def test_basic_math(types):
for x in types["all"]:
for y in types["all"]:
### Arithmetic
x + y
x - y
x * y
x / y
np.sum(x) # Sum of all entries of array-like object x
### Exponentials & Powers
x**y
np.power(x, y)
np.exp(x)
np.log(x)
np.log10(x)
np.sqrt(x) # Note: do x ** 0.5 rather than np.sqrt(x).
### Trig
np.sin(x)
np.cos(x)
np.tan(x)
np.arcsin(x)
np.arccos(x)
np.arctan(x)
np.arctan2(y, x)
np.sinh(x)
np.cosh(x)
np.tanh(x)
np.arcsinh(x)
np.arccosh(x)
np.arctanh(x - 0.5) # `- 0.5` to give valid argument
def haack_series(
x_over_L: np.ndarray,
C=1 / 3
):
theta = np.arccos(1 - 2 * x_over_L)
radius = ((
theta - np.sin(2 * theta) / 2 + C * np.sin(theta) ** 3
) / np.pi) ** 0.5
return radius
def length_day(latitude, day_of_year):
"""
For what length of time is the sun above the horizon on a given day?
:param latitude: Latitude [degrees]
:param day_of_year: Julian day (1 == Jan. 1, 365 == Dec. 31)
:return: Seconds of sunlight in a given day
"""
dec = declination_angle(day_of_year)
constant = -np.sind(dec) * np.sind(latitude) / (np.cosd(dec) * np.cosd(latitude))
constant = np.clip(constant, -1, 1)
sun_time_nondim = 2 * np.arccos(constant)
sun_time = sun_time_nondim / (2 * np.pi) * 86400
return sun_time
### Define velocity triangle components
U_a = airspeed #+ u_a # Axial velocity w/o induced eff. assuming u_a = 0
U_t = omega * radial_loc # Tangential velocity w/o induced eff.
U = (U_a ** 2 + U_t ** 2) ** 0.5 # Velocity magnitude
W_a = 0.5 * U_a + 0.5 * U * np.sin(Psi) # Axial velocity w/ induced eff.
W_t = 0.5 * U_t + 0.5 * U * np.cos(Psi) # Tangential velocity w/ induced eff.
v_a = W_a - U_a # Axial induced velocity
v_t = U_t - W_t # Tangential induced velocity
W = (W_a ** 2 + W_t ** 2) ** 0.5
Re = air_density * W * chord_local / mu
Ma = W / speed_of_sound
v = (v_a ** 2 + v_t ** 2) ** 0.5
loc_wake_adv_ratio = (radial_loc / tip_radius) * (W_a / W_t)
f = (n_blades / 2) * (1 - radial_loc / tip_radius) * 1 / loc_wake_adv_ratio
F = 2 / pi * np.arccos(np.exp(-f))
## Compute local blade quantities
phi_rad = np.arctan2(W_a, W_t) #local flow angle
phi_deg = phi_rad * 180 / pi
alpha_rad = twist_local_rad - phi_rad
alpha_deg = alpha_rad * 180 / pi
### Compute sectional lift and drag
cl = airfoil_CL(alpha_deg, Re, Ma)
cd = airfoil_CDp(alpha_deg, Re, Ma, cl)
gamma = 0.5 * W * chord_local * cl
### Add governing equations
opti.subject_to([