Cabin Class Fuel Allocation
jetfuelburn.utility.allocation ¶
footprint_allocation_by_area ¶
footprint_allocation_by_area(
fuel_per_flight,
size_factor_eco,
size_factor_premiumeco,
size_factor_business,
size_factor_first,
seats_eco,
seats_premiumeco,
seats_business,
seats_first,
load_factor_eco,
load_factor_premiumeco,
load_factor_business,
load_factor_first,
)Given the fuel burn per flight \(F\), the number of seats in each cabin class \(S_i\), the load factor in each cabin class \(L_i\) and the size factor of each cabin class \(s_i\), returns the fuel burn per passenger specific to each cabin class \(f_i\).
\[
f_i = \frac{1}{L_i} \frac{s_i F}{\sum_i s_i S_i}
\]
where
| Symbol | Unit (eg.) | Description |
|---|---|---|
| \(F\) | kg | Fuel burn per flight |
| \(f_i\) | kg | Fuel burn per passenger in seating class \(i\) |
| \(L_i\) | dimensionless | Load factor in seating class \(i\) |
| \(s_i\) | dimensionless | Size factor of seating class \(i\) |
| \(S_i\) | dimensionless | Number of seats in seating class \(i\) |
Summing over the fuel burn of all seating classes, we again get the total fuel burn per flight \(F\):
\[
F = \sum_i f_i S_i L_i = \sum_i \frac{1}{L_i} \frac{s_i F}{\sum_i s_i S_i} S_i L_i = F \frac{\sum_i s_i}{\sum_i s_i}
\]
The size factor of a class is defined as:
\[
s_i = \frac{A_i}{A_{economy}}
\]
where \(A_i\) is the area occupied by a passenger in class \(i\) and \(A_{economy}\) is the area occupied by a passenger in economy class.
This approach is suggested by both ICAO and IATA as the "allocation by area" method.
Notes
IATA RP 1726 (Section 2.4.2) recommends the following size factors:
| Economy | Premium Economy | Business | First | |
|---|---|---|---|---|
| Narrow-Body | 1.0 | 1.00 | 1.5 | 1.5 |
| Wide-Body | 1.0 | 1.5 | 4.0 | 5.0 |
Warnings
If a certain seating class is not present, all related parameters
(seats, size_factor, load_factor) should be set to 0.
References
Raises:
| Type | Description |
|---|---|
ValueError
|
If |
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
fuel_per_flight
|
float
|
Fuel burn per flight. |
required |
size_factor_eco
|
float
|
Size factor for economy class (1 by definition). |
required |
size_factor_premiumeco
|
float
|
Size factor for premium economy class. |
required |
size_factor_business
|
float
|
Size factor for business class. |
required |
size_factor_first
|
float
|
Size factor for first class. |
required |
seats_eco
|
int
|
Number of seats in economy class. |
required |
seats_premiumeco
|
int
|
Number of seats in premium economy class. |
required |
seats_business
|
int
|
Number of seats in business class. |
required |
seats_first
|
int
|
Number of seats in first class. |
required |
load_factor_eco
|
float
|
Load factor for economy class (between 0 and 1). |
required |
load_factor_premiumeco
|
float
|
Load factor for premium economy class (between 0 and 1). |
required |
load_factor_business
|
float
|
Load factor for business class (between 0 and 1). |
required |
load_factor_first
|
float
|
Load factor for first class (between 0 and 1). |
required |
Returns:
| Type | Description |
|---|---|
dict[float, float, float, float]
|
Fuel burn per passenger per flight in economy, premium economy, business and first class. |
Example
from jetfuelburn import ureg
from jetfuelburn.utility.allocation import footprint_allocation_by_area
footprint_allocation_by_area(
fuel_per_flight=14000*ureg.kg,
size_factor_eco=1,
size_factor_premiumeco=0,
size_factor_business=1.5,
size_factor_first=0,
seats_eco=154,
seats_premiumeco=0,
seats_business=24,
seats_first=0,
load_factor_eco=0.9,
load_factor_premiumeco=0,
load_factor_business=0.5,
load_factor_first=0,
)Source code in jetfuelburn/utility/allocation.py
def footprint_allocation_by_area(
fuel_per_flight: float,
size_factor_eco: float,
size_factor_premiumeco: float,
size_factor_business: float,
size_factor_first: float,
seats_eco: int,
seats_premiumeco: int,
seats_business: int,
seats_first: int,
load_factor_eco: float,
load_factor_premiumeco: float,
load_factor_business: float,
load_factor_first: float,
) -> dict[float, float, float, float]:
r"""
Given the fuel burn per flight $F$, the number of seats in each cabin class $S_i$,
the load factor in each cabin class $L_i$ and the size factor of each cabin class $s_i$,
returns the fuel burn per passenger specific to each cabin class $f_i$.
$$
f_i = \frac{1}{L_i} \frac{s_i F}{\sum_i s_i S_i}
$$
where
| Symbol | Unit (eg.) | Description |
| ------ | ------------- | -------------------------------------------- |
| $F$ | kg | Fuel burn per flight |
| $f_i$ | kg | Fuel burn per passenger in seating class $i$ |
| $L_i$ | dimensionless | Load factor in seating class $i$ |
| $s_i$ | dimensionless | Size factor of seating class $i$ |
| $S_i$ | dimensionless | Number of seats in seating class $i$ |
Summing over the fuel burn of all seating classes, we again get the total fuel burn per flight $F$:
$$
F = \sum_i f_i S_i L_i = \sum_i \frac{1}{L_i} \frac{s_i F}{\sum_i s_i S_i} S_i L_i = F \frac{\sum_i s_i}{\sum_i s_i}
$$
The _size factor_ of a class is defined as:
$$
s_i = \frac{A_i}{A_{economy}}
$$
where $A_i$ is the area occupied by a passenger in class $i$ and
$A_{economy}$ is the area occupied by a passenger in economy class.
This approach is suggested by both ICAO and IATA as the "allocation by area" method.
Notes
-----
IATA RP 1726 (Section 2.4.2) recommends the following size factors:
| | Economy | Premium Economy | Business | First |
| ----------- | ------- | --------------- | -------- | ----- |
| __Narrow-Body__ | 1.0 | 1.00 | 1.5 | 1.5 |
| __Wide-Body__ | 1.0 | 1.5 | 4.0 | 5.0 |
Warnings
--------
If a certain seating class is not present, all related parameters
(`seats`, `size_factor`, `load_factor`) should be set to 0.
References
--------
- [IATA Recommended Practice RP 1726: Passenger CO2 Calculation Methodology](https://web.archive.org/web/20230526103741/https://www.iata.org/contentassets/139d686fa8f34c4ba7a41f7ba3e026e7/iata-rp-1726_passenger-co2.pdf)
- [ICAO Carbon Emissions Calculator Methodology (Version 13.1)](https://web.archive.org/web/20240826103513/https://applications.icao.int/icec/Methodology%20ICAO%20Carbon%20Emissions%20Calculator_v13_Final.pdf)
- [World Bank Policy Research Working Paper 6471 _"Calculating the Carbon Footprint from Different Classes of Air Travel"_](https://documents1.worldbank.org/curated/en/141851468168853188/pdf/WPS6471.pdf)
Raises
------
ValueError
If `fuel_per_flight` < 0 or
(`load_factor_eco`, `load_factor_premiumeco`, `load_factor_business`, `load_factor_first`) not between 0 and 1.
Parameters
----------
fuel_per_flight : float
Fuel burn per flight.
size_factor_eco : float
Size factor for economy class (1 by definition).
size_factor_premiumeco : float
Size factor for premium economy class.
size_factor_business : float
Size factor for business class.
size_factor_first : float
Size factor for first class.
seats_eco : int
Number of seats in economy class.
seats_premiumeco : int
Number of seats in premium economy class.
seats_business : int
Number of seats in business class.
seats_first : int
Number of seats in first class.
load_factor_eco : float
Load factor for economy class (between 0 and 1).
load_factor_premiumeco : float
Load factor for premium economy class (between 0 and 1).
load_factor_business : float
Load factor for business class (between 0 and 1).
load_factor_first : float
Load factor for first class (between 0 and 1).
Returns
-------
dict[float, float, float, float]
Fuel burn per passenger per flight in economy, premium economy, business and first class.
Example
-------
```pyodide install="jetfuelburn"
from jetfuelburn import ureg
from jetfuelburn.utility.allocation import footprint_allocation_by_area
footprint_allocation_by_area(
fuel_per_flight=14000*ureg.kg,
size_factor_eco=1,
size_factor_premiumeco=0,
size_factor_business=1.5,
size_factor_first=0,
seats_eco=154,
seats_premiumeco=0,
seats_business=24,
seats_first=0,
load_factor_eco=0.9,
load_factor_premiumeco=0,
load_factor_business=0.5,
load_factor_first=0,
)
```
"""
if not fuel_per_flight > 0:
raise ValueError("Fuel burn per flight must be >0.")
if not (0 <= load_factor_eco <= 1):
raise ValueError("Load factor (economy class) must be between 0 and 1.")
if not (0 <= load_factor_premiumeco <= 1):
raise ValueError("Load factor (premium economy class) must be between 0 and 1.")
if not (0 <= load_factor_business <= 1):
raise ValueError("Load factor (business class) must be between 0 and 1.")
if not (0 <= load_factor_first <= 1):
raise ValueError("Load factor (first class) must be between 0 and 1.")
if size_factor_eco != 1 or seats_eco == 0:
raise ValueError("Economy class must have size factor 1 and at least one seat.")
fuel_eco = (
(1 / load_factor_eco)
* (size_factor_eco * fuel_per_flight)
/ (
size_factor_eco * seats_eco
+ size_factor_premiumeco * seats_premiumeco
+ size_factor_business * seats_business
+ size_factor_first * seats_first
)
)
if load_factor_premiumeco == 0 or seats_premiumeco == 0:
fuel_premiumeco = 0
else:
fuel_premiumeco = (
(1 / load_factor_premiumeco)
* (size_factor_premiumeco * fuel_per_flight)
/ (
size_factor_eco * seats_eco
+ size_factor_premiumeco * seats_premiumeco
+ size_factor_business * seats_business
+ size_factor_first * seats_first
)
)
if load_factor_business == 0 or seats_business == 0:
fuel_business = 0
else:
fuel_business = (
(1 / load_factor_business)
* (size_factor_business * fuel_per_flight)
/ (
size_factor_eco * seats_eco
+ size_factor_premiumeco * seats_premiumeco
+ size_factor_business * seats_business
+ size_factor_first * seats_first
)
)
if load_factor_first == 0 or seats_first == 0:
fuel_first = 0
else:
fuel_first = (
(1 / load_factor_first)
* (size_factor_first * fuel_per_flight)
/ (
size_factor_eco * seats_eco
+ size_factor_premiumeco * seats_premiumeco
+ size_factor_business * seats_business
+ size_factor_first * seats_first
)
)
return {
"fuel_eco": fuel_eco,
"fuel_premiumeco": fuel_premiumeco,
"fuel_business": fuel_business,
"fuel_first": fuel_first,
}