geometry

class description

class geometry.Geometry(**kwargs)

Bases: openmdao.core.explicitcomponent.ExplicitComponent

Compute geometrical parameters and ambient parameters along the trajectory.

The Geometry component requires the following inputs:

• inputs['x']: aircraft x-position [m]

• inputs['y']: aircraft y-position [m]

• inputs['z']: aircraft z-position [m]

• inputs['alpha']: aircraft angle of attack [deg]

• inputs['gamma']: aircraft climb angle [deg]

• inputs['c_0']: ambient speed of sound [m/s]

• inputs['T_0']: ambient temperature [K]

• inputs['t_s']: source time [s]

The Geometry component computes the following outputs:

• outputs['r']: distance source to observer [m]

• outputs['theta']: polar directivity angle [deg]

• outputs['phi']: azimuthal directivity angle [deg]

• outputs['beta']: elevation angle [deg]

• outputs['t_o']: observer time [s]

• outputs['c_bar']: average speed of sound between source and observer [m/s]

The Geometry component has the following options :

• settings: pyna settings

• n_t: number of time steps in the noise time series

• mode: mode for geometry calculations: “time_series” / “distribution”

compute(inputs: openmdao.vectors.default_vector.DefaultVector, outputs: openmdao.vectors.default_vector.DefaultVector)

Compute outputs given inputs. The model is assumed to be in an unscaled state.

Parameters

• inputs (Vector) – Unscaled, dimensional input variables read via inputs[key].

• outputs (Vector) – Unscaled, dimensional output variables read via outputs[key].

• discrete_inputs (dict or None) – If not None, dict containing discrete input values.

• discrete_outputs (dict or None) – If not None, dict containing discrete output values.

initialize()

Perform any one-time initialization run at instantiation.

setup()

Declare inputs and outputs.

Available attributes:

name pathname comm options

Warning

The Julia version of the Geometry component, geometry.jl, is not documented yet. However, it is very similar to the Python version, geometry.py. More information and examples on how OpenMDAO.jl components work can be found here.

theory

Given the aircraft position along the flight trajectory as a function of source time, i.e. \((x,y,z)(t_{s})\), the direction between the source and observer, \(\overrightarrow{r} = [x_{obs,x}, x_{obs,y}, -x_{obs,z}]^T-[x,y,-z]^T\), with magnitude \(r = || \overrightarrow{r} ||\). The normalized direction vector \(n_{so} = \frac{\overrightarrow{r}}{r}\). The elevation angle is given by:

\[\beta = \sin^{-1}(n_{so,z})\]

Euler transformation angles are used to change the normalized source-observer vector from the Earth-fixed axis system to the aircraft-fixed axis system:

\[\tilde{n_{so}} = \mathcal{T}_1(\Phi_B) \cdot \mathcal{T}_2(\Theta_B) \cdot \mathcal{T}_3(\Psi_B) \cdot n_{so}\]

where \(\mathcal{T}_i\) is the Euler transformation matrix around the i-th axis. For straight, horizontal flight, the angles \(\Phi_B, \Psi_B = 0\) and \(\Theta_B = \alpha + \gamma\). The polar and azimuthal directivity angles are given by:

\[\begin{split}\begin{aligned} \theta \quad &= \quad \cos^{-1}(\tilde{n_{so}}_x) \\ \phi \quad &= \quad \tan^{-1} \left(\frac{\tilde{n_{so}}_y}{\tilde{n_{so}}_z}\right) \\ \end{aligned}\end{split}\]

The average speed of sound between the source and the observer, \(\bar{c}\), is computed taking a numerical average of the speed of sound, \(c_0\), at 11 intermediate altitudes \(z_{intermediate}\) (including the endpoints). Finally, the observer time at each \(t_{o,i}\) is calculated using:

\[t_{o,i} = t_{s,i} + \frac{r_i}{\bar{c}_i}\]