“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)

Tuesday, March 31, 2009

Horsepower, fuel efficiency, and thermodynamic efficiciency

I received a comment to my post on the Moller Skycar Volantor suggesting that I "look up the Wankel rotary engine (Mazda RX8) - 1.3L = 200+ HP." I'm not completely sure what the commenter was getting at, but I think he or she was saying that it's possible to get the power claimed by Moller in a package of the type he claims to have it in. Let me be clear (quoting our President): I agree. There's no question in my mind that that's possible. I didn't discount that possibility in my post.

What I did say isn't possible is to develop that amount of power and still achieve 20 miles per gallon of fuel at the speed claimed. That is, the combination of airspeed, fuel economy, and engine power claimed is not realistic. I'd like to delve into this in a little more detail. An internal combustion engine works by taking some combustible fuel into an enclosed space and igniting it. This results in a large temperature rise, and the consequent increase in pressure is used to push down a piston, turn a rotor, or turn a turbine thus converting the potential energy in the chemical bonds of the fuel into mechanical energy and using it to do work.

Any given fuel has a fixed amount of energy available for release by oxidation for any given mass, volume, or number of "moles" of substance. In a perfect world, unencumbered by the second law of thermodynamics, we could harness 100% of this energy to do useful work. Even in such a perfect world, no more could be had. And once the time over which this chemical potential energy is converted by oxidation into internal energy or "heat" is noted, we can divide the energy in the quantity of fuel (energy available is the same as work that can be done) by the time, we have work divided by time, or power.

For example, my Piper Saratoga PA32R-301T will burn about 18 gallons of fuel per hour to go about 170 knots. A "knot" is one nautical mile per hour, and a nautical mile is 6080 feet or about 1.152 statute miles. So, the plane burns 18 gallons in an hour to go 170*1.152 or 195.6 miles. Thus it's achieving 10.9 m.p.g., but more to the point of this post, it's burning 18 gallons per hour. There are a variety of sites with somewhat differing values for the energy density of the 100LL avgas I burn in the Saratoga (see here and here for example) so I'll use an average of 32.6 megajoules/liter or 123.4 (easy to remember) megajoules/gallon.

So, I'm releasing 18*123.4 megajoules/hour of chemical potential energy. Since an hour is 3600 seconds that's 18*123.4/3600 megajoules per second or 617,000 joules per second. By definition, a joule/second is a watt so this is 617 kilowatts or 827 horsepower. This is interesting, my pilot's operating handbook says that the power setting producing this fuel flow is 70% of the 300 maximum continuous horsepower available, or 210 horsepower. Thus, I'm using (210/827)*100% or 25.4% of the heat released by burning the avgas. This is pretty close to the type of efficiency we've come to expect of internal combustion engines in typical applications.

The maximum possible efficiency allowed by the laws of thermodynamics for a "heat engine" was determined in the 19th Century beginning with the work of Sadi Carnot and is determined solely by the temperature of the working fluid (fuel/air mixture as it oxidizes in this case) and the cold reservoir (the atmosphere) and for reasonable temperatures, as stated in my post on the Moller Skycar, is about 82%. For a working internal combustion engine, the maximum efficiency is related to the compression ratio and, for a typical compression ratio of 10.5:1, works out to be about 61%. Various factors involving friction, the operating points of the engine, inefficiencies in the fuel delivery and exhaust, and many other factors cause the actual efficiency to be as low as it is. These considerations apply equally to the Wankel or rotary engines in the Moller Skycar.

But, if the rate of fuel burn in volume/time and the type of fuel are known (or can be calculated) then the maximum available power can be calculated. An estimate of engine efficiency can then give the power available to turn wheels, turn a propellor, turn a ducted fan, etc. This is what I did in the Moller Skycar post, using the miles per hour divided by miles per gallon to give gallons per hour and thus the heat energy available. This enabled me to demonstrate that the claims made by Moller for the Skycar are not feasible.


Anonymous said...

Good commentary regarding the Skycar.

I’ve never doubted that something that flies that way the Skycar is supposed to do could be flown and built. The Bell X-22A is proof that there’s nothing aerodynamically wrong with the concept. My concern has always been about other things:

1) Moller’s product is like a practical fusion reactor – It’s always just over the horizon (and has been for more than thirty years), but it never seems to get any closer). They seem to be very good at getting their craft featured prominently in magazines, and on the internet, but they never seem to do any actual test flying with it. (Note to Moller and Co. – those videos of the unmanned tethered test from 2003 are getting boring!).

2) The Skycar’s engines, and the claims made for them. You’ve addressed the concerns about energy content, fuel economy and range far more eloquently than I could, and generated hard numbers to back up the bad gut feelings I’ve had these for a long time. Another concern on this score – Moller claims that the Wankel engines that will power the Skycar are high performance, highly tuned engines designed to have an extremely high power: weight ratio. And yet, at other times they have made claims about how these high performance engines will work easily on a wide range of fuels. From my experience, these claims are contradictory – highly tuned, high performance engines usually require very specific fuels, while engines that can work on a wider range of fuels usually are compromised in performance as a result. At very least, these claims raise a red flag.

3) Assuming that it’s possible to build something like this and it does become a widely used form of transport – how do you keep thousands of people flying (and likely using cell phones, texting, etc. at the same time, like contemporary drivers) in the same airspace at the same time from colliding with each other? They have talked vaguely about completely automatic systems (both for piloting the craft, and for air traffic control), but it’s difficult to determine how realistic they are, on a craft that’s never flown untethered.

In summation – I’m prepared to believe that a craft that flies like the Moller Skycar could be built. But the claims made with regard to range can be shown to be total fiction. Based on this, all the other claims are suspect too – I can’t help thinking that some of the predicted performance numbers are based on what people would like to read, rather than on what’s actually practical. Until Moller can fly a Skycar from takeoff to hover to forward flight, and then back to hover and a normal landing (with something close to the proposed payload on board), their claims can’t be taken very seriously.

King of the Road said...

Thanks for the very thoughtful comment. I agree that the issues with the performance claims for the engines are only the start of the the areas for skepticism. His ultimate vision of pulling out of the garage and automatically taking off into an automated computerized network that whisks the craft to its destination is quite far-fetched as well. And you're quite right - Moller's tendency toward demonstrably impossible claims detracts from any credibility of his Company.

It's also a valid point regarding the fuels and the power to weight ratio, though I'm no expert on internal combustion engines.

All that said, I also agree that a craft that will take off vertically and achieve the speed stated for the Skycar violates no laws of thermo- or aero- dynamics.

Anonymous said...

I’m not an engine expert either, but I used to work in fuels refining and fuels R & D for a major oil company, so I do have some background in fuels and engine testing. I’m also an aviation historian with an interest in engines.

If it were possible to build something that can do all the wonderful things that Moller claims the Skycar will be able to do, I'd be first in line to buy one -- It would indeed be a revolution in transportation. But, to quote Carl Sagan: "Extraordinary claims require extraordinary evidence". And so far, there's next to no supporting evidence for this extraordinary claim.

Anonymous said...

One concern that I have is about the rotary engines durability and the maintenance required relative to the piston engine. Can anybody comment on that?

Anonymous said...

This discussion has actually been referenced on the Moller International blog page, and they have claimed that some of the assumptions made here are invalid. See http://www.moller.com/index.php?option=com_content&view=article&id=136:welcome-to-the-moller-blog&catid=37:blog&Itemid=108#JOSC_TOP , the entry dated July 20th by "A long time skeptic".

Anyway, they claim that in forward flight, the skycar only requires 120 HP (!) and that they are considering hybrid fuel-electric propulsion (!!) for possible future use. They also claim that they have a more detailed paper on the subject. I thought that this might make an interesting follow-up for you.

King of the Road said...

Thanks for the heads up. I'll respond to their claims as you've suggested.

Luke said...

The hybrid idea isn't bad. They want to use electric motors to supply a temporary boost of power for takeoff so that they can use smaller main engines that only have enough power for cruise flight. Not the safest option, since it might end up underpowered, but I guess it makes sense.

What I don't understand is how a vehicle that needs 8x180bhp engines will run on just 120bhp. Unless he means all 8 engines running at 120 bhp? That makes more sense, but still returns a fuel economy of 5.25 miles per US gallon*.

*In my comment to the previous article of this blog (this one: http://hamiltonianfunction.blogspot.com/2009/03/moller-sky-car.html ), I calculated an economy of about 3.5 miles per gallon at full throttle and at top speed. That's with the engines doing 180 bhp each. If they were to do 120 bhp each, and being very generous and assuming the speed remains almost the same at 330 mph, the new fuel economy is 180/120 * 3.5 = 5.25 miles per gallon. Things still don't add up. Unless he meant 120bhp total, in which case assuming half the top speed, i.e. 160mph cruise, we multiply the 5.25 by 8 (since we now have 1/8th the horsepower requirement) and divide by 2 (since half the speed) to get 5.25 *(8/2) = 21 miles per gallon. Not bad, but I seriously doubt it could do 160mph on just 120bhp when you compare it to contemporary piston-engined aircraft.

King of the Road said...


The previous post (the one you reference in your comment) wound up being cited on the Moller site and Bruce Calkins replied that the required horsepower in cruise is 120. Insufficient data is supplied in their web site and in their claims to address this fully, I did what I could in that regard in a further post (it also quotes the question and Bruce's answer) here.

Luke said...

Ahh, didn't realise you also gave an answer to his reply, though I did read the original post you're referring to on the Moller page. I read your answer, and I think we both agree - the performance numbers given for the skycar don't quite add up.