nyx_space/dynamics/

drag.rs

/*
    Nyx, blazing fast astrodynamics
    Copyright (C) 2018-onwards Christopher Rabotin <christopher.rabotin@gmail.com>

    This program is free software: you can redistribute it and/or modify
    it under the terms of the GNU Affero General Public License as published
    by the Free Software Foundation, either version 3 of the License, or
    (at your option) any later version.

    This program is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU Affero General Public License for more details.

    You should have received a copy of the GNU Affero General Public License
    along with this program.  If not, see <https://www.gnu.org/licenses/>.
*/

use anise::almanac::Almanac;
use anise::constants::frames::IAU_EARTH_FRAME;
use snafu::ResultExt;

use super::{
    DynamicsAlmanacSnafu, DynamicsAstroSnafu, DynamicsError, DynamicsPlanetarySnafu, ForceModel,
};
use crate::cosmic::{AstroError, AstroPhysicsSnafu, Frame, Spacecraft};
use crate::linalg::{Matrix4x3, Vector3};
use std::fmt;
use std::sync::Arc;

/// Density in kg/m^3 and altitudes in meters, not kilometers!
#[derive(Clone, Copy, Debug)]
pub enum AtmDensity {
    Constant(f64),
    Exponential { rho0: f64, r0: f64, ref_alt_m: f64 },
    StdAtm { max_alt_m: f64 },
}

/// `ConstantDrag` implements a constant drag model as defined in Vallado, 4th ed., page 551, with an important caveat.
///
/// **WARNING:** This basic model assumes that the velocity of the spacecraft is identical to the velocity of the upper atmosphere,
/// This is a **bad** assumption and **should not** be used for high fidelity simulations.
/// This will be resolved after https://gitlab.com/chrisrabotin/nyx/issues/93 is implemented.
#[derive(Clone)]
pub struct ConstantDrag {
    /// atmospheric density in kg/m^3
    pub rho: f64,
    /// Geoid causing the drag
    pub drag_frame: Frame,
    /// Set to true to estimate the coefficient of drag
    pub estimate: bool,
}

impl fmt::Display for ConstantDrag {
    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
        write!(
            f,
            "\tConstant Drag rho = {} kg/m^3 in frame {}",
            self.rho, self.drag_frame
        )
    }
}

impl ForceModel for ConstantDrag {
    fn estimation_index(&self) -> Option<usize> {
        if self.estimate {
            Some(7)
        } else {
            None
        }
    }

    fn eom(&self, ctx: &Spacecraft, almanac: Arc<Almanac>) -> Result<Vector3<f64>, DynamicsError> {
        let osc = almanac
            .transform_to(ctx.orbit, self.drag_frame, None)
            .context(DynamicsAlmanacSnafu {
                action: "transforming into drag frame",
            })?;

        let velocity = osc.velocity_km_s;
        // Note the 1e3 factor to convert drag units from ((kg * km^2 * s^-2) / m^1) to (kg * km * s^-2)
        Ok(-0.5 * 1e3 * self.rho * ctx.drag.cd * ctx.drag.area_m2 * velocity.norm() * velocity)
    }

    fn dual_eom(
        &self,
        _osc_ctx: &Spacecraft,
        _almanac: Arc<Almanac>,
    ) -> Result<(Vector3<f64>, Matrix4x3<f64>), DynamicsError> {
        Err(DynamicsError::DynamicsAstro {
            source: AstroError::PartialsUndefined,
        })
    }
}

/// `Drag` implements all three drag models.
#[derive(Clone)]
pub struct Drag {
    /// Density computation method
    pub density: AtmDensity,
    /// Frame to compute the drag in
    pub drag_frame: Frame,
    /// Set to true to estimate the coefficient of drag
    pub estimate: bool,
}

impl Drag {
    /// Common exponential drag model for the Earth
    pub fn earth_exp(almanac: Arc<Almanac>) -> Result<Arc<Self>, DynamicsError> {
        Ok(Arc::new(Self {
            density: AtmDensity::Exponential {
                rho0: 3.614e-13,
                r0: 700_000.0,
                ref_alt_m: 88_667.0,
            },
            drag_frame: almanac.frame_from_uid(IAU_EARTH_FRAME).context({
                DynamicsPlanetarySnafu {
                    action: "planetary data from third body not loaded",
                }
            })?,
            estimate: false,
        }))
    }

    /// Drag model which uses the standard atmosphere 1976 model for atmospheric density
    pub fn std_atm1976(almanac: Arc<Almanac>) -> Result<Arc<Self>, DynamicsError> {
        Ok(Arc::new(Self {
            density: AtmDensity::StdAtm {
                max_alt_m: 1_000_000.0,
            },
            drag_frame: almanac.frame_from_uid(IAU_EARTH_FRAME).context({
                DynamicsPlanetarySnafu {
                    action: "planetary data from third body not loaded",
                }
            })?,
            estimate: false,
        }))
    }
}

impl fmt::Display for Drag {
    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
        write!(
            f,
            "\tDrag density {:?} in frame {}",
            self.density, self.drag_frame
        )
    }
}

impl ForceModel for Drag {
    fn estimation_index(&self) -> Option<usize> {
        if self.estimate {
            Some(7)
        } else {
            None
        }
    }

    fn eom(&self, ctx: &Spacecraft, almanac: Arc<Almanac>) -> Result<Vector3<f64>, DynamicsError> {
        let integration_frame = ctx.orbit.frame;

        let osc_drag_frame = almanac
            .transform_to(ctx.orbit, self.drag_frame, None)
            .context(DynamicsAlmanacSnafu {
                action: "transforming into drag frame",
            })?;

        match self.density {
            AtmDensity::Constant(rho) => {
                let velocity = osc_drag_frame.velocity_km_s;
                // Note the 1e3 factor to convert drag units from ((kg * km^2 * s^-2) / m^1) to (kg * km * s^-2)
                Ok(-0.5 * 1e3 * rho * ctx.drag.cd * ctx.drag.area_m2 * velocity.norm() * velocity)
            }

            AtmDensity::Exponential {
                rho0,
                r0,
                ref_alt_m,
            } => {
                // Compute rho in the drag frame.
                let rho = rho0
                    * (-(osc_drag_frame.rmag_km()
                        - (r0
                            + self
                                .drag_frame
                                .mean_equatorial_radius_km()
                                .context(AstroPhysicsSnafu)
                                .context(DynamicsAstroSnafu)?))
                        / ref_alt_m)
                        .exp();

                // TODO: Drag modeling will be improved in https://github.com/nyx-space/nyx/issues/317
                // The frame will be double checked in this PR as well.
                // let velocity_integr_frame = self.cosm.frame_chg(&osc, integration_frame).velocity();
                let velocity_integr_frame = almanac
                    .transform_to(osc_drag_frame, integration_frame, None)
                    .context(DynamicsAlmanacSnafu {
                        action: "rotating into the integration frame",
                    })?
                    .velocity_km_s;

                let velocity = velocity_integr_frame - osc_drag_frame.velocity_km_s;
                // Note the 1e3 factor to convert drag units from ((kg * km^2 * s^-2) / m^1) to (kg * km * s^-2)
                Ok(-0.5 * 1e3 * rho * ctx.drag.cd * ctx.drag.area_m2 * velocity.norm() * velocity)
            }

            AtmDensity::StdAtm { max_alt_m } => {
                let altitude_km = osc_drag_frame.rmag_km()
                    - self
                        .drag_frame
                        .mean_equatorial_radius_km()
                        .context(AstroPhysicsSnafu)
                        .context(DynamicsAstroSnafu)?;
                let rho = if altitude_km > max_alt_m / 1_000.0 {
                    // Use a constant density
                    10.0_f64.powf((-7e-5) * altitude_km - 14.464)
                } else {
                    // Code from AVS/Schaub's Basilisk
                    // Calculating the density based on a scaled 6th order polynomial fit to the log of density
                    let scale = (altitude_km - 526.8000) / 292.8563;
                    let logdensity =
                        0.34047 * scale.powi(6) - 0.5889 * scale.powi(5) - 0.5269 * scale.powi(4)
                            + 1.0036 * scale.powi(3)
                            + 0.60713 * scale.powi(2)
                            - 2.3024 * scale
                            - 12.575;

                    /* Calculating density by raising 10 to the log of density */
                    10.0_f64.powf(logdensity)
                };

                // let velocity_integr_frame = self.cosm.frame_chg(&osc, integration_frame).velocity();
                let velocity_integr_frame = almanac
                    .transform_to(osc_drag_frame, integration_frame, None)
                    .context(DynamicsAlmanacSnafu {
                        action: "rotating into the integration frame",
                    })?
                    .velocity_km_s;

                let velocity = velocity_integr_frame - osc_drag_frame.velocity_km_s;
                // Note the 1e3 factor to convert drag units from ((kg * km^2 * s^-2) / m^1) to (kg * km * s^-2)
                Ok(-0.5 * 1e3 * rho * ctx.drag.cd * ctx.drag.area_m2 * velocity.norm() * velocity)
            }
        }
    }

    fn dual_eom(
        &self,
        _osc_ctx: &Spacecraft,
        _almanac: Arc<Almanac>,
    ) -> Result<(Vector3<f64>, Matrix4x3<f64>), DynamicsError> {
        Err(DynamicsError::DynamicsAstro {
            source: AstroError::PartialsUndefined,
        })
    }
}