## EHD thrusters performance analysis

© Engineer Xavier Borg - Blaze Labs ResearchSince different EHD thrusters have usually different sizes, geometry, air gaps, voltages, weight and thrust, one may obviously find it difficult to determine the best performer in terms of thrust per unit length. For this purpose, shown below, is a table which I have compiled to show which thrusters are able to obtain the highest performance in terms of thrust per unit element length. One can easily see how some of the engineering concepts developed within Blaze Labs Research group are actually improving performance over the basic triangular EHD thruster configuration aka Lifter. It is most clear, that although stacking gave higher thrusts, their actual efficiency per unit length deteriorates. This means that the more you stack vertically, the more 'dead' weight you get, and the less power available to lift external payloads. High performance EHD thrusters can convert the highest electrical power consumption into thrust in the minimum space.

Thruster comparision ordered by thrust per metre in decreasing order

Thruster typePhoto of prototypeDataThrust per metreTrough cell thruster V1.0

12/01/04F = 0.12 N

P = 57 W

d = 50 mm

V = 44 kV0.48 N/m

F/P = 0.21g/W

Plane grid thruster V1.0

10/01/04F = 0.05 N

P = 8.3 W

d = 35 mm

V = 33 kV0.25 N/m

F/P = 0.6g/W

Blaze Super V1.0 Cell

15/04/03F = 0.15 N

P = 14 W

d = 72 mm

V = 54 kV0.156 N/m

F/P = 1.07g/W

Blaze Low profile

modified pressure

19/06/02F = 0.39 N

P = 40 W

d = 70 mm

V = 50 kV0.144 N/m

F/P = 0.97g/W

Blaze Low profile

02/02/02F = 0.37 N

P = 40 W

d = 70 mm

V = 50 kV0.137 N/m

F/P = 0.92g/W

Spiral Hex V3

20/03/03F = 2.32 N

P = 210 W

d = 70 mm

V = 46 kV0.13 N/m

F/P = 1.10 g/W

Blaze Toroid

15/05/02F = 0.12 N

d = 55 mm

V = 50 kV0.12 N/m

F/P = 0.3g/W

Blaze EHD Thruster V1

Heated cathode

09/04/02F = 0.0347 N

d = 30 mm

V = 30 kV0.0578 N/m

F/P = 0.6g/W

JLN BBS V2 Saucer

22/11/02F = 0.06 N

P = 6.25 W

d = 50 mm

V = 40 kV~0.056 N/m

F/P = 0.96g/W

JLN Lifter V3

01/10/010.1977 N

d = 30 mm

P = 70 W

V = 30 kVF = 0.0550 N/m

F/P = 0.27g/W

Blaze 2 stage Hex Thruster

25/01/02F = 0.300 N

d = 60 mm

V = 30 kV0.0550 N/m

F/P = 0.51g/W

TDT Lifter V1

10/10/01F = 0.032 N

d = 35 mm

P = 24 W

V = 30 kV0.0533 N/m

F/P = 0.13g/W

JLN Lifter V2

10/10/01F = 0.093 N

d = 30 mm

P = 49 W

V = 30 kV0.0516 N/m

F/P = 0.18g/W

Blaze 3 stage V1

16/01/02F = 0.0850 N

d = 55 mm

V = 30 kV0.0469 N/m

F/P = 0.13g/W

JLN Colisseum

24/10/02F = 0.9934 N

d = 45 mm

P = 97 W

V = 30 kV0.0460 N/m

F/P = 1.02g/W

JLN 3 stage V2

25/09/02F = 0.2346 N

d = 35 mm

P = 80 W

V = 30 kV0.0434 N/m

F/P = 0.28g/W

JLN 3 stage V3

10/10/02F = 0.4581 N

d = 35 mm

P = 101 W

V = 30 kV0.0424 N/m

F/P = 0.45g/W

JLN Maximus

12/11/02F = 2.353 N

d = 50 mm

P = 276 W

V = 30 kV0.0384 N/m

F/P = 0.85g/W

Enhancing thruster performance

It has been experimentally shown that the EHD force generated in these devices is:

- Proportional to voltage to the power of 1.9
- Linearly proportional to dielectric constant of flowing medium
- Linearly proportional to length of element
- Dependent on a geometric factor which can be expressed in terms of its shape
Points 3 and 4 depend on the physical shape of the EHD thruster, which may be optimised to a certain point at which no further improvement would be possible. Point 2 can be utilised by somehow modifying the air taken in by the thruster into one with higher dielectric constant, but this would require extra tanks carrying the required 'dielectric fuel' to be injected. This point may find its use for space propulsion using these kind of thrusters. Next we will see why point 1 is definitely the most important of all.

Why our thrusters perform 270% better than normal lifters

Point 1, is most interesting, that is, the resulting thrust is proportional to the voltage powered to 1.9. This power dependency on voltage shows up also in ion thrust calculations as simulated in my Lifter Simulator for Windows. It also shows up in the dielectrophoresis effect. It is also reported in what is perhaps the most extensive and elaborate work carried on for the Air Force Astronautics Lab CA, in R.L. Talley's report (see links page). On page 66 of Talley's report we read "The measured total force at atmospheric pressure due to contribution from electric wind varies approximately as the 1.9 power of the potential difference applied to the asymmetric propulsion device tested".

This is most interesting for two reasons, first because for a unit increase in voltage we get the equivalent of unit of 1.9 power thrust increase, and secondly because such enhancement has no limits, that is we can get any thrust per unit length at our wish by just setting the required voltage. The only problem as regards autonomous flight, is that higher voltages will result in higher powers and heavier power supplies, so a compromise must be found.

This point is clearly proven by the comparison of two prototypes by myself and JLN. As you may note, in most cases I use my 50 kV power supply, whilst JLN's lifters are normally driven by his 30 kV supply. The ratio of our voltages is:

V_{Blaze}/V_{JLN}= 50/30 = 1.667

If we power this value by 1.9 we get 1.667^{1.9}= 2.64 or 264%

The average thrust per unit length for Blaze Labs thruster is approximately 0.140 N/m.

The average thrust per unit length for JLN Labs thrusters is approximately 0.052 N/m.

So we get a performance ratio of P_{Blaze}/P_{JLN}= 0.134/0.045 = 2.69 or 269%

The prototypes taken into account are the non stacked versions of each, so that the calculation will not reflect the performance deterioration due to cascading. As you see the result of 269% experimentally confirms one of the most fundumental ways to improve the thrust per unit length performance, which in this case was calculated to be 264%. Considering the average was taken on two thrusters of each lab, an error of less than 2% over the reported value from a military spec laboratory is better than we would expect. The result of this observation is empirically used to evaluate EHD cell thrust according to the relation F = kV^{1.9}in my Autonomous EHD Thruster calculator running under JAVA.EHD thrusters' Performance with atmospheric pressure & altitudeCurve showing air dielectric strength vs air pressure. This explains why EHD machines do not work in the pressure region shown as glow discharge area. It also explains the fact why they work better at sea levels than in very high altitude levels. Atmospheric pressure is much lower at high altitudes.

The absolute value for air pressure above sea level can be calculated as

p = 101325 * (1 - 2.25577E-5 * h)^{5.25588}

where p = air pressure (Pa) and h = altitude above sea level (m) The performance of EHD thrusters at different altitudes can be approximated by a simpler empirical approximation, which neglects air temperature variations with altitude:

P = P_{o}e^{(-h/7)}, which is a good approximation of how atmospheric pressure varies with altitude. P_{o}is their performance at sea level = 100%, and h is the altitude in km.

For 7000 ft. (approx. 2 km), Performance = e^{(-2/7)}*100% = 75%