“Be kind, for everyone you meet is fighting a hard battle” - Often attributed to Plato but likely from Ian McLaren (pseudonym of Reverend John Watson)

Monday, December 28, 2020

The Celera 500L

Image credit: Otto Aviation

As anyone who's spent any time reading my publications knows, I'm a pilot and have been involved (non-commercially) in aviation for over 40 years. As such, I keep track of developments in the field. Thus, I was fascinated by the news of the Celera 500L by Otto Aviation. The performance claims made for the airplane are spectacular, to say the least.

Otto claims that the aircraft has a range of 4,500 miles (statue rather than nautical as far as I can tell) at a speed of 460 m.p.h. (again, statute m.p.h., not knots, as far as I can tell). It's stated that the Celera 500L does so while burning "8 times lower fuel consumption" and "5-7 times reduction in operating cost." For those who don't follow general aviation (that is, all aviation other than air carriers and military), the claimed speed is well above the speeds of high end turboprop business aircraft and not far below those of business jets. For example, the King Air B360ER turboprop achieves 349 m.p.h. in high-speed cruise, the Cessna Latitude business jet has a maximum speed of 512 m.p.h. But the range of the King Air is 3,092 miles and that of the Longitude is 3,105 miles. Otto claims that the Celera 500L achieves 18 - 25 miles per gallon fuel economy. What might be considered a comparable small jet, the Embraer Phenom 300E will get, perhaps, 5 miles per gallon. 

Otto states that the Celera 500L achieves these spectacular specifications due to a design for laminar flow over both the wings and the fuselage. Laminar flow is a fluid flow state wherein there is minimal mixing between layers and the flow is "smooth" rather than turbulent. It is a flow regime that minimizes drag, and all (well, most) aircraft designers seek to maximize laminar flow. It is a well-known phenomenon and no aeronautical engineer looks at Celera's web site or the many web sites and YouTube channels featuring the Celera 500L and slaps him or herself on the forehead and says "laminar flow, why didn't I think of that?"
Image credit: RED Aircraft

 The engine for the Celera 500L is the "RED A03" by RED Aircraft, GmbH. This is a 
compression ignition (i.e., diesel) engine. The engine is stated to be a V12 configuration with each six cylinder side operating independently. It's also stated to be all-aluminum in construction. Per RED's website, the engine is approved by both the FAA and EASA (the European Union Aviation Safety Agency). While diesel engines are typically very efficient due to the high compression ratio required for combustion of the fuel-air mixture, they are also typically heavy as a consequence of the strength required due to that high compression ratio. I'm not aware of any other all-aluminum compression engines.

As can be seen in the photo above, the aircraft is a "pusher" configuration, the propeller is behind the aircraft and pushes the airplane rather than the standard configuration wherein the propeller(s) pulls the airplane. This configuration has the advantage of letting the wings "see" a flow undisturbed by prop wash. Of course, the propeller is composed of airfoils as well, and they now see air disturbed by the wings and the fuselage, though not nearly so much as the propeller causes, especially given the laminar flow claim. It's also the case that the propeller is more subject to damage from ice shed from the wings in icing conditions and, at the altitudes stated in Otto Aviation's material, icing is certainly possible.

With all of that said, what is the likelihood that Otto Aviation can live up to their claims for the Celera 500L? It's difficult to do a thorough analysis given that nearly 100% of the numbers given consist only of those claims. The only hard data I could find is the takeoff power of the engine. They do claim that drag has been reduced by approximately 59% in comparison to similar sized aircraft. What can we infer from this?

With thanks to "Simplex11" at aviation stack exchange for the approach, we'll use the "59% lower drag" claim along with figures for my airplane, a Cessa 441. My airplane cruises at about 345 m.p.h., using 450 horsepower per side in cruise, or a total of 900 horsepower. The Celera 500L cruises at 460 m.p.h. and a drag of 0.41 ("59% less") times that of a typical aircraft.

We then have that ~D1=\frac{1}{2}C_{D1}\rho S_{D1}V_{D1}^{2}~ and ~D2=\frac{1}{2}C_{D2}\rho S_{D2}V_{D2}^{2}~, where ~D1~ is the total drag on the Celera 500L and D2 is the total drag on the C441. The Cs, Ss, and Vs are the drag coefficients, reference areas, and velocities of the Celera 500L and the C441 respectively, and ~\rho~ is air density. We can then combine these to get ~\frac{D1}{D2}=0.41(\frac{V1}{V2})^{2}~. Then, we know that power is speed times force, so we have ~P1=D1V1~ and ~P2=D1V2~ and so ~\frac{P1}{P2}=0.41(\frac{V1}{V2})^{3}~. Plugging in numbers, we can calculate that the Celera 500L needs something like 875 horsepower* to achieve the claimed speed. These numbers are, of course, approximate, but note that the maximum continuous power of the RED A03 is 460. And, as a reminder, this assumes that the "59% reduction in drag" is true.

What about fuel economy? Otto claims "18 - 25 m.p.g." (again, as above, I assume statute miles). The fuel economy can be calculated from the speed, power, and energy density of Jet-A fuel. Should the hordes demand that I show my work, I'll show the calculations but, having already produced an equation dense post, I'll just give results. And, as above, these are approximations based on sparse information. If the power requirement calculated above is correct, the Celera 500L would achieve something like 11.5 m.p.g. If, on the other hand, the speed of 460 m.p.h. can be achieved with the 460 maximum continuous power of the RED A03 engine then a figure of about 21.8 m.p.g. could be achieved. But, as I indicate above, it does not seem plausible to travel at 460 m.p.h. with less than 875 horsepower. And, yet again, all of this is contingent on the Celera 500L achieving the claimed 59% drag reduction. Time will likely tell.

Further questions are raised by Otto's claim that "The Celera 500L has a glide ratio of 22:1 (typical GA aircraft of similar size have a glide ratio of < 9:1)." While I can't question the 22:1, the "<9:1" claim is absolutely false. My airplane has a glide ratio of 14.8:1. Many business aircraft do better. Possibly such airplanes as the Cessna 172 Skyhawk (a four seat, fixed gear airplane with wing struts) may have glide ratios in the range mentioned by Otto, but no light jets or turboprops do. When falsehoods are stated as facts on web sites, I have to question all of the information to be found there.

And finally, in the immortal words of Carl Sagan, "extraordinary claims require extraordinary evidence." Otto Aviation's claims for the performance specifications of the Celera 500L are, without a doubt, extraordinary and I've seen no evidence, let alone extraordinary evidence.

Otto Aviation has completed their A round of financing. They anticipate B round financing in 2021 and 2022, during which they plan to begin FAA certification. In 2023 to 2025, their web site calls for C round financing and the beginning of manufacturing and first commercial deliveries. Based on my strong skepticism, I'm not a participant in Otto's financing!

*It should be noted that Simplex11's calculations are slightly different and yield a larger power requirement for the Celera 500L.

Saturday, January 18, 2020

More on Eviation Alice

Image credit: Jasper Juinen/Bloomberg
I published a post on the "Alice," a fully electrically powered airplane being designed and built by the Israeli Company "Eviation." The Alice is being promoted as a "9+2" airplane, that is, two pilots flying nine passengers. It is claimed that the airplane will have a range of 650 miles at a speed of 260 knots. Cape Air had made a "double digit" (actual quantity not stated that I can find) order (the "launch order") for the Alice. I expressed considerable skepticism, particularly with respect to the battery pack and to the claimed range.
Image credit: Eviation

The latest news is that two more airlines have placed orders for the Alice, bringing the total ordered to over 150. So three airlines have made substantial orders and several well-known OEM vendors (Honeywell, Bendix, Siemens, Hartzell) are providing equipment for the airplane. Is my skepticism unwarranted?

In my previous post, because the parameters needed for a direct calculation were not given anywhere that I could find, I got my estimate for the range by comparing the energy stated for the battery pack in the Alice to the energy in the Jet A fuel in a Pilatus PC-12. The number I came up with was 258 miles, far short of the claimed 650 and likely a deal breaker for the orders. Can I derail a multi-million dollar endeavor by back of the envelope calculations on an obscure blog?

There are two factors contributing to my vagueness on the range calculations: actual energy available in the battery pack; and the drag force on the airplane in flight. A rudimentary dimensional analysis show that the range is directly proportional to energy available and inversely proportional to drag, that is, ~R\propto\frac{E}{F_{d}}~, where R is range, E is total energy available, and Fd is the drag force. This, of course, makes intuitive sense but, at the moment, I don't know the proportionality constant.

Eviation claims a capacity of 900 kWh in the battery pack, though it's not at all clear how this can be accomplished. Eviation states that they use Li-Ion chemistry and also make a claim for a proprietary aluminum-air chemistry. I don't see how the aluminum-air chemistry can be feasible in an airplane, but who knows? Per the Wikipedia page for the Alice, the aluminum-air battery will be used on a later evolution of the Alice.

But, for Li-Ion chemistry, the current state of the art is about 260 watt hours/kilogram. At this energy density, 900 kWh would require 3,460 kg, or a bit under 7,630 pounds. At a maximum takeoff weight of 6,350 kg, this leaves 2,890 kg or 6,371 pounds for airframe, power plants, passengers, pilots, and baggage. Again, I don't have any data on the weights of the airframe and power plants. And, in my effort to be generous, the 260 watt hours/kilogram doesn't include the pack.

As to drag, I found a site that stated that the "L/D" (lift to drag) ratio of the Alice to be 24. This is likely to be the maximum L/d. Now, in cruise flight, lift is equal to weight. We'll assume a full load, giving a weight of 6,350 kg or 62,230 Nt. With a L/D ratio of at a maximum of 24, drag would be at least 2,593 Nt. Clearly, this is generous to Alice but we'll use it. Now, drag=thrust in straight and level flight, so we're looking at a thrust delivered by the propeller of 2,593 Nt. And P=F*V where P is power, F is force (thrust) and V is speed. So we have P=2,593 Nt * 134 m/s (260 knots converted to meters/second) = 346,817 watts or 347 kilowatts required in cruise.

Now, a constant speed propeller may be about 90% efficient, so the electric motors must deliver 347/.9 = 385 kilowatts. We have 900 kilowatt hours available so that's 900 kWh/385 kW = 2.34 hours. IFR (instrument flight rules) flight requires a minimum 45 minute (0.75 hour) reserve (we'll hold it to the minimum though I doubt a procedures manual for an air carrier operator would do so, and my policy is to never fly into my last hour of fuel) so we now have 1.59 hours or an hour and 35 minutes of battery capacity for cruise. Note: the specifications page for the Alice has been updated since my earlier post and gives some numbers that aren't too far off of mine, but I'm sticking with mine because they're derived from Eviation's performance claims.

I'm ignoring climb and this is generous because more power is used in climb (though that may not be the case for an electric airplane) and is at a slower speed (in all airplanes). So we can cruise at 260 knots for an hour and 35 minutes for a range estimate of 413 nautical miles or 475 statute miles. And, given the minimal reserve and ignoring climbing at low speed, this is generous.

I will agree that my rough calculations result in a range estimate higher than that I got using the Pilatus comparison, but it's significantly less than the 650 miles claimed by Eviation (I can't determine whether this is nautical or statute miles).

And this might be practical for a flight from, say, John Wayne Airport in Orange County to Las Vegas McCarran International, a distance of 226 (statute) miles, or Kennedy to Dulles, a distance of 228 (statute) miles. You wouldn't want to fly it to Reagan Airport because flight to
or from Reagan requires an air marshall and now you've lost 11% of your paying passenger capacity. There are many such city pairs. At right are 300 statute mile radius circles centered on New York City, Chicago, Houston, and Los Angeles. Such city pairs  as NYC - Philadelphia, Chicago - Detroit, Houston - Dallas, and Los Angeles - Las Vegas seem to be feasible.

And the economics seem favorable. 900 kWh of electricity probably would cost something on the order of $100, and a crew of two might be $100/hour. Maintenance on electric motors is much less demanding than on turbine or piston internal combustion engines.

So, taking everything into consideration, and if the data that's been provided so far is accurate, I think there may be a role for such an airplane.

Friday, October 18, 2019

Am I safe to break in?

I saw a commercial for the Google Home Speaker in which the spokesperson was touting the speaker's ability to scare off burglars by playing the sound of a barking dog. I realize there are multiple systems out there to achieve this but that's not my point. I started thinking about this in terms of Bayesian inference. If I'm a burglar and, during an attempted intrusion, I hear the sound of a vicious dog, what's the likelihood that there's actually a dog ready to attack?

This is analogous to the archetypal example of Bayesian inference wherein the likelihood of actual breast cancer is evaluated in light of a positive mammogram ("test"). The "test" in this case would be listening for the sound of a barking dog prior to breaking into a home. A true positive would be hearing a barking dog when there is such a dog (analogous to a positive mammogram and actual breast cancer). A false positive would be hearing a barking dog when none exists, i.e., when the Home Speaker sounds a dog alarm but there is no dog.

In order to come up with an estimate of my safety when breaking in should I hear a barking dog, I need to have an estimate for:

  • The fraction of homes have appropriate (i.e., big and scary) dogs (analogous to how many women have breast cancer).
  • The fraction of homes have a barking dog sound generator (analogous to a false positive).
  • The fraction of the time that, if there is a big, scary dog in the house, it will bark and I will hear it (analogous to a true positive).
I'll estimate that 40% (0.4 fraction) of homes have a dog, and 30% of those are of a size that would deter me. I'll estimate that 2% (0.02 fraction) of homes have a dog sound generator. I'll estimate that 90% (0.9 fraction) that I case a home with an appropriate dog, that dog will bark and I will hear it.

In the table below, I've shown that 12% of homes have a big (barking) dog, and 88% do not. When I hear a big, scary dog, I'm in the "Test pos" row. The 0.108 entry is the 0.12 fraction of homes with a big, scary dog * the 0.9 fraction that the dog will bark and I will hear it. The 0.0176 entry is the 0.88 fraction of homes with no big, scary dog * the 0.02 fraction of homes with a barking dog sound generator.

Actual big dog No actual big dog
0.12 0.88
Test pos (heard barking big dog) 0.108 0.0176
Test neg (didn't hear barking big dog) 0.012 0.8624

Now, the probability of a true positive (I hear a big, scary dog and there's actually one in the house) is the number of true positives divided by the total number of positives, or 0.108/(0.108+0.0176)=0.8599 or about 86%. Of course, this number will vary, depending on the actual values for the needed parameters but I think that this is in the ballpark.

Moral of the story: If I'm intending to burgle a house and I hear a big, scary dog, I'd best move on.

Saturday, August 10, 2019

Solar energy is GREAT but...

Image credit: 4Patriots, LLC
As is pretty clear from previous posts (and despite my current vehicle, airplane, and travel itinerary), I'm a very big fan of renewable energy. And thus, also a fan of solar power. But sometimes solar isn't appropriate for a particular application. To the left is a collage from 4Patriots, LLC, let's see if this device is in the "inappropriate" category.

This is a charger for such electronics as cell phones, tablets, etc. Is this an appropriate application? Lithium ion battery in the device is specified on the advertising web site as storing 8,000 mAh (milliamp hours) or 8 amp hours. The solar array is specified as delivering 1.5 watts.

Let's first see if the 1.5 watts is reasonable. To do so, we'll need to estimate the size. Using the measuring tool in Tracker Video Analysis and Modeling Tool, I estimate that there is an area of about 0.0068 m^2 of solar cells. This is actually generous as I've used to whole area of the face of the charger with the cells. And, during bright sunlight at my location if I hold the device facing the sun I can count on about 350 w/m^2 over the course of a day of actual insolation. Let's give the solar cells an estimated efficiency of 18% (again, generous) and figure the charging can take place at the rate of 350*.18*0.0068=0.42 watts. Well, if we use a full 1000 watts/m^2, we get 1.22 watts. I'd say that the 1.5 specification is an exaggeration at best.

Well, let's go with the 1.2 as a compromise between the 1.5 watts claimed and the 0.42 watts by my best estimate. And let's think about an iPhone 8, standard model. Such a phone has a battery capacity of 1.821 amp hours at 3.7 volts. This means it will deliver 1.821 amps at 3.7 volts for 1 hour, or 3,600 seconds. Since volts * amps is watts, we have 6.7377 watts. Since joules of energy are the same as watt seconds, we can use 3,600 seconds * 6.7377 watts to determine that the iPhone 8 battery stores 24,256 joules. Charging at 1.2 watts, or 1.22 joules/second, we find that it will take 24,256 joules/1.2 watts = 20,213 seconds or 5.6 hours to go from complete discharge to full charge.

Of course, if you're in the middle of nowhere with no other way to charge your phone and you're completely discharged, you won't need to wait for 100% charge to use your phone. Below is a graph of time needed as a percentage of charge from complete discharge. You can click on it to enlarge. Keep in mind that this is specific to the iPhone 8, other phones with different (and typically larger) batteries will be different. The new Samsung Galaxy Note 10+, for example, will carry a 4,300 mAh battery pack, well over twice as large as that in the iPhone 8, and the Apple iPhone XS Max sports a 3,174 mAh battery pack. And, of course, charging is a non-linear process so don't use this as a "to the minute" guide. It's more of a very best case scenario.

Still, this is actually a lot better than I'd anticipated when I started. It would take about an hour to go from complete discharge to 20%, certainly enough to make a few calls or send some texts. Of course it assumes perfect efficiency in the charger circuit but the efficiency is likely to be fairly high. Even if we use the low end estimate for the area of the solar array, the device will still give usable energy in a not too extreme amount of time, though if we use the more conservative estimates for insolation and charging on a state of the art, top of the line phone, we'd be looking at something more like 7 hours to go from complete discharge to 20%. Nevertheless, unlike the two previously published posts I linked above, this seems to be a good use of a small solar panel.

Tuesday, August 06, 2019

Energy Vault Revisited

Image credit: Energy Vault
Two posts back I discussed Energy Vault, a "Swiss-U.S." company whose concept for energy storage is based on the use of tower cranes to  stack concrete blocks. The blocks would be raised with electric motors to store gravitational potential energy when energy is either plentiful or cheap  and lowered, turning generators, when energy is expensive (arbitrage) or unavailable from renewable sources.

I subscribe to a YouTube channel from a British chemist, Dr. Philip Mason, who calls himself
Image credit: drunken-peasants-podcast.wikia.com
"Thunderf00t" and, when he's not criticizing modern feminism or proselytizing for atheism, he "debunks" various concepts. Among several others have been Hyperloop (the linked video is one of several he's done on this topic), Solar Roadways (again, one of many videos he's done on this topic and a topic I've covered), and the Water Seer. His videos tend to be long, repetitive, and repetitive (see what I did there?) but, typically, are convincing.

Most recently, Thunderf00t targeted Energy Vault, concluding that it's a scam meant only to collect investor money. I'll summarize his points as I understand them and then state my reaction. Per Thunderf00t:
  • No working installation yet exists, the pilot project (video here) shown in various places does not come close to demonstrating the viability of such a system and, other than that pilot, there's nothing but CGI animation.
  • Such a scheme will not be effective in windy areas due to inability to control the precise placement of the concrete blocks and the inherent problems with cranes in wind.
  • The cost would be excessive in comparison with alternative gravitational storage systems (specifically, pumped hydro storage).
  • The system could not have the lifespan claimed due to its environmental exposure, intrinsic wear, fatigue, etc., especially in areas where sun and wind for renewable energy generation are plentiful, such as deserts.
  • The configuration envisioned by Energy Vault is not optimized to maximize the storage of potential energy because of the way the blocks are stacked.
It takes Thunderf00t 24 minutes to make these points. He repeatedly contrasts the Energy Vault system with pumped hydro storage systems in terms of both cost and of capacity. He glibly glosses over the fact that the geographic/geological situation that is optimal for such a system severely limits feasible locations. And, it should be noted, I agree completely that pumped hydro storage is a superb option where geography and environmental considerations permit. Unfortunately, there are not a lot of such locations.

Another point misunderstood by Thunderf00t is the of the claimed ability of the Energy Vault system to quickly "ramp up," in 2.9 seconds to full power according to Energy Vault. Thunderf00t posited that utilities aren't in need of such a quick ramp up, but this isn't correct. Utilities utilize a variety of systems to provide reliable power, from frequency response, to spinning reserve, to peaking, to base load in order of increasing ramp up times from less than a second through several hours. Thunder00t seems to be thinking only of peaking or base load. For application to supplying energy from solar or wind plants when "the sun doesn't shine and the wind doesn't blow" this analysis would be correct but this is undoubtedly not the only potential application envisioned by Energy Vault.

In any case, addressing the points above:
  • It's clearly true that no working demonstration at scale yet exists. However, the technology of lifting concrete with tower cranes is quite standard. I could go out to one of my company's projects tomorrow and watch such a thing happen. As mentioned in my earlier post (and as Thunderf00t mentioned repeatedly), the IP claimed by Energy vault isn't tower cranes or concrete, it's the software that controls the crane movements so as to maximize storage and production and precisely place the blocks even during windy conditions. The fact is that every innovation starts out as an idea with no working model at scale. Time (and investment) will tell if the concept is viable.
  • Thunderf00t only addresses the proposed use of the system for storage of wind generated electricity, presumably because that's what's shown in the renderings on Energy Vault's web site. Of course, the system would be equally suitable (if it works at all) for solar sites. But, as mentioned above, Energy Vault claims that their control software will enable the system to operate in windy conditions. Many tower cranes have a maximum wind speed limit of 20 meters/second or 44.7 m.p.h. Thunderf00t has pulled up a web site that appears to refer to a specific crane model that limits wind speed to 10 meters/second (he converts this to 30 m.p.h. though it's actually about 22 m.p.h.) but, even in the page he shows, it's stated that "typical values vary from 9 to 20 m/s." I'll concede that I'd need to see the control system operating in a 20 m/s wind though.
  • In his cost estimate, Thunderf00t states that "a tonne (here I assume he means a metric ton, 1000 kg. or 2,205 pounds) of concrete costs about $100." I don't know what it costs in Great Britain or the Czech Republic (where I believe he's working) but in the U.S. a pretty basic concrete mix costs around $100/yd^3 and that cubic yard weighs about 4,050 pounds or 1.84 tonnes. So Thunderf00t's tonne of concrete costs about $54. Later in the video, he does come down to a number near this. As I mentioned, he compares the cost to pumped hydro, but the locations shown in the renderings have no suitable geography. Given the need for storage, if pumped hydro were suitable everywhere, we'd see more of it. Thunderf00t mentions that the vast majority of energy storage IS pumped hydro but that's because there's so little storage!
  • With respect to duration, I concede that I also see serious problems. Energy Vault mentions a 30 year lifetime but does not mention maintenance! As Thunderf00t states, tower cranes consist of a massive collection of moving parts, many of which will be under significant stress and subject to cyclic loading. It's a recipe for all manner of mechanical failure.
  • As to optimizing stacking, it's very clear that it would be better to have all the blocks be able to go from ground to top and back to ground as Thunderf00t helpfully demonstrates with children's blocks on a table but the logistics of the system won't allow that. The question isn't whether some other configuration would be better but rather what is the best configuration that can be achieved.
When all is said and done (and, as the wag said, when all is said and done, much more is said than done), there are many reasons to question the feasibility of such a system and, before I'd invest my money in the venture, I'd need more than is shown on the web site. But Cemex Ventures has invested in Energy Vault. Cemex Ventures is the venture arm of Cemex, a large producer of cement, concrete and other building materials. The size of the investment is not stated.

I've covered a number of non-electrochemical (that is, other than batteries) storage companies and modalities in this blog, some seemingly credible and some seemingly ridiculous. This one seems to be somewhere in the middle. I'm not as certain as Thunderf00t and his commenters that it's a scam but I'm not ready to sink my nest egg into it!

Update: Energy Vault has received a $110 million investment from the SoftBank Vision Fund. Of course, the Vision Fund has been in the news a LOT lately and not in a good way, having had to bail out We Work and losing money from the IPO of Uber.

Sunday, July 14, 2019

Eviation Alice

Image Credit: Eviation
As I've mentioned in quite a few previous posts, I'm a pilot by avocation and a dedicated follower of all things aviation. My YouTube feed recently decided that I'd be interested in the Eviation Alice, an all-electric airplane currently being developed by Eviation Aircraft, an Israeli company.

On my first time through the video, I was quite skeptical. The performance claims seemed to be outside of the range of current or near future technology (see below). 

Image Credit: Eviation
As is well-known, the specific energy (energy/mass) of chemical batteries is far below that of aviation fuel and so my first thought was that a 900 kWh battery pack would make the airplane far too heavy to carry any significant payload. However, Eviation claims to have achieved a specific energy "surpassing the 400 Wh/kg mark." This is quite an achievement if true. Such a battery pack would weigh (using 400 Wh/kg and ignoring "surpassed") 2,250 kg., or 4,960 pounds.

On the other hand, Eviation also states that the battery is 65% of the airplanes weight. Let's work back. They state it's a 9+2 airplane, i.e., 9 passengers, 2 pilots. There is no fuel. A standard FAA adult weighs 170 pounds, we'll add a few for (ahem) girth growth and baggage, call it 185 pounds. 11*185 = 2,035 pounds or 923 kg. The maximum gross weight is shown as 6,350 kg. We subtract the payload and get 5,427 kg in airframe and power plant weight. Eviation states that the batteries comprise 65% of the aircraft's weight, yielding (an approximation, of course) an implied battery weight of 3,528 kg.
Image Credit: Eviation

In any case, current lithium ion technology achieves specific energies on the order of 250 wH/kg, but aluminum-air batteries can achieve much higher specific energies. Eviation states on their site (from which the graphic at right is copied) that they have a proprietary aluminum-air system in addition to (?) their lithium ion batteries. However, naive as I am, I don't see how this is feasible, given the fact that in an aluminum-air battery, the aluminum anode is consumed in the oxidation half-reaction. The electrode can be reprocessed, but this is hardly the same as plugging into a charging system! Until I know more about the proprietary system, my skepticism is intact.

But lets suppose that Eviation has conquered this issue and can achieve 400 wH/kg in a practical system. As mentioned, they state that the airplane is a 9+2 configuration (9 passengers and two pilots). The usual tradeoff of fuel for payload with which I deal (and which is a consideration for all fossil fuel powered aircraft) is not a factor here. But we have (at least, depending on which of Eviation's numbers we use) 2,250 kg of batteries and 923 kg of passengers and miscellaneous for a total of at least 3,173 kg and probably more. From the maximum gross weight, this leaves 6,350-3,173 = 3,177 kg for the airframe and power plant.

The YouTube video states that the current prototype uses three Siemens 260 kW electric motors. The best information I can find gives a weight of 50 kg for these motors, so the total is 150 kg. We're down to 3,027 kg for the rest of the aircraft - avionics, fuselage, wings, empannage, propellers, interior furnishings, and miscellaneous. And recall that this is the absolute maximum possible weight in that it assumes the absolute minimum battery weight. With more conservative (not to say plausible!) assumptions for battery specific energy something like 1,830 kg would be the maximum. It's stated that the aircraft is all composite, I'll say it had better be!

All in all, given the contradictory and confusing information on the web site and the weight considerations outlined above, I find it very hard to be anything but skeptical, though I wouldn't go so far (at this point) as to call it a fraud. According to the YouTube video, Cape Air made a double digit "launch order" (airline industry terminology for the first purchaser of a new model). With  such an order and with Honeywell (fly by wire controlls), Bendix (avionics), Siemens (motors), Hartzell (propellers) and others signed on to supply components, there seems to be at least some level of confidence. And Eviation is expecting type certification in 24 to 30 months for the unpressurized version. But I wouldn't book a seat just yet.

What about aerodynamic calculations? None of the key parameters are given to calculate from first principles, so I'll use comparisons to known aircraft. Proceeding in this manner, 260 kW is 349 horsepower (call it 350) so the total power available is 1,050 horsepower and the cruise airspeed is listed as 240 knots. The Pilatus PC-12 uses a Pratt and Whitney PT6A-67P gas turbine engine flat rated to 1,200 horsepower and cruises at 280 knots. The maximum takeoff weight of the PC-12 is 4,740 kg. So, on its face, it would appear that the Alice has sufficient power to produce the listed speed.

How about range? Here we have the statement that the range of the Alice is 650 miles (statute I assume). Again, using the Pilatus PC-12 as a measuring stick, that airplane has a normal range of 1,646 statute miles. It has a fuel capacity of 403 gallons and, if we assume 40% efficiency of the gas turbine engine and use 131 megajoules/gallon, the engine delivers 2.111*10^10 joules or 5,866 kilowatt hours to the propeller to go 1,646 miles. The Alice has a battery capacity of 920 "usable kilowatt hours" (yes, different than 900 used above, but the statements from Eviation are widely variable depending on which interview or site I look at). Then, if we take (920 kWH/5,866 kWH)*1,646 mi., we can estimate that the Alice should have a range of 258 miles. It's implausible that the Alice has an aerodynamic efficiency of over twice that of the PC-12 so, again, I'm very skeptical.

Eviation states that the Alice on display at the recent Paris Air Show is a flying prototype and they are only awaiting FAA approval to begin flight tests. They state that they expect to fly later this year. Given the lack of consistency of their claims and the rough estimates above, I'll await the results. But, despite the apparent confidence of the very reputable OEM suppliers listed above, I'm putting this in my "I'll believe it when I see it" file.

Saturday, June 22, 2019

Energy Vault: A mashup of two of my interests

Image Credit: Energy Vault
My occupation is as an executive in a firm that provides materials testing, inspection, consulting, and engineering in the construction space. We deal with all aspects of the built environment with the exception of single family housing. As such, concrete is a fundamental area of my firm's expertise. And, as is clear, energy in all its aspects is a personal interest, not to say obsession, of mine. Finally, as I've elaborated in multiple posts, to bring renewable energy to the level of being able to provide base load power, I contend that relatively inexpensive energy storage will be needed.

Energy comes, basically, in two forms: kinetic; and potential. And while storage via kinetic energy is possible (think flywheels and thermal storage), most forms of storage utilize potential energy. Batteries utilize chemical potential energy, compressed air energy storage utilizes mechanical energy, etc. And finally, gravitational potential energy is utilized in various systems. In fact, most grid scale storage currently in place uses pumped hydro storage.

But any system of raising a mass against the force of gravity has the potential (get it?) to be used for storage. And a Swiss firm called Energy Vault has constructed a prototype of a storage solution using concrete lifted by tower cranes. It's clear that the technology for producing concrete is not new, and tower cranes are ubiquitous in the developed world. The innovation claimed by Energy Vault lies in the software to efficiently determine crane movements to optimize storage of excess energy and to deliver energy when needed.

In a previous set of posts (the last one is here), I estimated that a 3 MW nameplate capacity wind turbine combined with 40 MWh of storage could reliably provide 725 kW of base load power. What would 40 MWh of storage look like with the Energy Vault system? Energy Vault's web site states that an operational plant would have the capacity to store "between 10 and 35 MWh" of electrical energy and be able to deliver that energy at a rate of from 2 to 5 MW. Based on this claim, perhaps two such plants would be sufficient to provide storage for our hypothetical 735 kW plant and would be able to deliver the energy at the needed rate.

So as not to subject my readers to endless calculations, suffice it to say that the energy stored by lifting a mass against gravity is simply the product of the mass of the object lifted, the height to which it is lifted, and the local gravitational acceleration constant. Let's say we'll settle for two storage plants, each with a capacity of 20 MWh. For calculating purposes, we need to convert 20 MWh to the 7.2*10^10 J (joules, the SI unit of energy). 

We have two "knobs" that we can control to determine how much energy is stored in a storage system of the nature of that of Energy Vault. We can control the height to which our masses are lifted and we can control the amount of mass. And (net of losses), energy stored by lifting a mass against gravity is E=mgh, where E is the energy, m is the mass, g is the acceleration of gravity, and h is height. However, for the purposes of the physical logistics of our plant, we're really concerned about the volume of concrete so we'll use m=ρ*v where ρ is density and v is volume. This yields E=ρvgh. To isolate the knobs we can control, a little algebra yields E/(ρg)=vh. Concrete is typically quoted as having a density of 2,400 kg/m^3, g is 9.8m/s^2 and we need 7.2*10^10 J. Plugging these in, we see that we need v*h=7.2*10^10/(9.8*2,300)=3.06*10^6. This is the required product of height in meters times volume in meters^3.

In order to determine the feasibility we need to understand what an actual installation might look like, and Energy Vault helpfully includes an animated video of a hypothetical production facility.

While there's not a lot of information on the Energy Vault site with respect to tower height, plant radius, etc., Quartz has a writeup on the system that states that a tower would be on the order of 120 meters tall and the diameter of the installation would be around 100 meters. For our 40 MWh system, we need two of these.

It's also stated that each concrete block weighs about 35 metric tons (35,000 kg) and so the volume of each block would be 35,000/2,400 = 14.6m^3. Judging from the video, the concrete height is about 100 meters, and clearly it's not possible to have each block raised from the ground to 100 meters and lowered back to the ground, the blocks have to be stacked. I'd assume that it would be possible to have the average of the lift and drop to be 50 meters.

Does all of this make sense in comparison to the numbers from the earlier paragraph? We need height times volume to be 3.06*10^6 m^4. This means that we need about 3.06*10^6/50 = 61,200 m^3 of concrete. The video shows the beginning configuration to be basically a cylinder of concrete about 100 meters tall and a radius of, I estimate, 13 meters. This yields a volume of about 53,000m^3. This is not too bad, given the accuracy of estimates for height, radius, etc.

Now, in the U.S., we typically measure concrete volume in cubic yards, where a cubic meter is 1.308 cubic yards, so we're talking about a little over 80,000 yd^3 of concrete. Right now, a cubic yard of generic concrete costs around $80/yd^3 so the concrete cost alone (not counting concrete for the foundation) would be on the order of $6.4MM. However, Energy Vault claims to have developed the capability to use discarded materials as aggregate. Further, the concrete really needs very little compressive strength and so the cement requirement could be very low. Let's generously cut the $6.4MM by two thirds and call it $2.13MM. So we see that the concrete cost might be on the order of $2.13MM/20MWh = $156,500/MWh or $156.50/kWh. This is similar to the current cost of a lithium ion battery storage but doesn't include the cranes, the foundation, the construction, the control system, or the power electronics. To be fair, Li ion storage costs also are higher than strictly the battery costs.

Among the advantages of the Energy Vault solution are: negligible degradation of capacity over time; no use of rare elements; no toxic chemicals; no danger of thermal runaway. Is this the answer for turning our 3MW wind turbine into a reliable 725kW base load energy system? Well... as in so many things, it boils down to economics. I'll cover that in a future post at some yet to be determined future time.