def m0_fn(Ma):
if Ma <= 0.9:
return (2 * math.pi) / numpy.sqrt(1 - Ma**2)
else:
return (2 * math.pi) / numpy.sqrt(1 - 0.9**2)
def Cd_fn(Cl):
return 0.0095 + 0.0040 * (Cl - 0.2)**2
nn = 101
h = 0 # m
v_inf = 70 # m/s
is_SI = True
atm = AtmData(v_inf, h, is_SI)
k = 1.4
R = 287
atm.expand(k, R)
numB = 3
radius = 2 / 2
RPM = 2400
Cl = 0.4
alp0 = numpy.radians(-2)
prop = Propeller(radius, numB, RPM, CP=0, CT=0, CQ=0, Cl=Cl, alp0=alp0)
T_req = 13000 / 8 # N (TOGW/(L/D))
r_vec, c_vec, beta_vec, P_design, T_design, Q_design, eta_P, theta_vec = prop_design(
atm, prop, T_req, m0_fn, Cd_fn)
in_line = [0] * len(r_vec)
plot_propeller_3D(r_vec, c_vec, beta_vec, prop, in_line)
T_design = [0] * nn
Q_design = [0] * nn
eta_P = [0] * nn
for ii in range(0, nn):
atm = AtmData(v_inf, h, is_SI)
atm.expand(1.4, 287)
prop = Propeller(radius,
numB,
RPM[ii],
eta_P,
CP=0,
CT=0,
CQ=0,
Cl=0.4)
[_, _, _, P_design[ii], T_design[ii], Q_design[ii], eta_P[ii],
_] = prop_design(atm, prop, T_req, m0_fn, Cd_fn)
label = "$V_\infty$ = " + str(v_inf) + " (m/s)"
plt.figure(1)
plt.plot(RPM, Q_design, label=label)
plt.figure(2)
plt.plot(RPM, eta_P, label=label)
plt.figure(3)
plt.plot(RPM, P_design, label=label)
# plt.figure(7)
# plt.plot(RPM,T_design,label=label)
try:
import formatfigures
formatfigures.formatsubfigures()
latex = True
except:
RPM = 2400
alp0 = numpy.radians(-2)
dens = atm_check.dens
CT = 0.0509
T_req = CT * dens * (RPM / 60)**2 * (radius * 2)**4
v_seq = numpy.arange(v_climb - 30 * 0.3048, v_climb + 126 * 0.3048, 2)
prop_check = Propeller(radius,
numB,
RPM,
eta_P=0,
CP=0,
CT=0,
CQ=0,
Cl=0.4)
r, prop_check.chord, prop_check.bet, P_design, T_design, Q_design, eta_P, prop_check.theta = prop_design(
atm_check, prop_check, T_req, m0_fn, Cd_fn)
ll = numpy.size(v_seq)
J_var = numpy.zeros((ll, ))
P_design_var = numpy.zeros((ll, ))
T_design_var = numpy.zeros((ll, ))
eta_P_var = numpy.zeros((ll, ))
deta_P = numpy.zeros((ll, ))
dT = numpy.zeros((ll, ))
delta_bet = numpy.zeros((ll, ))
RPM_fix = numpy.zeros((ll, ))
for ii in range(ll):
J_var[ii], P_design_var[ii], T_design_var[ii], Q_design_var[
ii], eta_P_var[ii], deta_P[ii], dT[ii], delta_bet[ii], RPM_fix[
ii] = prop_analysis_var_pitch(v_seq[ii], v_des, P_eng_data,
def STOL_power_req(m, dist_to, mot_distr, AtmData, Wing, Propeller_list):
'''
Provides calculation for the least required power of STOL aircraft
Inputs:
m: kg, airplane mass
dist_to: m, target rakeoff distance
motDistr: 1xn vector of motor power distribution
Wing.S: m^2, wing area
Wing.CL_max: max CL during takeoff
AtmData.dens: air density (to get ratio compared to standard sea level atm.)
Propeller_list: list of class "Propeller" for power calculation in FAR 25
Outputs:
outVec: if FAR 23, 1xn vector of motor power (hp)
if FAR 25, 1xn vector of motor thrust (N)
Calls:
{none}
Notes:
1. Function uses empirical expression provided in Roskam Part I
2. FAR 23/25 based on aircraft mass included
3. When integrating functions, mute the FAR23/25 fprintf sections
4. Not well tested yet
History:
2.9.2021, created by X.Tang in Matlab
2.14.2021, translated to Python by X.Tang
2.14.2021, still has problem in FAR25 power with [1,1] distr, power way too high
'''
std_sl_dens_SI = 1.225 # kg/m^3
std_sl_dens_Brit = 0.002377 # slug/ft^3
g = 9.81 # m/s^2
if AtmData.is_SI:
sigma = AtmData.dens / std_sl_dens_SI
else:
sigma = AtmData.dens / std_sl_dens_Brit
# FAR 23 / 25 check
dist_to_Brit = dist_to * 3.28084 # meter to feet
W = m * g # N
W_Brit = W * 0.224809 # N to lbf
S_Brit = Wing.area * 3.28084 ** 2 # m^2 to ft^2
bdy = 12500 * 0.453592 # kg
tol = 1e-3 # tolerance for compare between double
if m <= bdy: # FAR 23
a1 = 8.134
a2 = 0.0149
TOP23 = [0] * 2
delta = a2 ** 2 - 4 * a1 * (-dist_to_Brit)
# Check real
if delta > 0:
TOP23[0] = (-a2 + numpy.sqrt(delta)) / (2 * a1)
TOP23[1] = (-a2 - numpy.sqrt(delta)) / (2 * a1)
# Check positive num
if TOP23[0] > 0 and TOP23[1] <= 0:
TOP23_val = TOP23[0]
elif TOP23[0] <= 0 and TOP23[1] > 0:
TOP23_val = TOP23[1]
elif TOP23[0] > 0 and TOP23[1] > 0:
print("Error: TOP23 has two positive roots")
return
else:
print("Error: TOp23 has two negative roots")
return
elif abs(delta) <= tol:
TOP23_val = numpy.mean(TOP23)
if TOP23_val <= 0:
print("Error: TOP23 has one negative root")
else: # imaginary
print("Error: No real root for TOP23")
return
# Calculation for power in hp
PTO = (W_Brit ** 2 / S_Brit) / (TOP23_val * sigma * Wing.CL_max)
# Power distribution
if numpy.size(mot_distr) > 1:
sum_distr = sum(mot_distr)
power_vec = [0] * len(mot_distr)
for i in range(len(mot_distr)):
cur_distr = mot_distr[i] / sum_distr
power_vec[i] = cur_distr * PTO
else:
power_vec = PTO
# Can mute this following message
print("Aircraft category: FAR 23, motor POWER vector output")
return power_vec
else: # FAR 25
a3 = 37.5
TOP25 = S_Brit / a3
TTO_lbf = (W_Brit ** 2 / S_Brit) / (TOP25 * sigma * Wing.CL_max)
TTO = TTO_lbf * 4.44822 # from lbf to N
print("Thrust is " + str(TTO) + " N")
# Thrust distribution
if numpy.size(mot_distr) > 1:
sum_distr = sum(mot_distr)
power_vec = [0] * len(mot_distr)
for i in range(len(mot_distr)):
cur_distr = mot_distr[i] / sum_distr
cur_thrust = cur_distr * TTO
# Calculating power using propeller design function
_, _, _, power_vec[i], _, _, _, _ = prop_design(AtmData, Propeller_list, cur_thrust)
power_vec[i] *= 0.00134102 # Converts to hp
else:
_, _, _, power_vec, _, _, _, _ = prop_design(AtmData, Propeller_list, TTO)
power_vec *= 0.00134102 # Converts to hp
# Can mute this following message
print("Aircraft category: FAR 25, motor POWER vector output")
return power_vec
# 3 Blades
numB = 3
# Design condition
T_req = 13000 / 8 * 1.2 * 0.601 # N (TOGW/(L/D))
Cl = 0.4
alp0 = np.radians(-2)
v_design = 30
atm = AtmData(v_design, 0, is_SI)
atm.expand(1.4, 287)
Design_RPM = 3000
prop = Propeller(radius, numB, Design_RPM, eta_P=0, CP=0, CT=0, CQ=0, Cl=Cl)
output = prop_design(atm, prop, T_req, m0_fn, Cd_fn, num=401)
r, prop.chord, prop.bet, P_design, T_design, Q_design, eta_P, prop.theta = output
# Point reduction and interpolation
# Adjustment
num_len = len(prop.bet)
beta_75_index = int(num_len * 0.75)
x = np.linspace(0, 1, num_len)
x_need = x[x >= 0.15]
c_need = prop.chord[x >= 0.15]
AF = 10**5 / 16 * np.trapz(c_need / diameter * x_need**3,
x_need) # activity factor
CL_design = 4 * np.trapz(Cl * x_need**3, x_need)
print(
'====================== Propeller Design Parameters ======================'
def VTOL_power_req(m, g_factor, mot_distr, AtmData, Propeller_list):
def m0_fn(Ma):
if Ma <= 0.9:
return (2 * math.pi) / numpy.sqrt(1 - Ma**2)
else:
return (2 * math.pi) / numpy.sqrt(1 - 0.9**2)
def Cd_fn(Cl):
return 0.0095 + 0.0040 * (Cl - 0.2)**2
'''
VTOL_power_req
provides data and figures for required power of VTOL aircraft
Input:
m: kg, aircraft mass
g_factor = loading factor (1 = hovering)
mot_distr = Thrust distribution of motors (1xn)
Ex. Enter [1,1,1] for same distr. with 3 motors
Accepts single value
AtmData = Class "AtmData" including atmospheric information, see Class130 file
Propeller_list = list of Class "Propeller" including each propeller information, see Class130 file\
Please make sure the sequence are right!
Outputs:
powerVec = hp, list of power required by each motor
Inner function:
m0_fn: Kind of like lift curve slope function -- typical:
m0_fn = @(Ma) (2 * pi ./ sqrt(1 - Ma.^2)) .* (Ma <= 0.9) + (2 * pi ./ ...
sqrt(1 - 0.9^2)) .* (Ma > 0.9);
Cd_fn: Blade sectional drag coefficient -- typical:
Cd_fn = @(Cl) 0.0095 + 0.0040 * (Cl - 0.2).^2;
Calls:
prop_design_TVG: written by TGreenhill, translated and editted by XTang
History:
2.09.2021, created by XTang
2.13.2021, translated by XTang
2.13.2021, briefly debugged by XTang
'''
# Input size check
if numpy.size(Propeller_list) != numpy.size(mot_distr):
print("Error: Unequal number of propeller and motors")
print("Number of propellers: " + str(numpy.size(Propeller_list)))
print("Number of motors: " + str(numpy.size(mot_distr)))
return
g_accel = 9.81 # constant
T_total = m * g_factor * g_accel
if numpy.size(mot_distr) != 1: # Having a list of motor distribution
for item in mot_distr:
if item < 0:
print("Error: mot_distr entry values have to be at least 0")
return
sum_distr = sum(mot_distr)
power_vec = [0] * len(mot_distr)
eta_vec = [0] * len(mot_distr)
for i in range(len(mot_distr)):
cur_distr = mot_distr[i] / sum_distr
cur_T = cur_distr * T_total
[_, _, _, power_vec[i], _, _, eta_vec[i],
_] = prop_design(AtmData, Propeller_list[i], cur_T)
power_vec[i] *= 0.00134102 # Converts to hp
return power_vec, eta_vec
else: # Having only one motor
if mot_distr == 0:
print("Cannot have 0 as value of mot_distr")
return
_, _, _, power_vec, _, _, eta_vec, _ = prop_design(
AtmData, Propeller_list, T_total)
power_vec *= 0.00134102 # Converts to hp
return power_vec, eta_vec