# Principles of EmDrive – Microwave energy to thrust, without the need for propellant.

Explanation by SPR Ltd.

FAQ

Theory

1.
Q. Is the thrust produced by the EmDrive a reactionless force?
A. No, the thrust is the result of the reaction between the end plates of the waveguide and the Electromagnetic wave propagated within it.

2.
Q. How can a net force be produced by a closed waveguide?
A. At the propagation velocities (greater than one tenth the speed of light) the effects of special relativity must be considered. Different reference planes have to be used for the EM wave and the waveguide itself. The thruster is therefore an open system and a net force can be produced.

3.
Q. Why does the net force not get balanced out by the axial component of the sidewall force?
A. The net force is not balanced out by the axial component of the sidewall force because there is a highly non linear relationship between waveguide diameter and group velocity. (e.g. at cut off diameter, the group velocity is zero, the guide wavelength is infinity, but the diameter is clearly not zero.) The design of the cavity is such that the ratio of end wall forces is maximised, whilst the axial component of the sidewall force is reduced to a negligible value.

4.
Q. Does the theory of the EmDrive contravene the accepted laws of physics or electromagnetic theory?
A. The EmDrive does not violate any known law of physics. The basic laws that are applied in the theory of the EmDrive operation are as follows:

Newton’s laws are applied in the derivation of the basic static thrust equation (Equation 11 in the theory paper) and have also been demonstrated to apply to the EmDrive experimentally.

The law of conservation of momentum is the basis of Newtons laws and therefore applies to the EmDrive. It is satisfied both theoretically and experimentally.

The law of conservation of energy is the basis of the dynamic thrust equation which applies to the EmDrive under acceleration,(see Equation 16 in the theory paper).

The principles of electromagnetic theory are used to derive the basic design equations.

5.
Q. Why does the EmDrive not contravene the conservation of momentum when it operates in free space?
A. The EmDrive cannot violate the conservation of momentum. The electromagnetic wave momentum is built up in the resonating cavity, and is transferred to the end walls upon reflection. The momentum gained by the EmDrive plus the momentum lost by the electromagnetic wave equals zero. The direction and acceleration that is measured, when the EmDrive is tested on a dynamic test rig, comply with Newtons laws and confirm that the law of conservation of momentum is satisfied.

6.
Q. Is the EmDrive a form of perpetual motion machine?
A. The EmDrive obeys the law of conservation of energy and is therefore not a perpetual motion machine. Energy must be expended to accelerate the EmDrive (see Equation 16 of the theory paper). Once the EmDrive is switched off, Newton’s laws ensure that motion is constant unless it is acted upon by another force.

7.
Q. Why does the thrust decrease as the spacecraft velocity along the thrust vector increases?
A. As the spacecraft accelerates along the thrust vector, energy is lost by the engine and gained as additional kinetic energy by the spacecraft. This energy can be defined as the thrust multiplied by the distance through which the thrust acts. For a given acceleration period, the higher the mean velocity, the longer the distance travelled, hence the higher the energy lost by the engine.
This loss of stored energy from the resonant cavity leads to a reduction in Q and hence a reduction of thrust.

Test procedures

8.
Q. Has buoyancy been allowed for?
A. Buoyancy has been allowed for in the initial experiments and then eliminated by hermetically sealing the thruster.

9.
Q. Are there any convection currents which might affect the results?
A. Convection currents did not affect the results, as measurements were taken with the thrust vector up, down and horizontal. Test runs were also carried out using a thermal simulation heater to quantify the effects of change of coolant temperature.

10.
Q. Has stiffness in cables and pipes been allowed for?
A. The only connections to the balance were high flex electrical links

11.
Q. Has friction in any pivots been allowed for?
A. Static thrust measurements were carried out using 3 different techniques – a counterbalance rig with a knife edge pivot, a direct weighing method using a 16kg balance (0.1 gm resolution), and with the thruster suspended from a spring balance with the weight partly offloaded on to an electronic balance.

12.
Q. Have electromagnetic effects been taken into account? These include interactions between current-carrying conductors and between such conductors carrying RF currents and nearby metallic structures in which currents might be induced.
A. Stray electromagnetic effects were eliminated by using different test rigs, by testing two thrusters with very different mounting structures, and by changing the orientation by 90 degrees to eliminate the Earth’s magnetic field.

13.
Q. Is there any ionization within the air, which might cause electrostatic charging and resulting forces?
A. Electrostatic charges were eliminated by the comprehensive earthing required for safety reasons, and to provide the return path for the magnetron anode current.

14.
Q. Could RF pick-up measurement circuits have produced erroneous results?
A. EMC tests were carried out on the instrumentation to eliminate the effects of RF pick up.

15.
Q. Could acceleration be caused by spurious torques generated by the air bearing?
A. Dynamic tests are preceded by an acceleration calibration test, using standard weights to determine the air bearing friction.

16.
Q. Could acceleration be caused by anomalous thermal or electromagnetic effects?
A. Acceleration and deceleration tests have been carried out in both clockwise and anti-clockwise directions Acceleration from rest only starts when the magnetron output frequency matches the resonant frequency of the engine, following an initial warm-up period.

Applications

17.
Q. Can the technology be qualified for space applications?
A. Yes, all the basic microwave, power supply, thermal and control technologies are similar to flight equipment currently used on high power communication satellites.

18.
Q. How can the EmDrive produce enough thrust for terrestrial applications?
A. The second generation engines will be capable of producing a specific thrust of 30kN/kW. Thus for 1 kilowatt (typical of the power in a microwave oven) a static thrust of 3 tonnes can be obtained, which is enough to support a large car. This is clearly adequate for terrestrial transport applications.
The static thrust/power ratio is calculated assuming a superconducting EmDrive with a Q of 5 x 109. This Q value is routinely achieved in superconducting cavities.
Note however, because the EmDrive obeys the law of conservation of energy, this thrust/power ratio rapidly decreases if the EmDrive is used to accelerate the vehicle along the thrust vector. (See Equation 16 of the theory paper). Whilst the EmDrive can provide lift to counter gravity, (and is therefore not losing kinetic energy), auxiliary propulsion is required to provide the kinetic energy to accelerate the vehicle.

A Note on the Principles of EmDrive force measurement

# 1. Introduction

A number of research groups have asked questions about methods of measuring EmDrive forces. Answers to these questions require a basic understanding of the theory of operation of EmDrive, and a rigorous understanding of classic mechanics and Newton’s Laws. This note describes simple examples of test methods which will clarify experimental results.

The most important point to be made, is that to measure force, the cavity must experience acceleration. In a fully restrained cavity, thrust and reaction force cancel out.

Demonstration of this point clearly shows that EmDrive is a Newtonian machine, and the law of conservation of momentum is maintained.

# 2.  Operation of an EmDrive thruster

R = Ma

Fg2

Fg1

T

Fig 1.  Thruster Force Diagram

The net force (F) created within the thruster is given by the basic equation

FQFg1 Fg2

where Fg1 and Fg2 are the radiation forces caused by group velocities  Vg1 and Vg2 at the two ends of the thruster.

This internal force F is measured by an outside observer as the Thrust T, a force acting against the observer in the direction shown.

Newton’s laws state that T must be opposed by an equal and opposite reaction R, such that

RMa

where M = mass of the thruster            a = acceleration of the thruster in the direction shown.

Note that the reaction is either the acceleration a, or a force equal to Ma, but not both.

Clearly, in a static situation, where T and R both exist as forces, they will cancel out. Thus any attempt to measure them by simply placing the thruster vertically on a set of scales will fail. If however the thrust is sufficient such that a = -g, then the thruster could be made to hover above the scales.

A rigorous examination of measurement techniques is required, to determine how these forces can be measured.

3. Measurement of EmDrive forces in free space.

Fig 2. Thruster in Free Space

In free space, the thruster will simply accelerate at a m/s/s, and R will not be measurable. To measure R it is necessary to restrain the thruster against a fixed reference point.

However at rest, no force can be measured as R will cancel out T as in Fig 1.

This situation is unique to a propellantless thruster such as EmDrive and analogies with conventional devices are pointless.

To illustrate further, assume the thruster is mounted on a friction free trolley, (or is suspended from a pendulum), and is restrained against a fixed wall by a load cell as shown in Fig 3.

Fig 3. Restrained Thruster

Because the thruster is at rest, no force will be measured on the load cell. i.e.   F = T-R = 0

It therefore appears that a force measurement can only be made in a dynamic environment, ideally by allowing the thruster to accelerate, measuring that acceleration, and then calculating the thrust from T = -Ma.

This is not a very easy method, although the SPR Demonstrator Thruster was successfully tested in this way on a rotary air bearing.

# 4. Practical static measurement techniques

A number of methods have been used in the UK, the US and China to measure the forces produced by an EmDrive thruster. In each successful case, the EmDrive force data has been superimposed on an increasing or decreasing background force, generated by the test equipment itself.

Indeed, in the UK when the background force changes were eliminated, in an effort to improve force measurement resolution, no EmDrive force was measured. This was clearly a result of attempting to measure the forces on a fully static thruster, where T and R cancel each other.

UK flight thruster measurements employ this principle to calibrate the background noise on the force balance prior to carrying out force measurements.

To illustrate one possible measurement method, assume the thruster is restrained, in a composite force measurement apparatus, by two load cells with different spring constants K1 and K2 (mm/kg).The restraining points are on the end plates of the thruster as shown in Fig. 4.

Fig 4. Composite force measurement.

If there is no acceleration of the thruster, T and R will balance out, and no forces will be measured on the load cells.

However, in a practical measurement, dissipation of the input microwave energy will cause the thruster wall temperatures to increase, and the walls to expand. The axial length of the thruster will increase, as illustrated by the dashed end plate positions shown in Fig. 5, and this will be registered on the load cells as forces F1 and F2.

Fig 5. Force measurement with thermal expansion effects

The different values of K1 and K2 will cause the centre of mass of the thruster to move, thus artificially creating a dynamic situation where R or T can be measured as an increase or decrease in acceleration, whilst the centre of mass of the thruster is accelerating due to thermal expansion.

Clearly the values of K1 and K2 will determine whether R or T is measured, and what calibration factor must be applied to the raw data.

The value of R or T can be determined by the change in F1 or F2 after switch-on and switch-off of the microwave input. This is easily subtracted from the slow increase in F1 or F2 due to the wall expansion, which has a much longer time constant.

A review of the published test data from US and Chinese test programmes, together with UK measurements, supports the above principles.

All from http://emdrive.com/

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