# estimate_take_off_field_length.py
#
# Created: Jun 2014, T. Orra, C. Ilario, Celso,
# Modified: Apr 2015, M. Vegh
# Jan 2016, E. Botero
# Mar 2020, M. Clarke
# May 2020, E. Botero
# Jul 2020, E. Botero
# ----------------------------------------------------------------------
# Imports
# ----------------------------------------------------------------------
# RCAIDE Imports
import RCAIDE
from RCAIDE.Framework.Core import Data, Units
from RCAIDE.Library.Methods.Aerodynamics.Common.Drag import *
from RCAIDE.Library.Methods.Aerodynamics.Common.Lift import *
# package imports
import numpy as np
# ----------------------------------------------------------------------
# Compute field length required for takeoff
# ----------------------------------------------------------------------
[docs]
def estimate_take_off_field_length(vehicle,analyses,altitude = 0, delta_isa = 0, compute_2nd_seg_climb = False):
"""
Computes the takeoff field length and optionally the second segment climb gradient for a given vehicle configuration.
Parameters
----------
vehicle : Vehicle
The vehicle instance containing:
- mass_properties.takeoff : float
Takeoff weight [kg]
- reference_area : float
Wing reference area [m²]
- V2_VS_ratio : float, optional
Ratio of V2 to stall speed, default 1.20
- networks.*.number_of_engines : int
Number of engines per network
analyses : Analyses
Container with atmosphere and aerodynamic analyses
altitude : float, optional
Airport altitude [m], default 0
delta_isa : float, optional
Temperature offset from ISA conditions [K], default 0
compute_2nd_seg_climb : bool, optional
Flag to compute second segment climb gradient, default False
Returns
-------
takeoff_field_length : float
Required takeoff field length [m]
second_seg_climb_gradient : float, optional
Second segment climb gradient [unitless], only if compute_2nd_seg_climb=True
Notes
-----
The takeoff field length is computed using empirical correlations:
.. math::
TOFL = k_0 + k_1(V_2^2/T/W) + k_2(V_2^2/T/W)^2
where k₀, k₁, k₂ depend on number of engines:
* 2 engines: [857.4, 2.476, 0.00014]
* 3 engines: [667.9, 2.343, 0.000093]
* 4 engines: [486.7, 2.282, 0.0000705]
**Major Assumptions**
* Sea level standard conditions unless specified
* Standard V2 speed ratio (1.20 × stall speed)
* No wind conditions
* Dry runway surface
* For second segment climb:
- One engine inoperative
- Only validated for two-engine aircraft
**Theory**
Second segment climb gradient is computed as:
.. math::
\gamma = T/W - 1/L/D
where L/D includes effects of:
* Windmilling drag
* Asymmetric drag
* High-lift device drag
References
----------
[1] Stanford University AA241 Aircraft Design Course Notes http://adg.stanford.edu/aa241/AircraftDesign.html
See Also
--------
RCAIDE.Library.Methods.Aerodynamics.Common.Drag.windmilling_drag
RCAIDE.Library.Methods.Aerodynamics.Common.Drag.asymmetry_drag
"""
# ==============================================
# Unpack
# ==============================================
atmo = analyses.atmosphere
weight = vehicle.mass_properties.takeoff
reference_area = vehicle.reference_area
try:
V2_VS_ratio = vehicle.V2_VS_ratio
except:
V2_VS_ratio = 1.20
# ==============================================
# Computing atmospheric conditions
# ==============================================
atmo_values = atmo.compute_values(altitude,delta_isa)
conditions = RCAIDE.Framework.Mission.Common.Results()
p = atmo_values.pressure
T = atmo_values.temperature
rho = atmo_values.density
a = atmo_values.speed_of_sound
mu = atmo_values.dynamic_viscosity
sea_level_gravity = atmo.planet.sea_level_gravity
# ==============================================
# Determining vehicle maximum lift coefficient
# ==============================================
# Condition to CLmax calculation: 90KTAS @ airport
state = Data()
state.conditions = RCAIDE.Framework.Mission.Common.Results()
state.conditions.freestream = Data()
state.conditions.freestream.density = rho
state.conditions.freestream.velocity = 90. * Units.knots
state.conditions.freestream.dynamic_viscosity = mu
settings = analyses.aerodynamics.settings
maximum_lift_coefficient, induced_drag_high_lift = compute_max_lift_coeff(state,settings,vehicle)
# ==============================================
# Computing speeds (Vs, V2, 0.7*V2)
# ==============================================
stall_speed = (2 * weight * sea_level_gravity / (rho * reference_area * maximum_lift_coefficient)) ** 0.5
V2_speed = V2_VS_ratio * stall_speed
speed_for_thrust = 0.70 * V2_speed
# ==============================================
# Determining vehicle number of engines
# ==============================================
engine_number = 0.
for network in vehicle.networks : # may have than one network
engine_number += len(network.propulsors)
if engine_number == 0:
raise ValueError("No engine found in the vehicle")
# ==============================================
# Getting engine thrust
# ==============================================
# Step 28: Static Sea Level Thrust
planet = RCAIDE.Library.Attributes.Planets.Earth()
atmosphere_sls = RCAIDE.Framework.Analyses.Atmospheric.US_Standard_1976()
atmo_data = atmosphere_sls.compute_values(0.0,0.0)
p = atmo_data.pressure
T = atmo_data.temperature
rho = atmo_data.density
a = atmo_data.speed_of_sound
mu = atmo_data.dynamic_viscosity
conditions = RCAIDE.Framework.Mission.Common.Results()
conditions.freestream.altitude = np.atleast_1d(0)
conditions.freestream.mach_number = np.atleast_1d(0.01)
conditions.freestream.pressure = np.atleast_1d(p)
conditions.freestream.temperature = np.atleast_1d(T)
conditions.freestream.density = np.atleast_1d(rho)
conditions.freestream.dynamic_viscosity = np.atleast_1d(mu)
conditions.freestream.gravity = np.atleast_2d(planet.sea_level_gravity)
conditions.freestream.speed_of_sound = np.atleast_1d(a)
conditions.freestream.velocity = np.atleast_1d(a*0.01)
# setup conditions
segment = RCAIDE.Framework.Mission.Segments.Segment()
segment.state.conditions = conditions
thrust = np.array([[0.0, 0.0, 0.0]])
analysis = RCAIDE.Framework.Analyses.Vehicle()
energy = RCAIDE.Framework.Analyses.Energy.Energy()
energy.vehicle = vehicle
analysis.append(energy)
segment.analyses = analysis
for network in vehicle.networks:
network.add_unknowns_and_residuals_to_segment(segment)
for propulsor in network.propulsors:
segment.state.conditions.energy.propulsors[propulsor.tag].throttle = np.array([[1]])
network.evaluate(segment.state,center_of_gravity = vehicle.mass_properties.center_of_gravity)
thrust += conditions.energy.thrust_force_vector
# ==============================================
# Calculate takeoff distance
# ==============================================
# Defining takeoff distance equations coefficients
takeoff_constants = np.zeros(3)
if engine_number == 2:
takeoff_constants[0] = 857.4
takeoff_constants[1] = 2.476
takeoff_constants[2] = 0.00014
elif engine_number == 3:
takeoff_constants[0] = 667.9
takeoff_constants[1] = 2.343
takeoff_constants[2] = 0.000093
elif engine_number == 4:
takeoff_constants[0] = 486.7
takeoff_constants[1] = 2.282
takeoff_constants[2] = 0.0000705
elif engine_number > 4:
takeoff_constants[0] = 486.7
takeoff_constants[1] = 2.282
takeoff_constants[2] = 0.0000705
print('The vehicle has more than 4 engines. Using 4 engine correlation. Result may not be correct.')
else:
takeoff_constants[0] = 857.4
takeoff_constants[1] = 2.476
takeoff_constants[2] = 0.00014
print('Incorrect number of engines: {0:.1f}. Using twin engine correlation.'.format(engine_number))
# Define takeoff index (V2^2 / (T/W)
takeoff_index = V2_speed**2. / (thrust[0][0] / weight)
# Calculating takeoff field length
takeoff_field_length = 0.
for idx,constant in enumerate(takeoff_constants):
takeoff_field_length += constant * takeoff_index**idx
takeoff_field_length = takeoff_field_length * Units.ft
# calculating second segment climb gradient, if required by user input
if compute_2nd_seg_climb:
# Getting engine thrust at V2 (update only speed related conditions)
state.conditions.freestream.dynamic_pressure = np.array(np.atleast_1d(0.5 * rho * V2_speed**2))
state.conditions.freestream.velocity = np.array(np.atleast_1d(V2_speed))
state.conditions.freestream.mach_number = np.array(np.atleast_1d(V2_speed/ a))
state.conditions.freestream.dynamic_viscosity = np.array(np.atleast_1d(mu))
state.conditions.freestream.density = np.array(np.atleast_1d(rho))
# engine condition
num_propulsors = 0
for network in vehicle.networks:
num_propulsors += len(network.propulsors)
for propulsor in network.propulsors:
engine_out_location = propulsor.origin[0][1]
thrust = thrust * (num_propulsors -1 )/num_propulsors
single_engine_thrust = np.linalg.norm(thrust /num_propulsors)
# Compute windmilling drag
windmilling_drag_coefficient = windmilling_drag(vehicle,state)
# Compute asymmetry drag
asymmetry_drag_coefficient = asymmetry_drag(state, vehicle,engine_out_location, single_engine_thrust, windmilling_drag_coefficient)
# Compute l over d ratio for takeoff condition, NO engine failure
l_over_d = estimate_2ndseg_lift_drag_ratio(state,settings,vehicle)
# Compute L over D ratio for takeoff condition, WITH engine failure
clv2 = maximum_lift_coefficient / (V2_VS_ratio) **2
cdv2_all_engine = clv2 / l_over_d
cdv2 = cdv2_all_engine + asymmetry_drag_coefficient + windmilling_drag_coefficient
l_over_d_v2 = clv2 / cdv2
# Compute 2nd segment climb gradient
second_seg_climb_gradient = thrust / (weight*sea_level_gravity) - 1. / l_over_d_v2
return takeoff_field_length[0][0], second_seg_climb_gradient[0][0]
else:
# return only takeoff_field_length
return takeoff_field_length[0][0],0
