Applying the CO2 metric to the aircraft database: The numbers

Dimitri Simos
May 2013

A code extension to calculate values of ICAO's presumptive 'metric' for aviation CO2 emissions is now freely available to Piano-5 users. It can process, rank and plot an entire aircraft database automatically.

Key results are released into the public domain. This document provides implementation details for users together with assessments and background information for wider audiences.

• Definitions

The provisional form of the CO2 metric published here in June 2012 was not disputed by ICAO. To my best knowledge it is currently unchanged apart from a minor redefinition of 'low gross weight'. Caveats must however remain: ICAO (an agency of the United Nations) has thus far elected not to entrust the world community with its agreed metric - notwithstanding protestations that it is somehow a 'robust, objective and effective' system.

The metric definitions adopted here are:

Metric = 1/(SAR*RGF0.24)

SAR = specific air range (distance per unit fuel burn, km/kg)

RGF = 'reference geometric factor'. Despite its cryptic name this is an area (sq.m), not a factor. It is explained below.

1/SAR is to be evaluated at the following 3 postulated weights (kg) and then averaged, assuming 'optimum' conditions (maximum SAR) in each case:

1) High Gross Weight (GW) = 0.92 * MTOW
2) Mid GW = Average of High GW and Low GW
3) Low GW = 0.45 * MTOW + 0.63 * MTOW0.924

UPDATE: It is now possible to remove all caveats about the accuracy of this information. ICAO has acknowledged precisely the same definitions in its website: 1pdf/session 3/3-Dickson.pdf. Having taken responsibility for its metric, ICAO must address the questions raised here.

• What is RGF

The RGF is a Byzantine attempt to quantify 'cabin size', which ICAO inexplicably and untenably then considers to be a kind of 'proxy' for some unique but unstated payload - out of an infinity of possible payloads ranging from (MZFW-OEW) to zero. Indeed the word 'Payload' is not, on the face of it, sufficiently relevant to CO2 emissions to be mentioned anywhere in ICAO's metric sheet. Yet some of the participants in the process do hold compelling views about it.

For single-deck aircraft, RGF is defined as the part of the fuselage planform area (i.e. top view, external contours) constrained between the front and rear of the cabin. The precise proposed treatment of more intricate configurations is at this time less clear.

Piano readily calculates single-deck RGF from the fuselage shape and based on the existing parameters 'cabin-in-front-fuse-fraction' and 'cabin-in-rear-fuse-fraction'. It makes simple factored estimates for A380s and B747s. It is not aimed at interior layout details, so default inputs of cabin dimensions used in the database are for now mostly approximate. Cabin lengths and fuselage shapes can be adjusted by the user if required to set RGF precisely.

To allow for entirely arbitrary interior arrangements or revisions in ICAO's definitions, a new parameter 'co2-metric-rgf' is introduced, whose value is automatically determined by Piano unless it is explicitly input for a particular aircraft.

• Selecting optimum Mach and altitude

At each of ICAO's posited weights, Piano calculates the optimum combination of Mach number and altitude that maximises SAR. It incorporates operational ceiling restrictions of 100 ft/min (residual rate of climb) at maximum cruise rating and 300 ft/min at maximum climb rating.

There is significant potential for distortions (both analytic and practical) implicit in a loosely-worded choice of 'optimum' conditions, so ICAO will be forced to devise various qualifications. Several lightly-wing-loaded types could certainly improve their metric values through contrived engine rating options that would never be used in practice. (Unless clarified, the formal problem demands the calculus of variations for dynamic flight profiles; zoom-climbs could improve the metric).

ICAO's logic fails to reflect typical operational usage, or the widely differing but significant reasons why particular aircraft have the design characteristics that they do. Piano will happily crunch the requisite numbers, but the blinkered analysis of local optima is an academic exercise that is unrelated to fair CO2 comparisons of one type against another.

For individual aircraft, the metric is calculated by selecting the first item under the new 'CO2' menu, to produce a brief report such as this:
 B787-8 (502)pip v13ae                  CO2 Metric value = 1.422
 MTOW =    227930. kg.                            RGF = 233.4 m2.
 Span =     60.20  m.                    Cabin Length = 41.51 m.
 High GW   209696. kg.    Max.SAR .1674 km/kg @ M0.831, 36186.ft.
 Mid  GW   184246. kg.    Max.SAR .1912 km/kg @ M0.832, 38959.ft.
 Low  GW   158796. kg.    Max.SAR .2180 km/kg @ M0.830, 41719.ft.

(This is Piano's best estimate of current Boeing 787-8 CO2 metric levels, reflecting a more than 3% improvement over 2011 'entry into service' SARs - a substantial and creditable achievement by RR, GE and Boeing combined. Empty weights are another story.)

• Weight revisited

The metric definitions create the impression that ICAO does at least heed the critical importance of aircraft weight (after all, it uses three of them). It is best to disabuse the reader of any such thought. The CO2 emitted when an aircraft transports something to somewhere is determined by its empty weight (OEW). ICAO blithely ignores this. Instead, it bestows impossible powers on MTOW (the maximum combination of aircraft, fuel and payload weights legally allowed to take to the air), a number that is conveniently in the public domain.

In general (and particularly so within the aircraft emissions process), OEW is almost pathologically treated by the industry as information to be withheld from the public (though it is available to every pilot of every flight) precisely because it directly reflects on both the operator and the manufacturer through fuel burn (and CO2). MTOW is chosen by the manufacturer to suit design and marketing goals whilst satisfying regulatory safety rules. It does influence aircraft design strongly - it is a major sizing parameter. But it does not enter CO2 calculations in the slightest when comparing two aircraft over any payload and distance. It might restrict or extend capabilities, but MTOW is wholly irrelevant to CO2 over all shared operational regimes.

Put simply, ICAO is sheltering behind the crude fact that 'large' aircraft produce more CO2. Regulatory weights will naturally correlate statistically with CO2 over a sufficiently broad spectrum of aircraft size. This comprehensively ignores the key role of structures and materials.

According to ICAO's logic, two aircraft, one using old aluminium alloys and the other titanium, as long as they share their aerodynamics, engines and MTOW, are necessarily assigned precisely the same metric value. Yet their CO2 outputs would indeed differ substantially, over all shared operations. Selecting the same MTOW in this example merely exposes the insanity most clearly; the effect is just as real in the general case: An infinity of MTOW / sizing choices is open to the manufacturer depending on his design goals, but it is his use of materials and structures that will decide his CO2 credentials under all scenarios. ICAO's metric is universally blind to these technologies, and thoroughly insensitive to the weight of the actual aircraft.

In its press release, ICAO disingenuously tries to hide behind hollow phrases. It states that "[MTOW] accounts for the majority of aircraft design features which allow an aircraft type to meet market demand". The question is whether the metric accounts for how the physical weight of the aircraft alone affects CO2. It does not. A metric that fails to do that is nothing but a pretense.

• Data release: Running the metric on the aircraft database

Piano-5 users can select 'Sort+Plot Planes' from the 'CO2' menu to run the metric over their entire aircraft database (i.e. for all planes in the 'planes' directory) and produce a full output in this format:
 Provisional metric, based on SARs in km/kg, weights in kg, areas in m2:

 Rank  Aircraft                 CO2 Metric value        MTOW          RGF

   1. Eclipse (v00)                        0.097        2087.        5.18  
   2. Eclipse 500 (v04)                    0.141        2558.        5.12  
 ................................ etc ...................................
 495. Airbus A380-841 (qfa)                3.069      569000.      598.74
 496. Airbus A3XX-100R                     3.080      583000.      583.11
 497. Airbus A380-800F                     3.110      590000.      598.74
 498. Antonov An-124-210                   3.120      392000.      254.10
 499. Boeing model 763-246CER              3.148      532063.      366.68

Click here to view the ORIGINAL data release (May 2013).

Click here to view an UPDATED data release (July 2013).

If we were to take this list at face value, owning a small business jet (MTOW 2.5 tonnes) denotes the greenest of altruists whilst boarding an A380 (MTOW nearly 570 tonnes) condemns you as the most unspeakably crass polluter. This particular Alice-in-Wonderland ranking is not what ICAO suggests. ICAO recognises that the metric is meaningless in its direct form. And that it must therefore be bludgeoned into submission. Having resorted to the MTOW once, it resorts to the MTOW twice. This time it calls it 'The Correlation Parameter', assigns it to the X-axis of a plot, and places the metric values on the Y-axis. Here is the result:

The trend is not surprising. MTOW is one of many possible indicators of abstract 'aircraft size', so we get a straightforward sizing correlation. The bigger the MTOW, the higher the metric. The correlation is rough and nonlinear. Does this picture carry any information other than a mere sizing trend? Indeed it does, in a qualitative, weight-free sense: Since we have been evaluating SARs, it contains a broad technological trend attributable to the combined aerodynamic and engine qualities. This simply means that points significantly above the line are more likely to correspond to 1960s designs like DC-9s, 707s and IL-62s, and those significantly below the line are more likely to be modern designs. Overall trends are very loose (standard deviation 21.4%). They can of course be improved by selective culling of the data, like any statistic.

• An experiment

What role have ICAO's three postulated weights played in this picture? It is instructive to do a simple experiment: Let us replace all three weights by one. Take a wild guess and say an empty aircraft might weigh 50% of its MTOW and be rarely loaded above 90% of MTOW, so pick an average of 70%. We now define a 'modified metric' using (Low GW = High GW = Mid GW = 0.7 * MTOW) and re-run the entire database, including re-optimising Mach and altitude for maximum SAR. Here is what we get:

The correlation barely changes (in fact improves slightly to 21.2%. Y-values naturally differ). This begs the question: If this brutality made no difference, precisely what is the intended role of ICAO's three enigmatic weight definitions? A casual glance at the equations suggests that they address some intricate effect governed by MTOW. Do they have a utility beyond conveying that appearance? Let us move on from this mystery to another:

• One more experiment

Consider again ICAO's original metric with its 3 different weights. ICAO is not contemplating any simple straight-line regression as shown in the figures. It proposes to superimpose its own 'stringency' line and thereby create a compliance threshold that the CO2 metric of an aircraft must not exceed. This might take the form of an arbitrary multi-segment linear fit or curve, selected by fiat. The final act of the high-level political struggle is expected to be played out in somehow settling the location and contours of this mercurial 'Pass/Fail' line in the sand.

Whatever the ultimate line, one may well ask if some alternative simple correlation parameter can do any better than ICAO's omnipresent MTOW. There are other size-like candidates, for example geometric span. This too provides a trend - but even looser than the MTOW. What about simple span loading, which can often yield intriguing statistics? Defining this as the ratio of MTOW / span, we re-run the entire metric database (with the original ICAO weight definitions) against span loading. This is the result:

The correlation is noticeably tighter and more linear (standard deviation 15.4%). Why is that? There is no satisfactory single overarching reason, and in fact it remains a poor correlation - it merely happens to be noticeably better than ICAO's choice. These are trends, not causations.

The important lesson is this: An organisation that elects to base its key policies on voodoo statistics exposes itself to being out-voodoo'ed more or less at random. Is ICAO even minded to improve its metric format? It is a moot question. The ritualistic processes required to renegotiate the existing agreement (the relevance of span would need to be formally conceded) are so sclerotic as to make deviations in ICAO's insular and fact-free trajectory unlikely.

Additional views: labelled view, zoom 1, zoom 2, zoom 3, zoom 4, zoom 5

• Smoke and mirrors

The list shows that many business jets fare surprisingly well. That reflects their high standards of aerodynamic and engine characteristics (resulting in good SARs), but also the fact that the metric fails to correctly account for their normally miniscule payloads: The G650 is ranked very close to the CRJ 701LR (points 86 and 88 in the list; ICAO's stringency line makes no difference). The sheer folly of a scheme that assigns similar environmental credentials to premier business jets (carrying say 8 people) and regional jets (carrying 70 people) is self-evident.

One fatal flaw at the core of the charade is that the metric ignores payload and distance. Yet aircraft produce CO2 only because they carry payloads over distances. Bypassing elementary physics, ICAO chooses to sanctify an irrelevant concoction of ersatz cabin size and a certification weight restriction. It cannot work.

It is worth bearing in mind the arid information environment in which work is taking place. So far, minimal data provided by manufacturers to ICAO appear to be little more than prepared values of the metric. Flight conditions (Mach, altitude) are not revealed. Elements of self-certification might confer a final seal of irrelevance to the entire process.

Scientific analysis demands modelling aircraft correctly and disseminating data, methods and results publicly, with the participation of industry. Technical aspects of modelling are not difficult, despite protestations to the contrary. The pragmatic cooperation of manufacturers will follow from a practice of fair assessments.

Clearly aviation CO2 is intensely political, but this matter transcends politics. Politics cannot function absent a foundation of reason, which for quantifiable environmental emissions means scientific objectivity and true transparency. In this, ICAO is renouncing its responsibilities as a global body. It should stand up and act to the benefit of future generations. Smoke and mirrors are not a legacy to our children.

It would be wrong not to clarify that there are many good and competent people doing real work within the ICAO process. Personal contacts provided positive feedback and implied that such things needed to be said. At the organisational level, ICAO unsurprisingly did not respond to suggestions in the previous open letter. Failure to contact the author of the message did not extend to failure to contact some messengers and leave them in no doubt as to how it was received. Concentrating on a root-and-branch review of CO2 policies would have been time better spent.

• Notes for Piano-5 users

ICAO's CO2 metric remains 'work in progress'. The current code implementation is therefore provisional. It is issued free of charge as an extension to the latest version of Piano (5.2) and will be revised as and when definitions are formally frozen.

You will not require any new executable. The code is simply appended via existing patching mechanisms to your copy of Piano-5.2. If you are a supported Piano-5 user, the necessary source file with instructions will be emailed to you. A new 'CO2' menu lets you reproduce the results published here or apply the method to your own aircraft and engine models. Suggestions for other relevant features to go under the new menu are welcome. Code extensions are not supported in Piano-X.

Dimitri Simos