Summary: This paper proposes that a reaction-less (in the Newtonian sense) space drive thruster can be created by leveraging the Coriolis and Euler accelerations that are present within a rotating free vortex flow to provide a coherent thrust vector. The hurricane is utilized as an example of this phenomenon. The configuration and basis of the underlying physics is discussed and utilized to support the proposal.
If humankind is ever to be a space-faring society, it must devise a more efficient and effective propulsion system for use in spacecraft. Almost all of the techniques for interstellar travel under consideration today rely on the rejection of mass from the vehicle, and while that technique is moderately effective in lifting objects off from the surface of the Earth, as a strategy for interplanetary and interstellar travel, it is woefully inadequate. This article will propose a new propulsive system, based on leveraging the internal dynamics of vortex flow as a means to create an acceleration vector and thereby, thrust, in a system that can recycle the mass used to drive it by reacting against the planar aspects of the flow. In this sense, it is a non-Newtonian drive.
Vortex flow systems are not very well understood. Perhaps it is due to the fact that they are hard to generate and maintain for study in the laboratory or maybe that lack of knowledge is related to the static Euclidean type geometry that we generally use to define space. In either case, the fact is that we lack good theories and practical knowledge regarding the vortex, which is an extremely common form of nature in the universe that we inhabit.
A vortex is, by its very definition, a three dimensional phenomenon. It has two central features: a whirling planar flow that is concentrating to or dispersing from the middle and a central core which projects out from the plane of rotation at roughly a 90o angle as shown in Fig. 1.
Figure 1: The basic shape of a Vortex
There are many examples of free vortexes in everyday life, but some of the most common and distinctive examples are: tornados, hurricanes, water draining from a sink and a stirred container of liquid. Each of these examples has the same basic functional form, although they vary in rotation direction and the orientation of the core column with respect to the spiral field. In this paper, only the form that is most relevant to the topic will be discussed, and that is: the hurricane.
Hurricanes are by far the longest lived and most stable of the vortexes. The ‘Red Spot’ on Jupiter is presumed to be of that form and has been observed in continuous existence for hundreds of years. On Earth, hurricanes are almost exclusively an oceanic phenomenon, because only the ocean can provide the raw thermal power required to maintain and develop the flow characteristics necessary to create and feed one. Hurricanes are formed when a large body of hot air over the ocean starts rising to the stratosphere. This rapidly rising air creates a rising column and a low pressure cell below it that draws in air from the surrounding lower level atmosphere to replace that which is rising. As this air is pulled across the surface of the ocean, it picks up both heat and humidity, which in turn augments the process.
Since the Earth is a rotating system and the column is somewhat localized, this rising air creates a coriolis effect on the flow as it attempts to refill that low pressure zone and the air starts to swirl, forming the characteristic spiral that we have come to associate with such storms.
As this moving mass of air swirls toward the center, something amazing happens. At a certain point, when the air achieves a critical velocity, it stops moving inward and forms a discrete structure that continues to extend upward without continuing to expand or contract, creating what we call the “eye wall”. This column is enormous (see Fig. 2, below)
Figure 2: A diagram and relative scale of the Hurricane Eye
Rising almost 15 km (48,000’) above the seascape, it is the singular feature that defines and distinguishes the hurricane from the lesser storms. The Eyewall provides a stable core that allows the hurricane to become an organized entity, one that is coherent, long lived, independent and dangerous. It is there that the highest speed winds reside, as they whirl about with velocities greater than, for a Class 5 hurricane, 249 kph (155 mph).
These winds carry a tremendous force and can take roofs off of entire commercial buildings, completely destroy mobile homes and whip up the ocean to devastating heights with surge levels exceeding 6 meters with the low pressure at the core. The amazing thing is that for the life of the hurricane, these powerful winds continuously circle in a relatively tight band (30 – 60 kilometers in diameter) around that core, leaving the very center calm and, because the air currents tend to disperse at the top, clear and sunny. See Fig. 3. How is it that these winds can be contained to make such a thing possible?
Figure 3: A Space eye view of a Hurricane
Viewed from space, it is rather obvious that a hurricane is a rotational system following the right hand rule. A counterclockwise base rotation creates an upward column that is accelerated away from the Earth. This is very difficult to understand if one is using only ground level observations, although the viewpoint provided by an airplane can give one a better perspective. The heat transfer necessary to maintain this thermal flow system driven by the rising, warm, moist air is possible because the ocean is an ideal thermal storage medium. Being a liquid, it can continuously replenish the heat energy on its surface from the warm sea water below. At the root of this drive is gravity, whose presence is what causes the warm air to rise.
However, the gravity and Earth rotation driven coriolis, although sufficient to start the system rotating and create the basic form, does not create a sufficient amount of force or control to engender this hurricane system that exhibits such a tightly bound, energetic Eyewall. Some other system dynamic must be controlling this feature. It is these other forces that can create the acceleration necessary to accomplish the generation of the thrust for this space drive, and the equations presented in the next section will illustrate how they can accomplish that goal.
3.0 The Physics of Vortexes
There are four basic accelerations present in any non-rigid rotating system. They are: Centrifugal, Centripetal, Coriolis and the Euler accelerations. Each will be briefly defined below.
Centrifugal: This is the acceleration created by a rotating system in a direction outward from the axis of rotation. In a bound system it is seen as a force pushing on the inside boundary of the outside wall. For systems under constant rotation, the direction of this acceleration is coincident with the radius of the rotation and therefore perpendicular to the tangent of the arc of rotation at that point. Its magnitude is proportional to the mass times the radius and the rate of the rotation, squared (A Centrifugal = mrW2)
Centripetal: The acceleration required to counteract the centrifugal force, and maintain the boundary of the system.
Coriolis: Coriolis acceleration is created when a particle within a rotating system changes its radius with respect to that system, that is, it acquires a velocity with respect to the system radius that changes over time (dr/dt). In a hurricane, when the moving air tries to rush into the low pressure left by the rising hot air, its velocity with respect to the rotating Earth changes, causing it to veer counterclockwise in the Northern hemisphere. The defining equation for this acceleration is, however, a vector cross product:
Wsystem X dr/dt = A Coriolis
This will be very important.
Euler: The Euler acceleration is, in respects similar to Coriolis, except that it is due to a change in rotational frequency within the rotating system. It also is defined by a vector cross product, this time:
r X dw/dt = A Euler
These are all considered by conventional standards to be fictitious forces because they are only present in and generated by rotating systems, and their strongest influence is within them. However, if properly applied, the forces that they create can impact non-rotating systems.
With these equations in hand, let us examine the Eyewall of a hurricane. As the air rushes in on its spiral path toward the eye, it accelerates both in linear and rotational velocity. As it moves into a tighter and tighter circle, its radius decreases, and at a certain point, the drawing power of the low pressure center can no longer restrain the Centrifugal acceleration created by the whirling system. At this point, a boundary is created. Assuming that the system is to be maintained, some force or acceleration must counteract the centrifugal acceleration present to keep the system from expanding radially and dissipating. In a rigid system, this is called the Centripetal force (see Fig. 4), and we can express the equation at that boundary as:
A Centrifugal = A Centripetal
Figure 4: A cross sectional view of an idealized Hurricane Eyewall
However, in a free vortex system there is no obvious, top level physical mechanism to restrain the flow in this manner; that is, to provide the Centripetal acceleration required to create a stable system. However, there must be some mechanism other than the pressure differential created by the storm to maintain the Eyewall. Fortunately, there is, because in a free, spiraling vortex, the particles within the vortex are moving within the flow and both rising and resonating within it; thereby creating both Euler and Coriolis accelerations. The rising air causes these flow variances to begin, and once begun they are fed and reinforced by the rotating flow in a feedback loop of sorts. These accelerations, by virtue of being cross products, do not react directly against the main body of the general flow but can and do provide the acceleration and consequently the force required to constrain the wind to travel in a circular pattern. This allows the Eyewall to stabilize and grow to a height far in excess of what it could by means of its thermal gradient properties alone. See Fig. 5.
Figure 5: A diagram of the flow patterns within a Hurricane
It is these accelerations that can and must be constraining the flow, and providing the centripetal acceleration required to create the tight banded column that is the Eyewall. Therefore, at the simplified boundary we can write the following equation:
A Centrifugal = f (A Coriolis + A Euler)
From the previous diagram and the equation given above, it would appear that a straightforward equality could be stated, however, that would mean ignoring the physical attributes of the flow. Since each of these accelerations is the result of a cross product, then the contributing vectors must be perpendicular to the line of acceleration created, which would mean that if all of the acceleration created by them was directed in opposition to the Centrifugal one, the arc of rotation for that cross product would have to remain rigidly within and completely aligned with the flow. Please refer to Fig. 6.
Figure 6: A Diagram showing the relative orientation of the Coriolis acceleration generated by Vortex flow
If the particles of the flow were to remain completely within the column of the flow, it would not be possible to have the variations in diameter and rotation rate required to create the restraining forces. Therefore, the individual particles of the flow must be moving on axes that are tipped to that flow by some angle that allows them to rotate within the flow field while allowing and creating the variations sufficient to generate those Coriolis and Euler accelerations to replace the Centripetal acceleration. If we define this angle to be a variable, theta, then we can write:
A Centrifugal = cosine theta (A Coriolis + A Euler)
This means that there must be some portion of that force that is directed perpendicularly to the line of action of the Centrifugal acceleration. Since the Centrifugal acceleration is in an almost horizontal orientation, that left over quantity, sine theta (A Coriolis + A Euler), must be directed upwards to give the Eyewall its characteristic height and shape.
Why is this important? Because the hurricane is creating a vertical acceleration, in opposition to gravity, from a cross product that reacts against the rotational flow of the particles within it rather than against the outside environment. Put quite simply, a hurricane supports and raises the Eyewall column, accelerating it against gravity, without reacting against the Earth. A hurricane, and for that matter, any free vortex system, converts planar rotational inertia into an out of plane acceleration, thereby seemingly violating Newton’s Third Law of Motion that roughly states that “for every action there must be an equal but opposite reaction”. The core of any free vortex leverages the small variations within its basically planar rotation to create an acceleration that is directed along the perpendicular linear flow line that is characteristic for that particular system. In the case of the hurricane, that direction is ‘up’.
The Eyewall cannot be a feature controlled by the pressure driven storms that feed it because it towers above those circulating winds by a factor of two or better. Its flow remains constrained above them in the absence of a more obvious internal or external mechanism to keep it from dissipating. The Coriolis and Euler forces must be present in every free vortex flow; the only question is whether one assumes that they may be aligned within the system to produce a coherent acceleration. However, it is the position of this paper that this is no harder to accept than it is to believe in the co-magnetization of an iron object by the application of a magnetic field to it. Just as that applied magnetic field can align the atoms of the iron within their crystal lattice to induce secondary magnetism (and therefore a directional force field) in the subject in contact, so too can the prevailing linear field (in the case of the hurricane, the rising moist, heated air) align the vectors of the Coriolis and Euler accelerations to induce a coherent field.
A free vortex, by its very fundamental nature, converts rotational velocity into linear acceleration, and can, therefore, be utilized to create a ‘reaction-less’ space drive (in the purely Newtonian sense). Make no mistake, this is not a system creating energy from nothing. This is about conservation of inertia and the conversion of rotational to linear energy according to the right hand rule.
4.0 The Space Drive
What is needed is a device that can essentially create a hurricane in a ‘can’, and harvest the acceleration vectors that are created by it. It will require several distinct features. A free vortex requires a fluid and a flow path. This flow path will need to allow the circulation of the vortex, and provide a return path that will turn the flow and allow it to reenter the spiral field at a lower level and velocity.
Some force will be required to drive the flow, but a strictly linear potential along the center of the vortex may not be sufficient to drive it correctly without some augmentation to create the spiral character, especially for smaller scale devices. Therefore, a feature will probably need to be included to set the flow into circular motion to orient and engender the Coriolis and Euler accelerations.
The thermal gradients that create the upward flow in a hurricane will not work in space due to the absence of gravity, and probably only work on a large scale anyway. This makes the electric and/or magnetic forces obvious choices for that driving force.
Finally, there must be a method to harvest the acceleration. Figure 7 below illustrates one possible configuration.
Figure 7: A cross sectional view of the proposed Space Drive Thruster
In this concept, a containment vessel is constructed with a dome shaped housing. The outer container will need to be made of a strong and rigid material. Although early test units could be made using Lexan or another clear, strong material to allow visualization of the flow characteristics, eventually, metal will be required for this structure. A Baseplate will be required to anchor the thrust device to the structure of the craft. In order to segregate the vortex path from the return flow, a doughnut shaped spacer is placed within the enclosure. This ‘doughnut’ must have a sufficient inside diameter to allow a free vortex to form inside its interior column. The return path created next to the interior surface of the dome will naturally increase in volume as it approaches the outer circumference that connects with the boundary of the spiral portion of the field. The diameter of the inner vortex core will need to be adjusted based on the fluid choice, density and velocity.
Stators placed at the bottom of the chamber where the returning fluid flow transitions back into the horizontal flow field will help to induce the spiral flow at the base. Toward this end, they will be placed at strategic locations around the perimeter of the spiral flow zone to induce that flow. For the first test devices, these stators should be adjustable to allow experimentation to determine the most effective angles. Since hurricanes seem to be dominated by Phi, the golden ratio, it would be expected to be a good starting point. A cone shaped stator is also shown attached to the baseplate at a point directly beneath the center of the core. This may or may not be required, but it would appear to smooth the streamlines and will not absorb any of the vertical acceleration created by the system.
The flat plate positioned at the top of the vortex column will serve as an impact surface for the accelerated flow. The flow of the vortex, after having generated additional linear velocity from the Coriolis and Euler accelerations within itself will slam into this top piece and create the thrust in a true Newtonian fashion. It has been illustrated as being a solid, flat surface perpendicular to the axis of the flow, although some curvature may need to be added to this feature to better focus the accelerated fluid and increase the stability of the thrust vector. It will need to be hard, durable, and will probably need to be cooled for higher velocities and fluid densities in order to remove the inevitable heat buildup that accompanies the momentum transfer. It can also be used as a component of the linear drive system, as discussed below.
The force of that impact from the fluid is what will create the thrust. By securing the device to the craft, this momentum from the fluid will be transmitted to the structure of the device and will provide the motivating force required to accelerate the spacecraft. In this manner, the device will provide it with a constant acceleration vector, delivered by a system that is operating at a constant velocity; something that is forbidden in a strictly Newtonian system.
Once that excess linear energy has been transferred by impact to the outside housing, the ‘slowed’ fluid will be dissipated radially by returning to the spiral flow field through the increasing area and circumference of that external flow path. In this manner, the fluid may be recirculated. Although the ‘turning’ of the fluid from the vertical flow of the lower section of the return to the spiral field may induce some counter thrust, this effect will be greatly overpowered the inertia transferred to the housing at the top of the device and additional damping will be provided by the general inertia and path of the flow field.
Providing a sufficient and effective linear drive force may be the most difficult aspect. The electric force is the most powerful of the known forces and could be utilized for this purpose. If an ionized (charged) fluid were utilized, an electric potential applied between the baseplate and the top could be used to accelerate the fluid and would easily work in any level of gravitational field, that is, either on Earth or in deep space. There is a problem with an electric drive however, and that is, by using a strictly attractive force, it may be difficult to establish a flow when the particles all want to ‘stick’ to the top because that is where the potential difference between the charge of the fluid and the source is the greatest. This may be overcome by the overall inertia of the system, or by pulsing the field at a certain frequency to allow the particles of the flow to be ‘dislodged’ and continue along with the flow. The frequency required will be specific to the charge density, the velocity and the inertial mass of the fluid.
Alternately, one could use magnetism.
There is an interesting relationship between the magnetic force and some materials that fall into the category of being diamagnetic. Diamagnetic materials are repelled by magnetic fields, and notably, the stronger the magnetic field, the stronger the effect, that is, the closer the diamagnetic material is to the source of the magnetic field, the more forcefully the particle is repelled. It is the diamagnetic effect that causes a permanent magnet to float above a superconductive material. Very few materials exhibit this characteristic, but the list contains some fluids, notably nitrogen, water and mercury.
This source for acceleration would have the best configuration to establish the desired flow. By placing a magnet either around the vortex column in the spacer or in the conical stator and choosing a diamagnetic fluid, the repulsion provided by the magnet will repel the atoms of that fluid at the very location where the most acceleration is required and will dissipate at distance making it easier to turn the flow into the recirculation channel.
Because this is a mass-based thrust system, the greater the leveraged fluid mass, the greater the possible thrust, making mercury the best long term choice. Mercury is not only a fluid at room temperatures and has the highest mass of any low temperature fluid, but it also has the second highest diamagnetic value of any element, exceeded only by bismuth. Although bismuth is not a liquid, it may be possible to salt the mercury with bismuth to achieve higher levels of antimagnetic acceleration.
This magnetic-diamagnetic effect on fluid flow has already been demonstrated. Xiaodong Ruan et al showed in their paper from 2001 that a decreasing, stationary magnetic field induces a natural vortex in an established flow field containing nitrogen and increases the speed of the nitrogen flowing through that system over the flow velocity induced through the pressure differential alone, by a factor of almost 5 times.  The vortex flow was induced by the magnetic field in their test, and was created with the complete absence of stators or moving parts.
Although the idea of a self contained, ‘reaction-less’ thruster in a ‘can’ is somewhat unusual, it is not without precedent. Roger Shawyer has shown that by selectively eliminating some of the directional microwave energy stored in a resonance tube, such a self contained device can produce measureable thrust. 
5.0 Conclusion and Speculation
The question is not ‘if’ the Coriolis and Euler accelerations exist within a free vortex. They must; and they are definitely created by the action of a cross product of velocities. The only question is: can they be aligned to form a coherent acceleration that can transmit a force to the larger, outside world? Based on the examples provided by nature, the answer to this question must be ‘yes’.
It is expected that it will take some time to experiment with and capitalize on this concept. Smaller thrusters made using water or nitrogen will be more easily developed and will be very useful for long duration space missions. Since the thrust described here can be produced by a system with a constant motion or a constant force field utilizing a recirculated fluid, considerable mass will be saved over more conventional rocket based systems, even if the thrust produced is, at least for the initially designed systems, somewhat low.
However, this system design has almost no theoretical upper limit, and does not necessarily have any moving parts other than the fluid. As the mass, flow rate and the rate of rotation of the fluid is increased, so too is the thrust created. Although the circulating fluid must be constrained by the light speed limit, since this system reacts against itself rather than being dependent on the surrounding space, the craft that it is attached to may not be so constrained; especially since the acceleration produced by the system is constant.
The physics behind this system was actually derived during the creation of an alternate geometric system that utilizes velocities to describe space, rather than static axes and points, and that analysis makes this design and its conclusions, quite frankly, much more accessible, obvious and easier to describe. This drive is a natural outgrowth of realizing that the vortex is one of nature’s most fundamental forms, and that, in the rotational dimension, a constant velocity always creates a constant acceleration and that every action has a perpendicular reaction.
1. National Oceanic and Atmospheric Administration, U.S. Department of Commerce, “Hurricane Basics” May 1999 (Publication)
2. R. Xiaodong et al. “Particle Image Velocimetry Investigation of N2-Air Convection Induced by Magnetic Fields”, Japan Journal of Applied Physics, Vol. 40, pp. L648 – L650, Part 2, No. 6B, 15 June 2001 (Article in Journal)
3. R. Shawyer, “A Theory of Microwave Propulsion for Spacecraft”, V 9.4, Satellite Propulsion Research Ltd., 2006 (Paper)