**Updates coming very soon!!**
By Danny Kerr
Welcome. The basic idea presented here is that both Nikola Tesla and an Ancient Culture thought up similar systems for the distribution of electricity. No one has yet been able to replicate Tesla’s Earth Wave Vibration Theory or demonstrate a working model of the Giza Pyramids as a Power Plant. I try to show simple similarities between Tesla’s Wardenclyffe Tower and the Giza Pyramids without using math, and I present the idea that the Great Pyramid could function as a low-frequency thermoacoustic engine with the passages and chambers of the Pyramid in their current empty state.
The current egyptological explanation for the building and layout of the different chambers inside of the Great Pyramid is that the Pharoah Khufu just couldn’t make up his mind about where he wanted to be buried. Khufu first wanted to be buried in the Subterranean Chamber but before his workers finished the chamber, he changed his mind. Khufu then wanted to be buried higher up inside the Pyramid so he had his workers build the Queen’s Chamber, but after the Queen’s Chamber was completed Khufu changed his mind again and now he wanted to be buried even higher up in the Pyramid, in an even grander chamber, the King’s Chamber. This is the accepted explanation for why the Great Pyramid’s internal chambers are where they are and why they were built, and it doesn’t take into account why the granite of the King’s Chamber has been scorched and browned, or why the Queen’s Chamber had an inch and half of salt built up on the walls, or why the Subterranean Chamber shows signs of water erosion and cavitation. These effects can be explained by water hammer in the Subterranean Chamber, an electrochemical process in the Queen’s Chamber, and heat being applied to the King’s Chamber.
The Thermoacoustic Piezoelectric Regenerative Pulsejet Pyramid of Khufu
“The Hydroelectric Multispectral Transmitter”-Doug Keenan.
“The Giza Power Plant”-Chris Dunn
Below is a cross-sectional diagram of the Great Pyramid’s internal chambers and passages.
Hypothetically speaking, high amplitude sound waves are generated within the Pyramid by thermoacoustic means and a monotone note is produced and sustained. The dimensions of the King’s Chamber, Grand Gallery, and Queen’s Chamber, resonate sympathetically allowing good sustain of low-frequency oscillations. Water hammer is used to drive a piston and create pressure to generate steam in the upper chambers, the heat is captured by the granite of the King’s Chamber. The limestone of the Pyramid is made conductive by pumping water to the top of the pyramid then allowing the water to percolate down through the stone. The white Tura limestone exterior of the Pyramid reflects the Sun’s light and heat helping to maintain the temperature of the Pyramid. Electricity is generated through the conversion of heat into sound and then sound into electricity, through the piezoelectric response of quartz. The Kings Chamber is playing the role of a large transducer.
The Granite Blocks don’t plug the First Ascending Passage at all, I’ve seen them in person and they’re not set in tight. The Ascending Passage displays wear and tear on the limestone, as do the Granite Blocks. The First Ascending Passage width is narrower where it meets the Descending Passage giving the impression that the Granite Blocks are plugging the Ascending Passage. If a shockwave of water came up the Descending Passage the Granite Blocks would be forced up the Ascending Passage. The Granite Blocks would then act as a piston, compressing any gases inside the pyramid as well as pushing water into the upper Chambers. The Granite Blocks would also weigh a bit less when submerged in water.
John Cadman, an American Hydrologist, has been reverse engineering the Subterranean Chamber of the Great Pyramid for years and is constantly discovering new aspects of the design of the Chamber. He’s shown that water drains unrestricted through it, and that the shafts connecting to the Chamber are designed to reflect and a contain a compression wave, or water hammer. Mr. Cadman demonstrates how the system would’ve created a pulse that was directed up into the Pyramid, thus vibrating the Pyramid. Click the link to view a video of Mr. Cadman describing his pulse-generator model. https://youtu.be/NVFPsCPhpyk
This is a picture of John showing his various Subterranean Chamber models.
John Cadman’s Subterranean Chamber pump model does not like air in the system. The percolation shaft in the graphic above is located where there is a niche in the top NW corner of the Subterranean Chamber. The niche is in a spot where John, with inkjet testing, has shown that water would’ve flowed towards the niche. This is where water could be percolated up into the pyramid as well as relieve any air that would’ve been trapped inside the Subterranean Chamber, thus allowing the chamber to achieve the ram pump effect. With limestone being a sieve and the effect of gravity on the capillary effect of the limestone, water was likely pumped to the top of the Pyramid and allowed to percolate down through the stone.
The function of the Queen’s Chamber
Chris Dunn, an American engineer, describes in his book, The Giza Power Plant, how the Queen’s Chamber could have regulated a mixture of zinc solution with dilute hydrochloric acid to produce hydrogen gas. Mr. Dunn’s idea is a way to explain how salt could’ve built up on the Queen’s Chambers walls and Passage, by hydrogen gas generated in a chemical reaction and the gas reacting with the limestone of the Chamber. This is confirmed plausible by chemical engineers. Mr. Dunn has an exceptional website displaying his more than 30 years of research. http://www.gizapower.com
The Queen’s Chamber used to have salt encrusted on the walls and ceiling up to 3.75cm(1.5″) thick and the two small shafts that feed the Chamber used to each be blocked off with a limestone block that had a crack running through it. The Queen’s Chamber has now been cleaned down to the limestone and the limestone blocking the small shafts was chiseled away in search for treasure. A piece of copper in the shape of a dual hook and a stone ball were recovered from the shafts and are on display at a British museum. Pipe inspection cameras have since inspected up the shafts and it was discovered that the shafts are blocked by limestone blocks with two copper handles, or electrodes. It appears the fluid levels of the shafts were monitored by a float switch opening a circuit. With cracks in the limestone blocks that were between the shafts and the Queen’s Chamber, the fluids mixing would be regulated. Check out Chris Dunn’s model of Gantenbrinks door for a clearer picture. http://gizapower.com/Model2.htm
The small shafts could’ve signalled overpressure by closing a circuit, or signalled that fluid levels are getting to low by opening a circuit, like Dunn originally proposed.
The Earth has a natural negative charge and the Ionosphere has a natural positive charge. The Pyramid builders seemingly exploited this difference of potential for electrolysis production by building the pyramid, and Kings Chamber Vents, high in the air to draw in the natural positive charge. Think of the Queens Chamber as a negative electrode with salt build-up on it. The positive electrode in this case would be the Kings Chamber. Hydrogen would be generated at the Queen’s Chamber and Oxygen would be generated at the Kings Chamber. This was brought to my attention by Doug Keenan.
The Queens Chamber may have had a very simple function. It’s job may have been to just raise the total dissolved solids in the water coming into the upper chambers. The nile is fresh water, therefore the E.C. of the water is relatively low, adding some salt would raise the electrical conductivity of the water. The salt of the Queens Chamber could’ve been intentionally put there and allowed to mix with the incoming water. This would help facilitate what Doug Keenan has proposed, with the Queens Chamber producing Hydrogen, acting as a negative electrode.
From the Giza Power Plant, “salt was only ever found in the Queen’s Chamber and Queen’s Chamber Horizontal Passage. In 1978 a researcher, Patrick Flanagan, had the salt of the Queen’s Chamber analyzed and it was found to contain a mixture of calcium carbonate, sodium chloride and calcium sulphate.”
The Thermoacoustic Regenerative Pulsejet
The dimensions and flatness of the Pyramids internal Chambers and Passages all appear geared towards the tuning and function of a pulsejet(thermoacoustic) style engine which generates heat and sound within the King’s Chamber and Grand Gallery, and is using the resonance and heat of the system to keep the Pyramid vibrating. A pulsejet engine fits the pyramid power model very well, pulsejets generate high sound pressure levels, plenty of thrust and heat, and would require no maintenance. Fire could continuously be created through the combination of fuel, oxygen, and heat, requiring no spark for combustion with very little compression. The Grand Gallery is slanted which would help with the directing of heat and the mixing of gases. Hydrogen being light would travel from the bottom to the top of the room, and oxygen, being heavier, would fall from the top to the bottom of the room.
Here’s a link showing how radio frequencies can ignite water into a constant flame. In this video a lazy yellow flame is produced displaying unburnt fuel. The inventor, John Kanzius, was searching for a cure for cancer when he discovered a way to set fire to water. http://youtube.com/watch?v=p8xYUDiSGDk
A series of experiments at Penn State University’s Microwave Lab were done using test tubes of water containing 0.1 to 30% salt. At just 3% salinity, the youtube video of John Kanzius’ burning water was confirmed.
The radio frequency used to split the water in the link above is 13.56mHz at 300 Watts power. The Kings Chamber generates a 41mHz radio frequency at a power of 150 MegaWatts, and would feed that signal back into the Pyramid’s Chambers. Doug Keenan demonstrates in his book, Cycles of the Pyramids, how the King’s Chamber’s acoustic resonance stimulates standing waves of piezoelectric charge in the electromagnetic spectrum. Signal referenced from http://www.bigskymap.com/cycles/PIX/HMT08.jpg
A ram pump can also be combined with a trompe, a water powered air compressor. A system like this could provide both timing and air for an engine. https://en.wikipedia.org/wiki/Trompe https://youtu.be/bsTK-BiUgtg
It’s also possible that the pulsejet function inside the Great Pyramd could have no combustion of any kind is taking place. If steam permeated the device, that may be all that’s needed for the pulsejet to work. Here’s a link to a patent from 1975, on a heat engine in the form of a water pulsejet. https://patentimages.storage.googleapis.com/ac/67/b6/eeccf9baab69d5/US3898800.pdf
Displayed in the pulsejet patent link above in FIG. 11, a water cooling jacking is applied to the water pulsejet to make the reaction more efficient. It is well known to Egyptologists that walls of the Grand Gallery have a hollow space behind them, this may be what the empty space behind the Grand Gallery walls was for, a cooling jacket. Below image By David Lightbody.
Below is a picture copied directly from http://Gizapower.com in which Chris Dunn is pointing out scorch marks on the ceiling of the Grand Gallery after the gallery was cleaned. These scorch marks could be evidence of combustion or pressures generating a standing wave and leaving a pattern showing the nodes and anti-nodes of the frequency generated. The total length of the upper chambers is roughly (Grand gallery 46.68m + King’s Chamber 10.47 lm + Ante Chamber 6m + Queens Chamber Passage and Chamber 39.75m = 102.9m), so the resonant frequency of the system could be anywhere between 343/102.9X2 = 1.666Hz for air, 460/102.9X2 = 2.235Hz for steam, and up to 1270/102.9X2 = 6.171Hz for Hydrogen. There’s about 100-200 burn marks, or antinodes, and they could be an indication of the system running at a higher frequency than what’s being anticipated.
I’ve crawled around inside the Great Pyramid with a private group for over 2 hours, and while the entire tour I was with was in the King’s Chamber, I had the Grand Gallery all to myself. This gave me the opportunity to create a bang on the floor to make the walls of the Grand Gallery vibrate. I jumped from the 4th step up above the landing where the stairs meet above the Queen’s Chamber Passage entrance and landed on the roughly 6′ x 3′ floor boards. After the initial impact with the floor, the walls shook like the sound of a subwoofer. This showed me the that Chamber resonated freely. The blocks that make up the walls actually vibrated for a few seconds past me making the bang on the floor, it was unbelievable, it was like striking a nicely tuned drum. My friends on the tour came yelling asking what happened as everyone felt a shockwave roar past them. I felt assured that the Pyramid has a low fundamental frequency. The size, geometries and the materials used in the Great Pyramid are all geared towards low-frequency response. My ear told me the sound was around 45hz, the vibration of the walls anyways.
The granite slabs that are believed to have existed in the Ante-Chamber could’ve served as hot plates or a choke thus aiding the thermoacoustic process. The slabs wouldn’t have blocked the passage completely either as there is quite of bit of space above and around them in the Ante-Chamber. The spacing of the slabs would affect the sound of the process too. On the walls in the space of the Ante-Chamber there are many lateral concave grooves that held the slabs of granite in place. A thermoacoustic effect could also be possible without the granite slabs, as the walls of the Ante-Chamber could be made hot thus working as a thermoacoustic choke. With water cooling the Grand Gallery, heat being contained in the Kings Chamber, granite slabs placed in the path between the two Chambers, and a ram pump driving the process, the right conditions for thermoacoustics should arise. Thermoacoustics would enable a steady continuous tone to be emitted by the Pyramid. https://en.wikipedia.org/wiki/Thermoacoustics
Here’s a link to a demonstration of a thermoacoustic sound generator. https://www.youtube.com/watch?v=Q6WN3wFPnqw
Here’s a link which demonstrates how sound can be used to generate power, and which also indirectly explains the shape and configuration of the Grand Gallery and Kings Chamber. http://www.rexresearch.com/lucasmacrosonix/lucas.html
Besides driving a piston, the Cadman Pump appears to also be working like a speaker which is vibrating the pyramid from below. The King’s Chamber is working like a microphone, harnessing the vibrations of the Pyramid and the oscillating gases within the Chambers. Both the Cadman Pump and Thermoacoustics are beating the Kings Chamber and Pyramid into resonance, inside and out.
It also appears that steam could be the working-gas of the Pyramid thermoacoustic engine, and that no combustion of any kind is taking place. This would actually be the simplest design to execute, water is easily vaporized and condensed. The diagram below is similar to the Layout of the chambers inside of the Great Pyramid, with the Grand Gallery on the right, the Kings Chamber on the left, and the Ante-Chamber in between.
The Thermionic Configuration
The Great pyramid also resembles a basic thermionic device similar to a vacuum tube. The King’s Chamber is made entirely of granite and the walls of this chamber are barely in contact with the limestone of the Pyramid. A thermionic effect could be possible by heating the granite of the King’s Chamber and effectively negatively charging the granite. Granite can withstand higher temperatures when dry, so if the King’s Chamber was kept dry than the temperature of the stone could be made hot enough to emit electrons.
The Quartz in the granite is an exceptional piezoelectric material and it could potentially generate megawatts of power through the heat and pressures of the system. Through the ingenious use of water hammer, thermionics, thermoacoustics and piezoelectrics, it starts to sound possible that the Giza Pyramids generated enormous amounts of power.
Tesla’s Earth Wave Vibration Theory
Note: Electricity in a wire behaves like a gas.
In the Graphic above Tesla shows his analogy and realization of his Wireless Transmission Theory. The analogy is a hand pump pumping up a sphere and gauges responding all around the sphere. He states in his Analogy Graphic that each pulse of the pump is felt with equal force at all points of the sphere and that sphere could be a flexible, spherical envelope filled with a liquid or gas. Tesla then demonstrates in the Realization Graphic how the Earth could be used as a means for the distribution of electricity without wires utilizing the principle displayed in the Analogy Graphic.
There’s no “free energy” in this system. Tesla makes no mention of using the energy of the Earth to power the Wardenclyffe Tower. The Tower required a large generating station which was right beside the Tower. Tesla also wanted power from Niagara Falls, which wasn’t too far away.
Tesla’s Wardenclyffe tower contained two resonating Tesla Coils placed in series with Earth and a virtual ground terminating the circuit at the top of the Tower. The Tower was in a single phase configuration (single wire, mono phase) and a generating station provided the current for the Tower to transmit. Each Pyramid, Khafre and Khufu, are acting as a resonant conductor like a pair of Tesla Coils arranged in parallel configuration.
With the two largest Pyramids at Giza working as resonant generators, and both Pyramids fundamental frequencies being induced into the ground in such close proximity, the fundamental frequencies of the Pyramids likely clashed in a constructive and destructive manner. The frequencies generated would mix and create a beat frequency, or pulsation. The Pyramids seem to be pulsing acoustic and electromagnetic frequencies into the Earth, just the way Tesla simply describes in his Analogy Graphic –Tesla’s Earth Wave Vibration Theory. This arrangement could possibly set up a standing acoustic/electromagnetic wave within the Earth, and possibly the Ionosphere, for the transfer of wireless power! The waveform above demonstrates how the Ancients could have used beat-frequencies to generate low-frequencies. Couple this effect with hitting a resonant frequency of Earth and you have a resonant switched, resonant amplified signal being transmitted around the globe.At the speed of sound through the Pyramids, using P-waves(averaged at 6km/s), Khufu’s pyramid clocks in at around 13Hz and Khafre’s Pyramid in at around 14Hz. This leaves a difference of 1Hz, which a 1Hz modulation produces a 0.5Hz wave. The 4th octave of this waveform would be 8Hz.
Earth rotates at 465.1 metres per second and the Great Pyramid is argued to be between 230 and 232 metres, which 465.1/2 is 232.5. The Pyramids turn with the Earth and pass through space twice every second, this could be hinting at how the Pyramids are synced/clocked to the planet.
The Picture below was taken in a book of Tesla Patents from a Tesla Museum in Hungary. What’s depicted in Figure 4 doesn’t appear in any other Tesla patent on the internet, and is what would appear to be, a double tower version of the Wardenclyffe Tower. The arrangement is similar to the arrangement of the Pyramids, with two resonant transformers of a slightly different frequency paired together. Notice the length of the vertical coils, the one on the left is longer and would resonate at a lower frequency than the one on the right, just like the Khufu and Khafre Pyramids. Tesla originally wanted to build two towers at Wardenclyffe, but financing prevented Tesla from building his original vision. The details on how the twin tower system would work are still a mystery, though modulation may be the answer. Tesla coils apparently work best when the primary and secondary have an 8% difference in frequency, maybe this same concept was carried over into Tesla’s Wardenclyffe Tower.
The Pharaohs name Sneferu translates into double-harmony. Sneferu also built two Pyramids of different size in close proximity to each other, the Red Pyramid and Bent Pyramid. This lends to the Idea that the system employed by the Ancients used mainly two frequencies harmonizing with the Earth. The Red and Bent Pyramid are located in Dashur 21km south of the Giza Pyramids. Why would the Ancients build their structures so similarly if there was no master plan?If the Pyramids were resonators then the frequencies they generate would combine into the sum of the difference of the frequencies, resulting in beats. The Giza pyramids and the Red and Bent Pyramids may also have been coupled together, for they’d modulate in the same fashion.
By volume, the Pyramids Khufu and Khafre are similar to the Red and Bent Pyramids. Khafre being 85.5% the volume of Khufu, and The Bent Pyramid being 84.2% the volume of the Red Pyramid. These percentages may even be closer, Khufu’s Pyramid is argued by some Egyptologist as being a little bigger than 230m per side.
Below is a picture by Doug Keenan illustrating the electromagnetic resonant frequencies of the Giza Pyramids based on the latest Electromagnetic Survey of the Great Pyramid. Take the speed of light and divide it by the Base width of a pyramid and you’ll get the electromagnetic resonant frequency of that pyramid. Khufu’s Pyramid clocks in at 230m(or 1.304mhz), and Khafres is at 215m(or 1.395mhz). Therefore, the Pyramids should modulate at 91khz, producing a 45.5khz wave.
Here’s a link to the Survey Publication. Mikhail Balezin et al, Electromagnetic properties of the Great Pyramid: First multipole resonances and energy concentration, Journal of Applied Physics (2018). https://aip.scitation.org/doi/10.1063/1.5026556
Read about Tesla’s Wardenclyffe Tower here. https://en.wikipedia.org/wiki/Wardenclyffe_Tower
Tesla originally attempted this pulsation mechanically at 5khz pulses of a 230-250khz waveform. The pyramids appear to be in the same low frequency range in radio terms. The Pyramids actually appear to be mixing two mhz signals, modulating at roughly 91khz, which half of 91khz is 45.5khz, Eerily similar to Tesla’s own method of using a high-frequency pulsated at a lower frequency. Interestingly, Tesla claimed to be utilizing a longitudinal transmission through the Earth, and the Pyramids also appear to be doing just that, outputting low-frequency acoustic waves through the Earth.
Whether the output through the ground is electric or just low frequency sound, or both, the pyramids appear to modulate their amplitudes into a pulsation. The Pyramids produce sub-wavelengths at the speed of sound, and low frequencies in the electromagnetic spectrum. Both frequency ranges travel far and wide and possibly resonated with the planet with ease. Maybe the Pyramids are just using the Earth as a big transducer, vibrating the Earth at an optimum frequency could yield electric phenomena in a coordinated fashion. If the speed of sound through the Earth is averaged at 6km/s, and the Pyramids modulate at 1hz, then the wavelengths of the acoustic waves and electromagnetic waves are nearly identical. 299792458/45555=6580 meters, or 6.58km.
Rocks actually generate power, here’s a link to the “Time Resolved Study of Charge Generation and Propagation in Igneous Rocks,” By Friedemann Freund. https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/1999JB900423
Friedemann Freund has determined that a charge through granite Propagates at 100-200m/s. Interestingly, many pyramids in Egypt fall into this size range. Maybe pyramid dimensions reflect the time it takes a charge to make its way through the structure and be emitted.
The tip of a Pyramid is the perfect shape to facilitate electrical and discharges of static in and out of a virtual ground. If the tips of the Pyramids were gold, that would reinforce the similarities with the Wardenclyffe Tower. Gold is a great conductor and doesn’t corrode, therefore it would remain a steady ground. The Pyramid shape naturally wicks current into the atmosphere out the tip, and with the Pyramids negatively charged and the ionosphere positively charged, we have the proper configuration for ion/electron flow.
The geometry, resonance and current of the Pyramids could yield some very interesting effects through the feedback between the structures and the Earth. The Pyramids could be oriented in a way that promotes feedback of the tones generated to further bring out the notes. If you place a subwoofer on the floor of a room and turn it up, you can walk around the room and find the spot where the sub frequencies are loudest, this is where the Khafre pyramid could be located in relation to the Great Pyramid, and where the Bent Pyramid could be located in relation to the Red Pyramid.
The Giza Pyramids, and the rest of the Pyramids in Egypt, are on Earths magnetic equator. Therefore the Pyramids are 90 degrees out of phase with Earths magnetic field. This could be how some “free energy” was pulled from the Earth. Tesla was aware of this possibility but never got to prove it. The Wardenclyffe Tower was only 10 degrees North of the Pyramids.
Video courtesy of Doug Keenan.
Pyramid Power Uses
The pyramids generate sub-frequencies at the speed of sound, and low-frequencies in the electromagnetic spectrum. Both frequencies travel great distances and must’ve had an impact on the surrounding area, and maybe the entire planet. Acoustic and electric pressures in the ground could have had many uses, for example, Earthquake lights, or a mechanoluminescent process like piezoluminescence.
One of the interesting effects of quartz crystals is that they can emit light through an effect known as piezoluminescense. Maybe the Ancients had a piezoluminescent lighting system, essentially using rocks as lights. There are tunnels in Egypt kilometres long without any torch marks, so how did the Ancients see in the dark? There’s possibly a connection between piezoluminescense and piezoelectricity. Any monuments or temples built from stone containing quartz could very well have emitted light in ancient times. Seeing as so many ancient temples appear built in geometric proportion to one another, maybe these geometries reflect the harmonic intervals of the piezoluminescent effect of the stones used in construction. We seek out temples for enlightenment, maybe in ancient times that was literally what people went to temples for, to have light shed upon them. In the image below a drill bit is being pressed into a piece of quartz crystal and light is being emitted when the drill bit squeaks on the stone. This effect can arise in the kHz to mhz range, with brightness attributed to power. Watch the videos in the links below.
Other Possible Pyramid Uses
Doug Keenan, an American electronics engineer, has reverse engineered the Pyramid as a radio-telescope. His website’s, http://cyclesofthepyramids.com and http://bigskymap.dougkeenan.com, are incredible and he’s the first to properly reverse engineer the Great Pyramid. I firmly believe in a system like the one Doug presents on his website but I think the Pyramids might’ve continuously operated providing a continuous output through the Earth.
It’s been proven that loud rock music affects plant growth. It’s also been proven that electrical stimulus encourages plant growth. The Pyramids could’ve been built to allow plants to grow bigger and faster by energizing the ground with loud low-frequency pulses of current. The Land of the Dead could be where dead bodies were shipped to decompose, thus raising the EC of the water and land. Plants grow many times faster with abundant food sources.
So if the Pyramids aren’t Tesla-like power plants, than they’re very likely what Doug Keenan is proposing, which is a radio device. Nikola Tesla was the pioneer of radio, so this outcome, the pyramids being radio devices, is perfectly fitted to the research presented on this website. Doug adheres to the tenets.
No aliens, no religion, no magic, and no Khufu. Pyramids focus their energy down the middle. The word pyramid can be translated as, “fire in the middle.” The name for the great pyramid, Ahket Khufu, can be translated as, “Khufu’s mountain of light.” The name for obelisk can be translated as, “to the beat of a drum.” Maybe pyramids around the world are capable of harnessing an effect that we just haven’t realized yet. Maybe it’s piezolumenesence, or a earthquake/tsunami warning system, or an ancient form of communication. Whatever it ends up being, it’ll be a real verifiable effect of some sort. For now, pyramids remain temples and tombs, but possibly not for long. Cheers.