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use super::{
body::{object, Body},
Density, Ori, Vel,
};
use crate::{
consts::{AIR_DENSITY, LAVA_DENSITY, WATER_DENSITY},
util::{Dir, Plane, Projection},
};
use serde::{Deserialize, Serialize};
use std::f32::consts::PI;
use vek::*;
#[derive(Copy, Clone, Debug, PartialEq, Eq, Serialize, Deserialize)]
pub enum LiquidKind {
Water,
Lava,
}
impl LiquidKind {
/// If an entity is in multiple overlapping liquid blocks, which one takes
/// precedence? (should be a rare edge case, since checkerboard patterns of
/// water and lava shouldn't show up in worldgen)
#[inline]
#[must_use]
pub fn merge(self, other: Self) -> Self {
use LiquidKind::{Lava, Water};
match (self, other) {
(Water, Water) => Water,
(Water, Lava) => Lava,
(Lava, _) => Lava,
}
}
}
/// Fluid medium in which the entity exists
#[derive(Copy, Clone, Debug, PartialEq, Serialize, Deserialize)]
pub enum Fluid {
Air {
vel: Vel,
elevation: f32,
},
Liquid {
kind: LiquidKind,
vel: Vel,
depth: f32,
},
}
impl Fluid {
/// Specific mass
pub fn density(&self) -> Density {
match self {
Self::Air { .. } => Density(AIR_DENSITY),
Self::Liquid {
kind: LiquidKind::Water,
..
} => Density(WATER_DENSITY),
Self::Liquid {
kind: LiquidKind::Lava,
..
} => Density(LAVA_DENSITY),
}
}
/// Pressure from entity velocity
pub fn dynamic_pressure(&self, vel: &Vel) -> f32 {
0.5 * self.density().0 * self.relative_flow(vel).0.magnitude_squared()
}
/*
pub fn static_pressure(&self) -> f32 {
match self {
Self::Air { elevation, .. } => Self::air_pressure(*elevation),
Self::Water { depth, .. } => Self::water_pressure(*depth),
}
}
/// Absolute static pressure of air at elevation
pub fn air_pressure(elevation: f32) -> f32 {
// At low altitudes above sea level, the pressure decreases by about 1.2 kPa for
// every 100 metres.
// https://en.wikipedia.org/wiki/Atmospheric_pressure#Altitude_variation
ATMOSPHERE - elevation / 12.0
}
/// Absolute static pressure of water at depth
pub fn water_pressure(depth: f32) -> f32 { WATER_DENSITY * GRAVITY * depth + ATMOSPHERE }
*/
/// Velocity of fluid, if applicable
pub fn flow_vel(&self) -> Vel {
match self {
Self::Air { vel, .. } => *vel,
Self::Liquid { vel, .. } => *vel,
}
}
// Very simple but useful in reducing mental overhead
pub fn relative_flow(&self, vel: &Vel) -> Vel { Vel(self.flow_vel().0 - vel.0) }
pub fn is_liquid(&self) -> bool { matches!(self, Fluid::Liquid { .. }) }
pub fn elevation(&self) -> Option<f32> {
match self {
Fluid::Air { elevation, .. } => Some(*elevation),
_ => None,
}
}
pub fn depth(&self) -> Option<f32> {
match self {
Fluid::Liquid { depth, .. } => Some(*depth),
_ => None,
}
}
}
impl Default for Fluid {
fn default() -> Self {
Self::Air {
elevation: 0.0,
vel: Vel::zero(),
}
}
}
pub struct Wings {
pub aspect_ratio: f32,
pub planform_area: f32,
pub ori: Ori,
}
impl Body {
pub fn aerodynamic_forces(
&self,
rel_flow: &Vel,
fluid_density: f32,
wings: Option<&Wings>,
scale: f32,
) -> Vec3<f32> {
let v_sq = rel_flow.0.magnitude_squared();
if v_sq < 0.25 {
// don't bother with minuscule forces
Vec3::zero()
} else {
let rel_flow_dir = Dir::new(rel_flow.0 / v_sq.sqrt());
let power_vec = match wings {
Some(&Wings {
aspect_ratio,
planform_area,
ori,
}) => {
if aspect_ratio > 25.0 {
tracing::warn!(
"Calculating lift for wings with an aspect ratio of {}. The formulas \
are only valid for aspect ratios below 25.",
aspect_ratio
)
};
let ar = aspect_ratio.min(24.0);
// We have an elliptical wing; proceed to calculate its lift and drag
// aoa will be positive when we're pitched up and negative otherwise
let aoa = angle_of_attack(&ori, &rel_flow_dir);
// c_l will be positive when aoa is positive (we have positive lift,
// producing an upward force) and negative otherwise
let c_l = lift_coefficient(ar, aoa);
// lift dir will be orthogonal to the local relative flow vector.
// Local relative flow is the resulting vector of (relative) freestream
// flow + downwash (created by the vortices
// of the wing tips)
let lift_dir: Dir = {
// induced angle of attack
let aoa_i = c_l / (PI * ar);
// effective angle of attack; the aoa as seen by aerofoil after
// downwash
let aoa_eff = aoa - aoa_i;
// Angle between chord line and local relative wind is aoa_eff
// radians. Direction of lift is
// perpendicular to local relative wind.
// At positive lift, local relative wind will be below our cord line
// at an angle of aoa_eff. Thus if
// we pitch down by aoa_eff radians then
// our chord line will be colinear with local relative wind vector
// and our up will be the direction
// of lift.
ori.pitched_down(aoa_eff).up()
};
// induced drag coefficient (drag due to lift)
let cdi = {
// Oswald's efficiency factor (empirically derived--very magical)
// (this definition should not be used for aspect ratios > 25)
let e = 1.78 * (1.0 - 0.045 * ar.powf(0.68)) - 0.64;
c_l.powi(2) / (PI * e * ar)
};
// drag coefficient
let c_d = zero_lift_drag_coefficient() + cdi;
debug_assert!(c_d.is_sign_positive());
debug_assert!(c_l.is_sign_positive() || aoa.is_sign_negative());
planform_area * scale.powf(2.0) * (c_l * *lift_dir + c_d * *rel_flow_dir)
+ self.parasite_drag(scale) * *rel_flow_dir
},
_ => self.parasite_drag(scale) * *rel_flow_dir,
};
0.5 * fluid_density * v_sq * power_vec
}
}
/// Physically incorrect (but relatively dt-independent) way to calculate
/// drag coefficients for liquids.
// TODO: Remove this in favour of `aerodynamic_forces` (see: `integrate_forces`)
pub fn drag_coefficient_liquid(&self, fluid_density: f32, scale: f32) -> f32 {
fluid_density * self.parasite_drag(scale)
}
/// Parasite drag is the sum of pressure drag and skin friction.
/// Skin friction is the drag arising from the shear forces between a fluid
/// and a surface, while pressure drag is due to flow separation. Both are
/// viscous effects.
fn parasite_drag(&self, scale: f32) -> f32 {
// Reference area and drag coefficient assumes best-case scenario of the
// orientation producing least amount of drag
match self {
// Cross-section, head/feet first
Body::BipedLarge(_) | Body::BipedSmall(_) | Body::Golem(_) | Body::Humanoid(_) => {
let dim = self.dimensions().xy().map(|a| a * 0.5 * scale);
const CD: f32 = 0.7;
CD * PI * dim.x * dim.y
},
// Cross-section, nose/tail first
Body::Theropod(_)
| Body::QuadrupedMedium(_)
| Body::QuadrupedSmall(_)
| Body::QuadrupedLow(_)
| Body::Arthropod(_) => {
let dim = self.dimensions().map(|a| a * 0.5 * scale);
let cd: f32 = if matches!(self, Body::QuadrupedLow(_)) {
0.7
} else {
1.0
};
cd * PI * dim.x * dim.z
},
// Cross-section, zero-lift angle; exclude the wings (width * 0.2)
Body::BirdMedium(_) | Body::BirdLarge(_) | Body::Dragon(_) => {
let dim = self.dimensions().map(|a| a * 0.5 * scale);
let cd: f32 = match self {
// "Field Estimates of Body Drag Coefficient
// on the Basis of Dives in Passerine Birds",
// Anders Hedenström and Felix Liechti, 2001
Body::BirdLarge(_) | Body::BirdMedium(_) => 0.2,
// arbitrary
_ => 0.7,
};
cd * PI * dim.x * 0.2 * dim.z
},
// Cross-section, zero-lift angle; exclude the fins (width * 0.2)
Body::FishMedium(_) | Body::FishSmall(_) | Body::Crustacean(_) => {
let dim = self.dimensions().map(|a| a * 0.5 * scale);
// "A Simple Method to Determine Drag Coefficients in Aquatic Animals",
// D. Bilo and W. Nachtigall, 1980
const CD: f32 = 0.031;
CD * PI * dim.x * 0.2 * dim.z
},
Body::Object(object) => match object {
// very streamlined objects
object::Body::Arrow
| object::Body::ArrowSnake
| object::Body::ArrowTurret
| object::Body::ArrowClay
| object::Body::FireworkBlue
| object::Body::FireworkGreen
| object::Body::FireworkPurple
| object::Body::FireworkRed
| object::Body::FireworkWhite
| object::Body::FireworkYellow
| object::Body::MultiArrow
| object::Body::BoltBesieger
| object::Body::Dart
| object::Body::BubbleBomb => {
let dim = self.dimensions().map(|a| a * 0.5 * scale);
const CD: f32 = 0.02;
CD * PI * dim.x * dim.z
},
// spherical-ish objects
object::Body::BoltFire
| object::Body::BoltFireBig
| object::Body::BoltNature
| object::Body::Bomb
| object::Body::PotionBlue
| object::Body::PotionGreen
| object::Body::PotionRed
| object::Body::Pouch
| object::Body::Pumpkin
| object::Body::Pumpkin2
| object::Body::Pumpkin3
| object::Body::Pumpkin4
| object::Body::Pumpkin5
| object::Body::Pebble
| object::Body::IronPikeBomb
| object::Body::StrigoiHead => {
let dim = self.dimensions().map(|a| a * 0.5 * scale);
const CD: f32 = 0.5;
CD * PI * dim.x * dim.z
},
_ => {
let dim = self.dimensions().map(|a| a * scale);
const CD: f32 = 2.0;
CD * (PI / 6.0 * dim.x * dim.y * dim.z).powf(2.0 / 3.0)
},
},
Body::ItemDrop(_) => {
let dim = self.dimensions().map(|a| a * scale);
const CD: f32 = 2.0;
CD * (PI / 6.0 * dim.x * dim.y * dim.z).powf(2.0 / 3.0)
},
Body::Ship(_) => {
// Airships tend to use the square of the cube root of its volume for
// reference area
let dim = self.dimensions().map(|a| a * scale);
(PI / 6.0 * dim.x * dim.y * dim.z).powf(2.0 / 3.0)
},
Body::Plugin(body) => body.parasite_drag(),
}
}
}
/// Geometric angle of attack
///
/// # Note
/// This ignores spanwise flow (i.e. we remove the spanwise flow component).
/// With greater yaw comes greater loss of accuracy as more flow goes
/// unaccounted for.
pub fn angle_of_attack(ori: &Ori, rel_flow_dir: &Dir) -> f32 {
rel_flow_dir
.projected(&Plane::from(ori.right()))
.map(|flow_dir| PI / 2.0 - ori.up().angle_between(flow_dir.to_vec()))
.unwrap_or(0.0)
}
/// Total lift coefficient for a finite wing of symmetric aerofoil shape and
/// elliptical pressure distribution.
pub fn lift_coefficient(aspect_ratio: f32, aoa: f32) -> f32 {
let aoa_abs = aoa.abs();
let stall_angle = PI * 0.1;
if aoa_abs < stall_angle {
lift_slope(aspect_ratio, None) * aoa
} else {
// This is when flow separation and turbulence starts to kick in.
// Going to just make something up (based on some data), as the alternative is
// to just throw your hands up and return 0
let aoa_s = aoa.signum();
let c_l_max = lift_slope(aspect_ratio, None) * stall_angle;
let deg_45 = PI / 4.0;
if aoa_abs < deg_45 {
// drop directly to 0.6 * max lift at stall angle
// then climb back to max at 45°
Lerp::lerp(0.6 * c_l_max, c_l_max, aoa_abs / deg_45) * aoa_s
} else {
// let's just say lift goes down linearly again until we're at 90°
Lerp::lerp(c_l_max, 0.0, (aoa_abs - deg_45) / deg_45) * aoa_s
}
}
}
/// The zero-lift profile drag coefficient is the parasite drag on the wings
/// at the angle of attack which generates no lift
pub fn zero_lift_drag_coefficient() -> f32 { 0.026 }
/// The change in lift over change in angle of attack¹. Multiplying by angle
/// of attack gives the lift coefficient (for a finite wing, not aerofoil).
/// Aspect ratio is the ratio of total wing span squared over planform area.
///
/// # Notes
/// Only valid for symmetric, elliptical wings at small² angles of attack³.
/// Does not apply to twisted, cambered or delta wings. (It still gives a
/// reasonably accurate approximation if the wing shape is not truly
/// elliptical.)
/// 1. geometric angle of attack, i.e. the pitch angle relative to freestream
/// flow
/// 2. up to around ~18°, at which point maximum lift has been achieved and
/// thereafter falls precipitously, causing a stall (this is the stall
/// angle)
/// 3. effective aoa, i.e. geometric aoa - induced aoa; assumes no sideslip
// TODO: Look into handling tapered wings
fn lift_slope(aspect_ratio: f32, sweep_angle: Option<f32>) -> f32 {
// lift slope for a thin aerofoil, given by Thin Aerofoil Theory
let a0 = 2.0 * PI;
if let Some(sweep) = sweep_angle {
// for swept wings we use Kuchemann's modification to Helmbold's
// equation
let a0_cos_sweep = a0 * sweep.cos();
let x = a0_cos_sweep / (PI * aspect_ratio);
a0_cos_sweep / ((1.0 + x.powi(2)).sqrt() + x)
} else if aspect_ratio < 4.0 {
// for low aspect ratio wings (AR < 4) we use Helmbold's equation
let x = a0 / (PI * aspect_ratio);
a0 / ((1.0 + x.powi(2)).sqrt() + x)
} else {
// for high aspect ratio wings (AR > 4) we use the equation given by
// Prandtl's lifting-line theory
a0 / (1.0 + (a0 / (PI * aspect_ratio)))
}
}