Package Exports

velitherm
velitherm/dist/cjs/index.js
velitherm/dist/es/index.js

This package does not declare an exports field, so the exports above have been automatically detected and optimized by JSPM instead. If any package subpath is missing, it is recommended to post an issue to the original package (velitherm) to support the "exports" field. If that is not possible, create a JSPM override to customize the exports field for this package.

Readme

Velitherm

A library of basic thermodynamics equations for soaring flight.

As used by the weather site https://www.velivole.fr / https://www.meteo.guru

Zero-dependency!

If you are new to weather thermodynamics, you should probably start here: Basic Concepts of Thermodynamics for Soaring Flight

Si vous n'êtes pas à l'aise en thermodynamique appliquée à la météorologie, vous devriez peut-être commencer ici: Bases de la thermodynamique pour le vol libre et le vol à voile

Installation

npm install --save velitherm

Usage

Keep in mind that some equations are numerical approximations of differential equations that have no analytic solutions. The approximations used are the typical weather science approximations which produce good results for temperatures in the range of -40°C to +40°C and air pressures in the range of 1050hPa to 200hPa - which are the typical values in the troposphere - but often lack precision outside this range.

You can check velitherm-visu for a real-world example of using this library. It is hosted at aircalc.velivole.fr.

Common JS

const velitherm = require('velitherm');

// must be very close to 1000
const alt = velitherm.altitudeFromPressure(898.746);

ECMAScript 6

import * as velitherm from 'velitherm';

// must be very close to 1000
const alt = velitherm.altitudeFromPressure(898.746);

TypeScript

import * as velitherm from 'velitherm';

// must be very close to 1000
const alt = velitherm.altitudeFromPressure(898.746);

C++

#include "node_modules/velitherm/include/velitherm.h"

// must be very close to 1000
double alt = velitherm::altitudeFromPressure(898.746);

C

#include "node_modules/velitherm/include/velitherm.h"

// must be very close to 1000
double alt = altitudeFromPressure(898.746, P0, T0);

When using plain old C, you should be using C99 (otherwise gcc may include a deprecated and non-standard math function called gamma) and you should link the math library if it is not already linked.

Barometric and hypsometric equations

There is no single analytical equation that can be used to give a precise value for the altitude / pressure relationship. In fact, this relationship depends on the full vertical temperature and humidity profile and it is impossible to reduce to a single formula. There are two levels of approximation that are widely used:

The barometric formula, which is an ICAO standard and gives a rough value that does not take into account the pressure or the temperature of the day and it is always constant - in aviation it is referred by the callsign QNH
The hypsometric formula, which is commonly used in weather science and it is a better estimation that takes into account the pressure and the temperature of the day - so it varies from one day to another - in aviation it is referred by the callsign QFF

If you are coming from an aviation background, and QNH, QFF and QFE are altimeter settings to you, then you should know that they actually refer to different equations for calculating the altitude from the pressure. QFE refers to the surface pressure of a given site - airport or weather station - and not an equation. If you want to use velitherm to convert between altimeter settings, the right way to do it would be to convert the pressure to altitude using the input setting and then convert it back to pressure using the output setting.

Examples

General weather science

An air parcel with relative humidify of 75% and temperature of 25°C rises from 0m AMSL to 500m AMSL where the surrounding temperature is 20°C. What is its new relative humidity? What is its new temperature? Has there been condensation and did it form a cloud? Has the convective top (ceiling) been reached or will the air parcel continue to rise? The pressure of the day is 1017hPa and the relative humidity at 500m AMSL is 50%.

Solution:

import * as velitherm from 'velitherm';

// When the air rises, its specific humidity remains constant
const q = velitherm.specificHumidity(75, 1017, 25);
console.log('Specific humidity = ', Math.round(q), 'g/kg');
console.log('Dew point = ', velitherm.dewPoint(75, 25).toFixed(2), '°C');

// Find the current pressure at 500m AMSL
const P1 = velitherm.pressureFromAltitude(500, 1017, 25);
console.log('Pressure at 500m = ', Math.round(P1), 'hPa');

// Take into account the dry adiabatic cooling over 500m
const T1 = 25 - 500 * velitherm.gamma;
console.log('The new temperature of the air parcel at 500m = ', T1, '°C');

// Compute the new relative humidity of the air parcel at this pressure and
// temperature
const w1 = velitherm.relativeHumidity(q, P1, T1);
console.log('Relative humidity after rising to 500m = ', Math.round(w1), '%');

// If the air parcel has reached 100% relative humidity, then there is
// condensation
if (w1 < 100) {
  console.log('No, it did not form a cloud');
} else {
  console.log('Yes, it did form a cloud');
}

// If the density of the air parcel is still lower than the
// surrounding air at 500m AMSL, then it will continue to rise
const rhoParcel = velitherm.airDensity(w1, P1, T1);
const rhoAir500 = velitherm.airDensity(50, P1, 20);
if (rhoParcel < rhoAir500) {
  console.log('The air parcel will continue to rise');
} else {
  console.log('The ceiling has been reached');
}

You can run the example program with

npx tsx examples/risingAir.ts

Note that the dew point of the air parcel at sea level is 20.26°C, yet it does not form a cloud when cooled down to 20.12°C at 500m AMSL. The reason is that a dew point is valid only for a given pressure. At a lower pressure, the dew point will also be lower.

Flight instruments

I know that the surrounding air pressure is 821 hPa. How can I tell what is my current altitude? How can I tell what is my current flight level and how far I am from FL115?

My local weather information provider tells me that the mean sea level pressure of the day at my location is 1017 hPa. How can I improve the accuracy of my height estimate? And if I know that the mean temperature of the air below me is 23°C? How can I get an even better estimate?

What should I do if I don't have any idea about today's pressure and temperature of the air near the ground? How can I be sure to stay below FL115?

Solution:

import * as velitherm from 'velitherm';

const barometerInput = 821;
const pressureMSL = 1017;
const temperatureBelow = 23;

// Rough estimate of the height using only the pressure
// We round it to 50m because it is a rough estimate
const alt = Math.round(velitherm.altitudeFromStandardPressure(barometerInput) /
  50) * 50;
console.log('Rough estimate of the altitude is', alt, 'm');

// Better estimate of the height using the ground pressure
const alt2 = Math.round(velitherm.altitudeFromPressure(barometerInput,
  pressureMSL));
console.log('Better estimate of the altitude is', alt2, 'm');

// Even better estimate of the height using the temperature
const alt3 = Math.round(velitherm.altitudeFromPressure(barometerInput,
  pressureMSL, temperatureBelow));
console.log('Even better estimate of the altitude is', alt3, 'm');

// Flight levels are in pressure-feet, so we do not need
// anything but the barometer input (this is the very reason for this)
const fl = velitherm.FLFromPressure(barometerInput);
console.log('The current closest flight level is FL', fl);

// What is the current altitude for FL115?
// FL115 means 11500 feet measured at pressure at standard atmospheric
// conditions
const pressureFL115 = velitherm.pressureFromFL(115);
console.log('FL115 means the altitude at which the pressure is',
  Math.round(pressureFL115), 'hPa');

// Get the actual altitude for today
const altitudeFL115 = Math.round(velitherm.altitudeFromPressure(
  pressureFL115, pressureMSL, temperatureBelow));
console.log('Today FL115 is at', altitudeFL115, 'm');
console.log('You can climb', altitudeFL115 - alt3, 'm before reaching FL115');

// Get the most pessimistic (lowest) possible estimate for FL115?
// This is possible only with a minimum pressure and a minimum air temperature
// We suppose that we are not flying in winter storm conditions
// Let's define these as 1000 hPa and -20°C
// You should never be flying in an ultralight aircraft is pressure
// is below 1000 hPa
const altitudeMinFL115 = Math.round(velitherm.altitudeFromPressure(
  pressureFL115, 1000, -20));
console.log('FL115 should not be below', altitudeMinFL115,
  'm even in bad winter weather');
console.log('You can climb', altitudeMinFL115 - alt3,
  'm before reaching the pessimistic estimate for FL115');

Run this example with:

npx tsx examples/flightInstrument.ts

Please note the huge difference between the usual 3505m estimate for FL115 and the actual 3945m altitude for this given day or the 3237m altitude in bad winter weather!

API

velitherm
G
Cp
L
gamma
ELR
P0
T0
Rd
Rv
Md
Mv
R
K
feetPerMeter
altitudeFromStandardPressure
- Parameters
pressureFromStandardAltitude
- Parameters
altitudeFromPressure
- Parameters
pressureFromAltitude
- Parameters
waterVaporSaturationPressure
- Parameters
relativeHumidity
- Parameters
dewPoint
- Parameters
relativeHumidityFromDewPoint
- Parameters
mixingRatio
- Parameters
specificHumidityFromMixingRatio
- Parameters
specificHumidity
- Parameters
airDensity
- Parameters
LCL
- Parameters
gammaMoist
- Parameters
adiabaticExpansion
- Parameters
adiabaticCooling
- Parameters
- Examples
pressureFromFL
- Parameters
FLFromPressure
- Parameters

velitherm

velivole.fr/meteo.guru Basic Thermodynamics Equations for Soaring Flight

Licensed under the LGPL License, Version 3.0 (the "License") You may not use this file except in compliance with the License. You may obtain a copy of the License at: https://www.gnu.org/licenses/lgpl-3.0.en.html

All methods use:

Pressure in hPa

Temperature in °C

Height in meters

Relative humidity in % from 0 to 100

Specific humidity in g/kg

Mixing ratio in g/kg

Type: string

G

Earth's average gravity acceleration (m/s2)

Type: number

Cp

The thermal capacity of air (J/kg)

Type: number

L

The enthalpy of vaporization of water (J/kg)

Type: number

gamma

The adiabatic lapse rate of dry air (°C/m)

This is the rate of cooling of a rising air parcel without water vapor condensation.

See gammaMoist() for the condensation case.

Type: number

ELR

Mean environmental lapse rate of the troposphere (°C/m)

This is the mean rate of cooling of the troposphere when the air is calm and stable. It works best over large height differences. It is also the lapse rate of the standard atmosphere.

Type: number

P0

The average sea level pressure (hPa)

Type: number

T0

The temperature of the ICAO standard atmosphere (°C)

Type: number

Rd

The specific gas constant of dry air J/(kg*K)

Type: number

Rv

The specific gas constant of water vapor J/(kg*K)

Type: number

Md

Molar mass of dry air kg/mol

Type: number

Mv

Molar mass of water vapor kg/mol

Type: number

R

Universal gas constant J/(kg*mol)

Type: number

K

Absolute zero in °C

Type: number

feetPerMeter

Number of feets in one meter

Type: number

altitudeFromStandardPressure

Altitude from pressure using the barometric formula and ICAO's definition of standard atmosphere.

This is a very rough approximation that is an ICAO standard. It is used when calculating QNH. It does not take into account the pressure and temperature of the day.

Parameters

pressure number Pressure
pressure0 number? Optional sea-level pressure of the day (optional, default P0)

Returns number

pressureFromStandardAltitude

Pressure from altitude using the barometric formula and ICAO's definition of standard atmosphere.

This is a very rough approximation that is an ICAO standard. It is used when calculating QNH. It does not take into account the pressure and temperature of the day.

Parameters

height number Height
pressure0 number? Optional sea-level pressure of the day (optional, default P0)

Returns number

altitudeFromPressure

Altitude from pressure using the hypsometric formula.

This is a better equation that takes into account the pressure and the temperature of the day. It is not a standard and different weather institutions use slightly different parameters. It is used when calculating the QFF.

Parameters

pressure number Pressure
pressure0 number? Optional sea-level pressure of the day (optional, default P0)
temp number? Optional average temperature from the ground to the given level (optional, default T0)

Returns number

pressureFromAltitude

Pressure from altitude using the hypsometric formula.

Parameters

height number Height
pressure0 number? Optional sea-level pressure of the day (optional, default P0)
temp number? Optional average temperature from the ground to the given level (optional, default T0)

Returns number

waterVaporSaturationPressure

(Saturation) Water vapor pressure.

Clausius–Clapeyron equation - the most fundamental equation in weather science.

This is the Magnus-Tetens approximation.

Parameters

temp number Temperature (optional, default T0)

Returns number

relativeHumidity

Relative humidity from specific humidity.

This is from the Magnus-Tetens approximation.

Parameters

specificHumidity number Specific humidity
pressure number? Optional pressure (optional, default P0)
temp number? Optional temperature (optional, default T0)

Returns number

dewPoint

Dew point from relative humidity.

Approximation of the Magnus equation with the Sonntag 1990 coefficients.

Parameters

relativeHumidity number Relative humidity
temp number? Optional temperature (optional, default T0)

Returns number

relativeHumidityFromDewPoint

Relative humidity from dew point.

Approximation of the Magnus equation with the Sonntag 1990 coefficients.

Parameters

dewPoint number Relative humidity
temp number? Optional temperature (optional, default T0)

Returns number

mixingRatio

Mixing ratio from specific humidity.

Analytic equation from the definition.

Parameters

specificHumidity number Specific humidity

Returns number

specificHumidityFromMixingRatio

Specific humidity from mixing ratio.

Analytic equation from the definition.

Parameters

mixingRatio number Mixing ratio

Returns number

specificHumidity

Specific humidity from relative humidity.

Approximation of the Magnus equation with the Sonntag 1990 coefficients.

Parameters

relativeHumidity number Relative humidity
pressure number? Optional pressure (optional, default P0)
temp number? Optional temperature (optional, default T0)

Returns number

airDensity

Air density.

Analytic equation from Avogadro's Law.

Parameters

relativeHumidity number Relative humidity
pressure number? Optional pressure (optional, default P0)
temp number? Optional temperature (optional, default T0)

Returns number

LCL

Lifted Condensation Level.

This is the altitude at which a mechanically lifted air parcel from the ground will condensate.

It corresponds to the cloud base level when the clouds are formed by mechanical lifting.

This approximation is known as the Espy equation with the Stull coefficient.

Parameters

temp number Temperature at 2m
dewPoint number Dew point at 2m

Returns number

gammaMoist

Moist adiabatic lapse rate from pressure and temperature.

Copied from Roland Stull, Practical Meteorology (copylefted, available online).

Rather complex approximation based on the Magnus-Tetens equation and the barometric equation.

Parameters

temp number Temperature
pressure number? Optional pressure (optional, default P0)

Returns number

adiabaticExpansion

Adiabatic expansion rate from pressure change rate.

This equation allows to calculate the expansion ratio of an air parcel from the the previous pressure and the new pressure.

An adiabatic expansion is an isentropic process that is governed by the Ideal gas law in general and the constant entropy relationship in particular: (P / P0) = (V / V0) ^ gamma Where P=pressure, V=volume, gamma=heat capacity ratio (1.4 for air, a diatomic gas)

Analytic equation.

Parameters

volume0 number Old volume
pressure number New pressure
pressure0 number Old pressure (optional, default P0)

Returns number

adiabaticCooling

Adiabatic cooling rate from pressure change rate.

This equation allows to calculate the cooling ratio of an air parcel from the the previous pressure and the new pressure.

It is by combining this equation with the barometric equation that the adiabatic lapse rate of dry air can be obtained.

Keep in mind that if you intend to use this method to calculate a rate relative to height in meters, you will need very precise altitude calculations for good results. As the dry adiabatic rate is a constant that does not depend on the temperature or the pressure, most of the time you will be better off simply using the gamma constant.

https://en.wikipedia.org/wiki/Ideal_gas_law contains a very good introduction to this subject.

Analytic equation.

Parameters

temp0 number Old temperature
pressure number New pressure
pressure0 number Old pressure (optional, default P0)

Examples

// Compute the adiabatic cooling per meter
// when rising from 0m AMSL to 100m AMSL starting at 15°C

const gamma = (15 - velitherm.adiabaticCooling(15,
                      velitherm.pressureFromStandardAltitude(100),
                      velitherm.pressureFromStandardAltitude(0))
               ) / 100;

// It should be very close to the provided constant
assert(Math.abs(gamma - velitherm.gamma) < 1e-5)

Returns number

pressureFromFL

Convert a Flight Level to pressure

Flight levels are defined as pressure and not as a fixed altitude. This means that a flight level can always be converted to pressure without needing any other information in a fully deterministic way.

A flight level of 115 means 11500 feet measured by barometer using the ICAO standard atmosphere.

The returned pressure can then be converted to altitude using any of the above functions, taking into account the MSL pressure and temperature variations.

Parameters

FL number Flight Level

Returns number

FLFromPressure

Convert pressure to Flight Level.

A flight level of 115 means 11500 feet measured by barometer using the ICAO standard atmosphere.

The returned Flight Level can be a fractional number, this should be rounded to the closest integer as there are no fractional flight levels.

Parameters

P number pressure

Returns number

velitherm

Package Exports

Readme

Velitherm

Installation

Usage

Common JS

ECMAScript 6

TypeScript

C++

C

Barometric and hypsometric equations

Examples

General weather science

Flight instruments

API

Table of Contents

velitherm

G

Cp

L

gamma

ELR

P0

T0

Rd

Rv

Md

Mv

R

K

feetPerMeter

altitudeFromStandardPressure

Parameters

pressureFromStandardAltitude

Parameters

altitudeFromPressure

Parameters

pressureFromAltitude

Parameters

waterVaporSaturationPressure

Parameters

relativeHumidity

Parameters

dewPoint

Parameters

relativeHumidityFromDewPoint

Parameters

mixingRatio

Parameters

specificHumidityFromMixingRatio

Parameters

specificHumidity

Parameters

airDensity

Parameters

LCL

Parameters

gammaMoist

Parameters

adiabaticExpansion

Parameters

adiabaticCooling

Parameters

Examples

pressureFromFL

Parameters

FLFromPressure

Parameters