def __thrustTorqueDeriv(self, Np, Tp, dNp_dX, dTp_dX, dNp_dprecurve, dTp_dprecurve,
r, precurve, presweep, precone, Rhub, Rtip, precurveTip, presweepTip):
"""derivatives of thrust and torque"""
Tb = np.array([1, 0])
Qb = np.array([0, 1])
Npb, Tpb, rb, precurveb, presweepb, preconeb, Rhubb, Rtipb, precurvetipb, presweeptipb = \
_bem.thrusttorque_bv(Np, Tp, r, precurve, presweep, precone, Rhub, Rtip, precurveTip, presweepTip, Tb, Qb)
# X = [r, chord, theta, Rhub, Rtip, presweep, precone, tilt, hubHt]
dT_dNp = Npb[0, :]
dQ_dNp = Npb[1, :]
dT_dTp = Tpb[0, :]
dQ_dTp = Tpb[1, :]
# chain rule
dT_dX = dT_dNp*dNp_dX + dT_dTp*dTp_dX
dQ_dX = dQ_dNp*dNp_dX + dQ_dTp*dTp_dX
dT_dr = dT_dX[0, :] + rb[0, :]
dQ_dr = dQ_dX[0, :] + rb[1, :]
dT_dchord = dT_dX[1, :]
dQ_dchord = dQ_dX[1, :]
dT_dtheta = dT_dX[2, :]
dQ_dtheta = dQ_dX[2, :]
dT_dRhub = np.sum(dT_dX[3, :]) + Rhubb[0]
dQ_dRhub = np.sum(dQ_dX[3, :]) + Rhubb[1]
dT_dRtip = np.sum(dT_dX[4, :]) + Rtipb[0]
dQ_dRtip = np.sum(dQ_dX[4, :]) + Rtipb[1]
dT_dpresweep = dT_dX[5, :] + presweepb[0, :]
dQ_dpresweep = dQ_dX[5, :] + presweepb[1, :]
dT_dprecone = np.sum(dT_dX[6, :]) + preconeb[0]*pi/180.0
dQ_dprecone = np.sum(dQ_dX[6, :]) + preconeb[1]*pi/180.0
dT_dtilt = np.sum(dT_dX[7, :])
dQ_dtilt = np.sum(dQ_dX[7, :])
dT_dhubht = np.sum(dT_dX[8, :])
dQ_dhubht = np.sum(dQ_dX[8, :])
dT_dprecurvetip = precurvetipb[0]
dQ_dprecurvetip = precurvetipb[1]
dT_dpresweeptip = presweeptipb[0]
dQ_dpresweeptip = presweeptipb[1]
dT_dprecurve = np.sum(dT_dNp*dNp_dprecurve + dT_dTp*dTp_dprecurve, axis=1) + precurveb[0, :]
dQ_dprecurve = np.sum(dQ_dNp*dNp_dprecurve + dQ_dTp*dTp_dprecurve, axis=1) + precurveb[1, :]
# scalars = [precone, tilt, hubHt, Rhub, Rtip, precurvetip, presweeptip]
dT_ds = np.array([dT_dprecone, dT_dtilt, dT_dhubht, dT_dRhub, dT_dRtip, dT_dprecurvetip, dT_dpresweeptip])
dQ_ds = np.array([dQ_dprecone, dQ_dtilt, dQ_dhubht, dQ_dRhub, dQ_dRtip, dQ_dprecurvetip, dQ_dpresweeptip])
# vectors = [r, chord, theta, precurve, presweep]
dT_dv = np.vstack((dT_dr, dT_dchord, dT_dtheta, dT_dprecurve, dT_dpresweep))
dQ_dv = np.vstack((dQ_dr, dQ_dchord, dQ_dtheta, dQ_dprecurve, dQ_dpresweep))
return dT_ds, dQ_ds, dT_dv, dQ_dv
def __thrustTorqueDeriv(self, Np, Tp, dNp_dX, dTp_dX, dNp_dprecurve,
dTp_dprecurve, r, precurve, presweep, precone,
Rhub, Rtip, precurveTip, presweepTip):
"""derivatives of thrust and torque"""
Tb = np.array([1, 0])
Qb = np.array([0, 1])
Npb, Tpb, rb, precurveb, presweepb, preconeb, Rhubb, Rtipb, precurvetipb, presweeptipb = \
_bem.thrusttorque_bv(Np, Tp, r, precurve, presweep, precone, Rhub, Rtip, precurveTip, presweepTip, Tb, Qb)
# X = [r, chord, theta, Rhub, Rtip, presweep, precone, tilt, hubHt, yaw, azimuth, Uinf, Omega, pitch]
dT_dNp = Npb[0, :]
dQ_dNp = Npb[1, :]
dT_dTp = Tpb[0, :]
dQ_dTp = Tpb[1, :]
# chain rule
dT_dX = dT_dNp * dNp_dX + dT_dTp * dTp_dX
dQ_dX = dQ_dNp * dNp_dX + dQ_dTp * dTp_dX
dT_dr = dT_dX[0, :] + rb[0, :]
dQ_dr = dQ_dX[0, :] + rb[1, :]
dT_dchord = dT_dX[1, :]
dQ_dchord = dQ_dX[1, :]
dT_dtheta = dT_dX[2, :]
dQ_dtheta = dQ_dX[2, :]
dT_dRhub = np.sum(dT_dX[3, :]) + Rhubb[0]
dQ_dRhub = np.sum(dQ_dX[3, :]) + Rhubb[1]
dT_dRtip = np.sum(dT_dX[4, :]) + Rtipb[0]
dQ_dRtip = np.sum(dQ_dX[4, :]) + Rtipb[1]
dT_dpresweep = dT_dX[5, :] + presweepb[0, :]
dQ_dpresweep = dQ_dX[5, :] + presweepb[1, :]
dT_dprecone = np.sum(dT_dX[6, :]) + preconeb[0] * pi / 180.0
dQ_dprecone = np.sum(dQ_dX[6, :]) + preconeb[1] * pi / 180.0
dT_dtilt = np.sum(dT_dX[7, :])
dQ_dtilt = np.sum(dQ_dX[7, :])
dT_dhubht = np.sum(dT_dX[8, :])
dQ_dhubht = np.sum(dQ_dX[8, :])
dT_dprecurvetip = precurvetipb[0]
dQ_dprecurvetip = precurvetipb[1]
dT_dpresweeptip = presweeptipb[0]
dQ_dpresweeptip = presweeptipb[1]
dT_dprecurve = np.sum(dT_dNp * dNp_dprecurve + dT_dTp * dTp_dprecurve,
axis=1) + precurveb[0, :]
dQ_dprecurve = np.sum(dQ_dNp * dNp_dprecurve + dQ_dTp * dTp_dprecurve,
axis=1) + precurveb[1, :]
dT_dyaw = np.sum(dT_dX[9, :])
dQ_dyaw = np.sum(dQ_dX[9, :])
dT_dUinf = np.sum(dT_dX[11, :])
dQ_dUinf = np.sum(dQ_dX[11, :])
dT_dOmega = np.sum(dT_dX[12, :])
dQ_dOmega = np.sum(dQ_dX[12, :])
dT_dpitch = np.sum(dT_dX[13, :])
dQ_dpitch = np.sum(dQ_dX[13, :])
# scalars = [precone, tilt, hubHt, Rhub, Rtip, precurvetip, presweeptip, yaw, Uinf, Omega, pitch]
dT_ds = np.array([
dT_dprecone, dT_dtilt, dT_dhubht, dT_dRhub, dT_dRtip,
dT_dprecurvetip, dT_dpresweeptip, dT_dyaw, dT_dUinf, dT_dOmega,
dT_dpitch
])
dQ_ds = np.array([
dQ_dprecone, dQ_dtilt, dQ_dhubht, dQ_dRhub, dQ_dRtip,
dQ_dprecurvetip, dQ_dpresweeptip, dQ_dyaw, dQ_dUinf, dQ_dOmega,
dQ_dpitch
])
# vectors = [r, chord, theta, precurve, presweep]
dT_dv = np.vstack(
(dT_dr, dT_dchord, dT_dtheta, dT_dprecurve, dT_dpresweep))
dQ_dv = np.vstack(
(dQ_dr, dQ_dchord, dQ_dtheta, dQ_dprecurve, dQ_dpresweep))
return dT_ds, dQ_ds, dT_dv, dQ_dv