The concluding part of the Tau Zero Foundation’s examination of what is being called the ‘EmDrive’ appears today. It’s a close analysis of the recent paper by Harold ‘Sonny’ White and Paul March in the Journal of Propulsion and Power. Electrical engineer George Hathaway runs Hathaway Consulting Services, which has worked with inventors and investors since 1979 via an experimental physics laboratory near Toronto, Canada. Hathaway’s concentration is on novel propulsion and energy technologies. He has authored dozens of technical papers as well as a book, is a patent-holder and has hosted and lectured at various international symposia.

Hathaway Consulting maintains close associations with advanced physics institutions and universities in the US and Europe. Those familiar with our Frontiers of Propulsion Science book will know his paper on gravitational experiments with superconductors, which closely examined past methods and cast a skeptical eye on early claims of anomalous forces (an earlier paper, “Gravity Modification Experiment using a Rotating Superconducting Disk and Radio Frequency Fields,” appeared in Physica C). Like Marc Millis, Hathaway calls for continued testing of EmDrive concepts and increased rigor in experimental procedures.

By George Hathaway

Comments on “Measurement of Impulsive Thrust from a Closed Radio Frequency Cavity in Vacuum” (White, March et al, published online by Jnl. Prop. & Power November 17, 2016).


White et al are to be congratulated for attempting to measure the small thrusts allegedly produced by a novel thruster whose operating mechanism is not only not understood but purportedly violates fundamental physical laws. They have made considerable effort to reduce the possibility of measurement artifact. However it appears that there are some fundamental problems with the interpretation of the measurement data produced by their thrust balance. This document will analyse the measurement procedure and comment on the interpretation.

The following comments roughly follow the order in the original text by White et al

Analysis and Comments

1. Null Test Orientation

Tests were performed in both the “Forward” and “Reverse” direction as well as in a “Null” direction where the alleged force vector pointed towards the rotational axis of the balance (pg 23). Apparently no Null tests were performed with the force vector pointing away from the balance axis nor were any tests performed with the “test article” force vector pointing up or down. These additional orientations would have provided much needed control data given the magnitude of the allegedly purely thermal signal seen in their “Null” test.

In addition, the Forward and Reverse tests should also have been performed by just re-orienting the test article whilst keeping all other rotating components untouched. In this type of control experiment, the spurious effect of the rest of the components is largely eliminated.

2. Axis Verticality

An optical bench was used as a platform to mount the vacuum chamber containing the balance. It is not stated whether the optical bench was itself mounted on pneumatic legs, however, this is usually the case with optical benches. The correct operation of any balance of this geometry requires that the pivots around which the balance arm rotates must be perfectly aligned vertically one above the other (for a 2-pivot system). When the pneumatic legs of the table are inflated, the axis of the balance is not typically able to be kept perfectly vertical, as required to obtain the maximum balance sensitivity and repeatability. There is no indication in the text stating how such verticality was assured throughout the test campaign, especially since the balance was housed in a large vacuum chamber.

3. Flexural Bearings

There is no information presented to indicate whether the linear flexure bearings were operating within the manufacturer’s axial loading specification, especially when additional ballast weight was required for the non-“split configuration” tests. It would also have been useful to see data on the natural frequency of the balance when loaded with the equivalent weights used in the thrust tests, given the damping method described. Also missing is an explanation of why none of the traces of the optical displacement sensor return to starting baseline after the calibration and “thrust” pulses. There seems to be an inherent bearing stiction problem preventing the balance from returning to its original baseline after a test. This is not due to general balance drift and is typical for overloaded bearings of this type. Long-term balance stability/drift plots would be useful.

4. Electrostatic Calibrator

Evidently the calibration of the electrostatic “fin” method of applying calibration pulses was performed using an electronic balance (Scientech SA-210). Unfortunately no data was provided to show exactly how this calibration was performed. In particular, no data was provided to show that there was no electrostatic interaction between the high-voltage calibration voltages and the operation of the balance. Since the Scientech balance properly reports vertical forces only, was care taken to translate these vertical forces into the horizontal calibration forces required by the thrust balance? It would have been useful for the authors to have employed a second, independent horizontal force calibration to verify the Scientech method such as a strain gauge-type force gauge with interpolation.

5. Vacuum System

The authors note that although turbomolecular pumps were used to evacuate the vacuum chamber, they caused no artificial vibrational signals. Turbo pumps require mechanical backing pumps to evacuate them to atmosphere. These mechanical pumps are connected to the turbo pumps typically via thick and stiff vacuum hoses. These hoses can transmit backing pump vibrations to the turbo pumps which are usually rigidly connected to the vacuum chamber. Was this source of vibration taken into account as well?

Additionally, no evidence is provided to show how the interior of the test article was evacuated coincidentally with the chamber evacuation. This is a different concern to that stated in the paper (pp 27, 28) regarding outgassing of the dielectric. The concern here is that if the test article cannot be fully evacuated coincidentally with the chamber evacuation, residual gas inside the test article can possibly escape during the time of a test, causing spurious force signals. Moreover, if the test article is rather well-sealed, the shell of the test article, especially the end plates, could expand upon evacuation of the chamber due to air trapped inside prior to chamber pump-down. This would alter the center of gravity (COG) of the balance causing a spurious signal, especially if the trapped air is heated upon application of RF power of tens of watts.

6. Liquid Metal Connections

“Galinstan screw and socket” rotary connections were employed to prevent any unwanted torques from upsetting the balance due to hard-wire connections between the rotating test article and the power supplies, analytical instruments etc fixed to the lab frame. There must have been quite a few of these connections for DC power, Forward and Reverse RF power, various tuning and drive signals etc. The authors failed to indicate how these connections were arranged geometrically. The ideal mounting arrangement is for such liquid metal connections to be stacked one on top of the other exactly coaxial with the main rotational axis of the balance. It seems unlikely that the design constraints of the balance within the chamber shown would accommodate this tall a stack of connections. Thus it is assumed that these connections were not arranged coaxially with the balance axis. If so, there could be spurious side thrusts generated by Ampère currents set up within the galinstan. This should have been tested and reported.

7. Thermal Expansion and Control Tests

The White et al paper contains considerable information on the effects of thermal expansion of the various test article components. It would be beneficial to see control experiments in which the test article is replaced by a suitable control article such as a purely cylindrical cavity of approximately the same dimensions, materials and construction and which supports similar RF modes as the frustrated conical test article.

According to pg 10, the heat sink unsurprisingly is the greatest source of heat during operation. It would be useful to perform control tests by separating the heat sink mechanically from the rest of the rotating components in such a way as to allow it to be oriented in any direction relative to the rest of the components to see the effect on the optical displacement signal.

Evidently, the test article assembly produces a relatively large thermal “thrust” signal as measured by the optical displacement sensor. The only explanation given is the change in center of gravity (COG) due to thermal expansion of various components causes a spurious torque on the balance. In fact the presence of a thrust signal due to thermal effects is only inferred, not proven. Not only that but it is stated (pg 10) that this thermal effect causes the balance arm to shift “with the same polarity as the impulsive signal” in Forward or Reverse tests. Here also it is implied but not proven that an “impulsive thrust” signal is even present (see below). The authors need to perform such control tests as to ascertain with certainty that there is indeed a “thermal thrust” before assuming without proof that it causes the balance arm to shift “with the same polarity”. One such test would be to construct a “control article” of the same shape, material and weight as the test article but with guaranteed no “impulsive thrust” and substitute it for the test article. Instead of powering it with an RF signal, put a resistor or light bulb inside to simulate the thermal characteristics.

This lack of proof of the presence of either a thermal thrust or an impulsive thrust thus precludes statements such as “the thermal signal in the vacuum runs is slightly larger than the magnitude of the impulsive signal [due to convective issues]”.

8. Confirmation Bias in Thrust Analysis

The entire edifice of the analysis of the signals from the optical displacement sensor rests on the assumption of the correctness and correct application of Fig. 5 to the present test situation. Fig. 5 shows an ad-hoc superposition of two assumed signals, namely a thermal signal and a pulse (impulse) signal. This is presented initially as a “conceptual simulation” and is reasonable in its own right. However, it then takes on the value of an accepted fact throughout the rest of the paper. Fig. 5 represents what the authors expect to see in the signal from the optical displacement sensor. When they see signals from this sensor which vaguely look like the expected superposition signal as represented in Fig 5, they assume that Fig 5 must actually represent what is going on in their system under test. This is a clear inductive reasoning fallacy called Confirmation Bias. This problem leads to baseless assumptions about the timing of the onset of expected effects after application of the stimulus (RF power), their proper shapes, and the joint amplitudes and thus the individual (impulse vs thermal) magnitudes.

In particular, the authors assume that the “true” impulse signal from the test article will look just like the assumed signal shown in Fig. 5, namely that it will look just like their calibration signal. This will include an initial fast-rising but well-behaved exponential slope up to a flat-topped constant thrust followed by a slower exponential falling section back to baseline. Next they assume that the thermal signal will be a well-behaved double exponential starting exactly at the same time as the impulse signal, also as shown in idealized form in Fig. 5. An additional assumption made by the authors is that there are no other spurious effects which might be represented as additional curves in Fig.5. The simple addition of the amplitudes of the thermal and impulse signals produces the resulting superposition signal. This signal is used as a template against which the actual sensor signal is compared. By stretching the imagination, the sensor signal can be force-fit onto the idealized superposition signal and, voila, the simple analysis can proceed to extract the magnitude of the true impulse signal.

This method is applied to all the sensor signals except that in Fig. 10 showing the “split configuration”.

There are additional problems with this force-fitting routine. For example, in Fig. 7, which is analysed in some detail, the initial rising slope of the displacement sensor signal should be an asymptotically flattening exponential according to Fig. 5. But it is clearly an asymptotically rising signal, perhaps exponential in shape. About half-way through the RF power application period, this rising slope suddenly breaks into a markedly linear (rising) slope. According to Fig. 5, this part of the signal should show an asymptotically decreasing (flattening) exponential slope, definitely not a linear slope. The authors even use linear curve fitting in this region, evidence that even they do not consider this part of the slope exponential. All the optical displacement signals shown in the other relevant figures (Figs. 13, 16) show this characteristic as well.

Then a sleight-of-hand is used to tease out the contributions of the assumed thermal vs the impulsive signal. According to pg. 11, “the characteristics of the curve [superposition curve in Fig. 5] after this discontinuity [the break in slope of the rising exponential due to the onset of steady thrust] are used as the baseline to be shifted down so that the line projects back to the “origin” or moment when RF power is activated.” The amount of this baseline shift is taken to represent the “true” impulse signal. Naturally, this assumes that the onset of thrust (and the thermal signal) are all coincident exactly with the application of RF power (and are all of the ideal shape according to Fig. 5). According to Fig. 7, it also assumes that a straight line can be used as this “baseline shift” rather than the more likely broken exponential shaped line depicted in Fig. 5. This has the added bonus of arbitrarily increasing the “calculated” impulsive thrust.

Pg. 13 introduces a “Slope Filtering: Alternate Approach” to the force-fitting approach discussed above whereby the time derivative of the displacement sensor signal is plotted. This procedure produces a curve of magnitudes of slopes (Fig. 9). Sadly, this method starts off with the same assumptions as in the above approach. It compounds these problems by invoking an arcane procedure whereby the parts of the original displacement sensor curve with slopes lower a particular arbitrary (and unstated) value are removed and what’s left of the curve allegedly represents the “true” impulse curve. None of this procedure is shown in detail and only the final result is shown which, conveniently for the authors, is within ~20% of the previous analysis method. Of course, this convenient coincidence is entirely dependent on the arbitrary slope magnitude removal value.

9. Split Configuration

On pg. 15 we learn that by splitting the test article from the rest of the electronics – one on each end of the balance arm, the response time is reduced as expected due to the reduction in ballast weight required, and that the “true” thrust amplitude has been reduced from 106 uN to 63 uN, all other things being equal! Additionally, the displacement sensor curve (Fig. 10) is completely different in shape from the non-split configuration tests. The only explanation proffered for this discrepancy is that “the thermal contribution…is smaller in magnitude compared to the impulsive signal.” No proof of the correctness of this statement is provided. Since the split and non-split configuration curves are so radically different, the authors chose not to apply either of the analysis methods discussed above. They arbitrarily take the amplitude of the displacement signal at the instant it starts an exponentially asymptotic downward slope as the correct point. Why not use a variant of this method and apply it to the non-split configuration? Because it would result in relatively and apparently unacceptably huge (eg ~260 uN at 60 W) thrusts!

10. Difference between Forward and Reverse Thrusts

Tables 2 and 3 allow us to compare “calculated” thrusts (using the ideal curve force-fitting method discussed above) from Forward and Reverse non-split configurations. The Reverse thrusts are consistently lower than their Forward thrust counterparts. For example for 60 W, average Forward thrusts are 108 uN vs 60 uN for Reverse thrusts. For 80 W, these numbers are 104 uN vs 71 uN. No explanation is given for these differences, nor for the fact that in the Forward configuration, the 80 W thrust is lower than the 60 W thrust.

11. Null Thrust Test

It is stated on pg. 23 that “The [COG] shift from thermal expansion causes a downward drift in the optical displacement sensor.” Why not an upward drift? There is no justification given for this statement as no control tests were performed to ascertain what the result of a purely thermal effect might be, expansion or otherwise.

Further, the authors state “The results from the null thrust testing show no impulsive element…only the thermal signal.” This is also an unproven statement since no purely impulsive or purely thermal signal has been positively identified in shape or amplitude. The authors appear to have forgotten the thermal curve they used in Fig. 5, namely a double exponential. There is no evidence for any exponential part of the supposedly “thermal only” curve of the Null Test in Fig. 18. It appears completely linear and if there is a slight hint of an exponential, it is in the wrong sense (asymptotically falling, not flattening)! Another hint as to the problem of assigning a purely thermal explanation of the curve in Fig. 18 is the fact that exactly at the time of shutting off the RF power, there is no thermal lag or overshoot: the linear slope breaks suddenly to become essentially flat.

The implication of the Null Thrust test is that the thermal signal apparently seen in the Null Test would be the same as that seen in the Forward and Reverse tests. If so, then the curve force-fitting routine discussed above is invalid as it assumes a double exponential thermal curve (Fig. 5).

The Null Thrust test depicted in Fig. 18 was run at 80 W RF power. The Reverse Thrust test in Fig. 16 run at 80 W shows an apparent thermal signal of approx. 70 uN using the force-fitting routine. For the same period, the Null Thrust test shows an apparent thermal signal of approx. 275 uN. This is a huge discrepancy begging for detailed explanation.


In addition to mechanical and related considerations, the authors’ methods of analysis of sensor data to derive thrusts rests on untenable grounds. Not only is there an assumption of the presence of only a “true” impulse signal as well as a thermal signal, there is an assumption that the observed signal can be broken down into just these 2 components and amplitudes can be calculated based on an idealized superposition assumption. Therefore, until more control tests are performed allowing a more accurate method for estimation of thrusts, no faith can be placed in the thrust magnitudes reported in the paper.