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As discussed in Chapter#07section01 , Piano does not analyse the thermodynamic cycle of the engine. Emission calculations are therefore carried out according to a widely used empirical method based on knowledge of the fuel-flow and atmospheric conditions. This is usually referred to as the '**Boeing 2**' emissions method. It was originally implemented in Piano as per "Minutes of 17th meeting of ANCAT/EC Emissions Inventory Database Group, July 20, 1995, Dept. of Trade and Industry" and "Presentation to CAEP Working Group III Certification Subgroup, March 6, 1995".

The method covers oxides of nitrogen (NOx), unburnt hydrocarbons (HC), and carbon monoxide (CO). It requires certain baseline information on the emissions of specific engine types. This is readily available in the public domain. It was first published in the "ICAO Engine Exhaust Emissions Data Bank, ICAO Doc 9646-AN/943, First Edition, 1995". More recent data are in the CAA aircraft engine emissions homepage .

Piano calculates the instantaneous fuel flow at several points in the flight cycle. It uses the Reference Emissions Indices (REI) obtainable from the ICAO databank or other sources, corrects them for flight conditions according to the '**Boeing 2**' method, then integrates the emissions output over the entire flight profile.

To calculate NOx emissions, Piano needs only the variation of the Reference Emissions Index (REINOx) with fuel-flow. The REINOx is defined as grams of NOx per kilogram of fuel (g/kg) at the reference sea-level-ISA conditions. Such data are provided by the ICAO databank in the form of four points, normally corresponding to settings of 100%, 85%, 30%, and 7% of rated thrust. However, you can actually input as many arbitrary points as are available. These must be typed directly into the '**description**' file of the engine, in the format shown in the following example:

fuel-kg/s-EINOx-g/kg ( 0.21 4.30 0.58 7.50 1.53 36.2 1.88 52.7 )The numbers, which must be surrounded by parentheses, represent alternately the fuel flow in kg/second and the REINOx in g/kg. More details on '

As with all engine characteristics in Piano, the REINOx should correspond to an installed engine. The consistency of the ICAO databank in this respect is unclear. It is only noted here that certain factors are applied by some users to the ICAO fuel flow, typically:

setting factor 100% 1.010 85% 1.013 30% 1.020 7% 1.100It is entirely up to the user to include any such adjustments in the input data.

Interpolation between points is smooth (a spline fit). You can use the '**Ref. EINOx**' item under the '**Eng**' menu ('**Dimensional**' sub-menu), to see a plot of the fitted data.

Source codes: Piano's implementation of the NOx method corresponds directly to the equations used in '**Boeing 2**', through the following functions:

humidity-beta : The exponent 'beta' (a function of ambient temperature) used in calculating the saturation vapour pressure (Pv).

emissions-omega : The specific humidity 'omega', a function of ambient pressure (therefore altitude) and Pv. Boeing and RR have assumed a relative humidity of 0.6 (though alternatives can be specified in the 'patches' file via relative-humidity ).

humidity-correction : The humidity correction 'H'.

emissions-corrected-flow : The corrected fuel flow factor 'Wff' as a function of actual fuel flow, ambient delta , theta , and Mach number.

reference-einox : This is the interpolation function that finds the reference NOx emissions index (REINOx) from the ICAO data as a function of the emissions-corrected-flow . A spline fit of the data is used.

einox-g/kg : The final result of '**Boeing 2**', giving the actual EINOx at any altitude, Mach, and fuel flow. It is a function of the reference-einox , the humidity-correction , delta and theta .

During the step-by-step analysis of the flight profile, the function nox-kg is used to find the absolute value of NOx emissions in kg (for all engines) over a certain time interval. The integrated results for all phases are added up by tot-up-nox . Piano stores the totals for the climb, cruise and descent in the variables climb-nox , cruise-nox , descent-nox , and for other segments in taxi-out-nox , takeoff-nox , approach-nox and taxi-in-nox .

Note that the emissions for the taxi-out, takeoff, approach, and taxi-in segments depend solely on the user-specified parameters taxi-out-time , takeoff-time , approach-time , and taxi-in-time . There is no attempt to analyse these phases in detail. Average values are calculated, using the takeoff, idle, or approach fuel flows, as appropriate over the given times.

Calculations of hydrocarbon (HC) and carbon monoxide (CO) emissions follow a similar pattern to the NOx calculations. The reference data from the ICAO databank (or other sources) must be typed in the '**description**' file of the engine as shown in these examples:

fuel-kg/s-EIHC-g/kg ( 0.21 1.0 0.58 0.04 1.53 0.01 1.88 .04 ) fuel-kg/s-EICO-g/kg ( 0.21 15.44 0.58 1.71 1.53 1.23 1.88 1.01 )The numbers, which must be surrounded by parentheses, represent alternately the fuel flow in kg/second and the reference emissions index (REIHC or REICO) in g/kg, at sea-level-ISA. If no data are specified, Piano does not carry out any HC or CO calculations.

The variations of REIHC and REICO with fuel flow are far less smooth than is the case for REINOx. Therefore, simple linear interpolation is used to avoid oscillations. You can input as many extra points as you want, to improve the fit. A mere four points, as provided in the ICAO databank, generally result in a poor curve. Data can be plotted through the '**Ref. EIHC**' and '**Ref. EICO**' items (see '**Eng**' menu, '**Dimensional**' sub-menu).

Source codes: The equations for finding EIHC or EICO at arbitrary conditions as defined in '**Boeing 2**' are simpler than those for the EINOx and depend solely on delta , theta and the reference data. The relevant functions are eiHC-g/kg and eiCO-g/kg .

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