PL/R-Diagrams

jetfuelburn.diagrams

calculate_fuel_consumption_payload_range

calculate_fuel_consumption_payload_range(
    d,
    oew,
    mtow,
    range_point_A,
    payload_point_B,
    range_point_B,
    payload_point_C,
    range_point_C,
    range_point_D,
)

Given aircraft performance parameters from a payload/range diagram and a flight distance \(d\), calculates the required fuel mass \(m_F\) and payload mass \(m_{PL}\) for a given mission.

This function implements the simple "reading fuel mass off the payload/range diagram directly" method:

Payload/Range diagram of the Airbus A350-900 (data derived from manufacturer information). Note that in this figure, the y-axis shows total aircraft weight, not payload weight. Total aircraft weight can be computed by adding the operating empty weight (OEW) to the payload weight and fuel weight.

Notes

Key assumptions of this fuel calculation function:

Parameter	Assumption
data availability	excellent for existing aircraft (payload/range diagrams are public)
aircraft payload	maximum payload possible payload
climb/descent	implicitly considered
fuel reserves	depends on (sometimes unknown) manufacturer assumptions
alternate airport	depends on (sometimes unknown) manufacturer assumptions

Warnings

There is no manufacturer-independent convention for including reserve and alternate fuel in payload/range diagrams. Limited evidence suggests that eg. Boeing always assumes a 200nmi diversion distance (cf. Slide 43 in this Boeing presentation and this airliners.net discussion). The user is therefore cautioned against directly comparing aircraft of different manufacturers using this function.

References

• Burzlaff (2017), Fig. 3.10
• "Aircraft Payload-Range Analysis for Financiers", Fig. 5 ff.

Parameters:

Name	Type	Description	Default
d	float	Flight distance [length]	required
oew	float	Operating Empty Weight (OEW) of the aircraft [mass]	required
mtow	float	Maximum Takeoff Weight (MTOW) of the aircraft [mass]	required
range_point_A	float	Range at point A [length]	required
payload_point_B	float	Payload mass at point B [mass]	required
range_point_B	float	Range at point B [length]	required
payload_point_C	float	Payload mass at point C [mass]	required
range_point_C	float	Range at point C [length]	required
range_point_D	float	Range at point D [length]	required

Returns:

Type	Description
dict	'mass_fuel' : ureg.Quantity Fuel mass [kg] 'mass_payload' : ureg.Quantity Payload mass [kg]

Raises:

Type	Description
ValueError	If any of the input parameters are not pint Quantity instances of the correct dimension.
ValueError	If the distance is less than zero.
ValueError	If the distance exceeds the maximum range of the aircraft as per the payload-range diagram.

Example

Editor (session: default) Run

import jetfuelburn
from jetfuelburn import ureg
from jetfuelburn.diagrams import calculate_fuel_consumption_payload_range
calculate_fuel_consumption_payload_range(
    d=2000*ureg.nmi,
    oew=142.4*ureg.metric_ton,
    mtow=280*ureg.metric_ton,
    range_point_A=500*ureg.nmi,
    payload_point_B=54*ureg.metric_ton,
    range_point_B=5830*ureg.nmi,
    payload_point_C=25*ureg.metric_ton,
    range_point_C=8575*ureg.nmi,
    range_point_D=9620*ureg.nmi,
)

Output Clear

Source code in jetfuelburn/diagrams.py

@ureg.check(
    "[length]",
    "[mass]",
    "[mass]",
    "[length]",
    "[mass]",
    "[length]",
    "[mass]",
    "[length]",
    "[length]",
)
def calculate_fuel_consumption_payload_range(
    d: float,
    oew: float,
    mtow: float,
    range_point_A: float,
    payload_point_B: float,
    range_point_B: float,
    payload_point_C: float,
    range_point_C: float,
    range_point_D: float,
) -> dict[float, float]:
    r"""
    Given aircraft performance parameters from a payload/range diagram and a flight distance $d$,
    calculates the required fuel mass $m_F$ and payload mass $m_{PL}$ for a given mission.

    This function implements the simple _"reading fuel mass off the payload/range diagram directly"_ method:

    ![Payload/Range Diagram](../_static/payload_range_generic.svg)
    Payload/Range diagram of the Airbus A350-900 (data derived [from manufacturer information](https://web.archive.org/web/20211129144142/https://www.airbus.com/sites/g/files/jlcbta136/files/2021-11/Airbus-Commercial-Aircraft-AC-A350-900-1000.pdf)).
    Note that in this figure, the y-axis shows _total_ aircraft weight, not _payload weight_.
    Total aircraft weight can be computed by adding the operating empty weight (OEW) to the payload weight and fuel weight.

    Notes
    -----
    Key assumptions of this fuel calculation function:

    | Parameter         | Assumption                                                          |
    |-------------------|---------------------------------------------------------------------|
    | data availability | excellent for existing aircraft (payload/range diagrams are public) |
    | aircraft payload  | maximum payload possible payload                                    |
    | climb/descent     | implicitly considered                                               |
    | fuel reserves     | depends on (sometimes unknown) manufacturer assumptions             |
    | alternate airport | depends on (sometimes unknown) manufacturer assumptions             |

    Warnings
    --------
    There is no manufacturer-independent convention for including
    reserve and alternate fuel in payload/range diagrams.
    Limited evidence suggests that eg. Boeing always assumes a 200nmi diversion distance (cf. [Slide 43 in this Boeing presentation](https://web.archive.org/web/20250000000000*/http://aviation.itu.edu.tr//img/aviation/datafiles/Lecture%20Notes/FundamentalsofAirlineManagement20152016/Lecture%20Notes/10.1-ITU_Airplane_Performance.pdf) and [this airliners.net discussion](https://www.airliners.net/forum/viewtopic.php?t=764183#p11029989)).
    The user is therefore cautioned against directly comparing aircraft of different manufacturers using this function.

    References
    --------
    - [Burzlaff (2017), Fig. 3.10](https://www.fzt.haw-hamburg.de/pers/Scholz/arbeiten/TextBurzlaff.pdf)
    - ["Aircraft Payload-Range Analysis for Financiers", Fig. 5 ff.](http://www.aircraftmonitor.com/uploads/1/5/9/9/15993320/aircraft_payload_range_analysis_for_financiers___v2.pdf)

    Parameters
    ----------
    d : float
        Flight distance [length]
    oew : float
        Operating Empty Weight (OEW) of the aircraft [mass]
    mtow : float
        Maximum Takeoff Weight (MTOW) of the aircraft [mass]
    range_point_A : float
        Range at point A [length]
    payload_point_B : float
        Payload mass at point B [mass]
    range_point_B : float
        Range at point B [length]
    payload_point_C : float
        Payload mass at point C [mass]
    range_point_C : float
        Range at point C [length]
    range_point_D : float
        Range at point D [length]

    Returns
    -------
    dict
        'mass_fuel' : ureg.Quantity
            Fuel mass [kg]
        'mass_payload' : ureg.Quantity
            Payload mass [kg]

    Raises
    ------
    ValueError
        If any of the input parameters are not [pint](https://pint.readthedocs.io/en/stable/) Quantity instances of the correct dimension.
    ValueError
        If the distance is less than zero.
    ValueError
        If the distance exceeds the maximum range of the aircraft as per the payload-range diagram.

    Example
    -------
    ```pyodide install='jetfuelburn'
    import jetfuelburn
    from jetfuelburn import ureg
    from jetfuelburn.diagrams import calculate_fuel_consumption_payload_range
    calculate_fuel_consumption_payload_range(
        d=2000*ureg.nmi,
        oew=142.4*ureg.metric_ton,
        mtow=280*ureg.metric_ton,
        range_point_A=500*ureg.nmi,
        payload_point_B=54*ureg.metric_ton,
        range_point_B=5830*ureg.nmi,
        payload_point_C=25*ureg.metric_ton,
        range_point_C=8575*ureg.nmi,
        range_point_D=9620*ureg.nmi,
    )
    ```
    """

    #  all variables of the same dimension must use consistent units
    oew = oew.to("kg")
    mtow = mtow.to("kg")
    payload_point_B = payload_point_B.to("kg")
    payload_point_C = payload_point_C.to("kg")
    range_point_B = range_point_B.to("km")
    range_point_C = range_point_C.to("km")
    range_point_D = range_point_D.to("km")

    acft_weight_point_B = oew + payload_point_B
    acft_weight_point_C = oew + payload_point_C
    acft_weight_point_D = oew

    if d < 0:
        raise ValueError("Distance must be greater than zero.")
    if d < range_point_B:
        slope = (mtow - acft_weight_point_B) / (range_point_B - range_point_A)
        intercept = mtow - slope * range_point_B
        m_f = (slope * d + intercept) - acft_weight_point_B
        m_pld = payload_point_B
    elif range_point_B <= d < range_point_C:
        slope = (acft_weight_point_B - acft_weight_point_C) / (
            range_point_C - range_point_B
        )
        intercept = range_point_B * slope + acft_weight_point_B
        m_f = mtow - (-1 * slope * d + intercept)
        m_pld = (mtow - oew) - m_f
    elif range_point_C <= d < range_point_D:
        m_f = mtow - acft_weight_point_C  # max fuel
        slope = (acft_weight_point_C - acft_weight_point_D) / (
            range_point_D - range_point_C
        )
        intercept = range_point_C * slope + acft_weight_point_C
        m_pld = (-1 * slope * d + intercept) - oew
    else:
        raise ValueError(
            "Distance exceeds maximum range of aircraft as per payload-range diagram."
        )

    return {"mass_fuel": m_f.to("kg"), "mass_payload": m_pld.to("kg")}