Fuel Effeciency and Range

[mlefebvre]

What is the general consensus on getting the most hours per gallon of fuel, which in effect would extend the range of the aircraft. What kind of engine management is possible to increase the efficiency? What about engine choices to preserve POWER but increase efficiency?

 

You may have noticed that I have posted similar querries elsewhere in this forum but attacking the problem from a design point of view, now, I would like to explore this from a power plant point of view.

 

Marc

[yairgil]

55% OR less give more range.

[Dave Clifford]

Another consideration is engine choice. The rotary uses far less fuel than a Lycombing or Continental in comparable HP power.

[yairgil]

As far as I know rotary engines have very low reliability.

[mjgundry]

The guys flying rotary engines are noting BSFC of .47 to .51. Maybe as low as .45 when leaned way past peak like Tracy Crook does. That's about on par with the Lycs and Conts. Maybe a little worse, certainly not way better. They are very compact for for their power output, so that may lead to other efficiencies.

 

All indications are that the rotary is a very reliable engine. Just three moving parts that are not stressed very hard at all. Race guys run these engines multiple races while getting 200+ horsepower per rotor. Typical aircraft applications only demand 100 hp or so per rotor, so the stresses are even less.

 

Cheers,

[Marc Zeitlin]

Originally posted by mlefebvre

What is the general consensus on getting the most hours per gallon of fuel, which in effect would extend the range of the aircraft.

 

Hours/gallon is endurance, not range - there's an optimal speed/power setting for maximum range - just increasing endurance does not automatically increase range. See the Breguet Range Equation (BRE) for these calculations, given weights, specific fuel consumption, and aircraft characteristics.

 

What kind of engine management is possible to increase the efficiency? What about engine choices to preserve POWER but increase efficiency?

 

Running at the continually changing optimal power setting given the changing weight of the aircraft will give you the best range. This will generally be in the 50%-60% power region, but may be different - you'd have to use the BRE to tell.

 

As far as engine choices go, you'll want to use the Thielert turbocharged diesel. No other certificated engine has as low a specific fuel consumption. Maybe over time some of the other diesels coming on the market will make themselves known to be as good as the Thielert, but it's the only proven one at the moment (and you can't buy it for a homebuilt YET).

 

.....I would like to explore this from a power plant point of view.

 

As mjgundry has pointed out, rotaries are about the same SFC as aircraft engines, so won't get you much more range. The subaru engines might be slightly better, but not much. For best SFC, the diesel is the way to go. Not only that, but since SFC is measured in HP/lb/hr, and diesel fuel is denser than gasoline, you get a LOT more range for the same # of gallons of fuel.

[mlefebvre]

Originally posted by Marc Zeitlin

As mjgundry has pointed out, rotaries are about the same SFC as aircraft engines, so won't get you much more range. The subaru engines might be slightly better, but not much. For best SFC, the diesel is the way to go. Not only that, but since SFC is measured in HP/lb/hr, and diesel fuel is denser than gasoline, you get a LOT more range for the same # of gallons of fuel.

 

 

Is there a weight penalty with diesel being more dense? Ie. 100gal of diesel will weigh X, and 100gal of JetA will weigh Y, where X > Y? Which would affect the amount of usable weight that can be added minus the weight of fuel.

 

Thanks for the tips on the diesel. I will keep my eyes on that as a possibility in the future.

 

Marc

[Marc Zeitlin]

Originally posted by mlefebvre

Is there a weight penalty with diesel being more dense? Ie. 100gal of diesel will weigh X, and 100gal of JetA will weigh Y, where X > Y?

Diesel fuel and Jet A are about the same thing (variants of kerosene) and weigh about 6.8 lb/gallon. Gasoline (for otto cycle engines) weighs about 6 lb/gallon. This means that a gallon of diesel will weigh more than a gallon of gasoline by about 15% - i.e. if you've got 100 gallon capacity, the gasoline will weigh 600 lb, and the diesel will weigh 680 lb. However, if you achieve a SFC of 0.4 with the diesel, while the gas engine does 0.45 (if you're REALLY lucky), you'll be able to go ~25% further on the diesel than on the gas. If you only load 88 gallons of diesel, to weight the same as the 100 gallons of gas, you'll still have a ~10% further range.

[Jim Sower]

Optimum range has a lot of variables. It is initially defined as that point in zero wind conditions where you have maximum excess power - where the distance from drag bucket (power required) is farthest from the thrust curve (power available) - for the aircraft weight you are examining. It actually occurs, as Marc pointed out, at a range of speeds depending on weight. This is not a real big deal for our purposes since our weight variation during a flight (~15%) is not real dramatic (as compared, for example, with a long range jet whose takeoff weight can be nearly twice his landing weight) and the curves that determine the numbers are relatively gentle. But it will vary some, so if you want to nit pick, you'll have to come up with a range of speeds - start the trip faster, and slow down a little as you burn down.

 

A much bigger factor when contemplating max range is wind. In a 40 kt headwind, your best range airspeed will be around 10 kts faster than would be the case no wind, and conversely, with a tail wind, you slow down toward max endurance speed and let the wind carry you along. The reason this is so is that with most other consierations (climb rate, endurance, climb angle, etc) we are discussing only angle of attack, and therefore indicated airspeed for whatever aircraft weight is being examined. When range is being discussed, airspeed has to be massaged against ground speed.

 

Dramatic examples are easier to visualize, so imagine yourself in a Piper Cub, and your best range airspeed is 70 kts at 5 gph, and you're flying into a 50 kt headwind, you won't get much of anywhere at all. OTOH if you accelerate to max speed - like 90 kts at 6.5 gph, you've doubled your ground speed (which is the only thing that gets you to your destination) at a relatively modest penalty in fuel burn. Conversely, if you are downwind in the same cub, and can slow down to 50 kts at 3 gph fuel burn, you'll end up going further since the wind will carry you along for a much longer period of time burning the same fuel.

 

This phenomenon is always at work, but is pretty tough to pin down precisely. Our mpg doesn't vary as radically with speed as some airplanes and there's room for some fudging (gentler curves and all...). For my own purposes I use a rule of thumb of around 20% - 25% of wind speed as an airspeed correction. If I'm cruising, I will try and increase/decrease TAS 1 kt for every 4 or 5 kts of headwind/tailwind encountered.

 

I have worked quantitatively with this stuff with tactical jets (where the effects and consequences can be dramatic). I have seen some of the curves for some (I don't know which) GA airplanes, but haven't gotten into the tight details. That's why I use the rule of thumb nice round numbers that I do. Perhaps Marc can give us some detailed numbers on the effect of head/tail winds on optimum cruise speeds. I certainly would like to see some actual numbers to bump against my SWAGs.

[Marc Zeitlin]

Originally posted by Jim Sower

Optimum range has a lot of variables. It is initially defined as that point in zero wind conditions where you have maximum excess power - where the distance from drag bucket (power required) is farthest from the thrust curve (power available) - for the aircraft weight you are examining.

 

I have no idea where you got this definition from - it certainly doesn't have anything to do with the BRE. Maximum excess power will get you your maximum ROC (Vy), not range.

 

Maximum range will come at a speed that is close to the maximum on the L/D curve (drag polar for the aircraft as a whole). It will also be dependent upon the SFC curve of the engine (to operate at or near max L/D, you'll need to throttle back, but throttling increases the SFC, so there's an optimum point that will be FASTER than the max. L/D speed) and also on the propeller efficiency, which also changes with speed.

 

For Marc L.'s original question, this is all theoretical - he just needs to put in a diesel engine, which will increase the range tremendously by reducing the SFC. He then needs to fly up high at about 55% power, which with no throttle won't change the SFC much. Any differences in increased range that might be obtained by maximizing the BRE parameters will be unmeasureable in the real world with this plane, where the fuel weight is ~15% of the gross, as you point out.

 

Originally posted by Jim Sower

That's why I use the rule of thumb nice round numbers that I do. Perhaps Marc can give us some detailed numbers on the effect of head/tail winds on optimum cruise speeds. I certainly would like to see some actual numbers to bump against my SWAGs.

 

Again, for exact numbers, you'd have to know the SFC, prop efficiency, and drag polar curves for your plane (and none of us do). But let's ignore that, and assume they're constant.

 

----

Interlude for Physical Therapy appointment - I'll pick this up again when I get home tonight.

[No4]

....Edited to say Marc got there first whilst I was typing...

 

Have to disagree with you very slightly there Jim, but in all you are very much correct.

 

From the engines view point, flying for max range you would want to use full throttle (not choked), weak mixture, highest boost permissable for the mixture, and lowest rpm consistent with the charging of the generator and avoidance of detonation.

Without a CSU and supercharger the job is much easier.

 

From the airframes view point, the angle of attack that gives the best lift/drag ratio will give you best range, (the best glide speed,which will be very close to the maximum excess power available speed at sea level, which is best rate of climb). For a given weight this will give you an indicated airspeed for best range, regardless of height.

 

The altitude you choose will be decided by the engine and propeller efficiency, as long as you maintain the best glide indicated airspeed.

 

However that is in nil wind conditions, and you are correct regarding the speeding up / slowing down. The half rule of thumb I heard was to add half the headwind/ subtract half the tail wind, but I believe mathematicaly it is not quite correct and the equation is a bit of a monster. In a strong tailwind you would utimately want to fly at min power speed, ie max endurance.

 

 

[Jim Sower]

<... I have no idea where you got this definition from - it certainly doesn't have anything to do with the BRE. Maximum excess power will get you your maximum ROC (Vy), not range. ...>

 

I got it from working on SIOP mission profiles in the service where we had to plan various mission profiles with various contingencies pretty much down to a gnat's ass (launching a 12000# airplane with 9000# of fuel and a weapon on board and being within 50# of our planned fuel at the end of a hi-lo-lo-hi profile). It was a LOOOOONG time ago. I should have tried to find some of the reference material and refresh my fading memory.

 

I do recall that the best cruise was where a line from the zero point of the thrust/drag graph became tangent to the drag curve (plot of thrust v. airspeed superimposed over drag v. airspeed). Bottom of the bucket is dog/max endurance speed. I remember that unlike recips, the thrust available curve was not at all flat, so max excess thrust was not at the bottom of the bucket. Anyway, thrust increased with airspeed, and drag did too (but a lot faster). Best cruise was where a line from zero airspeed was tangent to the curve. Now I am remembering a little better - if you had 50 kts on the nose, you drew your line from 50 kts, 0 thrust/drag to tangent to the drag curve (and it happened further up the curve). When you had 50 kts on the tail, you drew the tangent from -50 kts (and it intercepted closer to the bottom of the bucket).

 

But you're right. It has nothing to do with max excess thrust. I was having a senior moment there with different graphs and objectives kind of merging into one another. Mea Culpa !!

 

I also agree that there almost certainly isn't any sufficiently accurate data on homebuilts to make a "proper" analysis. One could argue that it isn't a big enough deal to bother with on GA airplanes. Probably something on the order of 2 or 3 of gal on a 6-hr leg. But then, there's those days when you wish desperately that you had a little more fuel. I recall one day in particular when I would have sold my first-born into servitude two gal of go-juice

[Marc Zeitlin]

So where was I....But let's ignore that, and assume they're constant.

 

Take a look at the "Range" graph at:

 

http://www.cafefoundation.org/aprs/Cozy%20IV%20APR.pdf

 

at 12K ft. You'll see that the range increases as fuel flow (and speed) decrease, almost linearly and monotonically.

 

Also, look at the glide performance graph at:

 

http://www.cozybuilders.org/performance/glide.html

 

This indicates that at a weight of 1800 lb (let's use this as an average, in between gross weight at takeoff and minimum fuel weight at landing) you want to fly at 93 kt., or 105 mph. The graphs never indicate fuel flows at this speed, because NO-ONE ever wants to cruise this slow in a COZY - it's my downwind speed. I maintain this speed at 1500 RPM - I'm going to guess that this is 25% power or so, and maybe 3-4 gallons/hr., but that's only a guess.

 

Nat claims that the fuel flow will bottom out around 5 gal/hr - see:

 

http://www.cozybuilders.org/performance/cruise.html

 

At that power rate, the engine is NOT very efficient, so let's assume that we've got to fly a bit faster to actually maximize the range - I'll guess 150 mph, since we already know that 50% power at 6 GPH at 12K ft. at 178 mph does NOT maximize range, given the CAFE foundation's graph, and that the fuel flow does NOT decrease much beyond that.

 

Where does this leave us (we still haven't gotten to the wind part)?

 

Well, we know that if we fly at about 150 mph, we'll probably maximize the range of the COZY, and extrapolating from the CAFE graph, I'm going to guess we'll top out at around 1500 miles with the standard tanks and VFR reserves. Now, that's 10 freaking hours in the plane, by which time __I'll__ be raving mad, and covered in urine, but maybe you folks can last longer in a tiny space than I can :-).

 

Let's assume that we've got the max range speed now (well, close, anyway - it's gonna be somewhere between 105 and 150, but closer to the latter) - any faster or any slower will not get us as far.

 

What about wind? Since we've got the part of the curve FASTER than max range speed, let's look at headwinds first - maybe a 30 mph headwind. Here are some datapoints:

 

No wind (all approximate #'s, from the graphs and extrapolations):

 

150 mph 5.0 gal/hr 10 hours 1500 miles

186 mph 6.5 gal/hr 7.5 hours 1350 miles

195 mph 8.5 gal/hr 5.6 hours 1100 miles

186 mph 10. gal/hr 4.7 hours 875 miles

 

With 30 mph headwind:

 

120 mph 5.0 gal/hr 10 hours 1200 miles

156 mph 6.5 gal/hr 7.5 hours 1170 miles

165 mph 8.5 gal/hr 5.6 hours 924 miles

156 mph 10. gal/hr 4.7 hours 733 miles

 

We can see that there's a 150 mile difference in range between 150 mph and 186 mph with no wind, but for all intents and purposes they're identical with a 30 mph headwind. So, you don't gain anything by speeding up, but you don't lose nearly as much as you would have with no wind. Make it a 60 mph headwind, and:

 

90 mph 5.0 gal/hr 10 hours 900 miles

126 mph 6.5 gal/hr 7.5 hours 945 miles

135 mph 8.5 gal/hr 5.6 hours 756 miles

126 mph 10. gal/hr 4.7 hours 592 miles

 

Now, we can see a definite shift to faster being better (but not by a whole hell of a lot).

 

A tailwind will be a similar analysis, but going in the slower direction, rather than faster. Since we already know that we don't want to fly any slower, and we've got no clue what the datapoints look like below 150 mph, I'm not going to bother.

 

So, what's this all tell us, for everyday flying? Basically, fly any speed you want - there's very little difference at low wind speeds in the MAXIMUM range you'll achieve due to speed changes based on the winds, or in the amount of fuel you'll use in that speed range. Fly at the speed that makes you comfortable and gets you where you want to be in the time period you want to spend.

 

For REAL maximum range flights, such as record attempts or Hawaii - Mainland flights with minimum fuel loads, this type of calculation will need to be run with REAL numbers for low speed fuel flows and concurrent ranges. Graphing the results will give the most accurate answers, since getting a closed form solution for all the parameters together is non-trivial.

 

Using a diesel engine that can be run at very low fuel flows efficiently would allow you to fly much closer to the best L/D speed, and get even more range. Let's extrapolate - if it took 2 gal/hr in a diesel to keep the COZY in the air at the 105 mph speed for best L/D, we'd be able to stay in the air for 21 hours - that would get us a range of 2205 miles. Even if it used 3 gal/hr at that speed, we'd have 16.8 hours and 1767 miles.

 

Hope this helps, both with the concepts and the reality.

 

And for Jim's response, it seems that the curves are/will be substantially different for jets than for piston engine propellor planes, giving different optima.

[No4]

Sorry to pick holes again Jim,

You are correct except for a sentence in the middle.

"...thrust increased with airspeed, and drag did too (but a lot faster)...."

 

To quote A.C. Kermode's "Mechanics of Flight"

 

Whereas the thrust of a proppeller falls off as forward speed increases, the thrust of a jet is nearly constant at all speeds (at the same rpm).

Whereas the fuel consumption in a reciprocating engine is approximately proportional to the power developed, the fuel consumption in jet propulsion is approximately proportional to the thrust.

 

So dividing the drag by the air speed gives one an airspeed drag ratio. The lowest number ratio will be the best range cruise indicated airspeed, which will be higher than the min drag speed. The effects of altitude cause the True airspeed to increase, so the efficiency will be greatly increased, and range will be increased.

Thus to get range jets must fly high.

 

Your description of the graphs, and best endurance speed is spot on.

 

...edited to add, jeez Marc we've got a synchronised posting thing happening here

 

with regard to the diesel, it being turbocharged, if you were to consider oxygen and high altitude cruise, you would have the same improvement in range, AND get there a lot faster because the true airpeed would be higher for a corresponding indicated airspeed and drag. The winds up there are also stronger, which gives you the option of climbing high to catch the big tailwind, or staying low to avoid the worst of the headwind ....

 

I found this great site that covers all of what we discussed, and lots more; it refers to the Beech Bonanza, but is just as relative for the Cozy.

 

http://www.nar-associates.com/technical-flying/technical_flying.html

[Jim Sower]

No4,

...I remember that ... the thrust available curve was not at all flat...

... the thrust of a proppeller falls off as forward speed increases, the thrust of a jet is nearly constant at all speeds ...

Actually, that's pretty much what I was taught in school. Then, while working at Republic on the team that wrote the performance suppliment to the F-105 handbook, and later on in the fleet flying A4s, I discovered that thrust does sometimes increase with airspeed. Can't speak for all jets, but that was my experience. I would hazard a guess that it might have to do with the intake ducts - good recovery of the dynamic pressure will increase static pressure at the compressor face and .....

 

 

Marc,

The very first paragraph of this thread (which I have presumed sort of defines the thread) read:

What is the general consensus on getting the most hours per gallon of fuel, which in effect would extend the range of the aircraft. What kind of engine management is possible to increase the efficiency? What about engine choices to preserve POWER but increase efficiency?

The last sentence was jumped on and discussed at some length. There was nothing much I could add that hadn't been said. There are reams of postings here and there around engine choices. The first two sentences kind of caught my fancy. I have no recollection of any discussion at all around cruise optimization, either here or on your Cozy list. So I just had to pipe up (you know I'm weak)

 

at 12K ft. You'll see that the range increases as fuel flow (and speed) decrease, almost linearly and monotonically

And the data is pretty much restricted to the very top 10 mph that the airplane is capable of achieving. Well Duuuuhhhhh! Do ANY of us know of anything that operates "optimally" when it's flat out, balls to the wall? I certainly don't.

 

you want to fly at 93 kt., or 105 mph.

No, I do NOT! I never suggested any such a thing.

The graphs never indicate fuel flows at this speed, because NO-ONE ever wants to cruise this slow in a COZY

Nobody's arguing that. Nobody's suggesting you cruise at these speeds. And if I'm not mistaken, you you are quoting GLIDE speeds. This thread is about CRUISE. If you were to look more closely, you may note I suggest a downwind [cruise] airspeed of optimum cruise (your suggested 165 for the sake of argument) less 25% of the [40kt] tailwind, or 155 (of course, that's TRUE airspeed).

 

... so let's assume that we've got to fly a bit faster ... I'll guess 150 mph ... about 150 mph, we'll probably maximize the range ... and extrapolating from the CAFE graph, I'm going to guess we'll top out at around ... Let's assume that we've got the max range speed now (well, close, anyway... it's gonna be somewhere between ...

May I invite your attention to the part where I said:

Perhaps Marc can give us some detailed numbers on the effect of head/tail winds on optimum cruise speeds. I certainly would like to see some actual numbers to bump against my SWAGs

 

6 GPH at 12K ft. at 178 mph does NOT maximize range, given the CAFE foundation's graph

I didn't see ANY airspeeds under 186, 6.5 gph - are we on the same graph? I'm looking at page 8.

 

Now, that's 10 freaking hours in the plane, by which time __I'll__ be raving mad, and covered in urine, but maybe you folks can last longer in a tiny space than I can :-).

Nobody's arguing that, Marc. Top of this post, top of the thread - the guy is asking for optimum cruise management - NOT preferred or most popular or most comfortable or most expeditious cruise management, but OPTIMUM.

 

Back in the 70s Dick Rutan flew all over hell and half of Georgia breaking distance records. He holds about 100 of them IIRC. Not that was before I was around homebuilding, but I read a couple of articles about those flights. If I'm not mistaken, he cruised his Long-EZ at around 160 kts. Once, back and forth from Mojave to Oregon somewhere for about 24 hrs setting a distance record. I would hazard a guess that he was taking careful account of the wind and changing his airspeed northbound and southbound depending on the wind.

 

So, what's this all tell us, for everyday flying .... For REAL maximum range flights, such as record attempts or Hawaii - Mainland ...

I feel is a pretty good paraphrase of my last paragraph.

 

Basically, fly any speed you want - there's very little difference

As I recall, my own estimate of the fuel saved making upwind/downwind speed correcctions was "... a couple of gallons on a 6-hour leg ..."

 

And for Jim's response, it seems that the curves are/will be substantially different for jets than for piston engine propellor planes, giving different optima.

I thought I was pretty clear (I was certainly trying to be) that my whole post was a qualitative analysis based on what I knew from my jet experience, and that I was asking you for some more accurate numbers for GA recips.

 

Now, I do run on from time to time:) so folks can be forgiven if they miss disclaimers like "jets" and "forty years ago" and so forth. That said, I am disappointed that We got a lot more heat than light when I very specifically noted that I had a qualitative handle on the deal and what I needed from you was "... good, reliable, accurate numbers ... if you had any. A simple "... I don't have any accurate numbers around this subject, and don't really know where to get any ..." would have worked for me.

 

As regards the qualitative analysis, and general magnitudes of the parameters, it would appear that

"... once again, we find ourselves in violent agreement ..."

[No4]

Jim,

Would it be the ram air causing the rise in thrust? Anyway, wrong website for that. I'm not a jet driver yet but hope to be in the next couple of years.

 

Yes you are looking at the wrong page in the CAFE report. Page 8 is a chart of TRUE airspeed. Drag is relative to INDICATED airspeed.

If you look at the table on page 9, 8 lines down in the table headed Cruise Flight Data.

 

CAS 155mph, 12,000 feet, TAS 186 mph, 6.5 gph, 28.6 mpg, range 1338

 

It is highlighted to help you find it

 

That's the lowest indicated airspeed tested at 12,000 feet, and it returns the best range.

 

Marc,

Good work with the number crunching, personaly I thought it was a very good post.

 

[Jim Sower]

No4,

Would it be the ram air causing the rise in thrust

Not the ram itself air I don't think. I am very thin in this area, but I believe that sort of like the plenum in your Cozy. You want to convert the ram/kinetic energy into static pressure at the compressor face. Higher static pressure at the compressor face makes the engine think it's at a lower altitude ~ you're moving more air mass through the engine which converts to more thrust since trust is produced by accelerating mass to a higher velocity. Like I said, I'm no intake man and that's my intuitive guess. I didn't mean to imply that thrust curves were real steep, but just that they weren't as flat as the texts I used in school would have had me believe.

[gontek]

Allright,

I'll ask this question here because I searched for keyword "Drag Polar" and found this topic of discussion.

 

My query to you smart fellers involves determination of "Optimum Cruise Speed" and hence cruise Drag Polar for a canard aircraft. Based on my calculations, I can mostly figure it out but I want to narrow down the Equivalent Parasite Drag Area of a long EZ or a Cozy. I can do this by calculation or you can try to estimate or verify it by looking at the front view of your aircraft and guesstimation.

 

Knowns:

Weight

Geometry (S and b)

Standard Atmosphere

 

Assumptions:

Oswalds e = 0.6

Prop Efficiency = 0.85

 

Unknowns:

f = Equivalent Parasite Drag Area

L/D ratio in cruise config.

 

I wish to use this information for my reference in sizing aircraft based on the report AIAA-80-1847 Fuel Efficiency of Small Aircraft, BH Carson, 1980. Does not have to be accurate to 1/100th SF but I know some of you guys have probably figured this out before, or can point me to some useful numbers.

 

I'd estimate f for a longEZ to be very low, maybe 3 to 5 ft sq, but that range of error makes a big difference for my purposes. I can also speculate that the L/D in Cruise for a canard is high (15-25?) but once again that range is too great for me to assume much from it.

 

Actually all I need is best glide speed and I think I can figure it out, so what is that? However, feel free to do your own calculations to determine the parasite drag, or point out that this information is very obvious and I have overlooked it.

[emteeoh]

I'm pretty sure that I read that Rutan talked about this in one of the Canard Pushers. IIRC, I didn't read the article directly, but instead read Bill James' summary of it in his blog (EZ Chronicles. Always a good read!). I'll look for the article tonight.

[gontek]

Thanks for pointing that out, I based on your information I was able to find that article here: http://www.ezchronicles.com/2007/03/longez-more-practical-airplane.html

 

I might be able to look at the numbers here and plug them in to find the based on the author's assumptions the effective parasite drag and lift to drag. My calculations were of the very late at night variety so I'll go over everything later and see if I can't find any clues in this article.

 

 

 

BTW - here is another potential solution to the original question, when focusing on efficiency more than range:

http://cafefoundation.org/v2/research_cafeformula.php

the discussions that ensued are very informative though.

 

the report I am referencing is here, under

Engines/Motors/Fuels Papers"

http://cafefoundation.org/v2/pav_tech_lib.php

 

yet another gem of information I gleaned while lurking in the canardzone archives.

[gontek]

http://www.ezarc.org/downloads/army_ez_eval.pdf

 

has everything I wanted exactly.