Merge pull request #39 from oyve/copilot/fix-altitude-function-tests

Add altitudeFromPressureDifference function returning final altitude

Author: oyve

README.md

@@ -66,6 +66,7 @@ console.log(`Dew Point: ${dewPoint} K`);
 | Formula                     | Description                                                               |
 |-----------------------------|---------------------------------------------------------------------------|
 | **Freezing Level Altitude**  | Estimate the altitude where temperature drops below freezing. [🔗](https://en.wikipedia.org/wiki/Freezing_level) |
+| **Altitude From Pressure Difference** | Calculate the final altitude from a pressure difference using the hypsometric formula. [🔗](https://en.wikipedia.org/wiki/Hypsometric_equation) |
 
 ### Humidity
 | Formula                     | Description                                                               |

src/formulas/altitude.ts

@@ -1,3 +1,5 @@
+import * as c from '../constants';
+
 /**
  * Estimate the altitude (in meters) where the temperature drops below freezing (0°C).
  * Assumes a linear lapse rate (default: 0.0065 K/m).
@@ -16,3 +18,39 @@ export function freezingLevelAltitude(
     const altitudeDiff = (surfaceTemp - 273.15) / lapseRate;
     return surfaceAltitude + altitudeDiff;
 }
+
+/**
+ * Calculate the final altitude from a pressure difference using the hypsometric formula.
+ * Given a reference pressure at a known altitude and an observed pressure, this function
+ * returns the altitude at which the observed pressure occurs.
+ * 
+ * @param {number} referencePressure - Reference pressure in Pascals (Pa) at the reference altitude.
+ * @param {number} observedPressure - Observed pressure in Pascals (Pa) at the unknown altitude.
+ * @param {number} referenceAltitude - Altitude in meters (m) where the reference pressure was measured. Defaults to 0 (sea level).
+ * @param {number} temperature - Average temperature in Kelvin (K) between the two altitudes. Defaults to 288.15 K (15°C).
+ * @returns {number} The final altitude in meters (m) where the observed pressure occurs.
+ * 
+ * @example
+ * // Calculate altitude when pressure drops from 101325 Pa (sea level) to 89874 Pa
+ * const altitude = altitudeFromPressureDifference(101325, 89874, 0, 288.15);
+ * console.log(altitude); // ~1000 m
+ * 
+ * @see https://en.wikipedia.org/wiki/Hypsometric_equation
+ */
+export function altitudeFromPressureDifference(
+    referencePressure: number,
+    observedPressure: number,
+    referenceAltitude: number = 0,
+    temperature: number = c.STANDARD_MEAN_TEMPERATURE_KELVIN
+): number {
+    const g = c.DRY_AIR_CONSTANTS.gravity; // Gravitational acceleration (m/s²)
+    const R = c.DRY_AIR_CONSTANTS.gasConstant; // Specific gas constant for dry air (J/(kg·K))
+    
+    // Using the hypsometric formula: h = (R * T / g) * ln(P1 / P2)
+    // Where h is the altitude difference, R is gas constant, T is temperature,
+    // g is gravity, P1 is reference pressure, P2 is observed pressure
+    const altitudeDifference = (R * temperature / g) * Math.log(referencePressure / observedPressure);
+    
+    // Return the final altitude (reference altitude + altitude difference)
+    return referenceAltitude + altitudeDifference;
+}

src/index.ts

@@ -3,6 +3,7 @@ import * as temperature from "./formulas/temperature";
 import * as pressure from "./formulas/pressure";
 import * as wind from "./formulas/wind";
 import * as airDensity from "./formulas/airDensity";
+import * as altitude from "./formulas/altitude";
 
 import * as beaufort from "./scales/beaufort";
 import * as saffirSimpson from "./scales/saffirSimpson";
@@ -18,5 +19,6 @@ export {
     pressure,
     wind,
     airDensity,
+    altitude,
     scales
 };

tests/formulas/altitude.test.ts

@@ -1,4 +1,4 @@
-import { freezingLevelAltitude } from '../../src/formulas/altitude';
+import { freezingLevelAltitude, altitudeFromPressureDifference } from '../../src/formulas/altitude';
 import { cloudBaseHeight } from '../../src/phenomena/cloud';
 
 describe('freezingLevelHeight', () => {
@@ -29,6 +29,59 @@ describe('freezingLevelHeight', () => {
     });
 });
 
+describe('altitudeFromPressureDifference', () => {
+    it('should calculate altitude from sea level pressure', () => {
+        // Sea level pressure: 101325 Pa, pressure at ~1000m: ~89874 Pa
+        // Using hypsometric formula: h = (R * T / g) * ln(P1 / P2)
+        // With R = 287.05 J/(kg·K), T = 288.15 K, g = 9.80665 m/s²
+        const result = altitudeFromPressureDifference(101325, 89874, 0, 288.15);
+        // Calculated: (287.05 * 288.15 / 9.80665) * ln(101325 / 89874) ≈ 1011.49 m
+        expect(result).toBeCloseTo(1011.49, 0);
+    });
+
+    it('should return the final altitude, not just the difference', () => {
+        // If reference altitude is 500 m, the result should be 500 + altitude difference
+        const result = altitudeFromPressureDifference(101325, 89874, 500, 288.15);
+        // Should be approximately 500 + 1011.49 = 1511.49 m
+        expect(result).toBeCloseTo(1511.49, 0);
+    });
+
+    it('should return reference altitude when pressures are equal', () => {
+        // If pressures are equal, altitude difference is 0
+        const result = altitudeFromPressureDifference(101325, 101325, 100, 288.15);
+        expect(result).toBeCloseTo(100, 2);
+    });
+
+    it('should calculate lower altitude when observed pressure is higher', () => {
+        // Higher pressure means lower altitude
+        const result = altitudeFromPressureDifference(89874, 101325, 1000, 288.15);
+        // Should be approximately 1000 - 1011.49 ≈ -11.49 m
+        expect(result).toBeCloseTo(-11.49, 0);
+    });
+
+    it('should calculate altitude at high elevation from sea level', () => {
+        // Sea level pressure: 101325 Pa, pressure at ~5000m: ~54020 Pa
+        const result = altitudeFromPressureDifference(101325, 54020, 0, 288.15);
+        // Calculated value using hypsometric formula
+        expect(result).toBeCloseTo(5305.07, 0);
+    });
+
+    it('should work with default parameters', () => {
+        // Uses default referenceAltitude = 0 and temperature = 288.15 K
+        const result = altitudeFromPressureDifference(101325, 89874);
+        expect(result).toBeCloseTo(1011.49, 0);
+    });
+
+    it('should account for different temperatures', () => {
+        // Colder temperature should result in slightly different altitude calculation
+        const coldResult = altitudeFromPressureDifference(101325, 89874, 0, 273.15); // 0°C
+        const warmResult = altitudeFromPressureDifference(101325, 89874, 0, 303.15); // 30°C
+        
+        // Warmer air is less dense, so same pressure difference = larger altitude change
+        expect(warmResult).toBeGreaterThan(coldResult);
+    });
+});
+
 describe('cloudBaseHeight', () => {
     it('should calculate cloud base height at sea level', () => {
         // Temperature: 293.15 K (20°C), Dew Point: 283.15 K (10°C)