Table of Content

• How does it work
• U-Values
• Glossary
• Acknowledgments

For the given room temperature T_in and relative humidity RH, the calculator solves the defining Equation (1) for the Dewpoint temperature T_dp.

The solution is found numerically using Newton's Method and by initially guessing the room temperature as the dewpoint. The algorithm must be able to evaluate the saturation vapor pressure of water at arbitrary temperatures, and therefore relies on interpolation formulas for this quantity.

At freezing conditions (sub-zero Deg. C temperatures), the Dewpoint Calculator uses the saturation vapor pressure over ice, thus computing the frostpoint.

After finding the dewpoint temperature, the calculator determines the heat flux q W/m² through the window when its inner surface is at that temperature by using the relationship

q = (T_dp - T_out) ^x U_w

where T_out is the outside temperature and U_w W/m²K is the U-value of the window. It then determines the U-value U_s W/m²K of a shutter that is consistent with that heat flux by using the similar relationship

U_s = q / (T_in - T_dp)

To design a shutter, use the actual U-value of your window, the warmest temperature that you normally keep the room, the coldest outdoor temperature and the most humid that the room is likely to be.

According to Greenspec, with the addition of Passivhaus, typical available U-values are:

5.0	Single-glazing
3.0	Double-glazing
2.2	Triple-glazing
1.7	Double-glazing with low-e coating
1.3	Double-glazing with low-e coating and Argon filled
0.8	Passivhaus requirement
0.4	Triple-glazing with multiple low-e coatings and Xenon filled

Dewpoint T_dp

If a body is exposed to moist air and then cooled down, water will condense on its surface when the temperature drops below the dewpoint temperature. At freezing conditions, both dewpoint (now the dew is super-cooled water) and frostpoint can coexist.

Note: For a fixed relative humidity, neither dewpoint nor frostpoint depend on the atmospheric pressure. However, if a moist air sample is pressurized at a constant temperature and at a constant absolute humidity, both the relative humidity and the dewpoint will rize.

Dewpoint Versus Temperature Curve for RH=5%

Frostpoint T_fp

Corresponding to the dewpoint for freezing conditions, the frostpoint is the temperature at which ice will form on the cool body. The frostpoint for liquid water is slightly higher than the dewpoint. Because the formation of ice depends on a certain amount of impurity on the surface of the body, however, you may still experience dew at subzero temperatures.

Boiling point

The temperature at which the vapor pressure equals atmospheric pressure (about 101kPa at sea-level). Below the boiling point, the atmospheric pressure (which equals the pressure inside the water) will prevent evaporation inside the water body. At the boiling point, the water body becomes physically unstable in that vapor bubbles will start to form.

Relative Humidity RH

Degree of saturation of water in air. At a RH of 100%, the air is saturated and attains its most moist state. At a RH of 0%, no water is present. Relative humidity is defined by Equation (1) as a function of ambient temperature T and dewpoint T_dp only, and therefore does not depend on air pressure or altitude:

Pvs(Tdp)=RH Pvs(T).

Equation (1)

In practice, RH is often measured directly and propagated through weather reports.

Saturation Vapor Pressure Pvs

The intensity at which water vapor will evaporate from water (Pressure over liquid water) or from ice (Pressure over ice). The saturation vapor pressure is a function of temperature only. It can be measured directly, is recorded in Steam Tables, and can be evaluated with the help of interpolation formulas.

Chilled Sensor Hygrometer

Technique to directly measure the dewpoint by chilling on object (e.g. a mirror) to the point of condensation. Sensors of this type are quite accurate, but are expensive to operate and have a low response rate.

Capacitive RH Hygrometer

Type of sensor most commonly used to measure atmospheric humidity. These type of sensors have a typical accuracy of about 2% to 5% at RH between 10% and 90%. For very low or very high humidity, accuracy can be lower.

Temperature Scale

The Dewpoint Calculator uses the traditional temperature scales Deg.C = Deg.K - 273.15 and Deg.F = 9/5 Deg.C + 32.

Interpolation Formulas

There are a great deal of interpolation formulas for the saturation vapor pressure Pvs(T). These formulas are of varying accuracy and have different ranges of validity. The Dewpoint Calculator uses the formula put forward in 1997 by IAPWS, the International Association for the Properties of Water and Steam. It is very accurate for 273.15 K < T < 647.096 K, with the relative accuracy never exceeding 0.06%. For details, please consult the source code.

Newton's Method

To solve an equation of the form f(x)=y for x, Newton's Method computes the iterates xn

xn+1 = xn + (y-f(xn))/f'(xn),

Equation (2)

starting at a suitable initial guess x0. If the problem is not ill-conditioned, iterates will converge quickly to the solution x.

This calculator is based on the Dewpoint Calculator by Wolfgang Kühn, which does all the hard work.

It was amended for shutter calculations by Dave Howorth - scc at howorth dot org dot uk

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