Source code for RCAIDE.Library.Methods.Geometry.Planform.estimate_wing_internal_volume
# estimate_naca_4_series_internal_volume.py
#
# Created: ### ####, M. Vegh
# Modified: Jan 2016, E. Botero
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# Imports
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import numpy as np
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# Methods
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[docs]
def estimate_wing_internal_volume(wing, m, p):
"""Computes the volume of a wing with NACA 4-series airfoils.
Assumptions:
Wing has constant thickness to chord along the span
Front spar is at 10%chord and rear spar is at 60% chord
Source:
Wikipedia, based on Moran, Jack (2003). An introduction to theoretical and
computational aerodynamics. Dover.
Inputs:
m [-] percent camber (.1 is 10%)
p [-] location of max camber (.1 is 10% along chord)
wing.chords.
root [m]
tip [m]
wing.taper [-]
wing.thickness_to_chord [-]
wing.spans.projected [m]
chord_length [m]
Outputs:
volume [m^3]
Properties Used:
N/A
"""
#unpack inputs
t_c = wing.thickness_to_chord
taper = wing.taper
rc = wing.chords.root
tc = wing.chords.tip
span = wing.spans.projected
yc_front_spar_root = m*(.1*rc/p**2.)*(2*p-.1) #front spar is 10%chords
yc_rear_spar_root = m*((rc-.6*rc)/(1-p)**2.)*(1+.6-2*p)
yc_front_spar_tip = m*(.1*tc/p**2.)*(2*p-.1)
yc_rear_spar_tip = m*((tc-.6*tc)/(1-p)**2.)*(1+.6-2*p)
dy_dx_front_spar = (2.*m/p**2.)*(p-.1)
dy_dx_rear_spar = (2.*m/(1-p)**2.)*(p-.6)
theta_front_spar=np.arctan(dy_dx_front_spar)
theta_rear_spar=np.arctan(dy_dx_rear_spar)
x_front_spar_root = .1*rc
x_rear_spar_root = .6*rc
yt_front_spar_root = 5*t_c*rc*(.2969*(.1**.5)-.126*.1-.3516*.1**2+.2843*.1**3.-.1015*.1**4.)
yt_rear_spar_root = 5*t_c*rc*(.2969*(.6**.5)-.126*.6-.3516*.6**2.+.2843*.6**3.-.1015*.6**4.)
yt_front_spar_tip = 5*t_c*tc*(.2969*(.1**.5)-.126*.1-.3516*.1**2+.2843*.1**3.-.1015*.1**4.)
yt_rear_spar_tip = 5*t_c*tc*(.2969*(.6**.5)-.126*.6-.3516*.6**2.+.2843*.6**3.-.1015*.6**4.)
yu_front_spar_root = yc_front_spar_root+yt_front_spar_root*np.cos(theta_front_spar)
yl_front_spar_root = yc_front_spar_root-yt_front_spar_root*np.cos(theta_front_spar)
yu_rear_spar_root = yc_rear_spar_root+yt_rear_spar_root*np.cos(theta_rear_spar)
yl_rear_spar_root = yc_rear_spar_root-yt_rear_spar_root*np.cos(theta_rear_spar)
yu_front_spar_tip = yc_front_spar_tip+yt_front_spar_tip*np.cos(theta_front_spar)
yl_front_spar_tip = yc_front_spar_tip-yt_front_spar_tip*np.cos(theta_front_spar)
yu_rear_spar_tip = yc_rear_spar_tip+yt_rear_spar_tip*np.cos(theta_rear_spar)
yl_rear_spar_tip = yc_rear_spar_tip-yt_rear_spar_tip*np.cos(theta_rear_spar)
#create line between root and tip points
slopeu_front_spar = (yu_front_spar_root-yu_front_spar_tip)/(span/2.)
slopel_front_spar = (yl_front_spar_root-yl_front_spar_tip)/(span/2.)
slopeu_rear_spar = (yu_rear_spar_root-yu_rear_spar_tip)/(span/2.)
slopel_rear_spar = (yl_rear_spar_root-yl_rear_spar_tip)/(span/2.)
yu_front_spar_mid = (span/4.)*slopeu_front_spar+yu_front_spar_tip
yl_front_spar_mid = (span/4.)*slopeu_front_spar+yl_front_spar_tip
yu_rear_spar_mid = (span/4.)*slopeu_rear_spar+yu_rear_spar_tip
yl_rear_spar_mid = (span/4.)*slopel_rear_spar+yl_rear_spar_tip
slope_chord = (rc-tc)/(span/2.)
mid_chord = slope_chord*(span/4.)+tc
Aroot = ((yu_front_spar_root-yl_front_spar_root)+(yu_rear_spar_root-yl_rear_spar_root))*(rc*(.6-.1))/2.
Atip = ((yu_front_spar_tip-yl_front_spar_tip)+(yu_rear_spar_tip-yl_rear_spar_tip))*(tc*(.6-.1))/2.
Amid = ((yu_front_spar_mid-yl_front_spar_mid)+(yu_rear_spar_mid-yl_rear_spar_mid))*(mid_chord*(.6-.1))/2.
volume = 2*(span/12.)*(Aroot+4*(Amid)+Atip) #integrate a side and multiply by two
return volume
