Older and Contemporary Attempts for Inertial Propulsion
| Scientific Paper | |
|---|---|
| Title | Older and Contemporary Attempts for Inertial Propulsion |
| Read in full | Link to paper |
| Author(s) | Christopher G Provatidis |
| Keywords | propulsion, time dilation, Rotation |
| Published | 2011 |
| Journal | General Science Journal |
| No. of pages | 14 |
Read the full paper here
Abstract
In this paper we review and critically present the state-of-the-art of inertial propulsion means, which may cause motion of the object to which they are attached. At the same time, we indirectly overview some other advanced propulsion systems by direct reference to the main bibliography. First we refer to the rotation of two synchronized masses that move along a circular path (Dean-drive). We prove that they can conditionally cause motion of the object and temporal lift. We also present some of our previous results concerning masses moving along a figure-eight-shaped path on the surface of a hemisphere, which also rotates around the axis of symmetry. We give particular attention to the proper synchronization that may instantly cause loss of weight or create such instability so as the object can be easily displaced by external means. Since the rotation is the key to the inertial propulsion, we discuss the role of the rotation in gyros as well as the possibility of the existence of an aetherometric mesh or the possible influence of time dilation, as claimed by others. This work is an extension of a one-hour presentation at the conference SPESIF-2011 (March 15-17, 2011, at University of Maryland, USA).
Overview
This is a review, by a mechanical engineer, of the whole tradition of trying to move a vehicle by moving masses around inside it. It grew out of a one-hour presentation at SPESIF-2011 at the University of Maryland, and it surveys the field from the halteres of the ancient Greek long jump through Norman Dean's contra-rotating drive of the 1950s to twenty-first-century patents, gyroscopic weight-loss claims and relativistic frame-dragging proposals. Interleaved with the survey are the author's own analytical results on two mechanisms: the Dean drive itself, and a device of his own design in which masses run along a figure-eight path laid over the surface of a hemisphere that is itself spinning.
What distinguishes the paper from most of the antigravity literature is that its mathematics mostly comes out against the devices. Provatidis proves that the Dean drive delivers zero net impulse per revolution; he reports that his own figure-eight path likewise gives a maximum upward force exactly equal and opposite to the maximum downward one; and when one variant of his analysis does suggest a weight loss, he flags it himself as an apparent violation of momentum conservation "that has to be further explored". The paper's positive content is therefore narrow and conditional: certain synchronizations can produce temporary lift or hovering, or can destabilize an object so that it "can be easily displaced by external means".
The survey and the analysis
Ancient dumbbells and the Dean drive
The earliest use of swinging eccentric masses, Provatidis suggests, is the pair of halteres carried by ancient Greek long jumpers. His reconstruction is that the jumper rotates them in a vertical plane so that at lift-off their momentum points along the direction of the jump, and by landing their horizontal momentum has been transferred to the athlete's body, lengthening the jump. Twenty-five centuries later Norman Dean patented a device using two contra-rotating eccentric masses (US Patent 2,886,976, 1959) to convert rotary motion into unidirectional motion, and claimed it would produce thrust.
The refutation is elementary and Provatidis states it plainly. Each rotating mass passes through the same point at the same velocity once per revolution, so the change of linear momentum over a cycle is zero and, with no external force, the net impulse per period vanishes. Equivalently, the positive impulse while the mass traverses the upper half of the circle is exactly cancelled by the negative impulse over the lower half. Writing the two momenta explicitly, their sum is purely vertical, of magnitude 2mrω cosφ, while the total angular momentum vanishes, so no gyroscopic phenomena arise either.
The qualification "conditionally" in the abstract refers to what remains. Because the summed momentum oscillates, the initial phase at which the assembly is released matters: with the rods horizontal and moving upwards, the stored momentum is at maximum, and a large part of it can be transferred to the carrier body over the next quarter turn, launching it upward like a projectile — which then falls back. Provatidis has published closed-form times of ascent and return elsewhere. This is momentum transfer within a cycle, not propulsion.
Attempts to break the symmetry
Three families of fixes are reviewed. Shortening the radius on the lower part of the path is defeated by the reaction forces needed to pull the mass inward through an external shell, which cancel the supposed benefit. Varying the angular velocity between the upper and lower arcs fails for the same reason as before — the mass still returns to the same point every 360° — and Provatidis reports that even an exponential variation gives no positive result. What is possible is hovering: starting just after bottom dead centre and increasing the angular velocity according to a formula he derives, the carrier can be held entirely immobile for a while. But as the mass approaches top dead centre the required angular velocity diverges, and the hovering cannot be sustained through even half a cycle. He notes in passing that the singular denominator is "reminiscent of relativity theory, although it is probably irrelevant".
The figure-eight mechanism
The author's own device was inspired by the hummingbird, whose wings trace a figure-eight — a continuous stroke "like a Möbius strip" — at some 53 beats per second, allowing it to hover for up to fifty minutes. He deforms the circular path in two steps: fold the lower half around the vertical axis to give a crossed figure-eight in a plane, then bend that curve so it lies entirely on the surface of a hemisphere, above or below the centre. A prototype with two rods pinned at the centre of the sphere and carrying masses at their ends is shown. Even so, he reports, "it has been theoretically verified that the maximum upward force is equal and opposite to the maximum downward force thus net propulsion is still impossible".
The final move is a second rotation about the vertical axis of symmetry, at an angular velocity whose ratio to the first is irrational, so that the mass never passes through the same point of three-dimensional space twice. Combined with the variable elasticity of the rods — least stretched at the bottom, most stretched when horizontal — a "crude mathematical analysis" yields a vertical impulse split into a rigid-body part, 2mrω sin 2θ, and a tension part expressed as a short Fourier series in 2θ, 4θ and 6θ. That total suggests weight loss. Provatidis immediately asks the right question — "how it is possible to develop thrust using internal forces?" — and offers only the tentative answer that Solomon's theory, in which time dilation is the source of gravitational effects, might apply.
Gyroscopes and the weight-loss claims
A long section reviews the claim that spinning gyros lose weight. Bruce DePalma, a lecturer at MIT in Harold Edgerton's laboratory, reported photographic evidence of anomalous behaviour in falling and obliquely launched spinning balls, and some have linked this to an alleged deviation of Explorer 1 in 1958 — though Provatidis records that a senior American physicist with connections to von Braun's team assured him nothing strange occurred. Hayasaka and Takeuchi reported in Physical Review Letters in 1989 that a gyro spun with its spin vector downward lost weight in proportion to its revolutions per minute. Provatidis lists the rebuttals in full: null results from Faller and colleagues, from Nitschke and Wilmarth, from Quinn and Picard (who found "no dependence on speed or sense of rotation"), and from Imanishi and colleagues, together with critical correspondence from Adelberger, MacCallum and Salter. He also cites Luo and colleagues, who measured the differential acceleration between spinning and non-spinning gyroscopes with a double free-fall interferometer and found none at the level of 2 × 10−6, concluding that "the equivalence principle is still valid for rotating extended bodies".
Against this he sets Wayte's report of an 8 per cent weight loss in a re-examination of Laithwaite's experiments — noting parenthetically that the figure is a time integral of a measured impulse rather than a static weighing — and the Correas' aetherometric argument that the discrepancy is a matter of angular velocity: their calculated electron "gravitational oscillation" rate of 13,716.1 double swings per minute-org corresponds to about 12,859 rpm, close to the 12,000–13,000 rpm at which Hayasaka saw the largest effect, whereas the null experiments were run at 6,000 and 8,000 rpm. Provatidis wonders whether it is accidental that DePalma's 27,000 rpm is nearly double the critical value, and observes that Hayasaka's later free-fall runs at 18,000 rpm do not fit the pattern.
The paper closes with a chronological catalogue of antigravity approaches from Townsend Brown in 1920 to Solomon in 2011, Millis's classification of the field into twenty-six propellantless, four faster-than-light and nine energy-conversion methods, and a rhetorical coda: Kelvin's 1895 pronouncement that heavier-than-air flight was impossible, the Wright brothers, and the prediction that "the death of Rocket Science is only a matter of time".
Assessment
Provatidis is a far more honest guide to this subject than most of the writers he cites, and the paper's chief value lies exactly in its negative results. He proves the Dean drive cannot work, and gives the reason in one sentence that any reader can check. He reports that his own figure-eight geometry also nets to zero. He quotes the null gyroscope experiments in detail rather than burying them. The closed-form condition for temporary hovering is a genuine and correct piece of engineering: internal masses really can hold a body up for part of a cycle by trading momentum, and he is candid that the required angular velocity diverges before half a turn is complete. Read as an annotated bibliography of inertial propulsion with a competent mechanical analysis attached, the paper is useful.
The positive claim at its centre, however, does not survive the paper's own logic. The centre of mass of a closed system cannot be accelerated by internal forces; this is not an empirical generalization awaiting a counterexample but a direct consequence of Newton's third law, and adding elastic rods changes nothing, because elastic elongation stores and returns energy through internal forces whose reactions act on the frame. When a "crude mathematical analysis" produces a net vertical impulse, the overwhelmingly likely conclusion is that a reaction term has been dropped — most probably the force transmitted through the pinned ends into the support. Provatidis half concedes this by calling it a violation to be explored, but the paper then treats the result as a possible weight-loss effect rather than as a diagnostic of the calculation.
The proposed escape routes do not help. That an incommensurate second rotation prevents the mass from ever revisiting a point in space does not imply a non-vanishing time average: a bounded force that is antisymmetric about the equatorial plane averages to zero whether or not the trajectory closes. And time dilation cannot supply the missing physics at these scales; at a rim speed of tens of metres per second the fractional effect is of order 10−15, some twelve orders of magnitude below anything a laboratory balance could register, so invoking it as the source of a measurable thrust is an appeal without a magnitude.
The gyroscope material is where the paper is least critical. The empirical record it itself sets out is one positive result and five independent nulls, capped by a free-fall interferometer bound of 2 × 10−6 on any spin-dependent acceleration. The aetherometric rescue — that Hayasaka happened to spin at a resonant rate — is directly contradicted by Quinn and Picard's finding of no dependence on rotation speed at all, and the numbers offered in its support (13,716.1 double swings per minute-org; a graviton frequency of 426.95 s−1) arrive with no derivation a reader could check, while the one datum that does not fit, Hayasaka's 18,000 rpm run, is noted and set aside. Similarly, Wayte's 8 per cent figure deserves more scepticism than a parenthesis: a body lighter by eight per cent would be unmissable on any balance, so the fact that the number comes from integrating a transient reaction impulse is the whole story, not a footnote.
Finally, the sourcing is uneven for a review. Physical Review Letters and Nature citations sit alongside Wikipedia articles, YouTube links, a website's list of "21 principles to achieve antigravity", and books on suppressed wartime flying saucers, with no visible difference in the weight assigned to them. And the closing appeal to Lord Kelvin's failed prophecy about heavier-than-air flight is beside the point: the objection to inertial propulsion is not a prediction about engineering ingenuity but a theorem about closed systems, and no amount of past pessimism about aviation bears on it. The right response to the paper is the one its own analysis keeps supplying — that if a device appears to produce net thrust from internal motion, the accounting is incomplete.