Pulse Parameters Description

Table of Contents

1. Air Density & Air Velocity
- 1.1. Air Density
- 1.2. Air Velocity
2. Ambient Temperature
3. Atmospheric Pressure
4. Clothing Resistance
5. Emissivity
6. Mean Radiant Temperature
7. Relative Humidity
8. Respiration Ambient Temperature
9. Ambient Gas
10. Reference Values
References

This section will focus on the description of the parameters contained in the JSON file of the environment part of Pulse. There are several parameters that influence the ambient conditions on the human body. These will be detailed and explained below.

1. Air Density & Air Velocity

1.1. Air Density

In general, we know that some objects are heavier than others even though they have the same size. For example, a brick and a sponge of the same size have considerably different weights. It’s due to density.
In particular, the density of air is defined as the mass per unit volume of earth’s atmosphere. Especially for gases, whose molecules are free to move around, density can vary widely. In the atmosphere, molecules that are close to the earth’s surface are held together more tightly than molecules that are further from the surface. This is due to the earth’s gravitational force. In fact, with increasing altitude the density of air decreases as there are less molecules.
Also temperature, atmospheric pressure and humidity influence air density. For example, hot air is less dense than cool air and therefore will move upwards through the cold air.
Note that Pulse calculates the density of the air in an internal class. However, humidity plays an important role and therefore there exist 2 different formulas to calculate the air density. [AD2]

Dry air [AD1]:
Air density can be calculated by using the ideal gas law \(pV=nRT\) and thus we get:

\[\rho_{dry\; air}= \frac{p}{R_{dry\; air}T}\]

with:

\(\rho_{dry\; air}\): air density \((kg/m^3)\)
\(p\): absolute pressure \((Pa)\)
\(T\): absolute temperature \((K)\)
\(R_{dry\; air}\): gas constant for dry air \((287.058\; J/(kg \cdot K))\).

Note that \(R_{dry\; air}=R/M_d\), where \(R\) stands for the universal gas constant and \(M_d\) represents the molar mass of dry air.

Absolute Temperature and Absolute Pressure

The absolute temperature scale matches the temperature 0 to the absolute zero which is the coldest possible temperature (-273.15°C). The same goes for the absolute pressure.

Humid air [AD1]:
Humid air is obtained by adding water vapour to the air. This results in a decrease of the air density. In fact, the molar mass of dry air \((29\; g/mol)\) is higher than the one of water \((18\; g/mol)\). Knowing that, by the Avogadro’s Law, at a given pressure and temperature, any ideal gas has a constant number number of molecules for a specific volume. Consequently, by adding water molecules to a certain volume of air, the dry air molecules have to decrease in order to remain the temperature or pressure stable.
Therefore, the density of humid air can be calculated as the sum of 2 ideal gases.

\[\rho_{humid\; air}= \frac{p_{dry\; air}}{R_{dry\; air}T} + \frac{p_{water\; vapor}}{R_{water\; vapor}T}=\frac{p_{dry\; air}M_{dry\; air} + p_{water\; vapor}M_{water\; vapor}}{RT}\]

with:

\(\rho_{humid\; air}\): density of the humid air \((kg/m^3)\)
\(p_{dry\; air}\): partial pressure of dry air \((Pa)\)
\(R_{dry\; air}\): gas constant for dry air \((287.058\; J/(kg \cdot K))\)
\(M_{dry\; air}\): molar mass of dry air \((0.0289652\; kg/mol)\)
\(T\): temperature \((K)\)
\(p_{water\; vapor}\): partial pressure of water power \((Pa)\)
\(R_{water\; vapor}\): gas constant for water power \((461.495\; J/(kg \cdot K))\)
\(M_{water\; vapor}\): molar mass of water vapor \((0.018016\; kg/mol)\)
\(R\): universal gas constant \((8.31446\; J/(K \cdot mol))\)

1.2. Air Velocity

The effect caused by air moving from high to low pressure is called wind speed or wind flow speed. This is generally due to temperature changes. As in meteorology wind is defined as the horizontal movement of air, its SI unit is usually expressed in \(m/s\) or \(km/h\). To measure the air speed, an anemometer is typically used. Note, for example, that the weather service gives its measurements at a height of 10 \(m\) from the ground.
For people in motion, e.g. for runners, the air speed can influence in different ways. Having favourable wind can make running easier and increase the runner’s performance, while unfavourable wind can cause the opposite effect with extra effort required from the runner. Furthermore, people in a static position can have different sensations of heat depending on whether they are exposed to wind or not. [WS]

Implementation

"SurroundingType": "Air",   (1)
"AirVelocity": {    (2)
    "ScalarLengthPerTime": {    (3)
    "Value": 2.5,   (4)
    "Unit": "m/s"   (5)
    }
}

1	Human body is surrounded by air
2	Name of the parameter
3	Type of the parameter’s value
4	Input value
5	SI unit

2. Ambient Temperature

The ambient temperature is the average air temperature surrounding an object whether inside or outside. In meteorology, the ambient temperature is the same as the current air temperature as it doesn’t get influenced by wind or other factors. Thus, it only relates to the air temperature. The ambient temperature is generally expressed in \(°C\). [AT]

Implementation

"AmbientTemperature": {     (1)
    "ScalarTemperature": {  (2)
    "Value": 35.0,  (3)
    "Unit": "degC"  (4)
    }
}

1	Name of the parameter
2	Type of the parameter’s value
3	Input value
4	Unit in degrees Celsius

3. Atmospheric Pressure

Atmospheric pressure or barometric pressure is the force applied on a surface by the air above it as gravity pulls it to the earth. "The air around you has weight, and it presses against everything it touches.", explains National Geographics on its website [AP].
With increasing altitude, the atmospheric pressure decreases. This leads to a reduction in the amount of oxygen available. Some high-level athletes will regularly train at high altitudes to increase their breathing volume and endurance. When travelling by plane for example, an artificial air pressure is created to make travellers feel comfortable. But atmospheric pressure is also an indicator of weather. Low pressure is normally synonymous with wind and precipitation, while high pressure is more related to mild weather.
Atmospheric pressure is usually measured with a barometer containing a column of mercury in a glass tube. Therefore it’s most commonly measured in \(mmHg\) (millimeters of mercury).
Hence, the following formula can be used to calculate the atmospheric pressure.

Barometric formula [BF]:

\[P=P_0 \cdot \exp\left(-\frac{Mg}{RT}h\right)\]

where:

\(P\): atmospheric pressure \((mmHg)\)
\(P_0\): average sea level pressure \((760\; mmHg)\)
\(g\): gravitational acceleration \((9.807\; m/s^2)\)
\(M\): molar mass of earth’s air \((0.02896\; kg/mol)\)
\(T\): standard temperature \((288.15\; K)\)
\(R\): universal gas constant \((8.3143\; (N\cdot m)/(mol\cdot K))\)
\(h\): height over sea level \((m)\)

By substituting all the known values, we obtain the simplified formula depending only on the altitude:

\[P=760 \cdot \exp\left(-0.00012 \cdot h\right)\]

Implementation

"AtmosphericPressure": {    (1)
    "ScalarPressure": { (2)
    "Value": 760.0, (3)
    "Unit": "mmHg"  (4)
    }
}

1	Name of the parameter
2	Type of the parameter’s value
3	Input value
4	Unit in millimeters of mercury

4. Clothing Resistance

Clothing insulation refers to the thermal insulation provided by clothing. The main role is to protect the human body against weather in different situations. Depending on those situations, the clothing must be adapted in order to benefit from this protection, knowing that each human being has a different perception of heat and cold.
Taking the example of athletes, they generally have to confront the following four elements: cold, heat, rain and wind. Moreover, there is the aspect of aerodynamics in order to reduce the friction with air and to be as efficient as possible, and the ability of the textile to move sweat from the skin to the outer surface in order to promote faster drying of the material.
Of course, in all cases the material of the clothing plays a major role. For example, one garment can be much thinner than another and still have the same insulating effect. [CR1][CR2]

Clothing insulation is usually expressed in \(clo\) units [CR2]:

\[1\; clo = 0.155 \; K \cdot m^2 \cdot W^{-1}\]

or \(tog\) units [CR2]:

\[1\; tog = 0.1 \; K \cdot m^2 \cdot W^{-1}\]

Consequently,

\[1\; clo = 1.55\; togs\]

Implementation

"ClothingResistance": { (1)
    "ScalarHeatResistanceArea": {   (2)
    "Value": 3.0, (3)
    "Unit": "clo"   (4)
    }
}

1	Name of the parameter
2	Type of the parameter’s value
3	Input value
4	Unit in clo

5. Emissivity

The emissivity of the surface of an object is the percentage of effectiveness in emitting energy as thermal radiation. It’s the ratio of the thermal radiation from a surface to the radiation from an ideal black surface (blackbody) at the same temperature. Thus, it’s values vary from 0 (very shiny) to 1 (perfect black body) and have no unit. [EM]

Implementation

"Emissivity": { (1)
    "Scalar0To1": { (2)
    "Value": 0.90   (3)
    }
}

1	Name of the parameter
2	Type of the parameter’s value
3	Input value

6. Mean Radiant Temperature

Mean radiant temperature (MRT) is a measure of the average temperature of the surfaces that surround a particular point, with which it will exchange thermal radiation. If the point is exposed to the outside, this may include the sky temperature and solar radiation. [MRT1]
There are different ways to calculate the MRT. By applying its definition, the MRT can be calculated from the measured temperature of surrounding walls and surfaces and their positions with respect to the person. Thus, we need the angle factors between the person and the surrounding surfaces.

1^st formula [MRT3]:

\[MRT^4=T_1^4F_{p-1}+T_2^4F_{p-2}+\cdots +T_n^4F_{p-n}\]

where:

\(MRT\): mean radiant temperature \((K)\)
\(T_n\): temperature of surface nr \(n\) \((K)\)
\(F_{p-n}\): angle factor between a person and surface \(n\)

Another way to calculate the MRT is to use a black-globe thermometer. The centre of it contains a temperature sensor such as the bulb of a mercury thermometer, and it’s external surface absorbs the radiation from the walls of the enclosure.
This gives us the following formula.

2^nd formula [MRT3]:

\[MRT=\left[(GT+273)^4+\frac{1.1\cdot 10^8\cdot v_a^{0.6}}{\varepsilon \cdot D^{0.4}}(GT-T_a)\right]^{\frac{1}{4}}-273\]

where:

\(MRT\): mean radiant temperature \((°C)\)
\(GT\): globe temperature \((°C)\)
\(v_a\): air velocity at the level of the globe \((m/s)\)
\(\varepsilon\): emissivity of the globe
\(D\): diameter of the globe \((m)\)
\(T_a\): temperature of the air \((°C)\)

Using a standard globe with \(D=0.15\; m\) and \(\varepsilon=0.95\), we get:

\[MRT=\left[(GT+273)^4+2.5\cdot 10^8\cdot v_a^{0.6}(GT-T_a)\right]^{\frac{1}{4}}-273\]

Implementation

"MeanRadiantTemperature": { (1)
    "ScalarTemperature": {  (2)
    "Value": 10.1,  (3)
    "Unit": "degC"  (4)
    }
}

1	Name of the parameter
2	Type of the parameter’s value
3	Input value
4	Unit in degrees Celsius

7. Relative Humidity

Humidity is the concentration of water vapour present in the air. Relative humidity (RH) indicates a present state of absolute humidity relative to a maximum humidity at the same temperature, where absolute humidity represents the water content of air. In other words, relative humidity is the ratio of how much water vapour is in the air and how much water vapour the air could potentially contain at a certain temperature. RH consequently depends on the temperature and is expressed as a percentage.
Note that this ratio can be written as the division of vapour pressure by saturation vapour pressure, which leads us to the first approach to calculating RH. [RH3]

Approach 1 [RH1]:

\[Es=E_0 \cdot \exp \bigg[\frac{L_v}{R_v}\bigg(\frac{1}{T_0}-\frac{1}{T}\bigg)\bigg] = 0.611 \cdot \exp \bigg[5423 \cdot \bigg(\frac{1}{273}-\frac{1}{T}\bigg)\bigg]\]

\[E=E_0 \cdot \exp \bigg[\frac{L_v}{R_v}\bigg(\frac{1}{T_0}-\frac{1}{T_d}\bigg)\bigg] = 0.611 \cdot \exp \bigg[5423 \cdot \bigg(\frac{1}{273}-\frac{1}{T_d}\bigg)\bigg]\]

with:

\(Es\): saturation vapour pressure \((kPa)\)
\(E\): vapour pressure \((kPa)\)
\(T_0\): reference temperature \((273\; K)\)
\(E_0\): vapour pressure at \(T_0\) \((0.611\; kPa)\)
\(T\): temperature \((K)\)
\(T_d\): dew point temperature \((K)\)
\(L_v\): latent heat of vaporisation for liquid water \((2.5 \times 10^6\; J\cdot kg^{-1})\)
\(R_v\): water-vapor gas constant \((461\; J\cdot kg^{-1}\cdot K^{-1})\)

Therefore, we can use the following formula [RH1]:

\[\text{Relative Humidity: } RH=E/Es \cdot 100\%\]

However, it is possible to make simpler approximations between relative humidity, dew point and temperature. Therefore, the following approximation formulas can be used:

Approach 2 [RH2]:

\[T_d \approx T-\frac{100-RH}{5}\]

\[RH \approx 100-5(T-T_d)\]

where:

\(RH\): relative humidity
\(T_d\): dew point temperature \((K)\)
\(T\): temperature \((K)\)

Implementation

"RelativeHumidity": {   (1)
    "Scalar0To1": { (2)
    "Value": 0.45   (3)
    }
}

1	Name of the parameter
2	Type of the parameter’s value
3	Input value

8. Respiration Ambient Temperature

This parameter refers to the temperature of surrounding air for respiration. In most cases the value of respiration ambient temperature will be the same as for the ambient temperature and the MRT.

Implementation

"RespirationAmbientTemperature": {  (1)
    "ScalarTemperature": {  (2)
    "Value": 10.1,  (3)
    "Unit": "degC"  (4)
    }
}

1	Name of the parameter
2	Type of the parameter’s value
3	Input value
4	Unit in degrees Celsius

9. Ambient Gas

The ambient gas, i.e. the ambient air, is composed of 78% Nitrogen \((N_2)\), 21% Oxygen \((O_2)\), 0.04% Carbon Dioxide \((CO_2)\) and 0.96% of other gases such as Argon \((Ar)\). The Pulse implementation will mainly take into account the first three gases mentioned. [AG]

Implementation

"AmbientGas": [{
    "Name": "Nitrogen", (1)
    "Amount": { (2)
    "Scalar0To1": { (3)
        "Value": 0.7901 (4)
    }
    }
}, {
    "Name": "Oxygen",
    "Amount": {
    "Scalar0To1": {
        "Value": 0.2095
    }
    }
}, {
    "Name": "CarbonDioxide",
    "Amount": {
    "Scalar0To1": {
        "Value": 4.0E-4
    }
    }
}]

1	Name of the parameter
2	Amount of the gas
3	Type of the parameter’s value
4	Input value

10. Reference Values

In order to have a general idea of the values that these different parameters take, we will summarise some standard cases in a table.

Table 1. Reference Values for Pulse Parameters
Parameter	Value	Description
Air Velocity	\(3.5-5\; m/s\) \(14-16.5\; m/s\) \(>32\; m/s\) [RVAV]	Gentle breeze: leaves & small twigs move, light flags extend Moderate gale: whole trees sway, difficult to walk against wind Hurricane: violent destruction
Ambient Temperature	\(0°C\) \(15°C\) \(25°C\)	Cold with risk of ice Pleasant temperature Very hot days
Atmospheric Pressure	Measured at \(15°C\) and \(0\%\) humidity: \(760\; mmHg\) \(675\; mmHg\) \(600\; mmHg\) [RVAP]	Standard sea-level pressure \(1000\; m\) altitude \(2000\; m\) altitude
Clothing Resistance	\(0.90\; clo\) \(0.76\; clo\) \(0.36\; clo\) [CR2]	Winter gloves and a jersey under the fleece jacket Fleece jacket and long tights Shorts and short-sleeved jersey
Emissivity	\(0.97-0.99\) \(0.80\) \(0.10\) [RVEM]	Skin, human Polyester Chromium
Mean Radiant Temperature	\(0°C\) \(15°C\) \(25°C\)	Cold with risk of ice Pleasant temperature Very hot days
Relative Humidity	\(40\%-60\%\) \(<30\%\) \(>70\%\) [RVRH]	Normal feeling Increased static electricity and increased dust concentration in the air Significant microbial growth and condensation on cold surfaces
Respiration Ambient Temperature	\(<0°C\) \(>0°C\)	Feeling of freshness Normal feeling
Ambient Gas	Nitrogen: \(0.7901\) Oxygen: \(0.2095\) Carbon Dioxide: \(4 \times 10^{-4}\) [RVAG]	Composition of ambient gas (ambient air)

References

[AD1] Wikipedia (2021, June 17). Density of air. Retrieved from en.wikipedia.org/wiki/Density_of_air.
[AD2] NASA Glenn Research Center (2021, June 17). Density. Retrieved from grc.nasa.gov.
[WS] Wikipedia (2021, June 21). Wind speed. Retrieved from en.wikipedia.org/wiki/Wind_speed.
[AT] Designing Buildings Wiki (2021, June 21). Ambient temperature. Retrieved from designingbuildings.co.uk/wiki/Ambient_temperature.
[AP] National Geographic (2021, June 21). Atmospheric Pressure. Retrieved from nationalgeographic.org/encyclopedia/atmospheric-pressure/.
[BF] Math24 (2021, June 16). Barometric Formula. Retrieved from math24.net/barometric-formula.
[CR1] The Col Collective (2021, June 24). THE BASICS OF CLOTHING TECHNOLGY FOR CHANGING CONDITIONS. Retrieved from thecolcollective.com.
[CR2] Wikipedia (2021, June 24). Clothing insulation. Retrieved from en.wikipedia.org/wiki/Clothing_insulation.
[EM] Wikipedia (2021, June 25). Emissivity. Retrieved from wikipedia.org/wiki/Emissivity.
[MRT1] Designing Buildings Wiki (2021, June 28). Mean radiant temperature. Retrieved from designingbuildings.co.uk/wiki/Mean_radiant_temperature.
[MRT2] Healthy Heating (2021, June 28). Mean Radiant Temperature. Retrieved from healthyheating.com/Definitions/Mean%20Radiant.htm#.YMM1a_kzZPY.
[MRT3] Wikipedia (2021, June 28). Mean radiant temperature. Retrieved from en.wikipedia.org/wiki/Mean_radiant_temperature.
[RH1] GEOSCIENCES - LibreTexts (2021, June 28). Vapor Pressure at Saturation. Retrieved from geo.libretexts.org/Bookshelves/Meteorology.
[RH2] Wikipedia (2021, June 28). Dew point. Retrieved from en.wikipedia.org/wiki/Dew_point.
[RH3] Wikipedia (2021, June 28). Humidity. Retrieved from en.wikipedia.org/wiki/Humidity.
[AG] University Corporation for Atmospheric Research (2021, June 28). What’s In the Air?. Retrieved from scied.ucar.edu/learning-zone/air-quality/whats-in-the-air.
[RVRH] Energie+ (2021, July 5). Confort thermique: généralité. Retrieved from energieplus-lesite.be/theories/confort11/le-confort-thermique-d1/.
[RVAV] University of Maine Ocean Observing System (2021, July 2). Variable Description - Beaufort Wind Scale. Retrieved from gyre.umeoce.maine.edu/data/gomoos/buoy/php/variable_description.php?variable=wind_2_speed.
[RVAP] Wikipedia (2021, July 2). Atmospheric pressure. Retrieved from en.wikipedia.org/wiki/Atmospheric_pressure.
[RVEM] Optotherm (2021, July 2). Emissivity Values. Retrieved from optotherm.com/emiss-table.htm.
[RVAG] University Corporation for Atmospheric Research (2021, June 28). What’s In the Air?. Retrieved from scied.ucar.edu/learning-zone/air-quality/whats-in-the-air.