implement density calculation and HUD gauge

doc/research.md

@@ -44,8 +44,10 @@
 ## Jupiter
 
 - SRC1: [Thermal structure of Jupiter's atmosphere near the edge of a 5µm hot spot in the north equatorial belt](https://doi.org/10.1029/98JE01766)
+- SRC2: [NASA Jupiter Fact Sheet](https://nssdc.gsfc.nasa.gov/planetary/factsheet/jupiterfact.html)
+- SRC3: ["THE INTERIORS OF JUPITER AND SATURN" by Ravit Helled](https://arxiv.org/pdf/1812.07436)
 
-Based on Table 8 from SRC1:
+Based on Table 8 from SRC1, with additional values for altitude=0 from SRC2 and interior density values from SRC3:
 
 | Altitude (km) | Pressure (bar) | Temperature (K) | Density (kg/m³) |
 | ------------- | -------------- | --------------- | --------------- |
@@ -101,7 +103,10 @@ Based on Table 8 from SRC1:
 | 60 | 4.37E-02 | 122.6 | 0.009915 |
 | 40 | 1.36E-01 | 113.2 | 0.03335 |
 | 23.3 | 3.52E-01 | 122.9 | 0.07945 |
-| 0 | 1 | | |
+| 0 | 1 | 165 | 0.16 |
+| -62000 | ? | ? | 4500 |
+| -62500 | ? | ? | 20000 |
+| -70000 | ? | ? | 25000 |
 
 ### Regression analysis
 
@@ -112,12 +117,20 @@ Pressure:
 - 0km-200km: `p[bar](x[m]) = exp(-0.0020248515 - 0.0000454102 * x)`
 - <0km: `p[bar](x[m]) = -(1.45773e-16) * x^3 + 1` (low-effort cubic regression on `[(-70000km, 50Mbar), (0m, 1bar)]`)
 
+Density:
+
+- 500km-1029.2km: `rho[kg/m³](x[m]) = exp(-15.98781474626208 - 0.00000816092074*x)`
+- 200km-500km: `rho[kg/m³](x[m]) = exp(-4.22487505187567 - 0.00003251947782*x)`
+- 0km-200km: `rho[kg/m³](x[m]) = exp(-1.83275074106303 - 0.00004486861245*x)`
+- -62000km-0km: `rho[kg/m³](x[m]) = -0.0725781*x + 0.16` (linear regression)
+- -70000km-62000km: `rho[kg/m³](x[m]) = 25000.0 / (1 + exp(0.00580528 * x + 361.44394)))` (logistic regression)
+
 ### Designing the in-game atmosphere
 
 New mechanics:
 
-- [ ] Ambient Pressure
-    - [ ] Depends on altitude
+- [X] Ambient Pressure
+    - [X] Depends on altitude
 - [ ] Temperature
     - [ ] Ambient temperature
     - [ ] Space suit temperature
@@ -142,6 +155,7 @@ Relations between mechanics:
 - [ ] Death at pressure of ~400 bar through implosion (depending on vehicle)
 - [ ] Death at high temperatures through continuous damage when temperature exceeds 60°C
 - [ ] Hydrogen + Oxygen = Water, used for evaporative cooling (works only at right pressure/temperature)
+- [ ] Refill Hydrogen inside Jupiter's atmosphere
 
 ## Io
 

src/actor.rs

@@ -1166,8 +1166,10 @@ fn handle_atmosphere(
                 }
 
                 if player.is_some() {
+                    let density = nature::jupiter_altitude_to_density(distance);
                     settings.atmo_pressure = Some(pressure);
                     settings.atmo_altitude = Some(distance - nature::JUPITER_RADIUS);
+                    settings.atmo_density = Some(density);
                     reset_player_gauges = false;
                 }
 
@@ -1187,5 +1189,6 @@ fn handle_atmosphere(
     if reset_player_gauges {
         settings.atmo_pressure = None;
         settings.atmo_altitude = None;
+        settings.atmo_density = None;
     }
 }

src/hud.rs

@@ -877,6 +877,9 @@ fn update_speedometer(
         if let Ok(mut speed_text) = q_node_speed.get_single_mut() {
             // Atmospheric conditions
             let mut atmo = String::new();
+            if let Some(val) = settings.atmo_density {
+                atmo += format!("dens: {}g/m³\n", nature::readable_si(val*1000.0)).as_str();
+            }
             if let Some(val) = settings.atmo_altitude {
                 atmo += format!("alt: {}m\n", nature::readable_si(val)).as_str();
             }

src/nature.rs

@@ -297,6 +297,7 @@ pub fn format_seconds_to_hour_min(seconds: f64) -> String {
 }
 
 pub fn jupiter_altitude_to_pressure(altitude: f64) -> f64 {
+    // Units: meter (relative to 1-bar "surface") -> bar
     // See doc/research.md
     let x = altitude - JUPITER_RADIUS;
     if x >= 1030e3 {
@@ -310,3 +311,21 @@ pub fn jupiter_altitude_to_pressure(altitude: f64) -> f64 {
     }
     return -(1.45773e-16) * x.powf(3.0) + 1.0;
 }
+
+pub fn jupiter_altitude_to_density(altitude: f64) -> f64 {
+    // Units: meter (relative to 1-bar "surface") -> kg/(m^3)
+    // See doc/research.md
+    let x = altitude - JUPITER_RADIUS;
+    if x >= 1030e3 {
+        return 0.0;
+    } else if x >= 500e3 {
+        return (-15.98781474626208 - 0.00000816092074 * x).exp();
+    } else if x >= 200e3 {
+        return (-4.22487505187567 - 0.00003251947782 * x).exp();
+    } else if x >= 0.0 {
+        return (-1.83275074106303 - 0.00004486861245 * x).exp();
+    } else if x >= -62000e3 {
+        return -0.0725781 * x + 0.16;
+    }
+    return 25000.0 / (1.0 + (0.00580528 * x + 361.44394)).exp();
+}

src/var.rs

@@ -53,6 +53,7 @@ pub struct Settings {
     pub zoom_fov: f32,
     pub zoom_sensitivity_factor: f32,
     pub atmo_pressure: Option<f64>,
+    pub atmo_density: Option<f64>,
     pub atmo_altitude: Option<f64>,
     pub font_size_hud: f32,
     pub font_size_fps: f32,
@@ -203,6 +204,7 @@ impl Default for Settings {
             zoom_fov: 15.0,
             zoom_sensitivity_factor: 0.25,
             atmo_pressure: None,
+            atmo_density: None,
             atmo_altitude: None,
             font_size_hud: 24.0,
             font_size_fps: 14.0,