The CAFE Measure of Efficiency - Mooney Style!

[testwest]

In this thread

http://www.mooneyspace.com/index.cfm?mainaction=posts&forumid=1&threadid=869

JimR wrote about efficiency of our wonderful Mooneys. A great discussion of over 70 posts ensued, and many figures, techniques and thoughts were shared.

In doing the research for my thesis, I kept coming back to a fundamental question....what is the most appropriate measure of efficiency for personal airplanes? Is it speed, range, mpg, or some combination? In answering that question, I wrote nearly 22 pages of thesis material. No need to go through all that here, but I will refer anyone interested to this:

cafefoundation.org/v2/pdf_pav/PAV.CAFE.Formula.Deriv.7.7.pdf

The "Cliff Notes" version is this: The CAFE (Comparative Aircraft Flight Efficiency) measure of merit for efficiency is the parameter V**1.3 X MPG (** means "raised to the power of" when you don't have superscript typing capability) . According to CAFE, maximizing this parameter yields the most efficient flight, with the best balance of speed, range, and miles per gallon. V in this case is no-wind true airspeed (= groundspeed).

Some nifty obervations....maximizing:

V**-1 x MPG gives Max Endurance Speed

V**0 x MPG gives Max Range Speed

V**1 x MPG gives Carson's Speed (usually around 50% power in standard GA airplanes)

V**2 x MPG gives Max Level Flight Speed

The interesting thing about this V**1.3 x MPG CAFE speed is that it results in about 65% power for most GA airplanes. The exponent was developed based on the results of hundreds of CAFE race results from the 80s and early 90s as well as some very good research. The curve peaks based on percent power and is consistent for best power, best "economy" and LOP mixture control schemes.

Now, we look at the specific fuel consumption of our piston engines at varying mixtures.....the research from the Advanced Pilot seminars indicates that a mixture setting of 25 deg F LOP (lean of peak) gives the best BSFC (brake specific fuel consumption, see here http://en.wikipedia.org/wiki/Brake_specific_fuel_consumption ). And....the maximum power setting for which mixture can be set at this point relatively care-free (no red box) is.....about 65%, again.

Hmm.

So, let's look at some data. JimR's flight at around 9000' was reported as

The trip took a total of 7.2 hours and we averaged 140.76 knots, which works out to 18.94 nautical mpg.

140.76 ** 1.3 x 18.94 = 11,759.9 CAFE score. Power setting was about 20/2400 (~50-55% while LOP)

Now here is his "old skool" flight at ROP:  The trip took 6.3 hours, average 154.35 knots, and 14.96 nmpg.

154.35**1.3 x 14.96 =  10,471 CAFE score. Power was WOT/2400 (~63% best power mixture). These numbers should be familiar to any J driver.....10 gph, 155 KTAS, 9000 feet, right out of the book

Neglecting the (hopefully countervailing) climbs and descents to compare with the above, a 63% power 25 deg LOP power setting should yield ~155 KTAS at only 8.5 gph at around 9000'.

155**1.3 x (155/8.5) = 12, 833 CAFE score.

But what if we went 70% power LOP at the same conditions (it would take ~2650 RPM to do it, FF 9.4 gph, around 160 KTAS)

(160**1.3) x (160/9.4)= 12,484 CAFE score.  The score decreases on either side of "around" 65% power, but it is stil pretty high. And remember, this is no-wind.

So, for max endurance I fly max endurance. Max range, max range. I don't normally cruise at Carson's Speed because the BSFC falls off at the 50% power level (Carson missed this, he assumed BSFC was relatively constant).

For maximum efficiency I try to plan and fly ~65% power (maybe a little more in a headwind), 25 deg LOP, at whatever altitude gives the best groundspeed. It's too difficult right now to try to optimize the CAFE parameter inflight instead (with the stuff currently installed in the airplane or carried on board e.g. handheld GPS w/XM WX) because the required info is a bit too federated. Typically the minimum cruise altitude I use is where I can get 65% at WOT with some reasonable RPM, usually above 7000 feet. Some of the latest flight planners can optimize a planned altitude for a given route based on forecast winds during preflight planning (www.fltplan.com does this, as well as Foreflight and WingX, I think) , but I would like to see that done even better.

It is entirely feasible for the latest flight planning and operation tools (Foreflight, Ipad, Connected, etc) to optimize and refine in real time a ~65-70% LOP cruise flight for the maximum CAFE score (best efficiency) using datalink winds and known aircraft performance data.  The tools would output (during a flight) a recommended power setting and an efficient lateral and vertical flight path in real time. Such an output could easily be constrained to reasonable intervals for altitude and course changes for ATC purposes. Using something like the proposed "Connected" technology by Aspen could make such an optimization output to the avionics nearly automatic in flight.

JimR made a brilliant statement in his post:

LOP operations have started to gain a lot of attention these days as a means of operating our engines more efficiently...Little attention is being given these days, however, to operating our airframes more efficiently.  I know that it is sacrilege to admit here, but the only way to do this is to slow down.

If the meaning of efficiency is understood as CAFE describes it, then you may not have to slow down to the 50% engine power level...if you can fly a smarter path in 3D where WOT results in 65%ish power (a little more in a headwind). We are just now seeing the GA market produce affordable cockpit tools and avionics that make this idea of putting the airframe along its most efficient path not only feasible, but achievable for a regular pilot.

Comments?

[carusoam]

Norman,

Let me know if there is data that you would like to collect from flight of an M20R...

I would like to see your cafe calculations include the Ovation if possible.

Best regards,

-a-

[testwest]

You got it. I'll need some info...

What is your Vy speed?

What altitude do you normally fly for a long cruise? (answered my own question, 11000 feet from your sig, right?)

Best Power, Best Economy or LOP?

TAS and fuel flow at those points?

Thanks!

[carusoam]

Norman,

Vy = 105 KIAS

My favorite VFR alts are 11,500 and 12,500  (my sig block indicates my favorite IFR - east bound from here is cape cod)

I prefer the highest altitude I can get without O2 requirements.  More time and options for engine out operations.

I usually climb and set up the initial leg of the flight in accordance with the POH = ROP.

Roughly speaking:

GS=175kts at 15.5gph (50d ROP)  WOT 2,500rpm

GS= 160kts at 11.5 gph (50d LOP)  WOT 2,500rpm

Fuel use and speed are from memory until I can get better data for you.  This could take a while with Huricane Irene on her way through...

Best regards,

-a-

[testwest]

OK, got the data.

For your next climb, try climbing at 138 knots indicated until your climb rate drops to 500 fpm. Then hold 500 fpm until your speed drops to Vy (105 knots), or level off at altitude, whichever comes first.

Try using the 'Target EGT' method of mixture managment on the climb, adjusting mixture to maintain your takeoff EGT every so often. Doing it every 1000' may be too much work, but doing it only once during the climb may not be often enough.

Modulate your cowl flaps to maintain 380 dF or less on the hottest cylinder. You may be surprised that you can climb this way without much cowl flap open at all.

Your altitude data:

ROP: (175**1.3 x (175/15.5)) = 9304 CAFE Score

LOP: (160**1.3 x (160/11.5)) = 10,204 CAFE Score   ...this is about 61% power.

You should be able to run 65% power at 25 dF LOP safely.

GAMI's? Fine Wire Plugs? If no to both, think about the fine wires first. Tempest fines are $49, half of brand C's price.

[testwest]

Here is a comparative score from an airplane that may seem like a fuel hog, but shows the power of a brilliantly designed turbonormalizing system:

Aerostar 601P, TN-intercooled, 2 x IO-540-S1A5 engines, 290hp each

FL250 data, 67% ish power, 25 dF LOP....219 KTAS, 26 gph total

219**1.3 x (219/26) = 9290 CAFE Score  

 

Turbocharged low-compression airplanes are far less efficient. [All data are for 65%, best power]

Cessna 340 at best power, FL200 gets you 206 KTAS, 39.2 gph

206**1.3 x (206/39.2) = 5353 CAFE Score 

Baron 58P at best power, FL200 gets you 210 KTAS, 41 gph

210**1.3 x (210/41) = 5349 CAFE Score    

Duke at best power, FL200 gets you 212 KTAS, 48 gph

212**1.3 x (212/48) = 4670 CAFE Score  < squeeeel!!! >

[testwest]

Here is some fun...KSMooniac wrote in this thread: http://www.mooneyspace.com/index.cfm?mainaction=posts&forumid=3&threadid=1480

I am dreaming of a TN-201 that could be tickling 185-190 KTAS at 17,500' and perhaps 165-170 KTAS in the 11-12,000' range on 11.5 GPH.

185KTAS on 11.5 GPH in a TN-201 is entirely within the realm of possibility. The resulting NMPG is ~16 NMPG. Let's run the score:

185**1.3 x (185/11.5) = 14,250 CAFE Score.

But here is the other thing that is so good.....the range of available altitudes for which 65% power can be selected efficiently goes from 7000' to over 18000' in this scenario, allowing much more flexibility in optimizing the 3D path to take the greatest advantage of the winds....

And this is why the group of us mooniac e-nuts just froths at the mouth at the possibility of a really well executed TN 201.

[testwest]

Let's see how the Tornado Alley Turbo-modded Cessna Cardinal fares: 177 KTAS at 10.8 gph , 17,500 feet

177**1.3 x (177/10.8) = 13,706 CAFE Score. Not bad for a Zezzna.

More fun:

A pilot was preflighting an A36 a couple days ago.  he said at peak they run 165 knots, burn 17 GPH and at get there power, 20 GPH.  I just smiled.   Our plane makes 150 KTAS at around 8.8. [jetdriven]

A36: 165**1.3 x (165/17) =7409 CAFE Score. My Aerostar beats this hands down (9290 CAFE Score), at an incredible 54 knots faster. And it's pressurized. That's why I call it the twin Mooney.

Jetdriven's 201: 150**1.3 x (150/8.8) = 11,495 CAFE Score.  Jet put one of these after his quote statement above  {cool} . All I can say is "Ya got THAT right"

[David Mazer]

Norman, If you were to catagorize CAFE scores into exceptional, good, average, and poor, where would the approximate breaks be?  In other words, is anything above 10,000 excellent, 7,500-9,999 good, 5,000-7,499 average, etc?

[carusoam]

People,

 

What do we know about propeller efficiency?

 

To go along with engine efficiency and airframe efficiency is there a particular rpm that is most airfoil efficient?  Or are we maximizing the fuel burn and hope the prop has an optimized design at this rpm?

 

More direct to the point...should I cruise at a lower rpm if I want to be more efficient?  How low?  Does this improve fuel usage or prop efficiency or a compromise of both?

 

When driven efficiently, my 1992 chevy 2-seater gets 40mpg from it's 350cu small block.  When driven for speed, it gets 22mpg.   For best efficiency, select highest gear ratio and lowest rpm and don't hit the brakes.

 

Seems like I should be selecting a low rpm, unless the airfoil or engine efficiency has a lower limit.

 

Best regards,

 

-a-

 

[Shadrach]

Hi Norman,

Being that you're doing your thesis, I would like to see more about how you're using SFC relating to mixture, rather than just taking Gami's estimate.  I believe that the lowest BSFCs occur at fuel air ratios significantly lower than would be utilized at 25LOP (more in the range of ~35-65LOP, engine dependent). Moreover, Gami may or may not have been taking airframe efficiency into consideration when they came up with that number (I've personally don't recall 25LOP given as a "best SFC target, excepting for in this thread.).  I don't believe that the power level that generates the lowest BSFC in a specific engine necessarily correlates to the most efficient power setting for a given airframe (discussion limited to normally aspirated engines). I think that you already understand this and it will be a significant part of your thesis. However, In addition to flat plate area, I'd like to see how you're accounting for the increase in induced drag that can result from lower IASs at the reduced power levels being used to attain the lowest SFC. It seems to me that those values would change with altitude and from airframe to airframe. Thanks!

 

P.S. Do you still want the climb table from my M20F POH, or are you only wanting M20J info? 

[jetdriven]

Ross:

I often wonder about BSFC as a relation to degrees LOP. THe data really doesnt exist for 4 cylinder lycomings.  I do have a graph supposedly from Lycoming that shows peak BSFC at 50 dF LOP.  But the curve is flat from 20-50 LOP.  Our plane completely falls on its face below 50 LOP.  Down low below 3000' its no big deal, 100 LOP is fine qe have excess MP available.  I wonder if I can even make 75% (150 HP) power LOP at altitude. It would take 9.9 GPH and for us almost always thats ROP. I havent seen it yet.  I always end up 8.7-7.8 GPH depending on altiitude and 145-150 KTAS.  It seems the airplane is happiest around 120 KIAS regardelss of altitude.

EDIT: with the 25 degres of timing there is much morm "oomp" while LOP. We also modified our style of flying to 10-20 LOP and not 130 KIAS is the norm, and FF is ~9 GPH below 4K, 8.8-8 GPH between 4-8K. At 9500 its 7.8 GPH.

The airframe equation seems that further from max L/D the more you pay in drag.  But the engine's efficiency at 40% power to maintain that speed  (L/D MAX) is below its max efficiency range as well.  So the engine likes 55-65% power to maintain a  .39 BSFC  but the airframe likes the equivalent of 40% power.  There is a balance somewhere.  I think our typical 8.7 GPH 62% power LOP at 8500' is actualy a bit slow, we could make nearly the same trip burn flying faster.

Byron

1977 201 N201EQ

SN 24-0162

Quote: Shadrach

Hi Norman,

Being that you're doing your thesis, I would like to see more about how you're using SFC relating to mixture, rather than just taking Gami's estimate.  I believe that the lowest BSFCs occur at fuel air ratios significantly lower than would be utilized at 25LOP (more in the range of ~35-65LOP, engine dependent). Moreover, Gami may or may not have been taking airframe efficiency into consideration when they came up with that number (I've personally don't recall 25LOP given as a "best SFC target, excepting for in this thread.).  I don't believe that the power level that generates the lowest BSFC in a specific engine necessarily correlates to the most efficient power setting for a given airframe (discussion limited to normally aspirated engines). I think that you already understand this and it will be a significant part of your thesis. However, In addition to flat plate area, I'd like to see how you're accounting for the increase in induced drag that can result from lower IASs at the reduced power levels being used to attain the lowest SFC. It seems to me that those values would change with altitude and from airframe to airframe. Thanks!

 

P.S. Do you still want the climb table from my M20F POH, or are you only wanting M20J info? 

[testwest]

Thanks for all the great discussions, everyone!

For Mazerbase, I don't have any great cutoffs, but 10,000+ scores are pretty darn good for 4 seat airplanes. Very few normally aspirated airplanes get there, but turbonormalized high compression modded planes do rather well. The TN Cardinal is a really good example...as is the TN Bonanza and the TN Cirrus.

For carusoam, as usual, the answer is "it depends".

There are losses at either end of the RPM range....at high RPM (and cold) the prop tips start to get into a range where transonic drag rise becomes a problem. It's worse with big prop diameters and wide chord, square prop tips. This is one of the reasons we went with the 2-blade Hartzell Top Prop, the blade profile near the tip is a lower drag design at higher RPM.

Friction losses are basically constant for a given RPM, at high or low power. So at lower power, the percentage of hp lost in friction goes up. And, 4 cylinder engines don't have 33% less friction loss than 6 bangers, it's more like 20% less (thanks to George Braly for that one). As the friction losses start to kick in the BSFC starts to go back up....like at 50% power. This is one of the reasons Carson's Speed never really caught on as a cruise flight condition, his other math to the contrary...holding that speed at altitudes that don't require oxygen meant very low power settings.

WOTLOP is a given. ~65% power maximizes the CAFE score no-wind. The big tradeoff optimizes altitude, wind and RPM in prefilight planning, and refines it inflight. We need an app to do that. And there isn't one, yet.

As a general suggestion, however, if headwinds force you low, lower RPM will stiil get ~65% power while WOTLOP. With tailwinds, higher altitude and RPM is better, up to a point.

For Shadrach, the 25 dF LOP is straight from the Lycoming representative leaning diagram, here:

http://www.lycoming.textron.com/support/publications/service-instructions/pdfs/SI1094D.pdf

Your other points are well taken. I am trying to account for a lot of engineering trade-offs while coming up with some simple planning factors that are "sufficiently rigorous". I have found precise technical rigor satisfies other engineering types but tends to alienate the actual target audience. I probably already did that with this thread.

And I do have the info I need for the J, thanks though. That Vy for the F seems pretty high. Have you ever done a set of sawtooth climbs to check the Vy speed on your own?

[Shadrach]

I've not done a lot in the way of climb testing for 2 reasons. 

1) In my anecdotal experience, the actual change in climb rate is not that dramatic (<200fpm)  from 90 to 120mph.

2) I've never felt at a loss for climb performance. It'd be nice to have more, but I've never felt that I've needed more. 

 

I'm sure that if I was based out of Denver I'd feel differently.

Unless I'm at or near MGW, which is rare (useful of 1059lbs, I'm typically 400-500lbs under MGW), 120mph almost always yields 1000+fpm at DAs under 3000ft and provides good cooling, visibility and forward speed. 

I look forward to reading more as your research and analysis continues... 

 

Also, I would not put tremendous stock in that lycoming graph. AFAIK, It is conceptual in nature and not engine specific.

[testwest]

Hi everyone

In doing some more research, I found an amazing program called Benchmark. It runs on a Mac, and is currently available as a full version for free, until July 2012. The author, Alfred Scott of Sequoia Aircraft, is a recognized expert in airplane performance.

See it here: http://www.seqair.com/benchmark/index.html

Attached is a screenshot of the CAFE output for a modeled Falco. Notice at gross weight, the "best economy" power setting maxes the CAFE score at about 65% power. The model takes into account everything about the airplane, engine and propeller, just as several writers above have asked.

This program is much better than the spreadsheet I was using for the M20J drag polar. Looks like I can start to model a Mooney M20J right away. KSMooniac, JimR, Shad, jetdriven, carusoam, ya gotta see this thing.

Stand by........

[jetdriven]

Norman I saw benchmark and I even downloaded it. I just forgot about it after I didnt know how to load the data.  Perhaps we can get this thing going.

[KSMooniac]

Wow, that looks very interesting!  Too bad I'm not a Mac guy...  :/  

One disappointment I've had with my MT prop conversion is the fact that they optimized it for much lower RPM than I would otherwise choose for LOP cruise at 7k+ altitudes.  Now I have to run lower LOP power settings as running higher RPM actually reduces my cruise speed with this prop, which is unfortunate.  The solution is to TN my plane and recover the power with MP instead...

[testwest]

Hi Scott

The first Benchmark model I plan to develop will be a standard M20J with the McCauley B2D34C212 prop. Later, we can model your MT prop and a Hartzell BA. My neighbor is putting a BA on his Mooney that is otherwise basically stock. Lastly we'll look at 1JX with all the goodies. Jezzie's airplane should be a close match to that.

[jetdriven]

how much does a BA give you?

 

[testwest]

Hartzell says 2-4 knots, and I'll confirm that!

What I need to get you and everyone else excited about is participating in the data gathering for a Benchmark model of the M20J (and, for carusoam, the R). Once the baseline airframe is fully modeled, the old McCauley prop model can be removed and the new model for a Hartzell BA (or an MT, for that matter) can be put in for a comparison of performance increase (or decrease :/ ) across the entire envelope.

Everyone always asks what a performance increase will get for you on top speed. I have always maintained that the performance increase should be measured by the max attainable CAFE score, instead. That has never been easily done with an accurate model....

until now.

I can't tell you how jazzed I am at discovering Benchmark.

For KSMooniac, you don't have to be a Mac guy....you just have to know one. ;-). Please write to MT or look in your documentation for a specification called "blade activity factor". They will know what it is.

And for jetdriven, how "stock" is your Mooney? Any mods?

[aviatoreb]

Quote: testwest

Hartzell says 2-4 knots, and I'll confirm that!

What I need to get you and everyone else excited about is participating in the data gathering for a Benchmark model of the M20J (and, for carusoam, the R). Once the baseline airframe is fully modeled, the old McCauley prop model can be removed and the new model for a Hartzell BA (or an MT, for that matter) can be put in for a comparison of performance increase (or decrease :/ ) across the entire envelope.

Everyone always asks what a performance increase will get for you on top speed. I have always maintained that the performance increase should be measured by the max attainable CAFE score, instead. That has never been easily done with an accurate model....

until now.

I can't tell you how jazzed I am at discovering Benchmark.

For KSMooniac, you don't have to be a Mac guy....you just have to know one. ;-). Please write to MT or look in your documentation for a specification called "blade activity factor". They will know what it is.

[fantom]

OK, so I'm late to the party...what do you need from us, Norm; is there a checklist for data?

[testwest]

Thanks again, everyone. I know this is a really technical subject.

For JimR, the actual derivation of the full CAFE formula:

V**1.3 x MPG x Wp**0.6 (where Wp is payload (not fuel or oil) weight, to a maximum of 200 lb per certificated seat)

is partly analytical and partly empirical. The PAV paper I referenced at the beginning of the thread goes through the entire process, it is excellent. If you can't get at it, I'll email you a copy. It does favor speed somewhat, but the original CAFE formula V x MPG x Wp wound up restating Carson's Speed in a parallel effort in 1980. And Carson's Speed as a cruise speed has never gained any traction in GA, because the required power level of ~50% is just too slow for most owner-operators...BSFC is lower at that power setting, too.

For fantom, welcome! You are never late.

And yes, there is a checklist for data. I am working on making the test card "Mooney Friendly"...there is a little homework, though. Probably the first thing would be an accurate and recent weight and balance. There are several W&B spreadsheets floating around on the site here....

[testwest]

This is the airspeed calculator output on Benchmark.

[testwest]

And some notes on the MPG chart:

"Now that you have entered all of the data, analyzed all of the curves, you are ready to produce some aircraft performance charts. The most important of these—and the raison d’être of Benchmark—is the miles-per-gallon chart.

The miles-per-gallon chart concept was originally developed for the B-29 bomber. With that aircraft, it was imperative
that the flight engineer operate the aircraft for the greatest practical efficiency, which was no easy task when you
considered the large changes in aircraft weight, as well as other variables like winds and altitudes. In fact, on the B-29,
the flight engineer was supplied with charts that showed the most efficient power settings for four-, three- and twoengine
operation. These charts are extremely useful since they tell you at a glance for a given altitude which are the
most efficient power settings to use, how fast an aircraft will fly at various weights, the miles-per-gallon efficiency of
the aircraft, and a temperature correction chart for non-standard days.

These charts were first introduced for general aviation aircraft by Mooney Aircraft in the early 1980s and proved to be very popular with efficiency-conscious Mooney 201 pilots. The development of these charts was done with largely manual methods, using a series of look-up charts for this mathematically rigorous approach. In a few hours with Benchmark, you can duplicate the work that Mooney spent about $25,000.00 to accomplish—and with greater accuracy." [emphasis added] [from http://www.seqair.com/benchmark/BenchmarkManual.pdf , page 42]