Gray-EV: Primer

Project: Edwin V. Gray's "EMA" (electromagnetic association) motor, later sold as "EMS" (electro-magnetic system) power units, 1970s-80s. Inputs used: arbiter.md (final verdicts, including its "QE revision" section, which takes precedence), physicist.md, mathematician.md, contrarian.md, qe.md, the QE deep reads in deep/ (press clippings and US 3,890,548 read from page images or full OCR text), facts.json, and my own reading of two page images: the Crosby letter (crosby_letter.pdf) and the GB 2,030,801 specification page (gray2030801.pdf p.5). The worked example was re-derived and checked by example.py in this folder.

Revised after QE (Step 4b). The first version of this primer repeated three errors that came from garbled OCR of the press clippings: it gave the remark "would violate all the laws of physics" to a deputy District Attorney (it was a TRW scientist who watched a test), said that scientist's test "wasn't convincing" (he said "everything blew"), and said the patents never use the word "static" (US 3,890,548 does). These are corrected below. No verdict changed.

Source tags: [read] = from a document in the folder; [read: page image] = I or a reviewer read a rendered page image; [web] = Internet source with URL; [memory] = recalled from training, with confidence.

Source gap (revised after QE; repeated from claims.md and arbiter.md). All four patents (US 3,890,548; GB 2,030,801; US 4,595,975; US 4,661,747) now have full OCR text. US 3,890,548 (all 18 pages) and US 4,595,975 were read in full; GB 2,030,801 and US 4,661,747 rest on digests plus the GB specification page, and the drawings of GB 2,030,801 and US 4,595,975 were not read. The press clippings and the Crosby letter were read from page images, because their OCR text is garbled. What is still missing: (a) the Crosby test reports ("available at EvGray"), with instruments, waveforms and the method used to measure pulsed input; (b) any data from the Japanese firm's visit or the test the TRW scientist watched; (c) court and DA (District Attorney) records. So every statement about what the 1973-74 tests showed rests on promoter or tabloid reports, and the legal history (Claim 5) on a tabloid, one AP (Associated Press) item and a promotional feature; web checks of the legal facts failed. Where a conclusion below rests on [memory] alone, it says so.

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1. The idea in one paragraph

Edwin Gray built a motor that does not run on a steady current. Instead, batteries slowly charge high-voltage capacitors, and each capacitor is dumped in one sudden spark through a pair of electromagnets (one on the rotor, one on the stator) wound so they push each other apart. The rotor gets a kick, coasts to the next pair, and gets kicked again. Gray added circuits that catch the voltage surge produced when each coil's magnetic field collapses and send it back into a second battery or capacitor. Promoters said the result was a motor that delivered 10 horsepower while barely draining its batteries, running "cool" on a special "cold" electricity, and they said the 1974 police raid on Gray's company was meant to bury the invention. The mechanism is real engineering. The headline performance figure comes from a single promoter-side letter that contradicts itself, and it cannot be true if the batteries were the only energy source. Nobody ever measured the real machine properly: the only sceptical eyewitness on record, a TRW scientist, says the run he watched lasted about ten seconds "and then everything blew", and a Japanese team that came with instruments left without investing. Neither left any data.

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2. What you need to know first

Energy stored in a capacitor. A capacitor is two conductors separated by an insulator. Charged to voltage V, a capacitor of capacitance C (farads, F) holds charge Q = CV and stored energy E = (1/2)CV^2 (joules, J). Doubling the voltage quadruples the energy. This is the only energy a capacitor can deliver in one discharge, no matter how fast it discharges. Read: Griffiths, Introduction to Electrodynamics, the electrostatics chapter (section on capacitors and electrostatic energy); or any first-year text such as Halliday, Resnick and Walker, Fundamentals of Physics, chapter on capacitance.

Inductors and "back EMF". A coil of inductance L (henries, H) carrying current I stores energy (1/2)LI^2 in its magnetic field. Faraday's law says the coil resists any change of current with a voltage -L dI/dt. EMF means electromotive force, a voltage produced by a changing magnetic flux rather than by a battery. If you try to stop the current suddenly, dI/dt is huge and so is the voltage spike: that spike is the "inductive kick" or "back EMF" Gray captured. It carries only the (1/2)LI^2 that was put into the field. Read: Griffiths, chapter 7 (Electrodynamics: Faraday's law, inductance, energy in magnetic fields).

RLC (resistor-inductor-capacitor) circuits. A capacitor discharging into a coil oscillates: energy sloshes from (1/2)CV^2 into (1/2)LI^2 and back, with angular frequency w0 = 1/sqrt(LC), while the resistance R turns some of it into heat at the rate I^2R each second. It is a second-order linear ODE (ordinary differential equation), the electrical twin of a damped mass on a spring. Read: any intro E&M or circuits text, chapter on AC circuits / RLC oscillations (Halliday, Resnick and Walker cover it).

Power, energy and the first law. Power is energy per second: 1 watt (W) = 1 J/s. Energy is power multiplied by time: 1 watt-hour (Wh) = 3,600 J. "Watts per hour" is not a unit of power or energy; it would be a rate of change of power. The first law of thermodynamics (conservation of energy) says energy out of a closed system, as work plus heat, cannot exceed the energy that went in plus what it had stored. Mechanical power of a shaft is P = torque x angular speed. Read: Halliday, Resnick and Walker, chapters on work and energy and on the first law; Schroeder, An Introduction to Thermal Physics, chapter 1.

Measuring power of a pulsed supply. The true average power drawn from a source is the time average of v(t) x i(t), the product of instantaneous voltage and current. For a smooth DC supply this is just V x I. For short, tall pulses it is easy to measure wrongly: a meter may be in the wrong part of the circuit, may be too slow, or the reading may be of a recovery battery rather than the main supply. Read: Horowitz and Hill, The Art of Electronics, on measurement and switching circuits (no chapter number given; editions differ).

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3. The textbook view

3.1 Capacitor-discharge pulse drives

A capacitor C charged to voltage V0 is switched into a coil (inductance L, resistance R). Kirchhoff's voltage law around the loop:

L dI/dt + R I + q/C = 0, with I = dq/dt,

where q is the capacitor charge, I the current, t time. The current rises to a peak of order V0 / sqrt(L/C) in about a quarter period (pi/2) sqrt(LC), then the energy goes back and forth unless something stops it. The energy budget for the whole pulse is

(1/2) C V0^2 = (heat in R) + (mechanical work done) + (energy sent elsewhere, e.g. to a recovery battery) + (energy left in C and L at the end).

The force between two coils facing each other with like poles is repulsive and grows with the product of their currents, so a short, very large current pulse gives a strong impulse. That is how capacitor-discharge solenoids, coil guns, magnetic forming machines and capacitor-discharge ignition work [memory, high]. A spark gap is just a switch that closes by itself when the voltage across it reaches the breakdown voltage of the air or gas in the gap; spark gaps are robust but lossy switches [memory, medium].

3.2 Recovering the inductive kick

When current is flowing in a coil and you open the switch, the coil's (1/2)LI^2 must go somewhere. In a modern circuit a "freewheel" or "flyback" diode gives the current a path into a capacitor or battery, so that energy is recycled instead of burned in an arc. This is everywhere in power electronics: switch-mode power supplies, motor drives, switched-reluctance motors, regenerative braking [memory, high]. What recovery cannot do is return the energy that was turned into shaft work or heat. It recovers only what is still stored in the field.

3.3 Bookkeeping of a motor

For any motor fed by a battery:

energy taken from battery = mechanical work out + heat + (change in stored energy in capacitors, coils, flywheel).

Ordinary electric motors convert 80-95% of electrical input to work at best [memory, high]. Efficiency eta = (work out)/(energy in) is at most 1 (100%).

3.4 Atmospheric electricity

Near the ground in fair weather there is a vertical electric field of about E = 100 V/m and a tiny downward current density of about J = 2 pA/m^2 (2 x 10^-12 A per square metre) [web: https://en.wikipedia.org/wiki/Atmospheric_electricity]. The power available per square metre is at most E x J. It is real and measurable, but very small.

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4. Where this researcher departs

The fair way to put it: everything Gray patented is ordinary pulse-power engineering with an honest energy statement. The departure from physics is in the test letter and press claims built on top of it.

The Crosby letter, verbatim on the key lines [read: page image, crosby_letter.pdf, dated September 27, 1973, signed J. A. Maize, Director of Engineering]:

"The measured overall system efficiency exceeds 99%, utilizing the EvGray proprietary methods whereby additional electro-strictive power is developed, as well as the electro-chemical battery energy is recycled during the system operation. No external recharging generator was utilized during these tests." "The EMA motor was operated into a 10 H.P. (48 ft. lb.) dynamometer load at 1,100 R.P.M. This power output is 7,460 watts. The total battery power available from the four batteries was 5,454 watts for one hour. The total battery power consumed by the motor during a 21 minute run was only 9.75 watts; this equals 26.8 watts per hour." "The system will operate continuously for 203 hours or 8.5 days, at 10 H.P. and 1,100 R.P.M., with the four batteries, without recharge."

Context: the tests were run by "Pan World Enterprises Co., Ltd., and EvGray engineers", that is, the inventor's side and a prospective investor; the letter is addressed to Larry Crosby at the institute's own address; the notary seal attests the signature, not the measurements; "Tests reports ... available at EvGray" were not supplied [read: page image]. The tabloid TATTLER later says Maize tested "on behalf of Pan World Enterprises Company, Ltd., a Japanese conglomerate" [read: page image, various_articles.pdf p.3].

The other tests on record, all reported second-hand and with no data: - Spring 1973 demonstrations (press and promotional feature): a 6 V battery and capacitors, a voltmeter reading 3,000 V, a magnet thrown more than two feet; one reporter saw 2,500 rpm for over 20 minutes with the batteries "as fully charged as they were at the beginning", with no instruments or method stated [read: page images, per arbiter QE revision]. A 20-minute run on four batteries is possible at a draw of a few hundred watts, so this does not discriminate. - The TRW eyewitness (AP, Progress Bulletin, Pomona, 7 July 1975). Donald Cronin, a staff scientist at TRW Systems, "watched a test of the motor about a year ago" (so about mid-1974): "If he did what he says it does it would violate all the laws of physics ... It ran for about 10 seconds and then everything blew. A group of scientists from a big research firm in Japan had come with an elaborate amount of equipment - gauges, instruments, TV cameras - and were ready to sign a letter of intent. After the test, they packed it all up and went back to Japan." [read: page image p.2]. Gray told TATTLER, "We could have had all that Japanese money last year" [read: page image p.3]. - Whether the Japanese team Cronin saw is the Pan World party of the Crosby letter is unresolved: the letter is from September 1973, Cronin's test about ten months later, and no document links them (arbiter, QE revision item 3).

"Electrostriction" is the small change in shape of an insulating material in an electric field (strain proportional to E^2). It converts electrical energy into mechanical strain energy; it is not a source of energy [memory, high].

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5. Worked example: the energy ledger

Reproduced by example.py (run: .venv/bin/python review/Gray-EV/example.py). Every number below is from its output.

Step A. Is "48 ft-lb at 1,100 rpm = 10 hp" right? (units check)

• Torque: 48 ft-lbf x 1.3558 N m per ft-lbf = 65.08 N m.
• Angular speed: 1,100 rev/min x 2 pi rad/rev / 60 s/min = 115.19 rad/s.
• Power: P = 65.08 x 115.19 = 7,497 W = 10.05 hp (1 hp = 745.7 W).

The letter's 7,460 W is right to 0.5%. The output figure is self-consistent. Good start.

Step B. What does the battery budget say?

• Output/input = 7,460 W / 26.8 W = 278, an "efficiency" of 27,800%. The same letter says "exceeds 99%". At 99%, input would be 7,460/0.99 = 7,535 W. The two statements cannot both be true.
• Run figure: 9.75 Wh in 21 min = 9.75 / 0.35 h = 27.9 W, not 26.8 W (a 4% slip; and "9.75 watts" must mean watt-hours).
• 5,454 Wh / 26.8 W = 203.5 h, which is where "203 hours" comes from. So 203 h is an extrapolation from a 21-minute run, not a measurement.
• If the batteries had to supply the full 7,460 W, they would last 5,454/7,460 = 0.731 h = 44 min.
• Running 203 h at 7.46 kW is 1,514 kWh of work from a 5.45 kWh bank.

Now the fair point the contrarian reviewer made, which I checked: the 21-minute run at 7,460 W needs 7,460 x 0.35 = 2,611 Wh, 48% of the bank. So the demonstration itself was physically possible on battery power with nothing unusual going on. The anomaly is only in the meter reading of 9.75 Wh. That shifts the question from "were the laws of physics broken?" to "how was the 9.75 Wh measured?", and the letter does not say.

Step C. How big must each pulse be?

At 1,100 rpm the rotor turns 18.33 times a second, so 7,460 W means 407 J of work per revolution (more if conversion is lossy). From E = (1/2)CV^2, the capacitance that must be discharged each revolution is C = 2E/V^2:

• at 2,000 V (the voltage in GB 2,030,801 [read: page image p.5]): 203 microfarads per revolution;
• at 3,500 V (the voltage printed on Fig. 2 of US 3,890,548, "18 CAPACITORS 3500 VOLTS EACH" [read: page image p.2]): 66 microfarads per revolution, or about 3.7 microfarads per capacitor if all 18 fired once per revolution. The patent gives no capacitance, so this is a scale check only, not a reconstruction of Gray's engine.

That is a large but buildable pulse-power system. So a 10 hp pulse motor is not absurd. What it cannot do is get those 407 J per revolution from 26.8 W / 18.33 rev/s = 1.46 J per revolution of battery energy.

Step D. Follow one pulse through the recovery circuit

GB 2,030,801 describes three phases [read: page image p.5]: (A) a 24 V battery charges a capacitor to about 2,000 V through a DC-to-DC converter; (B) a switch dumps the capacitor through the inductive load and on through "energy recovery battery number 2"; (C) when the capacitor voltage reaches zero, switch 1 cuts the capacitor out "without interrupting the current", and the coil current keeps flowing round a closed loop through the load and battery 2.

The patent gives no values for L, C, R or battery 2's voltage, so example.py uses illustrative ones: C = 10 uF, V0 = 2,000 V, L = 10 mH, coil resistance R = 1 ohm, and a 20 ohm resistance R_w that stands in for the energy that leaves as mechanical work. (A resistor is a bookkeeping stand-in for "energy that leaves the circuit as work"; it is not a model of the rotor.) The equations integrated are

• phase B: L dI/dt = v_c - (R + R_w) I - V_b, and dv_c/dt = -I/C,
• phase C: L dI/dt = -(R + R_w) I - V_b, until I = 0,

where v_c is the capacitor voltage and V_b the recovery battery's voltage. The energy put in is (1/2)(10^-5)(2000)^2 = 20.00 J. Result:

What this teaches:

1. Every row sums to exactly the 20 J the source put in. Recovery moves energy around; it never adds any.
2. Recovery competes with work. The higher the recovery battery's voltage, the more it captures, and the less is left to push the rotor. In the 1000 V row, two-thirds is "recovered" but the work done falls to 4.2 J. A motor that recycles "most of its energy" is a motor that does little work.
3. A low-voltage battery absorbs little. Energy into a battery is V_b x (charge that flows through it). With V_b = 12 V and about 0.034 C of charge, that is only 0.4 J.
4. The net energy the source must provide per pulse is (20 J - energy returned), which is never less than (work + heat). An efficiency above 100% is not reachable by any choice of values.

The physicist reviewer's comparison is worth keeping in mind: a 10 mH coil carrying 20 A holds (1/2)(0.01)(20^2) = 2 J, a tenth of the 20 J in the capacitor. The residual coil energy is the most a flyback path can catch.

Step E. Could the air supply the missing power?

Power density of the fair-weather atmosphere: E x J = 100 V/m x 2 x 10^-12 A/m^2 = 2 x 10^-10 W/m^2 [web values: https://en.wikipedia.org/wiki/Atmospheric_electricity]. To collect 7,460 W you would need 7,460 / (2 x 10^-10) = 3.7 x 10^13 m^2 = 37 million km^2, about 7% of Earth's surface. (The field's stored energy density, (1/2)eps0 E^2 with eps0 = 8.854 x 10^-12 F/m the permittivity of free space, is 4.4 x 10^-8 J/m^3, equally tiny.) No collector or antenna appears in any document read. This rules out the fair-weather field; it says nothing about lightning, which no document proposes.

Step F. The 100 MW substation (a second claim, same method)

TATTLER reports that Gray planned a battery substation to "supply 100 megawatts of electricity at peak periods while expending only 40 kilowatts doing so" [read: page image, various_articles.pdf p.3]. The article itself notes experts call it a possible hoax.

• Ratio: 100 x 10^6 W / 40 x 10^3 W = 2,500.
• Reading 1, both are continuous average powers. Then output is 2,500 times input, and the energy budget of Step B rules it out just as it rules out 278:1 (Refuted by calculation).
• Reading 2, peak-shaving from a store. A store charged steadily at 40 kW for 24 h holds 40 kW x 86,400 s = 3.46 x 10^9 J (960 kWh). Discharged at 100 MW, that lasts 3.46 x 10^9 / 10^8 = 34.6 s per day, a duty cycle of 1/2,500. This is ordinary load levelling and breaks no law, but 35 seconds is not "peak periods".

The lesson: a power ratio means nothing until you know whether both numbers are averages over the same time. "Expending only" points to Reading 1. This is the arbiter's analysis (QE revision item 10); example.py section F reproduces the numbers.

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6. Evidence table

Was it dismissed without testing? For the physics, no: the remark that the device "would violate all the laws of physics" came from Donald Cronin, who had watched a test and seen it fail, not from a prosecutor (an earlier version of this primer, and the three reviews, got this wrong because they worked from garbled OCR). For the fraud case, partly: DA investigator Ran Novell told TATTLER "All he has is a starter motor run by some batteries" and admitted no one in the DA's office had tested the motor "or even started it" [read: page image, gray_suppressed.pdf, as relayed by a hostile tabloid]. No independent test was ever refused or blocked in any document read, and Gray, who held the machine and raised money on it, never published one. The suppression story's evidence is analogy (other inventors) and an anonymous DA-office source; no document links the DA to any auto company.

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7. What a learner should take away

Solid. - Capacitor-discharge pulse drives and repelling electromagnets are real and can produce strong, sharp impulses. A cool-running coil and a magnet thrown off but caught by hand are what low average power and short pulses look like; they are not signs of a new kind of electricity. - Catching the inductive kick and returning it to a battery or capacitor is good engineering and is standard today. Gray's GB patent describes it honestly as "an energy conserving system". - The letter's output figure (48 ft-lb at 1,100 rpm = 10 hp) is arithmetically correct.

Wrong, and why it is instructive. - "Current only flows for an instant, so it uses little energy." Energy per pulse is (1/2)CV^2 regardless of how short the pulse is; mean power is that energy times the pulse rate. Short pulses hide energy from slow eyes and slow meters; they do not remove it. - "Recycling makes it self-sustaining." The ledger in section 5 shows recovery and useful work draw on the same 20 J. Recovering more means doing less work. - A test letter that contradicts itself. "Exceeds 99%" and 7,460 W from 26.8 W cannot both be true. "Watts per hour" is not a unit. A 21-minute run cannot certify 203 hours. Learning to run these four checks (units, ratio, internal consistency, extrapolation) on any extraordinary claim is the main skill this case teaches. - Where to look for the real error. The 21-minute run fits inside the battery bank (48%). So the mundane explanation is a measurement problem with the 9.75 Wh, for example a meter on the recovery battery instead of the main supply, pre-charged capacitors, or a reading taken from battery voltage, which recovers after pulsed loads. These are hypotheses [memory, medium], not findings; no instrument details exist to confirm any of them.

Genuinely open (but not about physics). - What the 1973 meters actually measured, and where in the circuit. - What the Japanese team measured, why it left, and whether it is the Pan World party of the Crosby letter. - What blew in the run Cronin watched, and why. - What, if anything, the patent's "static floating flux field" coil was meant to do. - How the real machine would perform on a dynamometer with proper metering. The likely answer is an ordinary efficiency (perhaps 10-90%) but nobody measured it. - The court record of the 1974-76 case (charges, plea, fine) and what investors were told.

The single experiment that settles Claims 1-3: an independent lab runs the motor on a calibrated dynamometer for hours, with a wideband power analyser integrating v(t) x i(t) at every battery terminal (main and recovery), plus a before-and-after battery watt-hour discharge test.

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8. Check yourself

1. A 50 uF capacitor is charged to 3,000 V and discharged in 20 microseconds. How much energy does it deliver? Does making the discharge ten times faster change that energy? If a pulse motor fires 100 such pulses per second, what is the minimum average power its supply must provide, assuming no recovery?
2. TATTLER says Gray's substation would deliver 100 MW at peak while "expending only 40 kilowatts". Under what reading is this impossible, and under what reading is it ordinary engineering? Under the second reading, how long per day could it deliver 100 MW?
3. Using only the Crosby letter's numbers, give two independent reasons the letter cannot be a correct report of a battery-only test.
4. In the recovery-circuit table of section 5, why does raising the recovery battery's voltage from 24 V to 1,000 V lower the work done from 18.3 J to 4.2 J?
5. The fair-weather field is about 100 V/m. A promoter says, "a 2 m tall car sits in 200 V of free potential difference, so it can draw power from it." What is missing from this argument, and how much power could a 10 m^2 car roof collect?

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9. Further reading

Mainstream - David J. Griffiths, Introduction to Electrodynamics (any edition): electrostatic energy and capacitors (electrostatics chapter); chapter 7 for Faraday's law, inductance and magnetic energy; chapter 8 for conservation of energy in electrodynamics (Poynting's theorem). - Halliday, Resnick and Walker, Fundamentals of Physics: chapters on capacitance, inductance, RLC oscillations and the first law (chapter numbers vary by edition). - Paul Horowitz and Winfield Hill, The Art of Electronics: flyback/freewheel diodes, switching circuits, measurement pitfalls. - Ned Mohan, Tore Undeland and William Robbins, Power Electronics: Converters, Applications, and Design: energy-recovery snubbers and switched-mode converters. - Daniel V. Schroeder, An Introduction to Thermal Physics, chapter 1: energy, work, heat and the first law. - Atmospheric electricity overview: https://en.wikipedia.org/wiki/Atmospheric_electricity [web].

The researcher's own works (in the folder) - Edwin V. Gray, US Patent 3,890,548, "Pulsed capacitor discharge electric engine" (filed 1973, granted 1975) [web: https://patents.google.com/patent/US3890548A/en]. File: gray3890548.pdf. Read the background (p.9-10) for "conservation of energy" and "excess energy", p.11 for the "static floating flux field", and Fig. 2 for the 18 capacitors at 3,500 V. - GB 2,030,801, "Regenerative energy recovery system" (published 1980). File: gray2030801.pdf. - US 4,595,975 and US 4,661,747 (later recovery-circuit patents). Files: US4595975.pdf, gray4661747.pdf. - Crosby Research Institute letter, 27 Sept 1973. File: crosby_letter.pdf. - Promotional and press material: ems_electronic_power.pdf, ems_inverter.pdf, static_generator.pdf, gray_suppressed.pdf, various_articles.pdf. The most informative single page is various_articles.pdf p.2 (the 1975 AP profile with Cronin's eyewitness account and the charges); read it as an image, as its text layer is garbled.

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Answers

1. E = (1/2)(50 x 10^-6)(3000)^2 = 225 J. No: the energy depends only on C and V. A faster discharge gives a higher peak current and peak power (225 J / 20 us is about 11 MW for that instant), but the same 225 J. At 100 pulses per second: 225 J x 100 /s = 22,500 W = 22.5 kW. Short pulses do not reduce this; only fewer or smaller pulses do.
2. If 100 MW and 40 kW are both continuous averages, output is 2,500 times input: impossible by conservation of energy. If 40 kW charges a store all day and the store discharges at 100 MW, it is load levelling: 40 kW x 24 h = 960 kWh, which lasts 960 kWh / 100,000 kW = 0.0096 h = about 35 seconds per day.
3. Any two of: (a) 7,460 W out from 26.8 W in is 278:1, but the letter also says efficiency "exceeds 99%", which would require about 7,535 W in; (b) 203 h x 7.46 kW = 1,514 kWh of work from a 5.45 kWh bank, 278 times the stored energy, with "no external recharging generator"; (c) 9.75 Wh in 21 min is 27.9 W, not 26.8 W, and "watts per hour" is not a unit; (d) 203 h is extrapolated from 21 minutes.
4. The battery pushes back against the current with its voltage V_b, so it takes energy V_b x I every second. Energy it takes is energy the work resistor does not get. The capacitor's 20 J is shared: more to the battery means less to the work (and at 1,000 V the battery even stops the current before the capacitor is empty, leaving 2.2 J in it).
5. Potential difference alone is not power; power is voltage x current, and the air conducts only about 2 x 10^-12 A per square metre [web: https://en.wikipedia.org/wiki/Atmospheric_electricity]. A 10 m^2 roof intercepts about 2 x 10^-11 A; even at the generous 200 V that is 200 x 2 x 10^-11 = 4 x 10^-9 W, four nanowatts, versus 7,460 W claimed.