re: solar?, literacy, the zero, connection SOLAR.KnowledgePublications.com

re: solar?, literacy, the zero, connection
13 feb 1996
>hi nick and the sun lovers,

hiya tag,

>what is the % heat loss from a glass window?

% of what?

that depends on the temperature inside and outside the window. i usually
assume that a window with a single layer of glass has an r-value of 1 
in us units, and use "ohm's law for heatflow," 

u = (t1- t2)a/r,

where u is in btu/hour, the ts are the temperatures on each side of the
surface in degrees f, a is the area of the surface in ft^2, and r is the
us r-value from one side to the other through the surface.  

so if it's 72 f inside and 32 f outside, and the window has one square
foot of glass, 

u = (72 f - 32 f) 1 ft^2/r1 = 40 btu/hour.

if the sun is shining, about 300 btu/ft^2/hour fall on the glass, as a
maximum, or about 1,000 btu/ft^2/day on a south wall in winter where i live,
and i usually assume that all of that solar heat gets through the glass.
if 300 goes in, and 40 goes out, the percent heat lost from the window is
about 13%, and the solar collection efficiency is about 87%. pretty good.

if the temperature inside the window were 132 f, about 100 btu/hour would be
lost, and the solar collection efficiency would be 66%. still pretty good.

what would the temperature inside the glass be if the solar collection
efficiency were 0%, with this simple model? power in = power out...
(reality is more complicated.) 

you can do all this with watts and meters and degrees c too, btw.

>what is indices of reflection mean?

that's index of refraction, or the refractive index of a material.
that has to do with how fast light travels through a material. if
light travels slowly through the material, people say the material
has a high index of refraction, like glass.

if light travels fast, as in air, the material has a low index. the lowest
index is 1, in a vacuum, where light travels fast, about one foot per
nanosecond, one way, or 10 microseconds per mile, round trip. air is very
close to 1. glass and copper are close to 1.5, ie light and electricity
travel about 2/3 as fast in glass and copper as in air. (which slows down
computers and makes lenses bend light.)
 
whenever electromagnetic waves (eg light) travel from a substance with
one index to a substance with a different one, some of the light is
reflected back at the interface. this is called a fresnel loss or a
reflection resulting from an impedance mismatch. 

the amount of reflction depends on the angle of the light striking the
surface. grazing angles make good reflections. if light hits perpendicularly
on the surface of a material with index n, and the other surface is air,
the fraction of light reflected at each surface is ((n-1)/(n+1)), squared,
ie about 4% at each interface. some plastics have lower indices, so there
is less reflection, and glass can be treated with index matching coatings or
etchings to reduce this reflection to almost zero, but that can be expensive.
if a substance is very thin compared to a wavelength of light or heat, like
a very thin soap bubble wall, it apparently doesn't reflect much light at all. 

light that travels from a substance with index n1, and enters another with
index n2, at an angle a1 from the perpendicular, enters the n2 medium with
an angle from the perpendicular a2 such that

n1/n2 = sin a2/sin a1.

this is known as "snell's law." (some birds know this intuitively, as they 
dive for fish that look to be elsewhere.)

here is the last and most complicated part of the picture, how to predict
how much energy will be reflected from a surface if the sun is not shining
directly at it. for instance we might want to guess how much low-angle winter
sun will be reflected from a shallow pond in the winter, onto a solar house.

if light strikes a surface at angle a1 from the vertical, the fraction of
energy reflected is 

r = (rper + rpar)/2, where

rper = (sin(a2-a1)/sin(a2+a1))^2, and rpar = (tan(a2-a1)/tan(a2+a1))^2.

>p.s it may be asking to much to ask those who send technical articles
> to explain few words at end, i think it help the operative mind.

maybe that's a good idea. but then we wouldn't be techno-priests, would we?
 
>2p.s m, there are 70 million who do not know how to write in the u.s

really? that's a lot...

>  should connection heppen in the beginning or in the end.

is this something to do with chickens and eggs? :-)

nick