How does LENR stack up against electrochemical devices, chemical reactions, nuclear fission plants, fusion
and renewables? The Ragone Chart (rhymes with Zamboni) is one good way to compare energy sources. It tells
us how much energy a source has locked inside it and the rate at which it can be harvested.
The chart shows how densely energy is stored in an energy source along its vertical axis versus how fast that
energy is released along the horizontal axis. Both axes are with respect to mass (not volume). It is a logarithmic
chart showing data in powers of ten, not a linear chart, so even small distances on the chart indicate big differences
in the data. The best energy sources will be toward the top of the chart because they can provide a lot of energy.
For most applications instantaneous energy release (such as in an explosion) is undesirable; energy is needed at
specific rates for specific applications. For high power applications energy is needed fast -- energy sources
toward the right of the chart can better meet those needs. Energy sources with a slower rate of release, which
also has its uses, are found toward the left of the chart.
For chemical sources and storage technologies like batteries and capacitors there is often a range of both energy
release rate and energy storage capacity. The chart does not show the full ranges for these technologies; it only
shows a single representative point from within that range. In general, most "smearing" will be in the horizontal
direction, with specific energy values more narrowly defined. Because the main goal of the chart is to show how
LENR technology compares to other energy sources, this single point representation of these ranges is adequate.
The diagonal lines inside the chart are interesting. They represent constant lines of "burn time." If energy
source A contains 1 joule per kilogram and provides power at 1 watt per kilogram then a kilogram of that fuel will
be consumed in 1 second. The same would hold true for energy source B that contains 10 joules per kilogram (much
more than source A!) but provides 10 watts of power per kilogram (also much more than source A). Sources A and B
would have the same "burn time" and both lie on the same diagonal line. Moving up and to the left, each burn time
line is ten times longer than the one beneath it. High power energy sources with long burn times are generally
more useful than low power sources or sources that burn out faster. The time labels on the burn time lines are
approximate to make them easier to read.
The Grand Tour
So what does the chart say?
It says that electrochemical storage technologies like batteries, fuel cells and capacitors, shown in orange,
bring up the rear. There's only about a megajoule per kilogram available in our best storage technologies,
though they support a wide range of energy release rates.
Next up the energy ladder are chemical sources like wood, coal and natural gas, shown in black. These fuels
can be burned slowly like coal in a furnace or fast like an exploding stick of dynamite. The best of the bunch
in terms of specific energy is hydrogen (liquid, gas, doesn't matter, since the chart deals with mass and not
volume). With hydrogen you can get more than two orders of magnitude more energy out per kilogram than the best
batteries, fuel cells and capacitors. There are many chemical sources that aren't shown such as gasoline and
oil just to keep the chart from getting too crowded. They all tend to cluster in the same area.
Data points collected from three E-Cat test results between 2012 and 2014 (and also a prototype
specifications sheet in the case of Defkalion's Hyperion) occupy the next tier up and are shown in green.
All of the LENR test report data shows energy release per kilogram more than an order of magnitude
greater than one could achieve with a pure hydrogen system. This is what the scientists mean when they
say the anomalous
heat measurements cannot be explained by chemical processes. The best chemical source we know of, pure
hydrogen, doesn't come close to explaining the LENR energy data.
There are two shades of green used to represent the LENR data. The dark green points represent the
actual data published in tests reports describing partial burns of the nickel-hydrogen powder fuel over
limited time periods. However, as a result of the incomplete burns, the reports contain artificially
low calculated specific energy and power values.
The light green points indicate the LENR data extrapolated for 6 months run time before the fuel
is exhausted. A 6 month burn time is not yet supported by any public data but is the claimed life of
the fuel charges for E-Cats. Assuming the device creators' assertions are true
suggests that LENR devices release a lot more energy over a longer period of time than was shown in the
tests and would thus have higher specific energy values. The calculations for this extrapolation are
shared in the LENR Calculations section below.
There are three points on the chart for nuclear fission, shown in red, with one point representing the
actual performance of nuclear fission reactors in the U.S. Specific energy for this point was derived
from statistics of nuclear plant fuel usage and energy production. Obviously nuclear fission is a fantastic
energy source from a specific energy perspective. Its weaknesses lie in other areas such as radioactive waste,
safety concerns and cost.
Fusion, the blue point, is an even better energy source than fission, but so far the engineering and
technology of fusion power plants has proved elusive.
Points for renewable energy sources, in light blue, are included for comparison (after making some
convenient assumptions), but are imperfect candidates for inclusion in a Ragone Chart. Ignore them if you
find them confusing.
Low Energy Nuclear Reactions (LENR)
Net Energy 6 mo. (J)
2.333 x 104
1.188 x 103
2.771 x 107
1.361 x 109
5.8 x 104
1.848 x 1010
9.072 x 1011
4.8 x 103
1.415 x 106
7.465 x 1010
2.201 x 1013
3.456 x 105
1.674 x 103
5.785 x 108
2.452 x 109
7.093 x 103
1.004 x 1010
1.103 x 1011
4.176 x 105
4.46 x 102
1.863 x 108
1.863 x 1011
4.46 x 105
6.938 x 109
6.938 x 1012
2.765 x 106
2.107 x 103
5.825 x 109
5.825 x 1012
2.107 x 106
3.276 x 1010
3.276 x 1013
Aug '12 Penon test report:
Duration: 6.48 hours = 2.3328 x 104 s
Active fuel mass: 20.38 g = 0.02038 kg
Average power (net): 1.188 kW = 1.188 x 103 W (also 3.66 kW, under less conservative assumptions)
Specific power (avg.): 58 kW/kg = 5.8 x 104 W/kg (also 117 kW/kg under less conservative assumptions)
Specific energy: 378 kWh/kg = 1.3608 x 109 J/kg
Time factor: 6 mo / 6.48 hr = (6 mo x 30 d/mo x 24 hr/d) / 6.48 hr = 666.7
Net energy (6 mos): (1.188 x 103 W) x (6 mo x 30 d/mo x 24 hr/d x 60 min/hr x 60 s/min) = 1.848 x 1010 J
Specific energy (6 mos): 666.7 x 1.3608 x 109 = 9.072 x 1011 J/kg
Though there is a Hyperion test report it does not include the kind of data needed for the Ragone Chart.
Instead values from the product specification sheet Defkalion released for their prototype Hyperion
system are used:
Nominal 5 kW power at 285 deg C (558 deg K)
Net power: 5 kW - 200 W = 4.8 x 103 W
Reactor interior volume: < 1.256 cm3
Nickel powder bulk density: 1.8 - 2.7 g/cm3
Active fuel mass: 1.256 cm3 x 2.7 g/cm3 = 3.3912 g = 0.0033912 kg
Specific power: 4.8 x 103 W / 0.0033912 kg = 1.415 x 106 W/kg
Net energy (6 mos): (4.8 x 103 W) x (6 mo x 30 d/mo x 24 hr/d x 60 min/hr x 60 s/min) = 7.465 x 1010 J
Specific energy (6 mos): (1.415 x 106 W/kg) x (6 mo x 30 d/mo x 24 hr/d x 60 min/hr x 60 s/min) = 2.2013 x 1013 J/kg
Dec '12 Magnificent 7 E-Cat test report:
Duration: 96 hours = 3.456 x 105 s
Active fuel mass: 0.236 kg (includes the metal end caps)
Average power (net): 1674 W
Total net energy: 1674 W * 3.456 x 105 s = 5.785 x 108 J
Specific power: 7093 W/kg = 7.093 x 103 W/kg
Time factor: 6 mo / 96 h = (6 mo x 30 d/mo x 24 hr/d) / 96 h = 45
Specific energy: 6.81 x 105 Wh/kg = 2.4516 x 109 J/kg
Mar '13 Magnificent 7 E-Cat test report:
Duration: 116 hours = 4.176 x 105 s
Active fuel mass: 1 g = 0.001 kg (conservatively assumed to be 1 g even though their measurements indicated 0.3 g)
Average power (net): 446 W = 4.46 x 102 W (worst case; 532.5 W nominal)
Total net energy: 5.1736 x 104 Wh = 1.8625 x 108 J (worst case; 2.23 x 108 J nominal)
Specific power: 4.46 x 105 W/kg (using worst case power consumption)
Specific energy: 5.1736 x 107 Wh/kg = 1.863 x 1011 J/kg (using worst case power consumption)
Time factor: 6 mo / 116 h = (6 mo x 30 d/mo x 24 hr/d) / 116 h = 37.2414
Specific energy (6 mos) = 37.24214 * 1.863 x 1011 J/kg = 6.938 x 1012 J/kg
Mar '14 "Lugano" E-Cat test report:
Duration: 32 days = 2.765 x 106 s
Active fuel mass: 1 g = 0.001 kg
Average power (net): 2107 W = 2.107 x 103 W
Total net energy: 1.618 x 106 Wh = 5.825 x 109 J
Specific power: 2.107 x 106 W/kg
Specific energy: 5.825 x 1012 J/kg
Time factor: 6 mo / 32 d = (6 mo x 30 d/mo) / 32 d = 5.625
Specific energy (6 mos) = 5.625 * 5.825 x 1012 J/kg = 3.276 x 1013 J/kg
Consistency of the LENR Results
One would expect to see a relatively tight band of results for LENR devices in terms of specific energy because
that value represents a fundamental property of the fuel (in this case the energy available in the hydrogen-loaded
nickel powder charge). Specific power on the other hand could be expected to occupy a wider domain along the
horizontal axis because it is in part the result of engineering decisions. What does the chart show?
The Mar '14 and Mar '13 test results for the E-Cat (and the specifications for Defkalion's Hyperion prototype) align
quite well. Both the specific energy and the specific power of the 2013 E-Cat HT2 are lower
by about a factor of 3. Taking into account though that the E-Cat HT2 testers used a conservative value of 1 g for
the mass of active fuel in the Mar '13 test rather than the 0.3 g they actually measured and the factor of 3
difference evaporates. The continued improvement in both the specific power and specific energy of the E-Cat
demonstrated in 2014 is evidence of a massive research and development effort now bolstered by Industrial Heat's
The specific energy and power values determined in the Aug '12 E-Cat test of the previous model E-Cat prototype
(HT) trail the HT2 and the Hyperion by more than one order of magnitude. Not coincidentally the mass of the
active fuel is determined to be at least one order of magnitude higher than used in those two devices. There are
two ready explanations then for the discrepancy between the Aug '12 HT model test results and the Mar '13 HT2 model
test results. The first is that the later stage prototype makes more efficient use of the fuel due to engineering
advances. The second is that the Aug '12 test used a conservative value for the active fuel mass. For example,
the tester was unable to accurately measure all of the sealant putty after the test and the part he couldn't
measure was lumped into the mass of the active charge. It is impossible to know which explanation is correct,
if either, without additional testing and better measurement of the mass of the active charge. Perhaps it is
a combination of the two or some other issue.
The specific energy and power values determined in the Dec '12 test of the E-Cat HT are an order of magnitude
lower than Aug '12 E-Cat HT test results. On the face of it this should be cause for concern about the quality
of the tests or the validity of the devices being tested. Again however, the cause for the discrepancy appears
to be in the mass assumed for the active fuel. In the Dec '12 test that mass is determined to be over 200 g
(versus about 20 g for the Aug '12 test). The test report indicates that the mass of the two end caps of the
fuel charge cylinder could not be separated out and so were included in the mass of the active fuel. While
making such conservative assumptions might have suited the testers' purposes of determining that the reactions
were unquestionably not chemical in nature, they also had the effect of corrupting the specific energy and
power results, which have a strong dependence on the fuel mass.
Sensitivity to Active Fuel Mass
As discussed above, the specific energy and power results are quite sensitive to the mass of the active
fuel (inversely proportional). The measurements of this mass in the tests to date have ranged from 0.3 g to 238 g,
yielding a wide range of specific energy and specific power values. The testers have made a number of assumptions
in their reports that have made the active fuel mass artificially high and thus their specific energy and power
calculations artificially low. Future tests should make a greater effort to accurately determine the upper and
lower bounds of the active fuel mass. The LENR device creators could assist this effort by allowing accurate
measurements of all the components before and after assembly as well direct measurement of the mass of the actual
fuel powder before it is loaded.
Six Month Fuel Charge?
The creators of the E-Cat and Hyperion LENR prototype devices both claim that the fuel charges in the devices
last for at least six months before requiring replacement. This is not yet borne out by any public test results.
The six month value is used in the chart, taking the device creators' word for it. The "Lugano" test of the E-Cat
in 2014 ran for more than one month continuously, improving the situation. Still there is no public confirmation
of the six month run-time. Do these devices really produce energy non-stop for 180 days or for
not much more than the 32 days (the duration of the longest public test so far)?
Adjusting for the conservative mass and energy assumptions in the test reports is a necessarily imprecise but
still useful exercise. The adjusted values can help characterize the true potential of LENR energy sources
freed from the constraints of the debate over its chemical or nuclear origin and the minimized energy calculations
that debate produces.
Specific Power (W/kg)
Specific Energy 6 mo. (J/kg)
Mass Adjustment Factor
Energy Adjustment Factor
Combined Adjustment Factor
Adjusted Specific Power (W/kg)
Adjusted Specific Energy 6 mo.
5.8 x 1044
9.072 x 1011
1.74 x 105
2.722 x 1012
7.093 x 103
1.103 x 1011
1.702 x 105
2.647 x 1012
4.46 x 105
6.938 x 1012
1.619 x 106
2.518 x 1013
2.107 x 106
3.276 x 1013
2.107 x 106
3.276 x 1013
1.415 x 106
2.201 x 1013
Aug '12 adjustments: overestimation of the active fuel mass due to inclusion of some "putty" stuck on the
device, worst case assumption that inner temperature equals outer temperature.
Dec '12 adjustments: included the mass of 2 metal end caps in the active fuel mass, underestimated
temperature by using an emissivity of 1 in IR camera settings, did not include end cap radiation and included
surface area obscured by metal struts in radiation calculations.
Mar '13 adjustments: assumed 1 g of active fuel charge even though 0.3 g was deduced through precise
measurements of the mass of all components, use of worst case energy consumption in calculation of net energy.
The adjusted results show the two E-Cat HT model specific energy and power values in agreement and the more
advanced E-Cat "HotCat" models tested in 2013 and 2014 in rough agreement (along with the Hyperion specs).
There is about a one order of magnitude difference between the two groups. It's unclear whether this is due to
testing artifacts or reflects an evolution in the efficiency of the prototype devices. There is evident progress in
engineering in the 2014 model of the E-Cat; it is smaller and designed to more efficiently transfer heat. So
assuming the latter, LENR devices can be roughly characterized as:
Approximate specific energy, LENR: 3 x 1013 J/kg = 8.3 GWh/kg
Approximate specific power, LENR: 2 x 106 W/kg = 2 MW/kg
~8.3 GWh/kg @ ~2 MW/kg
Wow! For one kilogram of LENR fuel you can get two megawatts of thermal power, and more than 8 gigawatt
hours of thermal energy before it burns out after about six months. That is a very compact, energetic and long
lasting fuel that would revolutionize the energy industry: a new and better "fire" that rivals fissile materials
without the associated problems and high cost.
For reference, the average U.S. home uses under 12 MWh electrical energy over the course of a year. Assuming
a conversion efficiency of thermal power to electric power of 30%, one kilogram of LENR powder could provide
energy for 6 months to more than 200 houses!
One final observation about LENR based on this characterization. It is not "a little better" than chemical
energy sources. It is radically better than chemical sources and squarely in competition with fission and fusion
sources as can be seen on the Ragone chart. That the LENR data points wind up in the "nuclear neighborhood" --
once adjusted for fuel exhaustion and conservative assumptions -- and not in the no-man's land between nuclear
and chemical, is a strong indication that the underlying processes in Low Energy Nuclear Reaction devices are
Nuclear Fission Calculations
The chart includes a few points representative of the specific energy and specific power of materials used in
nuclear fission. The values for uranium and plutonium are known. A composite value is also included for
operational fission reactors in the U.S. based on actual energy produced and fuel consumed.
Electrical energy generated 2012: 7.707 x 1011 kWh = 7.707 x 1014 Wh = 2.775 x 1018 J
Approximate thermal to electrical conversion efficiency: 33%
Thermal energy generated, 2012: 8.324 x 1018 J
Approximate nuclear fuel (uranium) consumed: 18983 tonnes = 1.8983 x 107 kg
Specific energy: 8.324 x 1018 J / 1.8983 x 107 kg = 4.385 x 1011 J/kg
The composite specific energy and power are lower than the theoretical values of the raw materials due to
preprocessing of the fuels and other engineering realities.
Renewable Energy Sources
Typically, renewable energy sources like solar and wind for which characteristics other than mass dominate, are
not included on a Ragone chart. Nevertheless, one can get a feel for how they compare to other energy sources
by making some convenient assumptions.
In the case of a solar panel, if the weight of the solar panel is considered to be the weight of "fuel" and
it has an effective lifespan of 100 years, its data point would wind up toward the upper left (not very powerful
but very long lasting).
Typical mass of 250 W solar panel: 19 kg
Assume panel lifetime of 100 years = ~3.158 x 109 s
Total energy produced (lifetime): 250 W x 3.158 x 109 s = 7.895 x 1011 J
Specific energy: 7.895 x 1011 J / 19 kg = 4.155 x 1010 J/kg
Specific power: 250 W / 19 kg = 13.158 W/kg
Air can be considered to be the "fuel" and its kinetic energy and mass used for the calculations. Wind
doesn't pack as much power or energy as other sources with respect to mass, but is still useful because
there is an endless supply.
Typical off shore wind speed: 9 m/s
Mass of air: ~1.2 kg/m3 (varies with temperature/pressure)
Volume of air moving through 1 m2: 9 m/s x 1 m2 = 9 m3/s
Mass of air moving through 1 m2 in 1 second at 9 m/s: 1.2 kg/m3 x 9 m3/s x 1 s = 10.8 kg
Kinetic energy of one second's worth of wind moving through 1 m2: 0.5 x mass x velocity2 = 0.5 x 10.8 kg x (9 m/s)2 = 437.4 kg m2 / s2 = 437.4 J
Specific energy: 437.4 J / 10.8 kg = 40.5 J/kg
Maximum wind power extraction by turbine: 59%
Specific power: 0.59 x 40.5 J/kg x 1 s-1 = 23.9 W/kg
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