cape.convert: Unit and angle conversion utilities¶
Perform conversions such as (alpha total, phi) to (alpha, beta). It also contains various utilities such as calculating Sutherland’s law for estimating viscosity with the standard parameters, which are commonly needed tools for CFD solvers.
- cape.convert.AlphaBeta2AlphaMPhi(alpha, beta)¶
Convert angle of attack and sideslip to maneuver axis
- Call:
>>> alpha_m, phi_m = cape.AlphaBeta2AlphaMPhi(alpha, beta)
- Inputs:
- alpha:
float|numpy.array Angle of attack
- beta:
float|numpy.array Sideslip angle
- alpha:
- Outputs:
- alpha_m:
float|numpy.array Signed total angle of attack [deg]
- phi_m:
float|numpy.array Total roll angle
- alpha_m:
- Versions:
2017-06-26
@ddalle: Version 1.0
- cape.convert.AlphaBeta2AlphaTPhi(alpha, beta)¶
Convert angle of attack and sideslip to missile axis angles
- Call:
>>> alpha_t, phi = cape.AlphaBeta2AlphaTPhi(alpha, beta)
- Inputs:
- alpha:
float|numpy.array Angle of attack
- beta:
float|numpy.array Sideslip angle
- alpha:
- Outputs:
- alpha_t:
float|numpy.array Total angle of attack
- phi:
float|numpy.array Total roll angle
- alpha_t:
- Versions:
2014-06-02
@ddalle: Version 1.02014-11-05
@ddalle: Version 1.1, transpose w formula
- cape.convert.AlphaBeta2DirectionCosines(alpha, beta)¶
Convert angle of attack and sideslip to direction cosines
- Call:
>>> u, v, w = cape.AlphaBeta2DirectionCosines(alpha, beta)
- Inputs:
- alpha:
float|numpy.array Angle of attack
- beta:
float|numpy.array Sideslip angle
- alpha:
- Outputs:
- u:
float|numpy.array x-component of body-frame velocity unit vector
- v:
float|numpy.array y-component of body-frame velocity unit vector
- w:
float|numpy.array z-component of body-frame velocity unit vector
- u:
- Versions:
2019-06-19
@ddalle: Version 1.0
- cape.convert.AlphaMPhi2AlphaTPhi(alpha_m, phi_m)¶
Convert maneuver axis to missile axis angles
- Call:
>>> alpha_t, phi = cape.AlphaTPhi2AlphaMPhi(alpha_m, phi_m)
- Inputs:
- alpha_m:
float|numpy.array Signed total angle of attack [deg]
- phi_m:
float|numpy.array Total roll angle
- alpha_m:
- Outputs:
- alpha_t:
float|numpy.array Total angle of attack
- phi:
float|numpy.array Total roll angle
- alpha_t:
- Versions:
2017-06-27
@ddalle: Version 1.0
- cape.convert.AlphaTPhi2AlphaBeta(alpha_t, phi)¶
Convert total angle of attack and roll to alpha, beta
- Call:
>>> alpha, beta = cape.AlphaTPhi2AlphaBeta(alpha_t, beta)
- Inputs:
- alpha_t:
float|numpy.array Total angle of attack
- phi:
float|numpy.array Total roll angle
- alpha_t:
- Outputs:
- alpha:
float|numpy.array Angle of attack
- beta:
float|numpy.array Sideslip angle
- alpha:
- Versions:
2014-06-02
@ddalle: Version 1.0
- cape.convert.AlphaTPhi2AlphaMPhi(alpha_t, phi)¶
Convert missile-axis to maneuver-axis angles
- Call:
>>> alpha_m, phi_m = cape.AlphaTPhi2AlphaMPhi(alpha_t, phi)
- Inputs:
- alpha_t:
float|numpy.array Total angle of attack
- phi:
float|numpy.array Total roll angle
- alpha_t:
- Outputs:
- alpha_m:
float|numpy.array Signed total angle of attack [deg]
- phi_m:
float|numpy.array Total roll angle
- alpha_m:
- Versions:
2017-06-27
@ddalle: Version 1.0
- cape.convert.AlphaTPhi2DirectionCosines(aoap, phip)¶
Convert total angle of attack and roll to direction cosines
- Call:
>>> u, v, w = cape.AlphaTPhi2DirectionCosines(aoap, phip)
- Inputs:
- aoap:
float|numpy.array Total angle of attack
- phip:
float|numpy.array Missile-axis to body-z roll angle
- aoap:
- Outputs:
- u:
float|numpy.array x-component of body-frame velocity unit vector
- v:
float|numpy.array y-component of body-frame velocity unit vector
- w:
float|numpy.array z-component of body-frame velocity unit vector
- u:
- Versions:
2019-06-19
@ddalle: Version 1.0
- cape.convert.CriticalAreaRatio(M, gamma=1.4)¶
Get the area ratio to a Mach 1 area
- Call:
>>> AR = CriticalAreaRatio(M, gamma=1.4)
- Inputs:
- M:
float Mach number
- gamma: {
1.4} |float Ratio of specific heats
- M:
- Outputs:
- AR:
float Nozzle area ratio
- AR:
- Versions:
2016-04-13
@ddalle: Version 1.0
- cape.convert.DirectionCosines2AlphaBeta(u, v, w)¶
Convert direction cosines to angle of attack and sideslip
- Call:
>>> alpha, beta = cape.DirectionCosines2AlphaBeta(u, v, w)
- Inputs:
- u:
float|numpy.array x-component of body-frame velocity unit vector
- v:
float|numpy.array y-component of body-frame velocity unit vector
- w:
float|numpy.array z-component of body-frame velocity unit vector
- u:
- Outputs:
- alpha:
float|numpy.array Angle of attack
- beta:
float|numpy.array Sideslip angle
- alpha:
- Versions:
2019-06-19
@ddalle: Version 1.0
- cape.convert.DirectionCosines2AlphaTPhi(u, v, w)¶
Convert direction cosines to total angle of attack and roll
- Call:
>>> aoap, phip = cape.DirectionCosines2AlphaBeta(u, v, w)
- Inputs:
- u:
float|numpy.array x-component of body-frame velocity unit vector
- v:
float|numpy.array y-component of body-frame velocity unit vector
- w:
float|numpy.array z-component of body-frame velocity unit vector
- u:
- Outputs:
- aoap:
float|numpy.array Total angle of attack
- phip:
float|numpy.array Missile-axis to body-z roll angle
- aoap:
- Versions:
2019-06-19
@ddalle: Version 1.0
- cape.convert.ExitMachFromAreaRatio(AR, M1, gamma=1.4, subsonic=False)¶
Calculate 1D nozzle Mach number from input Mach and area ratio
- Call:
>>> M2 = ExitMachFromAreaRatio(AR,M1, gamma=1.4, subsonic=False)
- Inputs:
- AR:
float Nozzle area ratio
- M1:
float Input Mach number
- gamma: {
1.4} |float Ratio of specific heats
- subsonic:
True| {False} Whether or not M2 should be less than 1.0
- AR:
- Outputs:
- M2:
float Exit Mach number
- M2:
- Versions:
2016-04-13
@ddalle: Version 1.0
- cape.convert.PressureFPSFromRe(Re, T, M, R=None, gam=None, mu0=None, T0=None, C=None)¶
Calculate pressure from Reynolds number
- Call:
>>> p = PressureFPSFromRe(Re, T, M) >>> p = PressureFPSFromRe(Re, T, M, R=None, gam=None, **kw)
- Inputs:
- Re:
float Reynolds number per foot
- T:
float Static temperature [R]
- M:
float Mach number
- R:
float Gas constant [ft^2/s^2*R]
- gam:
float Ratio of specific heats
- mu0:
float Reference viscosity [slug/ft*s]
- T0:
float Reference temperature [K]
- C:
float Reference temperature [K]
- Re:
- Outputs:
- p:
float Static pressure [psf]
- p:
- See also:
- Versions:
2016-03-24
@ddalle: Version 1.0
- cape.convert.PressureMKSFromRe(Re, T, M, R=None, gam=None, mu0=None, T0=None, C=None)¶
Calculate pressure from Reynolds number
- Call:
>>> p = PressureMKSFromRe(Re, T, M) >>> p = PressureMKSFromRe(Re, T, M, R=None, gam=None, **kw)
- Inputs:
- Re:
float Reynolds number per foot
- T:
float Static temperature [K]
- M:
float Mach number
- R:
float Gas constant [m^2/s^2*R]
- gam:
float Ratio of specific heats
- mu0:
float Reference viscosity [kg/m*s]
- T0:
float Reference temperature [K]
- C:
float Reference temperature [K]
- Re:
- Outputs:
- p:
float Static pressure [Pa]
- p:
- See also:
- Versions:
2016-03-24
@ddalle: Version 1.0
- cape.convert.ReynoldsPerFoot(p, T, M, R=None, gam=None, mu0=None, T0=None, C=None)¶
Calculate Reynolds number per foot using Sutherland’s Law
- Call:
>>> Re = ReynoldsPerFoot(p, T, M) >>> Re = ReynoldsPerFoot(p, T, M, **kw)
- Inputs:
- p:
float Static pressure [psf]
- T:
float Static temperature [R]
- M:
float Mach number
- R:
float Gas constant [ft^2/s^2*R]
- gam:
float Ratio of specific heats
- mu0:
float Reference viscosity [slug/ft*s]
- T0:
float Reference temperature [R]
- C:
float Reference temperature [R]
- p:
- Outputs:
- Re:
float Reynolds number per foot
- Re:
- See also:
- Versions:
2016-03-23
@ddalle: Version 1.0
- cape.convert.ReynoldsPerMeter(p, T, M, R=None, gam=None, mu0=None, T0=None, C=None)¶
Calculate Reynolds number per meter using Sutherland’s Law
- Call:
>>> Re = ReynoldsPerMeter(p, T, M) >>> Re = ReynoldsPerMeter(p, T, M, **kw)
- Inputs:
- p:
float Static pressure [Pa]
- T:
float Static temperature [K]
- M:
float Mach number
- R:
float Gas constant [m^2/s^2*R]
- gam:
float Ratio of specific heats
- mu0:
float Reference viscosity [kg/m*s]
- T0:
float Reference temperature [K]
- C:
float Reference temperature [K]
- p:
- Outputs:
- Re:
float Reynolds number per foot
- Re:
- See also:
- Versions:
2016-03-24
@ddalle: Version 1.0
- cape.convert.SutherlandFPS(T, mu0=None, T0=None, C=None)¶
Calculate viscosity using Sutherland’s law using imperial units
This returns
\[\mu = \mu_0 \frac{T_0+C}{T+C} \left(\frac{T}{T_0}\right)^{3/2}\]- Call:
>>> mu = SutherlandFPS(T) >>> mu = SutherlandFPS(T, mu0=None, T0=None, C=None)
- Inputs:
- T:
float Static temperature in degrees Rankine
- mu0: {
3.58394e-7} |float Reference viscosity [slug/ft*s]
- T0: {
491.67} |float Reference temperature [R]
- C: {
198.6} |float Reference temperature [R]
- T:
- Outputs:
- mu:
float Dynamic viscosity [slug/ft*s]
- mu:
- Versions:
2016-03-23
@ddalle: Version 1.0
- cape.convert.SutherlandMKS(T, mu0=None, T0=None, C=None)¶
Calculate viscosity using Sutherland’s law using SI units
This returns
\[\begin{split}\mu = \mu_0 \\frac{T_0+C}{T+C} \left(\frac{T}{T_0}\right)^{3/2}\end{split}\]- Call:
>>> mu = SutherlandMKS(T) >>> mu = SutherlandMKS(T, mu0=None, T0=None, C=None)
- Inputs:
- T:
float Static temperature in degrees Rankine
- mu0: {
1.716e-5} |float Reference viscosity [kg/m*s]
- T0: {
273.15} |float Reference temperature [K]
- C: {
110.33333} |float Reference temperature [K]
- T:
- Outputs:
- mu:
float Dynamic viscosity [kg/m*s]
- mu:
- Versions:
2016-03-23
@ddalle: Version 1.0
- cape.convert.fstep(x)¶
Return -1 for negative numbers and +1 for nonnegative numbers
- Call:
>>> y = fstep(x)
- Inputs:
- x:
float|np.ndarray Input or array of inputs
- x:
- Outputs:
- y:
-1.0|1.0|np.ndarray Output step function or array of outputs
- y:
- Versions:
2017-06-27
@ddalle: Version 1.0
- cape.convert.fstep1(x)¶
Return -1 for nonpositive numbers and +1 for positive inputs
- Call:
>>> y = fstep1(x)
- Inputs:
- x:
float|np.ndarray Input or array of inputs
- x:
- Outputs:
- y:
-1.0|1.0|np.ndarray Output step function or array of outputs
- y:
- Versions:
2017-06-27
@ddalle: Version 1.0
