# Introduction

Roger Shawyer, a microwave engineering from the U.K., devised and built a series of copper asymmetrical resonating cavities starting in the year 2001 for a company he started called Satellite Propulsion Ltd..

Shawyer claims that "Thrust is produced by the amplification of the radiation pressure of an electromagnetic wave propagated through a resonant waveguide assembly."[1] Although the device clearly works, as shown below, the theory to explain it has generated considerable skepticism and controversy. It is clear from papers[2][3] that there is severe problems with radiation pressure as the source of the force.

A clear demonstration the device works: <dhflashplayer>file=Emdrive_Flight_Test_Flight_20Test_20DEM_20188.flv|width=480|height=360|path=http://curvity.org/w/images/%7Cflashvars=&image=http://curvity.org/w/images/vlcsnap-5123655.png</dhflashplayer>

Figure 8: First cavity - graph of results

Figure 8 shows a graph of power versus force for the first "Experimental Engine" shown in figures 1 and 2. Once the power is turned on, the force builds up after about 10 to 12 seconds. The slope of the force after power is turned off is also a rough estimate of the Q of the cavity because if the Q, i.e. the "resistance" is high the slope will be sharp, but if not, then it will "ring" for a considerable time after. The length of Shawyer's tests are also telling because the graph shows that for this test he only ran it for a minute.

# Why the Cavity is Evidence for Curvity

Each section here starts out with a quote directly from Fry's story and then shows what it matches in Shawyer's cavity.

## Resonance

The "two fields" mentioned are the electric and magnetic fields and inside Shawyer's cavity they are resonating.

TE0,1,nEnergy Density in a triangular cavity

## Asymmetrical

Shawyer's cavity is resonating in the TE0,1 mode, creating the energy density at the narrow end as shown. The TE0,1,n modes were chosen because they all have zero E fields around the circumference and do not loose more energy at higher modes.

Because of the shape of the cavity, a truncated "V" shape, the resulting resonance is asymmetrical, i.e. the center of mass of the cavity does not coincide with the center of resonance or the "center of force". As the cavity accelerates toward the center of resonance or force, the entire apparatus moves and like the wiener on a stick a dog can never reach in front of it, the center of resonance moves as well.

## Frequency based

The higher the frequency, the more energy it has and Shawyer's cavity is pumped by waves at microwave frequency, 2.45Ghz.

## Power versus Force

Below are measurements by Shawyer of the force being generated versus the Q factor of the cavity.

• 6mN at a Q of 5960
• 300mN at a Q of 50,000

The importance here is that while the Q went up 10 times, the force went up 20 times. The amount of force, although 300mN at best, is still a substantial amount considering the power used is only 800W. A similarly powered ion thruster can only produce tens of milli-newtons.

## Existing Explanations Fail

Endless skeptics have pointed out that radiation pressure on either side of the cavity, no matter the shape, will produce an identical force. Shawyer's explanations have failed to convince skeptics because the theoretical treatment has not been peer-reviewed and generally fails as a coherent explanation.

Shawyer's theory paper (v9.4) also makes something clear:

Thus the radiation pressure at the larger end plate is higher than that at the smaller end plate. The resulting force difference (Fg1 - Fg2) is multiplied by the Q of the resonant assembly.[4]

Forces, Fg1 and Fg2, inside the cavity

Where Fg1 and Fg2 are the forces on the plates as shown on the right.

But if you look carefully at his demonstrator engine video above, you will notice the device is travelling in the opposite direction it should, counter-clock wise, which suggests that Fg1 is less than Fg2.

When Shawyer was queried about his demonstrator motor going backward, he states:

The force difference creates a thrust in the F1 direction. Newtons 3rd law (and the conservation of momentum ) require that the engine accelerates in the opposite direction, as demonstrated in the dynamic test. Regards Roger Shawyer SPR Ltd

(It is great to talk to a future Nobel Laureate!!)

By "F1" that he means Fg1 but his explanation doesn't make much sense, even from the perspective of radiation pressure. If it really is a radiation pressure difference on the large end versus the narrow end, then, as his paper states, it should be Fg1 - Fg2 which still points in the direction of the large end. A simple analogy to explain the radiation pressure idea is that the photons are like balls, and as it bounces against the narrow end, the force is like a tennis ball and at the larger end, it is like a bowling ball. If we take Shawyer's explanation at face value then he is suggesting that because the radiation pressure results in a force toward the large end and in order to satisfy the conservation of momentum, another force, identical to Fg1-Fg2 but in the opposite direction, is magically created?!?

It is likely he doesn't understand why it works[5][6]

An engineer also took a look over Shawyer's "radiation pressure" theory paper and noted that:

I started to read the technical report on the EM drive and right away I found problems, for instance, in the Lorentz force equation, the velocity v is the velocity of a charged particle, but the author assigns it the "group velocity" of the radiation. Two things wrong, one, EM radiation consists of photons, not charged particles, and, two, "group velocity" is not the velocity any particle at all, not even a photon. The group velocity of a wave can far exceed the velocity of light!

It would seem that Shawyer's device works, but not for the reasons he thinks.

# Problems With Curvity's explanation

If Shawyer's cavity moves because of a modification of earth's local gravity field, it fails to explain why if gravity is a downward force vector, that a perpendicular force vector can be created.

1. Quote from the front page of EMdrive.com, July 12th, 2007
2. Why Shawyer's electromagnetic relativity drive is a fraud John P. Costella (2006).
3. Resonant Modes of a Conical Cavity Greg Egan (2007).
4. "EMdrive Theory Paper" (PDF), v9.4, emdrive.com
5. Video Evidence of the First Ever Gravitic Propulsion!!, Daniel Fry Dot Com, May 14th, 2007
6. Waveguide Theory and Why Radiation Pressure is Not The Cause, Daniel Fry Dot Com, May 17th, 2007