aircraft.flight_performance

ECAC Doc 29 flight performance: procedural steps into a flight profile.

A published departure or arrival procedure is not a trajectory. It is a list of procedural steps — “climb at take-off thrust to 1500 ft”, “accelerate to 210.6 kt at 984.3 ft/min”, “descend on a 3 degree slope from 3000 ft at 180 kt” — and the aeroplane’s own aerodynamic and engine coefficients. ECAC Doc 29 5th ed., Volume 2, Appendix B is the flight-mechanics model that turns the one into the other: a flight profile, an ordered list of profile points carrying distance along the ground track, height above the aerodrome, true airspeed and corrected net thrust per engine. Corrected net thrust is what the NPD tables of phonometry.aircraft.airport_noise are indexed on, so this model is what stands between a published procedure and a noise contour.

• Aerodrome — the aerodrome and its weather, and the five atmosphere ratios of B3 that every equation below reads.
• PerformanceAircraft with JetEngineCoefficients, PropellerEngineCoefficients and AerodynamicCoefficients — the ANP coefficient tables the equations take their constants from.
• DepartureStep and ApproachStep — one row each of a published procedure.
• departure_profile and approach_profile — the model, returning a FlightProfile of ProfilePoint.

Units are the standard’s and they are English throughout (B2): feet, knots, pounds, pounds of thrust per engine, degrees Celsius in the thrust equations and inches of mercury for pressure. Doc 29 keeps them “due to the history of the overarching method […] and the strong association that aviation has with English units”, and pins two conversion constants at deliberately imprecise legacy values that must not be improved (footnotes 30 and 31, folios B-7/B-8).

Departures run forward from brake release and arrivals run backwards from touchdown, which is why an arrival profile carries negative distances until the aeroplane is on the runway (folio B-5).

Source (clean-room, implemented from the published standard): ECAC.CEAC Doc 29, 5th edition, Volume 2 “Technical Guide”, Appendix B, folios B-1 to B-49.

Auto-generated from the source docstrings by scripts/generate_api_docs.py (make api-docs). Do not edit by hand.

Aerodrome(
    elevation_ft: float,
    temperature_c: float = 15.0,
    sea_level_pressure_inhg: float = 29.92,
    headwind_kt: float = 8.0,
    runway_gradient: float = 0.0,
)

The aerodrome, its weather and the runway a procedure is flown from.

Every atmosphere ratio of B3 is a function of altitude above mean sea level given these five numbers, and every equation of Appendix B reads at least one of them.

Attributes

The validity envelope Doc 29 claims for the coefficients is “air temperatures up to 43 degrees C, aerodrome altitudes up to 6,000 ft and across the range of weights specified in the ANP database” (B1). Nothing here enforces it: outside it the equations still evaluate, and the coefficients, not the arithmetic, are what stop being adequate.

Aerodrome.calibrated_airspeed_kt(
    true_airspeed_kt: float,
    altitude_ft: float,
) -> float

Calibrated airspeed from a true one at altitude_ft (Eq. B-8), kt.

Aerodrome.density_ratio(altitude_ft: float) -> float

Density ratio sigma at altitude_ft above MSL (Eq. B-5).

The ratio calibrated and true airspeed differ by: Eq. B-7 divides a calibrated airspeed by its square root to get the true one.

Aerodrome.pressure_altitude_ft(altitude_ft: float) -> float

Pressure altitude h for altitude_ft above MSL, ft (Eq. B-6).

The altitude the standard atmosphere would put this pressure at, which is what Eq. B-9’s Ga h and Gb h^2 terms read — not the geometric altitude. The two coincide only at a QNH of exactly 29.92 inHg; at 30.71 inHg over a sea-level aerodrome the aeroplane sits at 0 ft and flies at a pressure altitude of -723 ft.

Aerodrome.pressure_ratio(altitude_ft: float) -> float

Pressure ratio delta at altitude_ft above MSL (Eq. B-4).

Ambient pressure over 29.92 inHg. Every force balance in Appendix B divides the weight by it, because W/delta is the weight the thrust equations’ corrected thrust has to lift.

Raises

Aerodrome.temperature_c_at(altitude_ft: float) -> float

Air temperature at altitude_ft above mean sea level, degC.

Eq. B-2 lapses from the temperature at the aerodrome, not from a sea-level value: at field elevation the temperature is Tapt however high the field is. Eq. B-9 reads this as its T.

Aerodrome.temperature_ratio(altitude_ft: float) -> float

Temperature ratio theta at altitude_ft above MSL (Eq. B-3).

Air temperature at the aeroplane over standard sea-level temperature, both absolute. Eq. B-16 reads it directly and Eq. B-5 divides by it.

Aerodrome.true_airspeed_kt(
    calibrated_airspeed_kt: float,
    altitude_ft: float,
) -> float

True airspeed from a calibrated one at altitude_ft (Eq. B-7), kt.

AerodynamicCoefficients(
    drag_ratio: float,
    ground_roll_coefficient: float | None = None,
    speed_coefficient: float | None = None,
)

One ANP Aerodynamic_Coefficients row: a flap configuration.

Attributes

A missing coefficient is None, the dash the printed table prints, not a zero: a zero B is a take-off with no ground roll at all.

approach_profile(
    aircraft: PerformanceAircraft,
    steps: Sequence[ApproachStep],
    *,
    aerodrome: Aerodrome,
    weight_lb: float | None = None,
    procedure_id: str = '',
) -> FlightProfile

Fly an approach procedure’s steps into a flight profile (Doc 29 B7).

Approaches are solved backwards. Every airborne step computes its own Point1 from the following step’s Point1 (Eq. B-42, Eq. B-64), and the recursion is anchored by the Land step, whose Point1 sits at distance zero: hence the negative distances before touchdown. The rollout is then solved forwards from the same anchor, so touchdown is where the two sweeps meet.

Parameters

Returns: A FlightProfile with operation="A".

Raises

ApproachStep(
    step_type: str,
    flap_id: str,
    start_altitude_ft: float | None = None,
    start_calibrated_airspeed_kt: float | None = None,
    descent_angle_deg: float | None = None,
    touchdown_roll_ft: float | None = None,
    distance_ft: float | None = None,
    start_thrust_percent: float | None = None,
    bank_angle_deg: float = 0.0,
)

One row of an ANP approach procedural-step table (B7.1).

Attributes

Doc 29 Volume 3’s own workbook keeps a Level-Idle step’s length in the descent angle column, with the distance column empty. That is a defect of that workbook, not of the format: the length belongs in distance_ft here, where the ANP release also puts it.

property

The step type folded onto Doc 29’s own vocabulary, lowercase.

departure_profile(
    aircraft: PerformanceAircraft,
    steps: Sequence[DepartureStep],
    *,
    weight_lb: float,
    aerodrome: Aerodrome,
    procedure_id: str = '',
) -> FlightProfile

Fly a departure procedure’s steps into a flight profile (Doc 29 B6).

The profile is built forward from brake release, “the starting parameters for each segment being equal to those at the end of the preceding segment” (B1). Every step contributes one point, except the Take-off step, which contributes two, and any step that changes thrust rating, which is preceded by an inserted transition point (B6.1.6).

Parameters

Returns: A FlightProfile with operation="D".

Raises

DepartureStep(
    step_type: str,
    thrust_rating: str,
    flap_id: str,
    end_altitude_ft: float | None = None,
    rate_of_climb_ft_per_min: float | None = None,
    end_calibrated_airspeed_kt: float | None = None,
    energy_share_percent: float | None = None,
    distance_ft: float | None = None,
    bank_angle_deg: float = 0.0,
)

One row of an ANP departure procedural-step table (B6.1).

Attributes

Four of these are quantities the step type simply does not define, and the ANP table leaves each blank; they are None here and rendered as an em dash, never as a zero, since a zero rate of climb is a level acceleration and a zero distance is a step that goes nowhere.

A step given both a rate of climb and an energy share factor keeps both, and the model prefers the energy share factor: “The ROC-values are altitude and atmosphere conditions dependent whereas ESF values adapt to changing airport elevations and atmosphere conditions” (B6.1.3, folio B-21), so of the two only the energy share factor still means what the manufacturer intended at another aerodrome. B6.1.3 leaves the choice to the model, putting it as advice: “it is preferable to use ESF values”.

The bank angle is an input rather than something derived, because Eq. B-14 needs a turn radius and a turn radius needs the ground track, which this model does not build and Appendix B assumes it is given. Zero, the default, is straight flight, where every R/cos(eps) in Appendix B reduces to R.

property

The step type folded onto Doc 29’s own vocabulary, lowercase.

The raw step_type is kept as the table spells it so a transcription stays diffable against the sheet it came from; this is what the model branches on.

FlightProfile(
    aircraft_id: str,
    operation: str,
    procedure_id: str,
    points: tuple[ProfilePoint, ...],
)

A flight profile: the fixed-point trajectory a procedure flies (B1).

Attributes

This is the vertical-plane half of a Doc 29 flight path. Section 3.6 is what turns it into three dimensions — splitting segments at ground-track nodes, sub-segmenting the rolls and the climb, merging in the ground track — and none of that happens here.

property

Height above the aerodrome per point, ft.

property

Corrected net thrust per engine per point, lb.

property

Distance along the ground track per point, ft.

FlightProfile.plot(
    ax: Axes | None = None,
    *,
    language: str = 'en',
    **kwargs: Any,
) -> Axes

Plot the profile’s height and thrust against distance along the track.

property

True airspeed per point, kt.

JetEngineCoefficients(e: float, f: float, ga: float, gb: float, h: float)

One ANP Jet_Engine_Coefficients row: the Eq. B-9 thrust polynomial.

CNT = E + F Vc + Ga h + Gb h^2 + H T gives the corrected net thrust per engine in lb, for one aeroplane and one thrust rating.

Attributes

The units are the 5th edition’s symbol list (folio B-2) and the Volume 3 column headers; the 4th edition printed four units for these five symbols.

JetEngineCoefficients.corrected_net_thrust_lb(
    *,
    calibrated_airspeed_kt: float,
    pressure_altitude_ft: float,
    temperature_c: float,
) -> float

Corrected net thrust per engine, lb (Eq. B-9, and Eq. B-10 in kind).

Parameters

PerformanceAircraft(
    aircraft_id: str,
    engines: int,
    max_static_thrust_lb: float,
    max_landing_weight_lb: float,
    jet_coefficients: Mapping[str, JetEngineCoefficients] = ...,
    propeller_coefficients: Mapping[str, PropellerEngineCoefficients] = ...,
    aerodynamic_coefficients: Mapping[tuple[str, str], AerodynamicCoefficients] = ...,
)

One aeroplane’s Appendix B coefficient set.

Attributes

Which of the two thrust forms applies is decided by which table carries a row, not by the engine-type label: B4.1 is headed “jet and (certain) turboprop” for Eq. B-9 and B4.2 “piston and (some) turboprop” for Eq. B-12, and neither says which turboprop is which, so a turboprop appears under either heading and only its coefficient rows say under which.

property

Approach weight, lb: 90 % of the maximum landing weight (folio B-31).

Not the ANP Default_weights arrival entry, which is a different number for most of the fleet; Doc 29 names the aircraft table’s landing weight and the fraction explicitly, three times.

PerformanceAircraft.flap(
    operation: str,
    flap_id: str,
) -> AerodynamicCoefficients

Aerodynamic coefficients for one flap configuration.

Parameters

Raises

ProfilePoint(
    distance_ft: float,
    altitude_ft: float,
    true_airspeed_kt: float,
    corrected_net_thrust_lb: float,
)

One point of a Doc 29 flight profile.

Attributes

PropellerEngineCoefficients(efficiency: float, power_hp: float)

One ANP Propeller_Engine_Coefficients row: the Eq. B-12 thrust.

CNT = (326 eta Pp / Vt) / delta for a piston or turboprop aeroplane.

Attributes

PropellerEngineCoefficients.corrected_net_thrust_lb(
    *,
    true_airspeed_kt: float,
    pressure_ratio: float,
) -> float

Corrected net thrust per engine, lb (Eq. B-12).

Parameters

Raises