous Unidentified Aerial Vehicles. Entropy 21(10) (2019) [4] Knuth, K.H., Powell, R.M., Reali, P.A.: Estimating Flight Characteristics of Anomalous Unidentified Aerial Vehicles in the 2004 Nimitz Encounter. Proceedings 33(1) (2019) [5] Koskinen, H., Kilpua, E.: Physics of Earth’s Radiation Belts. Springer (2022). DOI 10.1007/978-3-030-82167-8 [6] Liperovsky, V.A., Meister, C.V., Mikhailin, V.V., Bogdanov, V.V., Umarkhodgaev, P.M., Liperovskaya, E.V.: Electric field and infrared radiation in the troposphere before earthquakes. Natural Hazards and Earth System Sciences 11(12), 3125–3133 (2011). DOI 10.5194/nhess-11-3125-2011 [7] Markson, Ralph: The Global Circuit Intensity: Its Measurement and Variation over the Last 50 Years. Bulletin of the American Meteorological Society 88(2), 223 – 242 (2007). DOI 10.1175/BAMS-88-2-223 [8] Office of the Director of National Intelligence: Preliminary Assessment: Unidentified Aerial Phenomena. https://www.dni.gov/files/ODNI/ documents/assessments/Prelimary-Assessment-UAP-20210625.pdf (2021) [9] Subedi, S.: Scattering Theory and Geometry. Ph.D. thesis, Miami U. (2022) [10] United States Department of Defense: Statement by the De- partment of Defense on the Release of Historical Navy Videos. https://www.defense.gov/News/Releases/Release/Article/2165713/ statement-by-the-department-of-defense-on-the-release-of-historical-navy-videos/ (2020) |
