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Is electric propulsion worth it?

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tilopa

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Quite a few giant companies build electric prototypes just for "green" advertising, even at loss.
Bob Lutz, the retired GM exec explanined this in his book. His GM Chevy Volt was not expected to make a profit.

I saw a Sikorsky electric helicopter shown at Oshkosh that never flew, quietly shelved. Same for Cessna, Boeing etc.
Yes, this is a marketing/PR strategy well known. Cessna's electric 172 program was (IMO) one of these. The Airbus has more of a track record with electric, having actually built and flown at least 2 planes. As you said the Sikorsky, and the 172, never flew. Airbus claims the E-Fan is being marketed as a trainer, given its one hour flight time that seems reasonable. But I'll leave it to your discernment to decide if you think the Airbus electric is just a "green" marketing strategy.
 

BBerson

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. Airbus claims the E-Fan is being marketed as a trainer, given its one hour flight time that seems reasonable. But I'll leave it to your discernment to decide if you think the Airbus electric is just a "green" marketing strategy.
Nope, I don't think Airbus will build trainer aircraft. No large company can risk the liability, with too many assets.
 

Sockmonkey

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The thing with "money spending" pet projects is that even if the project itself is a bust, the information gathered and technologies developed for them are often beneficial to other applications. Like how things they create for race cars often have commercial applications in production cars.

Regarding using the motors in a flying wing for yaw control, that would only be acceptable to me if you could apply braking force to the windmilling unpowered props so they could act as drag rudders in the event you run out of juice.
If the motor setup also functions as generators like in electric cars during regenerative braking, you might be able to recharge the battery just enough for a powered landing if you have enough altitude to begin with.
 

tilopa

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Never going to work. Physics can't be fooled. Anybody who masters the Breguet Range Formula (that's a layered statement) and understand the ratio of atom mass vs max electric potential will say the same for planes with any useful range.
I just read about the Breguet Range Formula. Basically it is saying range is a factor of the energy density of the fuel (battery), aerodynamic efficiency (ratio of production of lift to drag, engine efficiency, and weight.

I understand why you say the increased energy density of batteries is going to be slow in coming, but why can't aerodynamic efficiency be increased to meet the challenge, and lighter stronger materials be created. such as these:

The world's lightest material (Video)
Aerographite: Six times lighter than air, conductive, and super-strong | ExtremeTech

Why would increasing efficiency and reducing material weight go against your "physics can't be fooled" mantra?
 
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tilopa

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Well, I think there is a misunderstanding of Physics here.. and a big misconception about energy & gravity.
Hydroelectric power plants do NOT extract energy from gravity .. they extract indirect solar energy .. H2O molecules are lifted to higher potential energy (altitude) by radiant heat from the sun .. they condense and fall .. and their higher potential energy can be extracted with dams & turbines.

The same is true of gliders .. their source for propulsion power is the potential energy that was gained from a tow vehicle, driving to a hilltop, etc. .. sinking through a mass of air in a gravitational field is expending potential energy.
Power = weight * sink rate
Finding rising air is another way of extracting indirect solar energy . but you're still sinking through the air mass to sustain flight.
Nothing in our current technology extracts energy from gravity.
That's a big misconception? Your kind of knit picking a point don't you think? ALL energy on this planet is solar energy, all energy is created from the sun. Name a source of energy that is not.
 

tilopa

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Nope, I don't think Airbus will build trainer aircraft. No large company can risk the liability, with too many assets.
They are not risking liability by building the A380 which if crashed as a fault of the manufacturing or design could kill 525 people? Yes, the payoff for an A380 is great but the liability is equally great.
 

BBerson

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That's a big misconception? Your kind of knit picking a point don't you think? ALL energy on this planet is solar energy, all energy is created from the sun. Name a source of energy that is not.
The planet has a hot core that is left over from the birth of the earth, not related to the sun. The earth is also filled with radioactive elements that release energy not from the sun. Provides geothermal energy with steam. Nuclear power comes from uranium not the sun. Tidal energy is slightly from the sun, mostly the moon motion relative to the earth.
 

autoreply

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I just read about the Breguet Range Formula. Basically it is saying range is a factor of the energy density of the fuel (battery), aerodynamic efficiency (ratio of production of lift to drag, engine efficiency, and weight.
Weight RATIO. But batteries don't loose weight.That's why they have a much lower range as you'd expect, purely based on the energy density (joules/kg) for longer ranges.
I understand why you say the increased energy density of batteries is going to be slow in coming, but why can't aerodynamic efficiency be increased to meet the challenge, and lighter stronger materials be created. such as these:
Sure.
The Ventus 2 FES has an L/D of 50 and with 45 kg of batteries a range of 200 km @ 90 km/h. That's what's possible today.

Yet, that's not terribly practical for distance-going. Too slow, too extreme of an airframe, etc.

Why would increasing efficiency and reducing material weight go against your "physics can't be fooled" mantra?
It doesn't. But there's a hard limit, which occurs before battery-powered becomes feasible for real long trips (say 250+ miles)
 

DangerZone

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Well, I think there is a misunderstanding of Physics here.. and a big misconception about energy & gravity.
Hydroelectric power plants do NOT extract energy from gravity .. they extract indirect solar energy .. H2O molecules are lifted to higher potential energy (altitude) by radiant heat from the sun .. they condense and fall .. and their higher potential energy can be extracted with dams & turbines.

The same is true of gliders .. their source for propulsion power is the potential energy that was gained from a tow vehicle, driving to a hilltop, etc. .. sinking through a mass of air in a gravitational field is expending potential energy.
Power = weight * sink rate
Finding rising air is another way of extracting indirect solar energy . but you're still sinking through the air mass to sustain flight.
Nothing in our current technology extracts energy from gravity.

And Tesla's bladeless turbine design does work, but it has been tested and proven to be horribly inefficient compared to modern bladed turbines.. foolish internet rumors of it being Illuminati-suppressed technology not withstanding.
An honest research effort will show you that Tesla turbine proponents are on the fringe, and do not have any supporting test data to back their wild claims.

And all this has absolutely nothing to do with electric propulsion discussions on a homebuilt airplanes forum..
Theoretically, you are partially right. Technically, you would be wrong. A theoretical physicist will emphasize this could be solar energy just the way you did. He seeks to explore theory and analyze some aspects into great detail and discover new findings. A technician seeks practical solutions and wants to build technology which will allow us to use this energy in the most efficient way. So taking a theoretical physicist to make an electric airplane would be irrational as taking a plumber to solve electric problems in your house. So why is this statement IN REALITY only partially right?
1. Solar energy is electromagnetic energy. Thus, in this process even from a theoretical point of view we have electromagnetic energy through indirect solar energy. Indirect solar energy through acting on water molecules to a higher potential energy. Higher potential energy acting through gravity to mechanical work driving the turbine to electromagnetic energy. The only limit in this magic circle is the phyisicist's imagination, we could go on and on for hours ranting about theory and phylosophy. But the simple fact is we'd be transforming electromagnetic energy to electromagnetic energy through our natural and technical resources.
2. There is a reality problem if we'd look at this as only indirect solar energy. A technician seeks to make a system as simple, efficient and reliable as possible. So why not transform indirect solar energy directly to electromagnetic energy? First, this would not be simple. Efficiency might be reduced, even solar panels which use direct solar energy have less efficiency compared to a water turbine. Reliablity? Water turbines built by Nikola Tesla more than a century ago in our country still work. The lifetime of mono solar cells? Twenty years tops before reducing efficiency. Poly? Five to ten years and your cells go bellow 50%. Reliability? Yes, they can be reliable if they are built by NASA for space use, and even there they are sensitive to micrometeorites or molecular debris.
3. A hydroelectric turbine allows us to use energy even during the night or 200 days of cloud and fog, when bpth direct and indirect solar energy are at their lowest potential. This is what technicians do, they build systems which are best for an application, regardless of phyisics phylosophy. They use phyisics to find solutions, not to complicate things beyond imagination. And this is what Tesla was good at.

'Extracting' energy from gravity needs some understanding. We're not talking about a 'free ride' or 'free lunch' as you seem to imply. However, we can use gravity to speed up objects in space, and this principle has been used for years in space exploration. The slingshot principle I mentioned earlier is a great example. We have a satellite, use the orbit around a planet to spin it up to a higher velocity and with slight energy input send it in a previously calculated path to deeper space. It might be better to try to understand the principle that limit ourselves with words. There is a brilliant watercraft that uses both gravity and buoyancy to propell itself around the globe. It works, the Slovenians from Pipistrel are building a glider which will use the same principle. Things are a bit more complicated than simple words like 'extracting energy from gravity', but an engineer might be able to understand how this works without spending too much time on words forumation or grammar. If you know what I mean.

Now when it comes to Tesla's trubines, it would be irrational to think that a dead man could demonstrate you some supporting test data to back his claims. The other thing is that you seem to not understand that Tesla developed more than fifty models of turbines, and each was for a different application. Using a turbine from one application for another is ridiculous as mounting a supersonic jet turbine on an ultralight aircraft with a Vne of 350km/h. And yet, there were projects like that in the past, which reduces efficiency drastically. If you are not familiar with turbines try to put a high speed propeller on a slow flying aircraft like a trike and you'll instantly understand why people fail in understanding Tesla's turbines.

How does this relate to electric flying? A lot. You see, there are MANY projects which do exactly what we discuss here: they are all great at theory but fail as tachnicians. Without understanding electric propulsion they use wrong technical solutions for the right idea. They put high speed turbines/props on slow speed aircraft. They do not use the advantages of electric propulsion but get burried in inefficient projects. In electric propulsion we calculate the efficiency in grams per watts, or kilograms per kilowatt. If a system is less than 2.5 g per W then it is as good as the best ICE/prop or turboprop power systems, NPT good enough. A well optimized electric motor with an efficient prop should make from 2.5 g/W to almost double that. A ionic turbine makes from 10g/W up to almost triple that. And this is where only technicians like Tesla go, cause you have to build practical and real machinery to come to those figures. You can't rely on only theory and physics philosophy, that won't get you flying at all.

The analysis of the feasibility and motives of the company project is immaterial to the argument regarding the use of electric motors. The Airbus E-fan is flying with known specs.

However, I did go ahead and dig a little deeper into the technical details of the E-fan and what Airbus is trying to accomplish. Firstly, I find your comments about Airbus cynical, naive, and arrogant, somehow all at the same time. Airbus is an established, respected, aerospace engineering company - we're not talking about Terrafugia. And though they are large not all large companies operate as you claim. The idea that one guy is sitting around with a bunch of cash thinking about how he can shoot his wad is ridiculous. And the idea that "Airbus does not care if a project is feasible, rational, efficient or an actual improvement.", is absurd. If they're building airplanes that are failures it is going to hurt there reputation as an airplane manufacturer and overall hurt their business.

The E-Fan may not be the greatest airplane made from a performance standpoint but it is definitely very efficient and incorporates some innovative engineering. Such as the electric motor driven wheels, which allows for a more efficient take-off run. And though I cannot confirm this as I cannot find details about the electric motors I suspect that the two 40 HP of each motor is peak output and not continuous which means the plane is powered by somewhere around a total of 40 - 60 HP continuous power. About half the power of the comparable-role Cessna 152.


This is the part were you really should have taken your own advice and been a "detective to see what's behind a story". The electric Cri Cri was, in fact, an Airbus project. They built a Cri Cri, and modified it for electric propulsion.

Airbus Group - Electrical Aircraft Cri-Cri in front of A380
Airbus electric aircraft takes to the skies - CNN.com
It was not my intention to be arrogant or cynic, I was simply stating some facts.

And the fact is that there are four different electric Cri Cri platforms. When the E-Fan project showed inferior results to a Cri Cri aircraft, Airbus made a rational decision to buy a succesfull one and go on from there building their own. The E-Fan was a successor of the early Fantrainer project, which was ok in some aspects. But the results of the E-Fan were anticipated even before the project was actually built. So yes, Airbus spent millions for the E-Fan even though engineers knew it's results will be inferior to the electric Cri Cri. Even the aerodynamic shape and ducts show that whoever designed the E-Fan was either not experienced in aircraft design or had not much knowledge about electric propulsion. And I highly doubt Airbus people would not be intelligent, I regard them as smart and goal oriented. So, why not ask them why they spent millions of Euro to develop an idea which was futile in the first place if they bought the Electric Cri Cri after that? There's two possible reasons, either they had millions to spend and went to the most 'appealing' project or they lacked knowledge about electric aircraft and invested millions for a project which was doomed to inefficiency at the design table. The looks are usually crucial today, the electric Cri Cri looks like an ugly duckling compared to the shiny fancy E-Fan. The saddest part is that the E-Fan COULD be a great airplane only if they would have contacted someone who has experience in analyzing/building airplanes or has knowledge about electric propulsion/flight. You say it is underpowered? The Arnold AR-5 flew around 200 knots with similar power of an internal combustion engine. And on top of that, BLDC motors CAN be electrically adjusted for optimized loads, which means you could have more thrust with same power. Please feel free to dig deeper and I am sure you will agree that a respectable and known company as Airbus could have done better. Specially with millions available.

So yeah, you're right, it does not have to be that they deliberately spent millions on a futile project. It could have been just lack of knowledge about electric aircraft and propulsion.
 

BBerson

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Dangerzone, I think you may have missed Dan's point that gliders use potential energy .
Both technicians and physicists use the same words.
 

DangerZone

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Dangerzone, I think you may have missed Dan's point that gliders use potential energy .
Both technicians and physicists use the same words.
That is possible, I thought we were writing about electrical propulsion and electrical energy for powered flight. An internet forum is limited to typing so it sometimes takes a while to see each other's perspectives.
 

tilopa

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It was not my intention to be arrogant or cynic, I was simply stating some facts.

And the fact is that there are four different electric Cri Cri platforms. When the E-Fan project showed inferior results to a Cri Cri aircraft, Airbus made a rational decision to buy a succesfull one and go on from there building their own. The E-Fan was a successor of the early Fantrainer project, which was ok in some aspects. But the results of the E-Fan were anticipated even before the project was actually built. So yes, Airbus spent millions for the E-Fan even though engineers knew it's results will be inferior to the electric Cri Cri. Even the aerodynamic shape and ducts show that whoever designed the E-Fan was either not experienced in aircraft design or had not much knowledge about electric propulsion. And I highly doubt Airbus people would not be intelligent, I regard them as smart and goal oriented. So, why not ask them why they spent millions of Euro to develop an idea which was futile in the first place if they bought the Electric Cri Cri after that? There's two possible reasons, either they had millions to spend and went to the most 'appealing' project or they lacked knowledge about electric aircraft and invested millions for a project which was doomed to inefficiency at the design table. The looks are usually crucial today, the electric Cri Cri looks like an ugly duckling compared to the shiny fancy E-Fan. The saddest part is that the E-Fan COULD be a great airplane only if they would have contacted someone who has experience in analyzing/building airplanes or has knowledge about electric propulsion/flight. You say it is underpowered? The Arnold AR-5 flew around 200 knots with similar power of an internal combustion engine. And on top of that, BLDC motors CAN be electrically adjusted for optimized loads, which means you could have more thrust with same power. Please feel free to dig deeper and I am sure you will agree that a respectable and known company as Airbus could have done better. Specially with millions available.

So yeah, you're right, it does not have to be that they deliberately spent millions on a futile project. It could have been just lack of knowledge about electric aircraft and propulsion.
Dangerzone, I don't mean to be offensive, from some of your other posts I gather you are informed and intelligent. But on this subject you are making subjective and dubious statements. First, you're implying that the E-Fan is a complete failure though I have not seen any report that would suggest that. You are limiting its success as a project by its cost and speed performance, even comparing it to the Cri Cri and AR-5. Both the Cri Cri and the AR-5 are single seat aircraft with very different missions. The AR-5 has a 65HP engine but it is much lighter than the E-fan because it does not have to haul heavy batteries, is single seat, and was built to break speed records (cramped, short range, and minimal margins to keep the weight down) - quoting from Orion's comments here. Not a good comparison to a two-seat trainer, nor is the speed record holding electric Cri Cri. As for the cost, when you build a prototype, especially an unconventional (practically one-of-a-kind) airplane it is going to cost a lot. For an auto company to make a new prototype of a part like an intake manifold costs hundreds of thousand of dollars. Sure someone can build an E-Cri Cri for under 100K but again they are very different planes and missions.

As for the Fantrainer, which is an airplane that I've been interested in because I'm big on ducted fans, there is nothing about that airplane you can say was a failure. There may have been some challenges with fitting the engine in the fan and placement, any such issues were mitigated in the E-fan because of the small size and weight of the electric motor. Also the FT used a Turboprop which made if more expensive and therefore not as marketable as a trainer. The E-Fan may not be the most efficient plane in the world (it is still very efficient), but two points to consider about that. first, it is already an unconventional design because it uses all electric for its propulsion, to further design the airframe with unconventional innovations would be adding too many variables for, not only potential failures, but increased production complexity and cost. Second, Being designed as a trainer the plane needs to have docile characteristics. As BB mentioned the liability is already a concern, you don't want to build the thing to break speed records and compromise stability and control.

Lastly, the timelines you are stating do not correspond to my research, though to be honest I have not really dug that deep into it. But it appears that the Cri Cri was Airbus's first endeavor first being flown in 2010 and the E-Fan came later, first flown in 2014. Sure, I understand they could have been working on the E-Fan prior to the Cri-Cri, but perhaps they began on the Cri-Cri because it was a lot easier to convert to electric and gave them some insight into what all was involved in epropulsion. And not because it was showing "inferior results" to the Cri Cri.
 

henryk

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inefficient projects. In electric propulsion we calculate the efficiency in grams per watts, or kilograms per kilowatt. If a system is less than 2.5 g per W then it is as good as the best ICE/prop or turboprop power systems, NPT good enough. A well optimized electric motor with an efficient prop should make from 2.5 g/W to almost double that. A ionic turbine makes from 10g/W up to almost triple that. And this is where only technicians like Tesla go, cause you have to build practical and real machinery to come to those figures. You can't rely on only theory and physics philosophy, that won't get you flying at all.



.
https://www.youtube.com/watch?v=Mhm5IVB6gb4

=from 2:30=simple flapping thrusters can generate up to 2000 N thrust from 1 W !!! \dr Sorokodum,Moscow\.
 

DangerZone

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Dangerzone, I don't mean to be offensive, from some of your other posts I gather you are informed and intelligent. But on this subject you are making subjective and dubious statements. First, you're implying that the E-Fan is a complete failure though I have not seen any report that would suggest that. You are limiting its success as a project by its cost and speed performance, even comparing it to the Cri Cri and AR-5. Both the Cri Cri and the AR-5 are single seat aircraft with very different missions. The AR-5 has a 65HP engine but it is much lighter than the E-fan because it does not have to haul heavy batteries, is single seat, and was built to break speed records (cramped, short range, and minimal margins to keep the weight down) - quoting from Orion's comments here. Not a good comparison to a two-seat trainer, nor is the speed record holding electric Cri Cri. As for the cost, when you build a prototype, especially an unconventional (practically one-of-a-kind) airplane it is going to cost a lot. For an auto company to make a new prototype of a part like an intake manifold costs hundreds of thousand of dollars. Sure someone can build an E-Cri Cri for under 100K but again they are very different planes and missions.

As for the Fantrainer, which is an airplane that I've been interested in because I'm big on ducted fans, there is nothing about that airplane you can say was a failure. There may have been some challenges with fitting the engine in the fan and placement, any such issues were mitigated in the E-fan because of the small size and weight of the electric motor. Also the FT used a Turboprop which made if more expensive and therefore not as marketable as a trainer. The E-Fan may not be the most efficient plane in the world (it is still very efficient), but two points to consider about that. first, it is already an unconventional design because it uses all electric for its propulsion, to further design the airframe with unconventional innovations would be adding too many variables for, not only potential failures, but increased production complexity and cost. Second, Being designed as a trainer the plane needs to have docile characteristics. As BB mentioned the liability is already a concern, you don't want to build the thing to break speed records and compromise stability and control.

Lastly, the timelines you are stating do not correspond to my research, though to be honest I have not really dug that deep into it. But it appears that the Cri Cri was Airbus's first endeavor first being flown in 2010 and the E-Fan came later, first flown in 2014. Sure, I understand they could have been working on the E-Fan prior to the Cri-Cri, but perhaps they began on the Cri-Cri because it was a lot easier to convert to electric and gave them some insight into what all was involved in epropulsion. And not because it was showing "inferior results" to the Cri Cri.
Please do not confuse the Fantrainer aircraft of Rhein Flugzeugbau and the E-Fan of Airbus. The first RF Fantrainer started as a twin ducted fan aircraft and it was a vaulable platform to see the limitations of ducted fans. The second (last) version had a single fan and a more powerful engine, it was quite capable and you should not call it a failure. It was a good aircraft but had less efficiency due to the ducted fan. I would also not call the E-Fan a failure because it shows how not to design and build an electric aircraft. I call the E-Fan inefficient and designed beneath the level of expertise a company like Airbus should have.

Concerning the dates it might have helped you visiting the Aero Expo in Friedrichshafen, Germany, the last couple of years. The electric aircraft started showing around 2009 over there, and it might have given you a better perspective than internet web pages. A respectable record of electric flight (around 250 km/h) was set in 2009 by a two seater electric Alpi Pioneer 300 in Torino, Italy. It is more efficient compared to both the E-Fan and the electric Cri Cri, seats two persons, formidable to fly and with beautiful aircraft lines. Bear in mind that the Alpi Pioneer 300 stalls around 59km/h and it's top speed is over 250km/h with less power than the E-Fan. Naturally, it would be rational to expect better from future projects, not less like in the case of the E-Fan. Hopefully you will understand this, I wish Airbus would have done a better job with the E-Fan but the amount of design and technical errors was too high to make it a success.

Lastly, don't confuse other people's elecric Cri Cri aircraft with the one from Airbus, there were around four different electric Cri Cri aircraft. Let's not be limited to only electric Cri Cri aircraft, there are other good electric aircraft which seat two persons like the Pipistrel Wattsup. Good slow speed and high speed comparable to the electric Alpi Pioneer 300 but with a better range, 90 minutes of flight time with a reserve of 30 minutes and the aircraft weighs around 300kg. THAT is an efficient platform and I was simply surprised Airbus went the hard way rather than to learn from other people's experience first. Hopefully this explanation satisfies you and I wish you successful exploring of the world of electric propulsion.

https://www.youtube.com/watch?v=Mhm5IVB6gb4

=from 2:30=simple flapping thrusters can generate up to 2000 N thrust from 1 W !!! \dr Sorokodum,Moscow\.
Does that really look like being capable of 2kN of thrust..?
 

danmoser

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That's a big misconception? Your kind of knit picking a point don't you think? ALL energy on this planet is solar energy, all energy is created from the sun. Name a source of energy that is not.
Well, to continue my "nit picking" .. nuclear fission powerplants are generating power that is not indirect solar energy.. though the Uranium we find on Earth did come from other exploded stars, it didn't come from Sol.

My beef is with the "energy from gravity" nonsense previously spewed forth.
Call it nit-picking, if it makes you feel better to trivialize my point .. but it is 100% incorrect.
 

Topaz

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If we really want to be proper with the energy bookkeeping, since that's where this discussion is going, the aforementioned "slingshot" maneuver performed by some spacecraft on their way to the outer solar system isn't something that gets its energy from gravity, either. Gravity acts as the link that transfers a small amount of the planet's kinetic energy to the spacecraft. Every time a probe uses Jupiter to speed up, the planet actually slows in its orbit by an infinitesimally small amount.

Nothing is free. Everything is a transfer of energy from one place to another.
 

DangerZone

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If we really want to be proper with the energy bookkeeping, since that's where this discussion is going, the aforementioned "slingshot" maneuver performed by some spacecraft on their way to the outer solar system isn't something that gets its energy from gravity, either. Gravity acts as the link that transfers a small amount of the planet's kinetic energy to the spacecraft. Every time a probe uses Jupiter to speed up, the planet actually slows in its orbit by an infinitesimally small amount.

Nothing is free. Everything is a transfer of energy from one place to another.
Guys, thank you for clearing that up, I will chose my words better next time when writing here.
 

DangerZone

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=sorry=typeerror=

2kN of thrust force from 1kW power \NOT 1W!!!\=circa 40*helicopter rotor specific thrust...
Well that part was pretty obvious, the electric motor looks like some of those standard 1kW ones. However, there is scepticism about the surface size which should produce 2kN of thrust. Without an explanation there is no possibility to decipher the practical use of this and the real static thrust.
 

henryk

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Well that part was pretty obvious, the electric motor looks like some of those standard 1kW ones. However, there is scepticism about the surface size which should produce 2kN of thrust. Without an explanation there is no possibility to decipher the practical use of this and the real static thrust.
https://www.youtube.com/watch?v=Mhm5IVB6gb4

=2:30=controll boxes for 12 small flappers for 2kg flying soucer...
=5:55=big flapper thrusters for man flying trike \10:15\ with SOLO 210 engine...
 
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