Earlier this month, at a meeting between ministers from Australia, China, and Malaysia, the countries involved in the search for MH370 announced that, in the event that the plane was not found within the current search zone by the end of mission in May, the area would be **increased** “to extend the search by an additional 60,000 square kilometres to bring the search area to 120,000 square kilometres.” (The **new area** is outlined in red in the image shown here.)

I think it’s worth considering the logic behind this decision.

Last year the ATSB spent months carefully calculating the boundaries of the original 60,000 sq km area. What they wound up with was **a rectangle** about 1200 km long and ranging in width from **48 to 62 kilometers wide**, straddling the 7th arc.

This area fit what the ATSB believed to be the most likely scenario for the final phase of the plane’s flight: that it flew straight on a southerly heading on autopilot and then shortly after 0:11 ran out of fuel — first one engine, then the second. After the second engine stopped, a backup system called the Auxiliary Power Unit (APU) would have kicked in, restoring a limited amount of electrical power. The plane’s satellite communications system would have rebooted, leading to the final “half ping” at 0:19.

As soon as the second engine failed, the engine would have entered a unpowered glide, much as the “Miracle on the Hudson” A320 did after its engines ingested a flock of geese. In this case, however, there would have been no pilot at the controls to guide the plane in for a smooth landing. What’s more, the power interruption would have turned off the autopilot. Uncontrolled, the plane would have gradually banked into a turn, which then would have grown steeper, devolving into a tight spiral dive that would have ended with the plane impacting the water at high velocity.

Let’s call this the “Unpiloted Fuel Exhaustion Scenario,” or UFES.

Under these circumstances, it would be virtually impossible for the plane to have traveled very far from the 7th ping arc. In a paper released last week, IG member **Brian Anderson** calculates that by 0:19 the plane would low and have been traveling downward at a tremendous rate:

… the 7th arc position calculation should assume that the aircraft was at or near sea level (the surface of the reference ellipsoid) at time 00:19:38, and hence only a little above sea level at 00:19:29, and descending rapidly.

The UFES, combined with careful analysis of the Inmarsat data, adds up to a clear and falsifiable hypothesis about the location of MH370’s final resting place: it should lie within a few kilometers of the 7th arc, and certainly be within the ATSB search area. The search team has consistently expressed absolute confidence in the hypothesis. Indeed, their language has only gotten stronger with the passage of time. Earlier this month, a Fugro executive told **Bloomberg,** “We’re absolutely in the right spot — all the analysis has been done. It’s actually getting more exciting as we get closer.”

The fly in the ointment is that the search area described in the area is now almost completely scanned, and the plane is not inside it. When the last square kilometer of the current 60,000 square kilometer search zone is scanned sometime next month, the hypothesis will have been falsified. The UFES will have been shown to be incorrect.

The failure to find the plane in the search area should not be regarded as failure. Rather, it is an important piece of information about the fate of MH370. It allows us to narrow down the list of possibilities going forward.

But it does force us to confront a difficult question: How do we best rationally proceed?

One approach would be to assess the different assumptions that underlie the UFES, judge which ones are most likely wrong, and then examine the available alternatives. Perhaps, for instance, the 0:19 half-ping was not caused by fuel exhaustion, but some other event. In that case, the plane might have flown on for an unknown period of further time.

Perhaps aircraft performance calculations, which would rule out scenarios like that proposed by Simon Hardy, are incorrect and the plane really did fly far to the southwest.

Another alternative is that the airplane was not unpiloted, but that a conscious individual was actively flying the plane at the time of fuel exhaustion. If that were the case, then the plane could have glided a considerable distance before impacting the sea; the ATSB’s June report states “the aircraft could glide for 100+ NM.”

A fourth alternative is that, **as I have suggested**, the BFO data upon which the UFES is predicated cannot be trusted, because it was tampered with by sophisticated hijackers. Indeed, we know that the system that generates the BFO data was indeed tampered with, in a way that implies sophisticated knowledge by whoever carried it out. If such a spoof were carried out, then the plane would likely be many thousands of miles from the southern Indian Ocean—most likely, in Kazakhstan. That scenario would explain why no debris has been found in the southern Indian Ocean, and provide a link to what would otherwise be an extremely unlikely coincidence: the Russian shoot-down of a second Malaysian Airlines 777 just four months later.

The ATSB has as yet given no indication that they realize that the the UFES is incorrect, or what kind of scenario would be compatible with the new search area. They have **specifically stated** that they view the Kazakhstan scenario as impossible, but have not revealed any evidence that would rule out a spoof.

The only insight we have into the ATSB’s actual line of reasoning is by looking at the new search area that they have laid out. Essentially what they’ve done is to take the current search area and make it bigger in every direction. There doesn’t seem to be any operational principle besides “let’s keep looking.”

The ATSB’s proposed new search area might simply be an example of what psychologists call “perseveration.” This is a pattern of behavior often seen in individuals who are highly stressed to the point of panic, and, unable to come up with a solution to their problem, simply continue to repeat the same unsuccessful actions over and over again. (An example I cite in my book *Extreme Fear* is the case of Civil War soldiers who, after suffering a misfire in their muskets, simply continue to cram more and more cartridges down their rifle barrels; after one battle guns were found stuffed with 10 or 11 cartridges.)

Perhaps the time has come for the taxpayers funding the SIO search to demand a more rational approach.

UPDATE: Soon after I put up this post, one reader commented via **Twitter** that continuing to search the southern Indian Ocean at least provided jobs and did no actual harm. I disagree. Apart from spending taxpayers’ money unnecessarily, it serves to put the mystery of MH370 on ice–allowing the authorities can say “we’re doing the best we can” while running out the clock on the public’s interest in the case. They’re buying the right to pretend, for one more year, that their assurances haven’t been empty and that the UFES is still a reasonable (indeed, the only reasonable) possibility. This means that more profitable lines of inquiry will continue to be ignored.

Dr. Bobby Ulich’s recommended location is ouside the aircraft performance envelope.

@LGH: I supported Bobby’s location back in August. It took what I deemed the best approach (path reasonability as OBJECTIVE function, with signal data error as CONSTRAINT, rather than vice versa). And both the ATSB and NTSB – in March, 2014, anyway – did rule such paths fuel-feasible; and we are in fact looking for paths right on the performance MARGIN (since arc7, we are told, bears the hallmarks of impending impact).

But ALL credible SIO theories predict surface debris – including his. Its failure to show up on Australian shores suggests STRONGLY that an SIO impact never occurred. And Bobby’s location WAS searched by air – it appears (to my eye) that, by Mar.24, 2014, the air search ranged out to E83.6, and from S39 to S42 at that western boundary:

https://s3-ap-southeast-2.amazonaws.com/asset.amsa.gov.au/MH370+Day+7/Charts/2014_03_24_cumulative_search_handout.pdf

Inasmuch as prevailing currents take surface debris INTO this search area, I find “the wind blew it all away (or up, or down)” arguments less than convincing.

Also counter-indicating any SIO path is the obfuscation by search leaders extensively documented elsewhere. One pertinent example (among dozens): the ATSB changed its mind a few months later about the fuel feasibility of Bobby’s path – and, a year after THAT, will (I predict) change its mind again (citing, as usual, “brand new” analysis of data that, as usual, hasn’t ever changed).

But to me, the most damning counter-evidence against his (and any similar) location has been the FAUX evidence paraded before our eyes these past few months. To me, that really cemented my conviction that the SIO theory is not being TESTED; it is being SOLD.

It is time to investigate the investigators.

I pitched this imperative – strenuously – to the IG last November. I was told to wait and see what the Fugro ships turned up. “First few passes”, I was told. “Within 1-5 nmi”, I was told. So I watched. And waited.

I’m done waiting. Let’s find out what search leaders are hiding.

@Brock,

Here is the same map with my proposed location marked on it.

https://drive.google.com/file/d/0BzOIIFNlx2aUWjNkbUlRV1ZOM3c/view?usp=sharing

It is very slightly beyond the air search area. In addition, currents in that area sometimes run west, so debris might not have drifted into the air search area. It is possible that impact debris at that location might not have been overflown by the air search.

@Gysbreght,

My location is in fact reachable by 9M-MRO if it flew above FL350 on the southbound leg. The average PDA needed, assuming FL380 – FL400, is about 2.4%. Your statement that this location is outside the aircraft performance envelope is incorrect.

@Dr. Bobby Ulich,

The aircraft performance boundaries for southern turn priorto 1840 at MRC speed and reachable altitudes has been defined by the ATSB in the October Update. Why do you need a PDA, doesn’t that reduce the range by 2.4%?

Gysbreght –

As Brock has pointed out, the ATSB figures show ranges at 25,000, 30,000, & 35,000 feet for a turn at 1828 and and adds the range at 40,000 feet for a turn at 1840. They seem to have excluded a track at 40,000 feet together with a turn at 1828. I think Brock suggested that this was omitted because it shows an impact location outside of the search area. According to the performance manual a B-777 with Trent 892 Engines can reach 40,400 feet as long as the weight is 210,000 Kg or below. My quick calculation shows MH370 should have been down to 210,000 Kg or below by 1828.

Niels,

Agree. My only purpose is to get comments and opinions from professionals in these areas, where I have little to zero expertise. But comments from IG members (except Victor; Jeff is not in IG), who may possess respective knowledge, are virtually absent if questions are not compatible with their “AP+FMT+N571” hypothesis. This is in contrast to the situation a year ago, when very active discussions took place.

Lauren H-

“… a B-777 with Trent 892 Engines can reach 40,400 feet …”

Sure, but it seems that an MRC path based on a turn near the first arc at 1828 (Figure 2) would not reach the 7th arc and, even if it did, would not intersect the 7th arc at a latitude south of 40S.

@Gysbreght: “it seems that an MRC path based on a turn…at 1828 (Figure 2) would not reach the 7th arc and, even if it did, would not intersect the 7th arc at a latitude south of 40S.”

The key word in your paragraph: SEEMS.

Now read my report’s Concern #7, and its supporting appendix. The principle of rotational symmetry PROVES that 18:28->E84 is JUST as fuel-feasible as 18:40->E88.

My beef with S40 is not “moving there is a waste of time” – it is “not moving there was a waste of time”.

And this is not an isolated incident, but part of a PATTERN of hiding poor search decisions behind intuitive-but-faulty reasoning.

If Lucy puts the football down at E84 NEXT year, I don’t think there are many of us left willing to try another kick.

@Brock McEwen

Where can I read your report?

http://www.dailytelegraph.com.au/news/nsw/mh370-only-one-conclusion-makes-sense/story-fni0cx12-1227346739023?sv=d217b24c7b7110e572aca4595dda4665

Gysbreght – Re the assumptions – agreed. But some of these assumptions are pretty far reaching and they were best guesses(however well researched) and they needed to line up for the plane to show up in the hotspots. No surprise to me – and others – that they didn’t. At the same time there was a projection of authority, confidence, even derision for suggesting otherwise. The pilot I have linked above sounds extremely experienced and well connected but even he has had to venture out into the idea of a relatively tidy ditching in wild seas to account for the situation. A big glide takes a lot of assumptions off the table, and still does not guarantee the data. The thing is, they always thought they would find it, now they have to confront. I’m sure there are some venerable and good guys in the IG as well as Inmarsat but what did we just witness? I was criticized for being a sideline detractor and told to go ahead and actually publish something that contributes towards finding the plane, but there is no plane so noone can really claim to have done anything of the sort as yet. The reasoning was predicated on the assumption that it was in the box, end of story. Ahem.

Gysbreght – Forgot to mention – scientists began to play with BFO as if it was some thoroughly understood and highly predictive tool. Eventually that may not sit well alongside the glittering CV’s on the table. “But it’s all we had” you could say. You could also say it was a free for all.

@Gysbreght,

You said “Sure, but it seems that an MRC path based on a turn near the first arc at 1828 (Figure 2) would not reach the 7th arc and, even if it did, would not intersect the 7th arc at a latitude south of 40S.”

Your conclusion is incorrect. Here is why. My fuel consumption model is essentially identical to the one first used by Victor, except for the speed used. I use the Boeing fuel burn tables for the correct aircraft and engines. Starting at 17:07 and knowing the fuel on board then, I integrate the fuel consumption every second. The speed is assumed to be Long Range Cruise at Mach 0.84 with climb as needed to stay within +/- 2,000 feet of the optimum cruise altitude for M0.84 at the current aircraft weight. The “margins” in both the endurance and range to a position past the 6th arc and nearing the 7th arc at the time of fuel exhaustion (00:15:50 for the second engine) are both approximately 2 1/2 % for an early turn and an end point near 40S 84 E. That means that engines with typical performance degradations would quit at just the right place and at the right time if 9M-MRO was flown as I have described. As Lauren has noted, the plane weight was appropriately low enough for a climb to have been made above FL350 near 18:28. As ALSM has noted, it would be expected that an even altitude would be used flying westward, so it is possible a climb was made then, or shortly thereafter, to FL380 or FL400. That allows efficient long-range cruising until 00:16.

End points farther up the 7th arc can also be reached at fuel exhaustion but at somewhat lower speeds. Since we don’t know the speed control method actually used, it is difficult to say which is more likely based solely on fuel models. However, it does appear that much of that area has already been searched by the ATSB with negative results. Either 9M-MRO is farther from the 7th arc in the ATSB search area or it is farther down the 7th arc. In my opinion, the latter case is more likely because that route also demonstrates remarkable air speed stability.

@Matty

Thanks for the Byron Bailey thread. He really nailed it.

>But some of these assumptions are pretty far reaching and they were best guesses

I can’t speak for the ‘Constrained Autopilot Dynamics’ model (as per the IG and most of the discussion here) but the assumptions for the ‘Data error optimisation’ models are pretty simple (straight-line, constant speed and variations around that). That doesn’t make them correct of course.

The Constrained Autopilot model clearly has a great deal of influence inside the Investigation since three-quarters of the Fugro boat time has been expended in searching the area it predicts. Perhaps is it because the leaders of the Investigation are old pilots and like the pilots whose ideas have been published (e.g. the Daily Telegraph story) they imagine what they themselves would have done in that unfortunate situation. The BFO driven Data Error models, which predict destinations in the North of the search area, seem to come from the non-pilot community (such as Inmarsat) and have been given lower priority. Quite when the last 25% of the original area will be finished remains to be seen since the weather has now been declared as keeping the focus in the South.

So IMHO the fat lady has not sung on the original search area.

@DrBobbyUlich

I’m still curious why you need a PDA. It reduces range and endurance, so how does it help to reach your location?

My reference is the performance boundary in the ATSB report. ATSB enjoys the participation of Boeing, and who knows better how to calculate the range and endurance of the airplanes they manufacture? They know, and you don’t, what went into the performance data they published in their manuals, and how to interpret anything that may be known about the past performance of this particular tailnumber.

The performance boundaries in the October Update are based on MRC speed. LRC is a higher speed, at the expense of reduced range (1%) and endurance (4 – 5%). If the airplane climbed near 18:28 from FL 350 to FL 380 or FL400 you have to account for the extra fuel used during climb. Increasing the cruise altitude from FL350 to FL390 (the optimum altitude for range) will increase the still air range by about 67 NM, and reduces the endurance by about 19 seconds.

The fact that sofar the airplane has not been found in the area searched, together with the lack of debris, make the unpiloted hypothesis even more improbable than it was before the search.

@DrBobbyUlich

P.S.

Based on a rough estimate the extra fuel for climbing from FL350 to FL390 is equivalent to 14 NM range, reducing the gain in SAR from 67 to 53 NM.

@Gysbreght,

It’s not clear you understand what the PDA means. If a particular route required 0% PDA to be reachable, then one would conclude that is quite unlikely because the engines in 9M-MRO were not new. They are likely to have PDAs between 1-3%. That implies that a route that reaches an end point near the 7th arc at the correct time with 2-3% PDA is much more likely to be correct.

It’s not that “I need a PDA”, as you said. It’s that the aircraft has one that is not zero, and the correct route must include that loss of engine efficiency.

Since neither the ATSB nor Boeing has released any of the assumptions made (very early on)in calculating their “performance limit”, it is difficult to evaluate its relevance today. Similarly, they have withheld the engine PDA values. This gives the appearance they did not want to be second-guessed. In addition, they did not include results for an 18:28 turn and a 40,000 foot altitude, as Lauren pointed out.

The fuel used in the climb is effectively included in the table values because of the integration method that interpolates the table values. Climbing to higher altitude in LRC mode is a net win because the reduced drag offsets the cost of the climb.

My confidence in a 40S 84E end point is bolstered by the following observations:

1. That route is consistent, within the expected noise, with the satellite data indicated by Inmarsat as being reliable.

2. It can be flown very simply on autopilot using a standard speed control mode.

3. The RMS variation in the true air speed is within ~1 knot after compensation for wind and temperature along the route.

4. The calculated endurance and range are both consistent within a percent or so with typical engine PDAs.

If you believe any other route is equal or superior in terms of these metrics, please publish it for others to evaluate.

IMHO the obvious explanation is that the 40,000 foot altitude path calculated by them did not reach the 7th arc.

“The fuel used in the climb is effectively included in the table values because of the integration method that interpolates the table values. Climbing to higher altitude in LRC mode is a net win because the reduced drag offsets the cost of the climb.”

I’m not sure which table you’re referring to. The FCOM table “Long Range Cruise Control” doesn’t include climb. Yes, the ‘net win’ in the cruise segment is 53 NM starting at a weight of 210 tons at FL350 and ending at a weight of 174.4 tons at FL390.

“If you believe any other route is equal or superior in terms of these metrics, please publish it for others to evaluate.”

As I wrote earlier, the unpiloted autopilot theory is losing credibility. Inmarsat has published a route that comes equally close to your ‘metrics’ after 19:41.

@Bobby: I have not repeated your calculation with the climb, so I will not comment on whether I get the same result. However, if you have not done so, it is important to include the additional fuel consumption due to temperatures higher than the ISA static air temperature (SAT). For instance, a 10K increase in total air temperature (TAT) will produce a 3% increase in fuel consumption, i.e., 0.3% increase per TAT (K) offset. At M=0.84, TAT/SAT = 1.14, so there is about a 0.26% increase per SAT(K) offset.

Depending on how you have arranged your calculation, it may be helpful to note that the specific air range (SAR) of TAS/FF (NM/kg of fuel) does not change with ambient temperature at a given Mach-number, because TAS and FF both change as the sqare root of absolute ambient temperature.

Gysbreght: I was referring the fuel flow rate, not the fuel mileage. The correction factor of 3%/10K TAT offset is a footnote to the LRC tables taken from the FPPM for the B777-200ER with GE engines. I assume that B777 equipped with either GE or RR engines will have similar temperature effects on fuel rate.

I do believe that the fuel mileage does increase temperature, although not as much as the fuel flow rate because of the offsetting effect of speed. The reason for the increase I believe is due to two effects:

1. The temperature effect has an exponent of 0.6, not 0.5.

2. Reynolds number effects increase the drag slightly with temperature.

Let’s assume ISA temperature at a cruise altitude is 218K and M=0.84, or TAT/SAT = 1.14. At ISA+10K, the total temperature offset is 11.4K, and the fuel flow increase is 11.4 x 0.3% = 3.4%. Meanwhile, the speed increase is sqrt(228/218)-1 = 2.3%. The net reduction in fuel mileage is 3.4 – 2.3 = 1.1%, which is smaller than the 3.4% increase in fuel flow, but not zero.

@VictorI:

I don’t think that is correct. Where do you get that the temperature effect has an exponent of 0.6? Why do you bring in TAT/SAT which is a function of Mach and applies for both temperatures? I noted that in an earlier post of you that I didn’t understand and I fear you are misinterpreting something. Can you point me to your references?

Victor,

I trust there are many parameterisations of fuel rate. A different parameterisation is suggested in “Aircraft Propulsion and Gas Turbine Engines” by El-Sayed, CRC Press, 2008:

fuel rate/thrust = (a+b*M)*sqrt(Ta/Tref),

where a and b are constants, M – mach, Ta – air temperature, Tref = 288.2K.

So, power 0.6 vs 0.5 can hardly be used as an argument.

———-

Bobby,

You wrote “The RMS variation in the true air speed is within ~1 knot after compensation”. I bet you do not account for gusts and turbulence.

In my opinion the problem in you scenario is not in metrics. The problem is to explain the sudden change of heading in less than 15 minutes with the use of AP. If the aircraft climbed to FL400 during 18:25-18:40, it would reappear on the same radar, but it did not. If it climbed later, why nobody picked the call 18:40? Anyway I am missing something: why do you need to ‘implement’ a climb to FL400 into your model?

Richard Cole – Yes, it looks like they will just fall short this season but where is it at exactly. ATSB have become increasingly vague about the area covered ever since they passed the half way. They say over 3/4 but ALSM calculated with his routine aplomb it was at 76% a month ago.

@VictorI:

Now I found the equation in the opening post of “Guest Post: Northern Routes …”.

That is a very strange equation. Where did you get it? Perhaps the context explains the conditions for which it applies, it cannot be true for turbine engines in general.

@Gysbreght and @Oleksandr: The exponent of 0.6 was offered as a suggestion as to why fuel mileage reduces slightly as temperature increases. I don’t know the exact number for our B777-200ER. However, the actual numbers I presented do not make an assumption about the exponent.

The references I cite are both from Boeing: 1) Flight Planning and Performance Manual (FPPM), 777-200ER, GE90-94B, Revised Dec 10, 2010.

2) Jet Transport Performance Methods, Walt Blake, (c) 2009, Boeing.

Specific citations:

a) In (1), as a footnote to the LRC tables on pages 3.2.12 – 3.2.21 and the .84M Cruise Tables on pages 3.2.22 – 3.2.23, it says “Increase/decrease fuel flow 3% per 10C above/below standard TAT”. That seems unambiguous to me.

b) In (2), Chapter 32: Normal Cruise, Section Cruise Fuel Mileage, Effect of Temperature of Fuel Mileage. I can’t quote every relevant phrase, but it discusses how fuel flow goes as sqrt(Tt/Tref)^x for a given thrust, where x = 0.61 for a B757-200, and drag increases with temperature due to Reynolds number change. It gives a specific example for a B757-200 in which an ISA+20 condition at FL350 and M=0.8 causes a 6.2% increase in fuel flow but only a true airspeed increase of 4.5%, causing a 1.7% decrease in fuel mileage. This example is also unambiguous.

It is clear that Boeing believes that for its planes, fuel mileage decreases as the temperature increases from ISA conditions. I’ll trust that Boeing is correct.

Upon further reflection I’ll partially retract my last post. Except for the exponent of 0.6 the equation can be correct. What is missing is the definition of ‘corrected’ thrust-specific fuel consumption and the conditions for which it can be assumed to be constant (i.e. in order to compare apples to apples and not to oranges).

@Gysbreght,

You said “As I wrote earlier, the unpiloted autopilot theory is losing credibility. Inmarsat has published a route that comes equally close to your ‘metrics’ after 19:41.”

I am unaware of any basis for your first claim.

Your second claim is incorrect. The route published by Inmarsat has ground speeds that vary from 800 to 829 kph from 19:41 to 00:19. In addition, it has no wind compensation. It is not a constant air speed nor a constant Mach number, and it is not very steady. Inmarsat’s bearings vary from 179 to 186 degrees. It it not a true track route, nor is it a great circle route. It is not flyable on autopilot. It requires bearing and speed changes during the last 4 1/2 hours. If you choose to believe a pilot made those course and speed changes, you can do so. In my opinion, a route consistent with full autopilot control after 19:41 is more likely to be correct.

Matty

The exact search area was never published, only the 60000sq.km. figure and a small scale map. My read is that since the expanded search area was agreed the search in the South has already expanded outside the original 60000sq.km. area, on the basis that general area will not be accessible for weather reasons for many months (as hinted in the recent ATSB updates). Hence progress on the original 60000sq.km. has stalled (in the South). When the Fugro boats return from their next port call we will see if they continue in the South, or move North to complete the original search area.

@ Dr. Bobby Ulich:

You can twist yourself into knots to argue that your location can be reached with the available fuel and perhaps a favourable tailwind, the fact remains that it is outside the ATSB’s Performance Boundary. That’s what I wrote on May 8.

@Gysbreght: here’s a link to my report, per your request:

https://drive.google.com/file/d/0B-r3yuaF2p72ZkNWN1U5bklEbTA/view?usp=sharing

@ Brock:

Thanks, I’ll read it.

@ VictorI:

To continue from my post on May 9 at 6:52 PM:

On the exponent: According to dimensional analysis, the theoretical value of the exponent is 0.5. The author may have found an empirical value of 0.6 to provide a better fit in some experiment, but that value is not generally used.

On the relation in your “Guest post”:

Since thrust specific fuel consumption is fuel consumption per unit of thrust, the definition of ‘corrected’ TSFC implied by that relation must be TSFC devided by the square root of the expression between braces. For practical purposes it may be considered to be constant a given engine at constant “corrected thrust” and Mach number, where “corrected thrust” is thrust divided by ambient pressure.

@ Brock McEwen:

I’ve read the items of your paper that you indicated in your post.

Firstly, I’m not sure that items 1 through 4 in Appendix B are neglible.

Secondly, you missed the fact that fuel consumption is approximately proportional to airplane weight, and that the paths originating from turns at 1828 and 1840 cross the arcs at different weights and therefore the fuel consumed between arcs is different.

@Gysbreght: No. The corrected thrust can be used to find how engine thrust rating varies with pressure, or how corrected fuel consumption varies with corrected N1, but the actual fuel consumption (after temperature correction) is proportional to thrust, not the corrected thrust.

I have tested these relationships against the fuel consumption values for the B777-200ER with success in the range of conditions of my study. In fact, I am working on a more general and more accurate methodology to be applied across the entire operating range of the engine. More on that later.

The relations I have presented are consistent with how Boeing does its calculations as I have shown in the references. I trust Boeing to know how to do the calculations, including how to calculate the temperature effect on fuel mileage, which you insist is zero. Your disagreement is with Boeing, not with me.

If you think you have a more accurate methodology, I encourage you to write it up and test it against the published values in the LRC tables over a range of altitudes. I’d be curious as to your ability to match the data using your methods.

True, but what I wrote is that the corrected TSFC is approximately constant for constant corrected thrust and Mach.

However, a complicating factor is that the bleedair extracted from the engine for cabin air conditioning and pressurization, expressed as a fraction of the total engine massflow, increases with altitude. That affects the TSFC and is apparent as a residual altitude effect in the ‘generalized’ LRC mileage data shown in this graph:

https://www.dropbox.com/s/h86kds7n1zuf6q4/B777_LRC_RF_Wcor.jpg?dl=0

@ VictorI,

If you are only interested in the temperature correction on fuel flow for given weight, altitude and Mach, the relation you gave simplifies to:

FF1 = FF_ISA*sqrt(Ts1/Ts_ISA) for absolute static temperatures Ts1 and Ts_ISA.

I am somewhat sceptical about your attempt to derive Cd’s from the fuel flow data. LRC is essentially a constant Cl, Cd condition, except that at high Mach the optitum Cl reduces slightly with increasing Mach. Since there is no indepent variation of Cl and Mach, you cannot separate the Cd variation due to Cl from that due to Mach.

The only other conditions you have data on is Holding and engine-out cruise. That gives you a second Cl,Cd point. You can assume that Cd varies linearly with Cl^2, which is a reasonable approximation for intermediate Cl’s, but not for high Cl or high Mach.

@Gysbreght: You said, “If you are only interested in the temperature correction on fuel flow for given weight, altitude and Mach, the relation you gave simplifies to…”

I am interested in fuel flow for varying weight, altitude, and Mach number. That was the point of the exercise.

You said, “LRC is essentially a constant Cl, Cd condition, except that at high Mach the optitum Cl reduces slightly with increasing Mach. Since there is no indepent variation of Cl and Mach, you cannot separate the Cd variation due to Cl from that due to Mach”

That’s not true. Neither Cl or Cd is constant for various LRC conditions. Prove it to yourself by going to the LRC table for a given pressure altitude (Ps/Pref = constant)and you will see that Cl varies considerably with weight.

You said, “You can assume that Cd varies linearly with Cl^2, which is a reasonable approximation for intermediate Cl’s, but not for high Cl or high Mach.”

This is false. There is a significant drag component that is not “induced”, that is independent of lift. I assure you that you will not get the correct answer if you ignore this effect.

You keep insisting my methodology is wrong while not presenting fuel flow results based on a model of your own. I have shown that my model is consistent with Boeing’s recommendations and predicts the fuel flow over a range of conditions. Rather than continue this debate, please present your own model and we can compare results.

I will also repeat that I have an even more accurate model that I will present in the future. I have found a way to use available data to more accurately calculate Cd from Cl and M. I have not made the documentation of this model a high priority because it does not fundamentally change the conclusions I reached regarding the feasibility of reaching various northern airports. However, if there is general interest, I will find time in the future to present the results.

@VictorI

Sorry, I somehow missed your post of May 9, 2015 at 6:47 PM, in which you gave a reference to Boeing’s JTPM.

So you are right and I was wrong.

My apologies.

Yes, I know that. You misread what I wrote.

But thanks anyway.

@Gysbreght: Yes, I see you said Cd is linear with Cl^2, not proportional. I agree.

Boeing’s JTPM is a gold mine of information. Relative to plane performance, it is my primary reference. To the best of my ability, my model replicates the methods presented therein.

Victor –

A couple of days ago, you made reference to temperature guidelines you used from a manual for a B777-200ER w/GE Engines. On 1/17/2015 Dave Reed posted this link http://lukas1992.bplaced.net/_777-family.pdf to a Boeing Flight Crew Operations Manual that includes performance tables for GE, RR & PW engines including the effect temperature has on various parameters. I do not know if these tables might give you different results but they do show slightly different maximum operating altitudes for the GE versus RR Engines at ISA+10°C, ISA+15°C, & ISA+20°C.

@Lauren H: Thank you for the link. I don’t see where the effect of temperature on fuel flow is explicitly stated as it was in the FPPM for the GE engines. However, the manual does contain the fuel flow for “Holding Flaps Up”, which was supplied to me confidentially. I am glad this is now in the public domain as others can use it.

Victor-

Glad I could help.

Below the Tables in the Performance Dispatch Sections (PD21.9-PD21.11 for Rolls Royce) there is a list of “Adjustments” the second of which states “Increase fuel required 0.8% per 10°C above ISA.”

I missed that earlier because I had only checked the “Performance Inflight” Tables. The adjustment amount is the same for all 3 Engine Manufacturers.

Lauren H: The fuel adjustment you cite is based on a different scenario than inflight LRC. To quote, “Based on: Emergency descent to 10000 ft, level cruise at 10000 ft, 250 KIAS descent to 1500 ft, 15 minutes hold at 1500 ft, approach and land.” The fact that the same adjustment is used for both engine types is relevant, though.

Well, I did look at the cL’s and it turns out that you are lucky. There are 6 points that are not on the line of optimum cL vs Mach because they are limited by a maximum IAS of 325 kt. Not to prove anything, just curiosity triggered by your remark.

https://www.dropbox.com/s/nxrk8jluesewgg4/B777_LRC_cL.jpg?dl=0

@Gysbreght: the two FL400 (constant speed)paths – the one plotted in Fig.3, and the one suppressed from Fig.2 – cross each arc at the exact same (required) times, and thus at the exact same weights. Period.

The two paths cover the exact same distance – both in total, and between each arc.

Other than the four negligible (and offsetting) items I list, this is a stone-cold mathematical PROOF. If you can demonstrate materiality of ANY of the four, I’d be thrilled to see it.

Agreed. You may have noted that in the section on holding it discusses the variation of fuel flow with thrust and Mach, and that TSFC is not constant.

Agreed.

“The two paths cover the exact same distance – both in total, and between each arc.”

That depends on the details in Appendix B that you claim to be negligible.

@Gysbreght: Thank you. No doubt the development of the fuel flow model is complicated with the limited data at hand. Let’s wait until I have documented the full model and we can discuss the inaccuracies. I encourage you to develop your own and we can compare results. Perhaps we can together work on an improved model.