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Shutter Condensation Calculator Explained
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 (subzero 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/m^{2} 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/m^{2}K is the Uvalue of the window. It then determines the Uvalue U_{s} W/m^{2}K 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 Uvalue 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 Uvalues are:
5.0  Singleglazing 
3.0  Doubleglazing 
2.2  Tripleglazing 
1.7  Doubleglazing with lowe coating 
1.3  Doubleglazing with lowe coating and Argon filled 
0.8  Passivhaus requirement 
0.4  Tripleglazing with multiple lowe coatings and Xenon filled 
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% 
RH
P_{vs}(T_{dp})=RH P_{vs}(T) 
Equation (1) 
P_{vs}
Deg.C = Deg.K  273.15
and
Deg.F = 9/5 Deg.C + 32
.
P_{vs}(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.
f(x)=y
for x
, Newton's Method computes the iterates x_{n}
x_{n+1} = x_{n} + (yf(x_{n}))/f'(x_{n}) ,

Equation (2) 
x_{0}
. If the problem is not illconditioned, 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