Even an uninsulated drape can trap up to one third of the heat lost through an ordinary window pane. An insulated drape can trap 50%.
Problem Restatement:
An uninsulated drape can reduce heat loss from a window by one third.
An insulated drape can reduce heat loss by one half.
Governing Equations and Required Input:
Where U is the thermal conductance which is the inverse of the more widely known thermal resistance or R-value. The R-value is calculated as R = l/k where l is the thickness of the material and k is the thermal conductivity.
The thermal resistances for the window with and
without drapes are:
For single glazed windows, adding drapes reduces heat loss by 37%. Adding the same drapes to double glazed windows reduces heat loss by 30%. Adding insulated drapes to a single glazed window reduces heat loss by 56% (48% for double glazed windows).
So, for single and double glazed windows, both claims are approximately true. The reduction in heat loss is smaller for double glazed windows than it is for single glazed windows.
However, This Answer Made Some Important Assumptions:
The air in the gap between the drapes is perfectly still.
This is a bad approximation. Cool air trapped between the drape
and the wall would fall to the floor. Warm air would enter the
space from above the window, cool down, and fall. This process
would create a convective loop that would serve to mix the air
in the room better and also cause more heat to be lost to the
outside. This mixing can actually cause greater heat loss than
if there were no drapes.
The exact details of how much heat loss drapes
cause or save depends on:
a) The thickness and types of the drapes.
b) The thickness of the gap between the drapes and the wall.
c) The inside-outside temperature difference.
The use of insulated drapes can cause severe problems in very
cold climates. The air trapped between the window and the drape
can drop below the dew point of the air which leads to condensation
on the window. This can lead to rotting of wood window frames
or mold growth. If the temperature drops below freezing, the condensed
water that permeates a window frame can expand and seriously damage
the windows. This happened in numerous houses with insulated drapes
and has lead to lawsuits between insulated drape manufacturers
and homeowners. These extreme conditions happen most frequently
in very cold climates.
Drapes can reduce heat loss. In extreme conditions,
they can also increase heat loss or cause other problems.
Deeper Issues:
Double glazed windows are required by building
or energy codes in many places in North America and the rest of
the world. When we repeated the analysis with a double glazed window,
the effect of the curtain is much lower. The strength of the convective
loop will also be smaller. Overall windows are very important to
the heat loss of a building [For more information see
http://www.efficientwindows.org].
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