$12 for 9 sheets and some double sided tape – is it worth it?

A window insulation kit of crystal clear shrink film for ~$12 with 9 sheets and some double sided tape –
is it worth it?  How does it compare to the rule of thumb for a 3% savings on your heating bill for every degree
that you set back your thermostat?  The short answer, it depends.

If you live in an old farmhouse with single pane windows that leak like a screen door it should be obvious that
just about anything will save you $.  But….if you live in a house built a bit more recently the answer isn’t quite
as crystal clear. In my case, it looks like I'll get half the advertised savings ($90 in energy savings).

So let’s look at how much it could save me – I have nine 30” x 62” double pane windows installed 25 years ago
and assuming that any difference in thermal losses are dominated by convection at these temperatures, I’ll
compare how installing an insulation kit changes the overall heat transfer.  For a second data point, I’ll also
measure the losses for single pane windows in my basement.

Measuring temperatures outside my house, on the interior window surface and room temperature over the
winter months gives the data set below

Using this, we can look at the expected convection heat transfer coefficient for a window based on the inside
surface temperature.  

Window Height:		24	inches
Window Width:		62	inches
Outdoor Temperature:		6.6	° C
Indoor Room Temperature		19.6	° C
Indoor Glass Temperature (without plastic):		14.8	° C
Average air temperature in the boundary layer:	T_fluid-avg =	17.2	° C
kinematic viscosity of air:	ν =	1.489E-05	(m2/s)
Prandlt number:	Pr = ν/α =	0.827
Thermal conductivity:	k, avg =	0.025	(W/m-K)
Thermal diffusivity:	α = k/ρc_p =	1.80E-05
Rayleigh number:	Ra = Gr x Pr = [β[ΔT]gL³/ν^2]Pr =	1.37E+08
Volumetric expansion of a fluid:	β = -([ρ/ρ_0]-1)/ΔT =	0.00345	1/K
Heat capacity of air:	c_p =	1005	(J/kg.K)
Average fluid density:	ρ =	1.408	kg/m3
Indoor fluid density:	ρ_0 =	1.397	kg/m3
Temperature difference between boundary layer and bulk fluid:	ΔT =	4.8	K
Nusselt Number:	Nu_avg = (0.825 + ((0.387*(Ra^(1/6)))/((1+((0.492/Pr)^(9/16))^(8/27)))^2 =	68.5
Convection heat transfer coefficient:	h_inner = (k/L)Nu =	2.86	W/m²K
Heat Loss
	Q = h_inner *A*dT =	13.2	W

This value aligns with typical convection heat transfer coefficients for glass which are in the range of 1 - 2 W/m2K.  With this value, we can use this to calculate the approximate ‘R’ value for the windows at each measurement point in our dataset

R value:

=(T_indoors-T_outdoors)/Q =

0.98

K. m²/W

Looking at the average performance the added shrink film increases the double pane window R-value from 1.2 to 3.3 and increases the single pane window from 0.63 to 2.3.  

You can see the difference in exterior temperature by looking at a thermal image.  The window on the left has
plastic is installed on the top section and nothing is installed on the right-hand window.

Now that we’ve gotten this, we can compare the heat losses for each window and look at the savings.  To
estimate this, I’ll use convert the price I pay per therm of natural gas to joules (yes we are neglecting the fan
wattage, but….).

Then we just take the difference to get the savings; the heat loss with plastic on the single pane window is

11.5 watts less, saving $0.0007 in the first hour.    

Doesn’t look like a whole lot per hour…but thanks to my tax dollars hard at work; we can use this method to
compare the savings over the heating season of November through April (I used historical 2016 data from
Pittsburgh published by Uncle Sam).  For the indoor temperature, we can use the thermostat program settings
(lower temps at night and during the workday). After the first week, the savings for covering a single pane window are $0.36.

Over the course of the winter for a single covered single pane window, I would save an estimated $20 per
window, or $180 for the package, netting me a $170.  Covering the double pane window I do have, the savings
drops to $9 per window, but still enough for a round of beers during happy hour. Worth the hour and a half it
took me to clean, cut, tape, stretch, and shrink.

If we look at a home in the burgh using electric heat, where a $0.12 kwH converts to $0.000000033 per joule
we would save about twice as much.

We also see greater savings increasing the indoor temperature, using a schedule between 70 °F and 75 °F our
savings increase to over $10 per double pane window.  

Let’s circle back to the first question – what if I have leaky windows?  Values vary, but if we assume an efficient
window with about 0.1 cfm per foot of window sash, our window with ~15 feet of sash will leak ~1.5 cfm when
we have a differential pressure.  And if we assume the furnace runs around 15 minutes an hour (generating a
differential pressure with the outdoors) we see a leakage of 23 cubic feet or 0.65 cubic meters per hour. If the
window leak rate is higher (some studies show 1 cfm per foot of sash) this cost is higher than the convection
losses.  The most convincing estimate I found was in "Studies of Exterior Wall Air Tightness and Air Infiltration
of Tall Buildings, ASHRAE Transactions, Vol. 82(I), 1976 which pegs the mean value for residential windows at
~0.5cfm/ft of sash. We can add the cost to heat that air for either data set using the same 2016 weather data set.

As you might expect, for a leaky window the savings are significant, but they are not a large with a well
installed leak tight window.

Back checking this against the total heating bill for my house shows how significant the overall savings is.  
Approximating my house as a 33’x52’x40’ box and assuming the bulk of heat transfer is to the air (there is a
finished and well-insulated basement, but I’ll neglect that) we can use the same formula as before -
Q = hAΔT = 5.7×Area*ΔT/R.  

Home Surface Area	1031.4	m² (without windows)
Home R_average	22.2	m²°C/W
Double Pane Window Area	40	m²
R for Double Pane Windows	1.237	m²°C/W
Single Pane Window Area	3	m²
R for Single Pane Windows	0.628	m²°C/W
Home R_average with Windows	12.9	m²°C/W
Estimated total heating cost	$753.41
	$125.57	Per month

Applying the same Pittsburgh temperature data set and the windows without plastic R values, the per
month heating bill is ~$125 a month which is a little high, but on par with my billing.

Home Surface Area	1031.4	m² (without windows)
Home R_average	22.2	m²°C/W
Double Pane Window Area	40	m²
R for Double Pane Windows	3.275	m²°C/W
Single Pane Window Area	3	m²
R for Single Pane Windows	2.261	m²°C/W
Home R_average with Windows	17.9	m²°C/W
Estimated total heating cost	$540.75
	$90.13	Per month

The $35 a month savings for covering 21 windows is 30% savings on my heating costs and goes a lot farther
than a 3% savings on your heating bill for knocking the temperature down a degree.  

In the end, if you have electric heat and leaky single pane windows this $12 kit is a bargain - giving the false
sense of a window replacement at a fraction of the cost and saving several hundred dollars per season
(assuming you don’t just want to use curtains).  Even for a home with older double pane windows like mine,
using the 9-pack kit saves around $90 (about half the advertised max) and is worth the evening of hassle it
takes to install.