`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

Outputs:

alpha_m: float | numpy.array: Signed total angle of attack [deg]
phi_m: float | numpy.array: Total roll angle

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

Outputs:

alpha_t: float | numpy.array: Total angle of attack
phi: float | numpy.array: Total roll angle

Versions:

2014-06-02 @ddalle: Version 1.0
2014-11-05 @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

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

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

Outputs:

alpha_t: float | numpy.array: Total angle of attack
phi: float | numpy.array: Total roll angle

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

Outputs:

alpha: float | numpy.array: Angle of attack
beta: float | numpy.array: Sideslip angle

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

Outputs:

alpha_m: float | numpy.array: Signed total angle of attack [deg]
phi_m: float | numpy.array: Total roll angle

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

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

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

Outputs:

AR: float: Nozzle area ratio

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

Outputs:

alpha: float | numpy.array: Angle of attack
beta: float | numpy.array: Sideslip angle

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

Outputs:

aoap: float | numpy.array: Total angle of attack
phip: float | numpy.array: Missile-axis to body-z roll angle

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

Outputs:

M2: float: Exit Mach number

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]

Outputs:

p: float: Static pressure [psf]

See also:

cape.convert.SutherlandFPS()
cape.convert.ReynoldsPerFoot()

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]

Outputs:

p: float: Static pressure [Pa]

See also:

cape.convert.SutherlandMKS()
cape.convert.ReynoldsPerMeter()

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]

Outputs:

Re: float: Reynolds number per foot

See also:

cape.convert.SutherlandFPS()
cape.convert.PressureFPSFromRe()

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]

Outputs:

Re: float: Reynolds number per foot

See also:

cape.convert.SutherlandMKS()
cape.convert.PressureMKSFromRe()

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

$μ = μ_{0} \frac{T_{0} + C}{T + C} {(\frac{T}{T_{0}})}^{3 / 2}$

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]

Outputs:

mu: float: Dynamic viscosity [slug/ft*s]

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

$\begin{array}{r} μ = μ_{0} \\ f r a c T_{0} + C T + C {(\frac{T}{T_{0}})}^{3 / 2} \end{array}$

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]

Outputs:

mu: float: Dynamic viscosity [kg/m*s]

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

Outputs:

y: -1.0 | 1.0 | np.ndarray: Output step function or array of outputs

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

Outputs:

y: -1.0 | 1.0 | np.ndarray: Output step function or array of outputs

Versions:

2017-06-27 @ddalle: Version 1.0

`cape.convert`: Unit and angle conversion utilities¶

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cape.convert: Unit and angle conversion utilities¶

`cape.convert`: Unit and angle conversion utilities¶