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trajectory.py
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trajectory.py
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import numpy as np
import matplotlib.pyplot as plt
import matplotlib.ticker
import time
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm
from air_data import change_air_data
from qprop_sweep import opt_dbeta, get_nums
from qmil_design import design_prop
plt.style.use('seaborn')
def follow_trajectory(ts, hs, vs, thrusts, npt=60, optimize=True, show=False,
prop="best_prop", save=True):
"""
Calculate propulsion parameters over a cycle trajectory and saves data
to "cycle.npz" using QProp
Requires time, altitude, airspeed, and thrust over the 24 hour trajectory
Parameters
----------
ts : array-like
Points in time
hs : array-like
Altitudes at given time points
vs : array-like
Airspeeds at given time poitns
thrusts : array-like
Required thrust at given time points
npt : int, optional
Number of time samples to evaluate/optimize at
unopt : boolean, optional
If checked, variable pitch is not allowed
show : boolean, optional
If checked, will show discretized altitude and airspeed over cycle
prop : string, optional
Propeller to use for analysis
save : boolean, optional
If true, the trajectory data will save as an npz file
Returns
---------
eff : float
Average efficiency over 24h cycle
"""
step = len(ts) // npt if npt <= len(ts) else 1
result = []
last_h = 0
# Iterate through time steps
for i, t in enumerate(ts[::step]):
i *= step
h, v, thrust = (hs[i], vs[i], thrusts[i])
p = thrust * v
# If alt change > 100m, recalculate air data
# if abs(h-last_h) > 10:
change_air_data(h)
# last_h = h
if optimize:
opt = opt_dbeta(v, thrust, prop=prop)
dbeta = opt.x
eta_opt = -opt.fun
else:
dbeta = 0
data = get_nums(dbeta, v, thrust, prop=prop)
rpm = data[1]
Q = data[4]
Pshaft = data[5]
eta = data[9]
J = data[10]
result.append([t, h, v, p, thrust, rpm, Q, Pshaft, J, dbeta, eta])
result = np.array(result)
# print("Average Efficiency:", np.mean(result[:,10]))
if show:
plt.figure()
plt.title('24 Hour Trajectory')
plt.subplot(211)
plt.plot(result[:,0], result[:,1]/1000, 'o-')
plt.ylabel('Altitude [km]')
plt.subplot(212)
plt.plot(result[:,0], result[:,2], 'o-')
plt.ylabel('Airspeed [m/s]')
plt.xlabel("time [hr]")
plt.show()
if save:
savefile = "cycle" if optimize else "cycle_unopt"
np.savez(savefile, res=result)
return np.mean(result[:,10])
def plot_trajectory(data_file="cycle.npz"):
"""
Plot various propulsion parameters from cycle.npz
Parameters
----------
data_file : str, optional
Name/Address of file containing plot data (from follow_trajectory())
"""
result = np.load(data_file)["res"].T
t, h, v, p, thrust, rpm, Q, Pshaft, J, dbeta, eta = result
night = int( len(t) * 7.5 // 24 )
day = len(t) * 18 // 24
res_day = np.concatenate((result[:,:night], result[:,day:]), axis=1)
res_night = result[:,night:day]
t_d, h_d, v_d, p_d, thrust_d, rpm_d, Q_d, Pshaft_d, J_d, dbeta_d, eta_d = res_day
t_n, h_n, v_n, p_n, thrust_n, rpm_n, Q_n, Pshaft_n, J_n, dbeta_n, eta_n = res_night
print("Avg RPM", rpm_n[0], "PShaft", Pshaft_n[0], "Q", Q_n[0])
print("Max RPM", max(rpm_d), "PShaft", max(Pshaft_d), "Q", max(Q_d))
fig = plt.figure(figsize=(12,7.5))
ax1 = plt.subplot(321)
fig.suptitle("24 Hour Cycle for each Propeller")
ax1.plot(t_d, h_d/304.88, ".-", label="Day", color="cornflowerblue")
ax1.plot(t_n, h_n/304.88, ".-", label="Night", color="midnightblue")
ax1.set_ylabel('Altitude [kft]', color="midnightblue")
ax1.legend()
ax12 = plt.subplot(322)
ax12.plot(t_d, rpm_d, ".-", label="Day", color="indianred")
ax12.plot(t_n, rpm_n, ".-", label="Night", color="maroon")
ax12.set_ylabel("RPM", color="maroon")
ax12.legend()
# ax12.grid(None)
# ax12.set_yticks(np.linspace(ax12.get_yticks()[0], ax12.get_yticks()[-1], len(ax1.get_yticks())))
ax2 = plt.subplot(323)
ax2.plot(t_d, thrust_d, ".-", label="Day", color="cornflowerblue")
ax2.plot(t_n, thrust_n, ".-", label="Night", color="midnightblue")
ax2.set_ylabel('Thrust [N]', color="midnightblue")
ax22 = plt.subplot(324)
ax22.plot(t_d, eta_d, ".-", label="Day", color="indianred")
ax22.plot(t_n, eta_n, ".-", label="Night", color="maroon")
ax22.set_ylabel(r'$\eta$', color="maroon")
# ax22.grid(None)
ax3 = plt.subplot(325)
# plt.plot(t, dbeta)
# plt.ylabel(r'$d\beta$')
ax3.plot(t_d, Pshaft_d, ".-", label="Day", color="indianred")
ax3.plot(t_n, Pshaft_n, ".-", label="Night", color="maroon")
ax3.set_ylabel('Shaft Power [W]', color="maroon")
ax32 = plt.subplot(326)
ax32.plot(t_d, Q_d, ".-", label="Day", color="indianred")
ax32.plot(t_n, Q_n, ".-", label="Night", color="maroon")
ax32.set_ylabel('Required Torque [Nm]', color="maroon")
ax3.set_xlabel("Time from Solar Noon [hr]")
ax32.set_xlabel("Time from Solar Noon [hr]")
# ax32.grid(None)
plt.figure()
plt.plot(J, eta, ".-")
plt.xlabel("Advance Ratio")
plt.ylabel(r"$\eta$")
plt.title("Advance Ratio vs Efficiency")
plt.figure()
plt.plot(rpm, Q, ".-")
plt.xlabel("RPM")
plt.ylabel("Torque Requirement [N/m]")
plt.title("Motor Torque Requirement vs RPM")
# plt.show()
def plot_motor_eff(Kv, R, I0):
"""
Calculate and plot motor efficiency over various torque and RPM ranges.
The RPM/Omega used in the calculations and Kv should be in units of
rad/s instead of rpm.
"""
Qs = np.linspace(5, 15, 50)
RPMs = np.linspace(200, 1800, 60)*np.pi/30
mot_effs = np.zeros((50, 60))
for i, Q in enumerate(Qs):
for j, RPM in enumerate(RPMs):
# I = Q*Kv + I0
# V = RPM * Kv + I*R
# mot_effs[i, j] = (1 - I*R/V) * (1 - I0/I)
mot_effs[i,j] = (Kv*RPM/(Kv*RPM+Q*R*Kv+I0*R))*(Q*Kv/(Q*Kv+I0))
# return np.mean(mot_effs)
print(np.mean(mot_effs))
plt.figure()
X, Y = np.meshgrid(RPMs*30/np.pi, Qs)
plt.contourf(X, Y, mot_effs)
plt.xlabel("RPMs")
plt.ylabel("Torques")
plt.title("Motor Efficiencies over Operating Range")
plt.colorbar()
plt.show()
def rpm_trade(rpms, ts, hs, vs, thrusts, optimize):
"""
Trade study of design RPM vs average efficiency over cycle. Given a range
of rpms, redesign "test_prop" to be optimized at the given rpm and use
the output propeller to get average efficiency over cycle
"""
effs = np.zeros(len(rpms))
for i, rpm in enumerate(rpms):
print("Design rpm:", rpm, "Design eff:", -design_prop(rpm, "test_prop"))
effs[i] = follow_trajectory(ts, hs, vs, thrusts, npt=200,
optimize=optimize, show=False,
prop="test_prop")
# plt.figure()
# plt.plot(rpms, effs)
# opt_title = "with Variable Pitch" if optimize else ""
# plt.title("Design RPM vs Average Efficiency " + opt_title)
# plt.xlabel("QMil Design RPM")
# plt.ylabel(r"Average $\eta$ over 24 Hour Cycle")
# plt.show()
return effs
if __name__ == "__main__":
num_motor = 4
data = np.load('time_altitude_airspeed.npz')
ts = data['t']/3600
hs = data['h']
vs = data['v']
thrusts = data['thrust']/num_motor
# plt.plot(ts, hs)
# plt.show()
# For motor study
# plot_motor_eff(8*np.pi/30, 0.3, 1.1)
# Kvs = np.linspace(3, 10, 10)
# I0s = np.linspace(1, 5, 15)
# effs = np.zeros((10, 15))
# for i, Kv in enumerate(Kvs):
# for j, I0 in enumerate(I0s):
# effs[i,j] = plot_motor_eff(Kv*np.pi/30, 1.1, I0)
# plt.figure()
# X, Y = np.meshgrid(I0s, Kvs)
# plt.contourf(X, Y, effs)
# plt.title("Average Efficiencies for Various Motors")
# plt.xlabel(r"$I_0$")
# plt.ylabel("Kv")
# plt.colorbar()
# plt.show()
# start = time.time()
# eff_opt = follow_trajectory(ts, hs, vs, thrusts, npt=200, optimize=True)
# print("Average Efficiency Var Pitch:", eff_opt)
# plot_trajectory("cycle.npz")
# print(time.time() - start)
eff_unopt = follow_trajectory(ts, hs, vs, thrusts, npt=200, optimize=False)
print("Average Efficiency Fixed Pitch:", eff_unopt)
plot_trajectory("cycle_unopt.npz")
plt.show()
# print(time.time() - start)
# result = np.load("cycle.npz")["res"].T
# result2 = np.load("cycle_unopt.npz")["res"].T
# t, h, v, p, thrust, rpm, Q, Pshaft, J, dbeta, eta = result
# plt.figure()
# plt.plot(t, rpm, label="Variable Pitch")
# plt.ylabel('RPM')
# result = np.load("cycle_unopt.npz")["res"].T
# t, h, v, p, thrust, rpm, Q, Pshaft, J, dbeta, eta = result
# plt.plot(t, rpm, label="Fixed Pitch")
# plt.xlabel("Time [hr]")
# plt.title("RPM over cycle")
# plt.legend()
# plt.show()
#