Net energy transfer measurement methods, apparatus and systems with solar energy and control applications

Heat flux sensors respectively painted black and white and mounted to a passive solar energy window intercept solar radiation and change the temperature of part of the window. The sensors, and differentially connected thermocouples attached to them, couple data to an electronic computer by which the solar radiation, reradiation, and conduction/convection thermal loss through the undisturbed balance of the window can be deduced. The computer outputs the net energy transfer NET to a recorder, a two-state indicator, and a window insulation control unit. The circuitry of the control unit responds to an ordinary thermostat and the NET from the computer to produce a condition signal, senses the position of the insulation, and repositions the insulation when necessary in response to the condition signal. The insulation is moved to block the window when the direction of NET is into the building and the inside temperature is higher than the thermostat limit temperature, and when the direction of NET is outward and the inside temperature is lower than the thermostat limit temperature.

BACKGROUND OF THE INVENTION 
The present invention relates to the field of energy transfer measurement 
methods, apparatus, and systems. More specifically, the present invention 
relates to methods, apparatus and systems for measuring, and in some 
embodiments controlling, net energy transfer by radiation, convection and 
conduction through a fenestration, such as a window or translucent panel. 
The invention has applications in a variety of industrial and consumer 
fields, and it is emphasized that the background of the invention is 
discussed herein by way of comparison with merely one specific field of 
application, that of passive solar energy. 
In the prior art, various systems have been proposed for operating solar 
heated buildings. For instance, it is known to use movable insulation to 
reduce heat loss through glazed openings such as windows, skylights, 
clerestories, and Trombe walls in a well-insulated building. Such movable 
insulation can be of hand operated variety, thermally sensitive type, or 
motor-driven type. Motor-driven applications are either manually activated 
or controlled by automatic timers, thermostats or light sensitive 
devices--examples are foam beads blown between double glazing, and 
motor-driven sliding insulation, blinds, or panels. Such systems feature 
relatively crude control of the insulation relative to the energy 
considerations which must be accounted for, thus wasting solar energy and 
consequently building heat. 
In the passive solar heating of buildings, the solar energy should be 
turned on only when it is needed, so as to avoid overheating; and the 
solar energy should be turned off only when it is not needed, so as to 
avoid overcooling. Unfortunately, determining the threshold decision 
points is not a simple problem in the solar energy field. If the solar 
energy is to be controlled by movable insulation, it must be recognized 
that the highly time-variable solar radiation entering the building is 
accompanied by complex heat convection and conduction processes between 
building and environment, as well as reradiation. Unlike a furnace or 
electric heater which when energized always provides net heat energy flow 
from itself into the interior of the building, the control of the sun by 
means of movable insulation introduces variable radiation, convection, and 
conduction processes which often work at cross-purposes to each other. It 
is as if there is a "furnace" which can cool a building when it should be 
heating, and which can heat the building when it should be cooling, unless 
some means of accurate control can be found. 
Accordingly, the accurate control of the timing of the use of solar energy 
in passively heated buildings is a significant problem, which a mere 
timer, wall thermostat, or light-sensitive cell is insufficient to solve. 
The reason is that accurate control depends on continuing knowledge of a 
quantity denominated herein as "net energy transfer (NET)". Net energy 
transfer is the actual solar energy available to pass into the building 
through a fenestration when the movable insulation is retracted or 
unblocked, net of losses by reradiation, convection, and conduction. Since 
an important advantage of passive solar energy is low cost, it is 
essential that the additional cost of such accurate measurement and 
control be kept small. Accordingly, the economical and convenient 
measurement of net energy transfer NET is an objective of the present 
invention. 
Although it has just been stated that the ordinary wall thermostat is 
insufficient to provide the necessary accurate control of the solar 
energy, the consumer of energy usually finds it convenient and 
advantageously familiar to be able to control the building temperature by 
means of such a thermostat. Accordingly, it is a further objective of the 
present invention not only to accurately measure the net energy transfer 
NET through solar energy windows but also to control the solar energy with 
comparable convenience to the thermostatic manner in which natural gas, 
heating oil, and electric heating sources of energy in buildings are 
controlled in the prior art. 
An additional problem in the solar energy field is accomplishing optimal 
control of more than one solar energy window in a passive solar building. 
In such a situation, it is not readily apparent whether all such windows 
should be blocked or unblocked at the same time, and if so when; or 
whether some windows should be blocked and others unblocked, and if so, 
which ones and when. Accordingly, it is a still further objective of the 
invention to provide accurate control for each additional solar energy 
window at relatively insignificant additional expense. 
Other objectives and advantages of the present invention will be evident 
from the description of the invention hereinbelow. 
SUMMARY OF THE INVENTION 
In the present invention it has been discovered that intercepting the solar 
energy itself and using the intercepted solar energy to change the 
temperature of part of the fenestration makes it possible to deduce not 
only the amount of incoming solar radiation, and the reradiation, but also 
the amount of heat flux being transferred by thermal processes through the 
rest of the fenestration which is undisturbed. These amounts are precisely 
those needed to determine net energy transfer NET. Measurement devices, 
known as transducers, mounted in thermal contact with the fenestration not 
only gather thermal data but also are themselves used as the means of 
intercepting the solar energy and changing the temperature of the part of 
the fenestration with which they come into thermal contact. An automatic 
computing device such as an inexpensive microprocessor receives data from 
the transducers, reduces it to NET and outputs the NET to a display 
device, recording equipment, or real-time window insulation control 
apparatus. 
The practice of the invention is compatible with use of thermopile heat 
flux sensors, and inexpensive thermocouples differentially connected for 
generating electrical analogs of temperature differences. In this way, the 
use of expensive pyranometer equipment for measuring radiation is avoided, 
and the cost of temperature reference units and electronic thermometers is 
eliminated where these are not desired. 
The inventive instrumentation is suitably used for energy audits of windows 
in residential and commercial structures, and for continuous, accurate 
measurements of window structure thermal properties in research 
applications. In an additional advantageous feature, the instrumentation 
need not be modified to permit measurements of energy transfer through 
opaque walls. 
In window insulation control applications, at least one window is provided 
with equipment for moving insulation so as to controllably block and 
unblock the window. A convenient thermostat device is provided which 
permits the user to designate a nominal or limit temperature (or upper and 
lower limits of a desired temperature zone) near which the inside 
temperature of the building is to be maintained, and the thermostat 
determines or registers whether the inside temperature is higher or lower 
than the nominal temperature. 
The invention provides computation and control apparatus which receives 
information from the transducers and thethermostat and computes the net 
energy flow or transfer NET and provides window insulation control so that 
blocking occurs when the direction of net energy flow is inward and the 
inside temperature is higher than the limit temperature and when the 
direction of net energy flow NET is outward and the inside temperature is 
lower than the limit temperature. In this way the convenience of 
thermostatic control is incorporated in passive solar energy window 
insulation control by putting NET information into the system. 
The computation and control functions in window insulation control 
applications are suitably provided in a computer or microprocessor to 
which the transducers and thermostat are coupled, or provided by a NET 
computer and a separate controller unit to which the thermostat, NET 
computer, and motorized window blocking equipment are connected. The 
invention is comprehensive of such alternatives. 
In those cases in which a separate controller unit is used, a further 
feature of the invention involves arranging the controller to include 
three sets of apparatus: (A) circuit for producing a condition signal in 
response to the thermostat and the NET from the computer, (B) circuit for 
sensing position of the insulation and driving the blocking equipment in 
response to the condition signal, and (C) circuit for sensing position of 
the insulation and driving the blocking equipment to unblock the window in 
response to the logical complement of the condition signal. 
Optimal control of more than one solar energy window in a passive solar 
energy building is readily accomplished by the invention with relatively 
insignificant additional expense. When the additional windows are oriented 
and illuminated with sunlight in the same manner as the first window 
having instrumentation, no additional transducers are needed as the NET 
cutover points are the same for the additional windows. Movable insulation 
equipment is provided for the additional windows and controlled in tandem 
with that for the first window by the same computation and control 
apparatus. 
When the additional windows are illuminated differently, window transducers 
are merely added for each differently illuminated window and coupled to 
the same computer. The computer calculates NET for each such window 
individually, and the movable insulation equipment for the additional 
windows is controlled individually according to the respective NET 
measurements. 
The present invention is applicable in a variety of environments in which 
energy is being transferred by radiative and thermal processes between 
adjacent regions and there is a need for accurate measurement, or 
measurement and control, of the energy transfer. For example, applications 
in which the fenestration divides water from air, divides water from 
water, divides organic liquid from gaseous medium, and gas from gas are 
contemplated. Such applications include underwater and undersea equipment, 
and assemblies for a variety of land-based industrial large-scale 
processes. Moreover, the invention is applicable in respect of any 
electromagnetic or particle radiation which can be intercepted and used to 
thermally disturb the fenestration for its measurement purposes.

DETAILED DESCRIPTION OF THE DRAWING 
In FIG. 1 the sun provides incident shortwave solar radiation energy 
S.sub.1 to double glazing 10. Double glazing 10 includes glass panes 12 
and 14 separated by airspace 13 by means of frame 11. Shortwave 
reradiation S.sub.2 from the opposite direction is a radiative energy loss 
component. Thermal loss Q occurs by longwave radiation and convection 
processes 4A, 4B and 4C and conduction 6A and 6B. The loss Q becomes 
negative, or becomes not a loss but a gain, when the convection, longwave 
radiation, and conduction cause heat to flow in the same direction as the 
incident solar radiation S.sub.1. The net energy transfer NET is regarded 
as the incident solar radiation S.sub.1 less the reradiation S.sub.2 less 
the thermal loss Q. The ambient temperature T.sub.2 outside double glazing 
10, in region 16, is suggested by thermometer 17 of ordinary mercury type, 
and the ambient temperature T.sub.1 inside glazing 10, in region 18, is 
suggested by similar thermometer 19. 
Inventive NET measurement system 1 includes radiation absorbing 
black-painted heat flux sensor 22 and white-painted heat flux sensor 24, 
thermocouples 26,28,30, and 32 and computer 34 having analog-to-digital 
converting (A/D) inputs and keyboard 35. Computer 34 outputs NET to chart 
recorder 36, window insulation control device 38, and two-state indicator 
having amplifier 40 and oppositely-connected light-emitting diodes (LEDs) 
41 and 42. 
The outside surface of pane 12 and the inside surface 15 of pane 14 
separate regions 16 and 18 respectively. Black heat flux sensor 22 is 
mounted in thermal contact with inside surface 15 of pane 14, as is white 
heat flux sensor 24. Sensors 22 and 24 cover the part of inside surface 15 
of pane 14 corresponding to sensor forward surfaces 21 and 25, leaving the 
balance 20 of inside surface 15 of pane 14 uncovered. Both forward surface 
21 and back surface 23 of sensor 22 are painted black to intercept 
radiation S.sub.1 and reradiation S.sub.2 with equal absorptivity a.sub.b 
respectively. Similar provision is made for painting the front surface 25 
and back surface 27 of sensor 24 with white flat paint for equal 
absorptivity a.sub.w to the radiation S.sub.1 and reradiation S.sub.2. 
Thermocouple temperature measuring elements are respectively provided in 
thermal contact with each heat flux sensor by physically placing 
thermocouple elements 26 and 28 between heat flux sensors 22 and 24 and 
inside surface 15. In this way thermocouples 26 and 28 are in both 
physical contact and thermal contact with their respective heat flux 
sensors 22 and 24 and pane 14. 
Inside ambient temperature thermocouple 30 is exposed to temperature 
T.sub.1 in region 18, and outside temperature thermocouple 32 is exposed 
to temperature T.sub.2 in region 16. Each ambient temperature thermocouple 
30 and 32 is provided with radiation shield 31 and 33 respectively for 
more accurate measurement. 
Heat flux sensors 22 and 24 are relatively inexpensive commercially 
available thermopile elements having copper lead pairs respectively 
providing electrical analog voltages corresponding to heat fluxes Q.sub.b 
and Q.sub.w passing through the sensors normal to their broadside surfaces 
23 and 27. Heat fluxes Q.sub.b and Q.sub.w are thermal quantities which 
are affected by interception of radiated solar energy S.sub.1 and 
reradiation S.sub.2 by the heat flux sensors 22 and 24. As such, heat 
fluxes Q.sub.b and Q.sub.w depart substantially from the undisturbed 
window thermal loss heat flux Q in the presence of substantial radiation 
S.sub.1 and S.sub.2. Moreover, the different absorptivities a.sub.b and 
a.sub.w of the black and white painted sensors 22 and 24 intercept 
radiation so as to cause measurably different heat fluxes Q.sub.b and 
Q.sub.w to be sensed by the sensors 22 and 24 and to cause measurably 
different temperatures T.sub.b and T.sub.w to be presented to 
thermocouples 26 and 28 respectively. Heat flux sensors 22 and 24 are 
suitably spaced apart so that their warming effect on pane 14 in the 
presence of radiation does not significantly affect the measurements of 
each sensor in the presence of the other sensor, i.e. sensors 22 and 24 
are suitably in thermal isolation from each other. 
All four thermocouples 26,28,30, and 32 are suitably copper-constantan 
junctions of inexpensive commercially available type. The constantan lead 
from each thermocouple 26,28,30, and 32 is brought into common connection 
29. The copper lead from each thermocouple 26,28,30, and 32 is brought to 
the A/D converter inputs on computer 34 for analog-to-digitally converting 
the temperature-difference data presented thereby. It will be noted that 
the four copper leads from the thermocouples 26,28, 30, and 32 can be 
organized into six possible pairs (the number of combinations of 4 taken 2 
at a time=4.multidot.3.multidot.2.multidot.1/(2.multidot.1) 
(2.multidot.1)=6) representing the temperature differences (T.sub.2 
-T.sub.1),(T.sub.w -T.sub.1), (T.sub.b -T.sub.1), (T.sub.w -T.sub.b), 
(T.sub.b -T.sub.2), (T.sub.2 -T.sub.w). Further, if any three of the six 
differences, being such that all four subscripts 2,1,b, and w appear in 
the algebraic representation of such three, be selected, then the rest of 
the differences can be derived in the computer 34 by appropriate additions 
or subtractions. Accordingly, the four copper leads from the thermocouples 
26,28,30, and 32 are brought advantageously to only three A/D converter 
inputs on computer 34, and the three differences (T.sub.2 -T.sub.1), 
(T.sub.w -T.sub.1), (T.sub.b -T.sub.1) are somewhat arbitrarily selected 
and shown in FIG. 1. These differences are provided by connecting the 
copper lead from thermocouple 30 to all three A/D converter inputs, and 
the copper leads respectively from thermocouples 26,28, and 32 to each of 
the A/D inputs as shown. 
In an advantageous feature of the invention, it has been discovered that 
the computer 34 can be programmed with an algorithm for calculating net 
energy transfer NET, as well as the radiation S.sub.1 and reradiation 
S.sub.2 and the amount Q of convection, longwave radiation and conduction 
through part 20 of window surface 15, which utilizes only Q.sub.b, 
Q.sub.w, and differences in measured temperature. Because as to 
temperature, only difference data is needed, no temperature reference 
units are needed for the thermocouples at a considerable saving in 
expense, and connection of the thermocouples at common 29 suffices. 
Connection of the devices at a common is termed "differentially connected" 
herein in order to identify such manner of connection that analog 
differences are generated for presentation and coupling to the computing 
apparatus. 
The measurement system of FIG. 1 is readily capable of calculating NET 
repeatedly for indefinite periods of time and recording the physical 
representation of NET generated by computer 34 on recorder 36. When NET is 
an analog voltage generated by the computer 34, amplifier 40 causes LED 42 
to light when NET exceeds zero level and causes only LED 41 to light when 
NET is less than zero (net heat loss through glazing 10). Amplifier 40 
can, of course, be biased to change the LED indication at any 
predetermined level of NET. Such bias is advantageously applied, for 
instance, when a signal for opening insulation manually is desired 
whenever NET is positive or when NET is negative but loss is not in excess 
of a predetermined magnitude. When NET is a digital signal, amplifier 40 
is connected so as to respond to the sign bit of the NET signal. 
When it is not inconvenient to enter quantities through keyboard 35, the 
thermocouple 32 is readily dispensed with, and the quantities T.sub.1 and 
T.sub.2 are simply read from thermometers 17 and 19 and entered into the 
computer 34 memory via keyboard 35. The temperature difference between the 
first and second regions 16 and 18 whether obtained from thermocouples, 
reading of thermometers 17 and 19, or from electrical thermometers of 
other types, is stored in the computer and updated continuously (as in 
FIG. 1) or occasionally as the skilled worker may elect. 
FIG. 2 illustrates multiple-window instrumentation according to the 
invention, by means of window measurement and control system 100. 
Thermocouples 104 and 106 are exposed to and in thermal equilibrium with 
the inside and outside regions having ambient temperatures T.sub.1 and 
T.sub.2 respectively. Single-glazed window 101 is instrumented with a 
white and black pair of heat flux sensor-thermocouple combinations 114,112 
and 124,122. The constantan leads of thermocouples 104,112,122, and 106 
are connected to common 105. Heat flux sensors 114 and 124 are coupled to 
the computer via analog-to-digital converters 116 and 126 which receive 
copper lead wires from the heat flux sensors 114 and 124. In a feature of 
the invention which keeps the amount of lead wire from the instrumentation 
low, the copper lead wire from thermocouple 112 is connected directly to 
one of the copper wires of white heat flux sensor 114 and the copper lead 
from thermocouple 122 is connected directly to one of the copper wires of 
black heat flux sensor 124. In this way the temperature differencing 
thermocouples 104,112,122 are coupled to A/D converters 110 and 120 in 
part by some of the lead wires from the heat flux sensors 114 and 124. The 
number of cable conductors from windows to computer can thus be kept 
essentially equal to the number of transducers in the system, instead of 
twice their number as might be presumed. 
For window 101, A/D converter 110 receives (T.sub.w -T.sub.1), converter 
116 receives Q.sub.w, converter 120 receives (T.sub.b -T.sub.1), converter 
126 receives Q.sub.b, and converter 130 receives (T.sub.2 -T.sub.1). 
Computer 158 is provided with keyboard-CRT terminal 151 and receives 
digital inputs from A/D converter input cards 
110,116,120,126,130,140,146,150,156,160 and 166. Computations according to 
an algorithm for NET, an example of which is described hereinbelow, are 
performed and the NET for window 101 is output on line NET-101 from the 
computer 158, to a window insulation control apparatus 170 for window 101. 
Window 102 is of double-glazed type like window 10 of FIG. 1. It is 
suitably instrumented by white heat flux sensor 144, thermocouple 142 and 
by black heat flux sensor 154 and thermocouple 152. In other words, a 
plurality of thermocouples and heat flux sensors coresponding to each 
window or fenestration is provided in addition to thermocouple 104. For 
window 102, A/D converter 140 receives Q.sub.w, converter 146 receives 
(T.sub.w -T.sub.1), converter 156 receives (T.sub.b -T.sub.1) and 
converter 150 receives Q.sub.b. Since (T.sub.2 -T.sub.1) is already 
available from thermocouples 106, 104 and A/D converter 130, it is 
unnecessary to duplicate these components for window 102. 
In an additional feature of the invention, part of window 102 is also 
changed in temperature when warmed by a heat flux sensor 164-thermocouple 
162 pair having absorptivity intermediate between black and white. Flat 
grey or flat colored paint is suitably used for sensor 164. Sensor 164 is 
exposed to a heat flux Q.sub.c and thermocouple 162 is exposed to a 
temperature T.sub.c. The data are conveyed to A/D converter 160 for 
Q.sub.c and converter 166 for (T.sub.c -T.sub.1). The pair 162,164 make 
possible an advantageous redundancy in that a malfunction in any one 
sensor 144,142,154, 152,164,162 can be readily detected and avoided by 
using the others. Also, all the pairs 144,142; 154,152; and 164,162 are 
suitably used for redundant calculations of NET and thereby averaging out 
measurement errors or manufacturing variations in the instrumentation 
characteristics. The NET for window 102 is calculated by computer 158 and 
output on line NET-102, for use by window 102 insulation control assembly 
180. 
Window control assembly 170 includes reversible motor 178 for moving 
window-blocking insulation (not shown) between a blocking position and an 
unblocked position relative to window 101. Sensing switch 176 detects when 
the insulation is fully blocking the window 101, and sensing switch 177 
detects when the insulation has been moved to the fully unblocked 
position. The assembly of motor 178 and sensing switches 176 and 177 is 
mounted with the window-blocking insulation on or near window 101 as 
assembly 101A. An insulation position switch 174 has three alternative 
positions for either automatic insulation operation, or overriding the 
automatic features of system 100 to block the window 101 at all times 
(manual close), or overriding the automatic features of system 100 to 
unblock the window 101 at all times (manual open). Controller apparatus 
172 receives information from position switch 174, sensing switches 176 
and 177, thermostat 190, and the NET for window 101. Then controller 
apparatus 172 operates motor 178 along cable 236 in the appropriate manner 
that will be more fully described. 
Window control assembly 180 is identical in construction to window control 
assembly 170 and includes sensing switches 186 and 187 corresponding to 
sensing switches 176 and 177 respectively, and reversible motor 188 
corresponding to motor 178. Sensing switches 186 and 187 and motor 188 are 
mounted on or near window 102 as assembly 102A for moving additional 
window-blocking insulation (not shown) relative to window 102. Controller 
apparatus 182 and its insulation position switch 184 are identical to 
controller apparatus 172 and its insulation position switch 174 
respectively. Controller apparatus 182 is fed by thermostat 190 in the 
same manner as controller apparatus 172, but controller apparatus 182 
receives the distinct NET representation for window 102 on line NET-102. 
Accordingly, controller 182 operates independently of controller 172 and 
controls window 102 separately in an optimal manner specific to window 
102. Because window insulation control assemblies 170 and 180 are 
identical in construction, no additional description of assembly 180 is 
undertaken. 
Thermostat 190 is next described with reference to FIG. 2 for exterior 
description and with reference to its diagram in the lower portion of FIG. 
3 for interior and electrical detail. 
Thermostat 190 includes thermometer pointer 195 indicating inside 
temperature T.sub.1 on scale 199. Pointer 195 is driven by bimetal spiral 
element 195B which in turn is fixedly mounted as a self-contained 
thermometer on thermostat cover plate 197. 
Temperature-limit-designating tab arms 191 and 193 are disposed over 
temperature scale 198 and respectively set the high temperature limit 
(T.sub.H) and the low temperature limit (T.sub.L), as of a comfort zone of 
temperature in a building. Winter-summer toggle switch 196 is set for the 
seasonal conditions. Thermostat 190 is connected to backup air 
conditioning (A/C) 250 and backup heater (HTR) equipment 260 in addition 
to the passive solar window control assemblies 170 and 180. 
In the interior of thermostat 190, shown diagrammatically in the lower 
portion of FIG. 3, bimetal spirals 191B and 193B are respectively affixed 
centrally to tab arms 191 and 193. Occasional adjustment of the angular 
positions of the bimetal spirals 191B and 193B is made around stiff pivots 
191P and 193P by finger adjustment of tab arms 191 and 193. Bimetal 
spirals 191B and 193B are coaxially mounted on axis 191A so that tab arms 
191 and 193 are adjustable with reference to the single temperature scale 
198 provided for them. (Bimetal spirals 191B and 193B are shown displaced 
from each other and in the plane of the paper on FIG. 3 to facilitate 
disclosure, but it is to be noted that the spirals 191B and 193B are 
coaxial and adjacent so that axis 191A is perpendicular to the paper in 
the actual thermostat assembly being represented.) Two illustrative 
positions T.sub.L and T.sub.H on scale 198 for tab arms 193 and 191 are 
shown in FIG. 3 corresponding to their positions in FIG. 2. 
Mercury switches 192 and 194 are respectively attached tangentially on the 
outer circumference of spiral 191B and 193B respectively. Mercury switch 
192 is mounted and arranged together with spiral 191B so that mercury 
switch 192 is electrically open when the ambient temperature T.sub.1 is 
less than high temperature limit T.sub.H and electrically closed when the 
ambient temperature T.sub.1 is above the high temperature limit T.sub.H. 
Decreasing the T.sub.H setting of tab arm 191 below the ambient 
temperature T.sub.1 moves mercury switch 192 counterclockwise around stiff 
pivot 191P from the position shown in FIG. 3 and permits mercury bead 192M 
therein to bridge electrodes 192E. This closes the switch 192, thereby 
connecting a supply voltage V to backup air conditioning 250 and to the 
winter pole of section 196A of winter-summer switch 196. Bimetal spiral 
191B is coiled in the proper sense so that at any setting T.sub.H of tab 
arm 191, a rise in the ambient temperature T.sub.1 above T.sub.H moves 
mercury switch 192 counterclockwise from the position shown in FIG. 3 
around stiff pivot 191P and also permits the mercury bead 192M therein to 
close switch 192. 
Mercury switch 194 is mounted and arranged together with bimetal spiral 
193B so that mercury switch 194 is electrically open when the ambient 
temperature T.sub.1 is greater than low temperature limit T.sub.L and 
electrically closed when the ambient temperature T.sub.1 is below the low 
temperature limit T.sub.L. Increasing the T.sub.L setting of tab arm 193 
above the ambient temperature T.sub.1 moves mercury switch 194 clockwise 
around stiff pivot 193P from the position shown in FIG. 3 and permits a 
mercury bead 194M therein to bridge electrodes 194E. This closes the 
switch 194 thereby connecting the supply voltage V to backup heater 260 
and to the summer pole of section 196A of winter-summer switch 196. Spiral 
193B is coiled in the proper sense so that at any setting T.sub.L of tab 
arm 193, a fall in ambient temperature T.sub.1 below T.sub.L moves mercury 
switch 194 clockwise from the position shown in FIG. 3 around stiff pivot 
193P and also permits the mercury bead 194M therein to close switch 194. 
In thermostat 190, double-pole-double-throw (DPDT) winter-summer switch 196 
has sections 196A and 196B. Section 196A selects a connection to mercury 
switch 192 or 194, previously described, for transmission of an 
out-of-zone digital voltage (T) to controller apparatus 172. Section 196B 
provides a digital voltage (W) indicating the switch 196 setting to 
controller 172. For instance, the winter setting of section 196B 
corresponds to voltage-on or Boolean 1. The summer setting of section 196B 
corresponds to voltage-off or Boolean 0 (not-winter). 
The thermostat 190 circuit in FIG. 3 is arranged to make thermostat 190 
control passive solar heating and passive window cooling processes, reduce 
temperature excursions from nominal or from the comfort zone, and maintain 
inside temperature T.sub.1 with a minimal reliance on the backup air 
conditioning 250 and heating 260. 
Winter-summer switch 196 selects the best system operating mode for the 
weather conditions. If set to winter, the system uses passive solar energy 
to heat to the high temperature limit T.sub.H if possible, since future 
cold conditions are anticipated. Since backup heater 260 is not used 
whenever the inside temperature exceeds the low temperature limit T.sub.L, 
it is apparent that passive solar energy is used to reduce or eliminate 
energy demand of backup heating 260. If winter-summer switch 196 is set to 
summer, the system uses passive window cooling to cool to the low 
temperature limit T.sub.L if possible, since future hot conditions are 
anticipated. Since backup air conditioning 250 is not used whenever the 
inside temperature is lower than the high temperature limit T.sub.H, 
passive window cooling is used to reduce or eliminate energy demand by the 
backup air conditioning 250 as well. 
The remainder of FIG. 3 provides details of the controller apparatus 172 in 
addition to switches 174,176,177 and motor 178 in window insulation 
control assembly 170, previously discussed in connection with FIG. 2. 
Controller apparatus 172 takes account of the thermostat 190 digital 
voltages for winter-summer (W) and out-of-zone (T) and also the net energy 
transfer NET for its window 101. DC voltage source 238 provides supply 
voltage V for the logic. It will be noted that the supply voltage lines 
from voltage source 238 are not shown, for clarity on the drawing, and 
that the symbol "V" is provided at thermostat 190 and switches 174,176 and 
177 to indicate that the supply voltage from source 238 is conducted to 
each. 
Digital voltage SC from sensing switch 176 is on only when the 
window-blocking insulation (not shown) for window 101 is in the blocked 
position. Voltage SO from sensing switch 177 is on only when the 
window-blocking insulation is in the fully unblocked position. In other 
words, sensing switch 176 is closed and thereby connects voltage V from 
source 238 as a voltage-on Boolean 1 condition of voltage SC for 
controller apparatus 172 only when the window insulation is in the blocked 
position. At all other times the voltage SC is zero corresponding to 
Boolean 0. On the other hand, sensing switch 177 is closed and thereby 
connects supply voltage V from source 238 as a voltage-on Boolean 1 
condition of voltage SO for controller apparatus 172 only when the window 
insulation is in the fully unblocked position. 
Insulation position switch 174 provides a voltage-on Boolean 1 condition 
for the digital input voltage MC only when switch 174 is set to the manual 
close position, thereby connecting supply voltage V from source 238 to the 
line designated MC on FIG. 3. Switch 174 provides a voltage-on Boolean 1 
condition for the digital input voltage MO to controller apparatus 172 
only when switch 174 is set to the manual open position, thereby 
connecting supply voltage V from source 238 to the line designated MO on 
FIG. 3. When switch 174 is set to the center position for automatic 
operation of the window insulation, no voltage is provided for MO and MC, 
so that these are both Boolean 0. NOR-gate 206 in the controller apparatus 
172 provides a Boolean 1 at its output when both MO and MC are zero, 
corresponding to this automatic-operation center position of switch 174. 
In controller apparatus 172, a first output CLOSE INSULATION (C) is 
provided by relay 224 contacts 230 when controller 172 connects AC power 
source 234 along cable 236 to motor 178 to cause the motor to block the 
window. A second output OPEN INSULATION (O) is provided by relay 228 
contacts 232 when controller 172 connects AC power source 234 in reversing 
manner along cable 236 to motor 178 to cause the motor to run in reverse 
and unblock the window 101. In its totality, controller 172 implements the 
Boolean logic equations: 
CLOSE INSULATION (C)={[NOT WINTER AND NET ENERGY TRANSFER IN AND NOT COLDER 
THAN T.sub.L) OR (NOT WINTER AND NET ENERGY TRANSFER NOT IN AND COLDER 
THAN T.sub.L) OR (WINTER AND NET ENERGY TRANSFER NOT IN AND NOT HOTTER 
THAN T.sub.H) OR (WINTER AND NET ENERGY TRANSFER IN AND HOTTER THAN 
T.sub.H)] AND [WINDOW NOT BLOCKED AND NOT MANUAL OPEN AND NOT MANUAL CLOSE 
]} OR {MANUAL CLOSE AND WINDOW NOT BLOCKED}. 
OPEN INSULATION (O)={[NOT WINTER AND NET ENERGY TRANSFER IN AND COLDER THAN 
T.sub.L) OR (NOT WINTER AND NET ENERGY TRANSFER NOT IN AND NOT COLDER THAN 
T.sub.L) OR (WINTER AND NET ENERGY TRANSFER NOT IN AND HOTTER THAN 
T.sub.H) OR (WINTER AND NET ENERGY TRANSFER IN AND NOT HOTTER THAN 
T.sub.H)] AND [WINDOW NOT UNBLOCKED AND NOT MANUAL OPEN AND NOT MANUAL 
CLOSE]} OR {MANUAL OPEN AND WINDOW NOT UNBLOCKED}. 
Inspection of the above Boolean equations indicates that the logic of the 
controller 172 regards T.sub.H and T.sub.L as examples of a selectable 
nominal temperature to be responded to in the same way once the choice of 
one or the other is made by the winter-summer switch 196. From a hardware 
standpoint, controller 172 has a hardware section for producing a 
condition signal CS in response to the thermostat 190 outputs W and T and 
in response to the net energy transfer NET on line NET-101 so that the 
condition signal changes corresponding to each change in a logic quantity 
defined as: 
[(NET ENERGY TRANSFER IN AND SAID INSIDE TEMPERATURE HIGHER THAN SAID 
NOMINAL TEMPERATURE) OR (SAID NET ENERGY TRANSFER NOT IN AND INSIDE 
TEMPERATURE NOT HIGHER THAN SAID NOMINAL TEMPERATURE)]. 
In controller 172 the condition signal is produced at the output of 
exclusive-OR gate 204 having two inputs respectively receiving the 
thermostat 190 output T signalling when the inside temperature in the 
building is higher than and not higher than the nominal temperature 
selected by the winter-summer switch 196 and receiving the output of 
exclusive-OR gate 202. Exclusive-OR gate 202 has two inputs respectively 
receiving the physical representation of NET (Boolean 1 if NET is positive 
or "in", and Boolean 0 if NET is negative or "not in") and receiving the 
winter-summer signal W. (Excl.-OR of A,B is A.multidot.B+A.multidot.B.) 
In the automatic mode, or center position, on switch 174 (MO.multidot.MC) 
the hardware of controller 172 provides two sections for providing the 
INSULATION CLOSE (C) and OPEN INSULATION (O) outputs respectively. The 
first section includes SC switch 176, inverter 208, AND-gate 210, 
three-input AND-gate 212, OR-gate 222 and relay 224. The first section 
senses the position of the insulation and provides the first output C for 
driving the motorized insulation 178 to block the window, the first output 
C corresponding to the condition signal CS except when the insulation is 
already in the blocking position. 
The second section includes SO switch 177, inverter 216, NOR-gate 214, 
AND-gates 218 and 220 and OR-gate 226 and relay 228. The second section 
senses the position of the insulation and provides the second output O for 
driving the motorized insulation 178 to unblock the window, the second 
output O corresponding to the logical complement (NOT) of the condition 
signal CS except when the insulation is already in the unblocked position. 
Taking all positions of mode switch 174 into account, together with its 
NOR-gate 206, the first hardware section producing the CLOSE INSULATION 
output C is a digital logic circuit for driving relay 224 according to a 
logic function MC.multidot.SC+MO.multidot.MC.multidot.SC.multidot.CS. The 
second hardware section for producing the OPEN INSULATION output O is 
correspondingly a digital logic circuit for driving relay 228 according to 
a logic function MO.multidot.e,ovs/SO/ +MO.multidot.e,ovs/MC/ 
.multidot.e,ovs/SO/ .multidot.e,ovs/CS/ . 
It will be apparent that a variety of design approaches can implement the 
same Boolean expressions and logic functions and that FIG. 3 is merely 
illustrative of a preferred embodiment for the practice of the invention. 
FIG. 3 furthermore illustrates an approach in which the controller 172 is 
outboard of the computer 158 of FIG. 2 or the computer 34 of FIG. 1. It is 
contemplated that the logic of the controller 172 is suitably implemented 
in software as desired by the skilled worker for execution in a computer 
when necessary. Switches 174,176, and 177 with thermostat 190 are in such 
alternative connected along with the transducers to A/D converters at the 
input to the computer. Window control output lines (not shown) are added 
to the computer 158 and drive relays 224 and 228 to the motor 178, and all 
logic gates of FIG. 3 are dispensed with. In such approach the computer 
absorbs most of the functions in the computation and control apparatus 
needed to run the window insulation. 
FIGS. 4A and 4B respectively show front and cross-sectional views of a 
sensor assembly unit 300 for conveniently bringing heat flux sensor and 
thermocouple combinations 322 and 324 into thermal contact with a window 
together and springably holding them there. "O" shaped rectangular base 
frame 302 is painted with low absorptivity flat white paint. Flat springs 
or straps 312 and 310 bridge the space between frame 302 parts 304 and 308 
and hold heat flux sensor and thermocouple combinations 322 and 324 from 
which triple-leads 330 and 332 emanate. The flux sensors are of the rigid 
plate type rather than thin foil design in this assembly so that 
durability is enhanced. Flat springs 310 and 312 are anchored at each end 
as by crimps 314 and 316. The flat springs are selected to be of low 
thermal conductivity (high thermal resistance) and are painted the same 
color in each part of their length as the respective color of the sensor 
over which each part passes. The heat flux sensor and thermocouple 
combinations 322 and 324 are physically separated for thermal isolation so 
that space is left around each heat flux sensor and between the heat flux 
sensors and the base frame 302. (The thermocouples, which are relatively 
small, are not shown.) Frame 302 is grooved or recessed so that flat 
springs 310 and 312 pass between frame 302 and glazing 101, and frame 302 
rests flat on glazing 101. 
Assembly 300 permits simultaneous mounting as a combination each of a 
plurality of pair of thermocouples in contact with their respective heat 
flux sensors on the inside surface of window 101. Assembly 300 is 
temporarily fastened to window 101 by white, or light-colored, 
commercially available adhesive tape shown as pieces of tape 320 and 321. 
Permanent mounting is accomplished by glue or cement for causing frame 302 
to adhere to window 101. 
FIG. 5 depicts an appropriate placement of sensor assembly 300 when 
blowable insulation beads 370 are provided in window 360. Sensor assembly 
300 is placed upward on the inside surface of window 360 just above the 
highest level assumed by the beads 370. Such placement permits the 
reception of solar radiation 350 and correct calculation of NET at all 
times. In this way, the measurement apparatus can calculate when the need 
for the presence of the insulation 370 to block the window has passed, and 
the insulation is then removed automatically from glazing 360 by a window 
insulation control unit, not shown. Similarly, when alternative movable 
insulation such as motor-driven shutters or a sliding panel is used, the 
physical arrangement is suitably made to permit sensor reception of solar 
radiation and correct calculation of NET at all insulation positions. 
FIGS. 6A, 6B, and 6C depict alternative physical positions of thermocouple 
410 and heat flux sensor 412 relative to the inside surface of window 400. 
In each case flux sensor 412 is in thermal contact with window 400 so that 
it both intercepts solar energy 405 and changes the temperature of the 
window 400. In FIG. 6A thermocouple 410 is in both physical and thermal 
contact with window 400 and the forward surface of heat flux sensor 412 in 
the arrangement contemplated by the mathematical model equations presented 
hereinafter. In FIG. 6B, thermocouple 410 is provided onto the back 
surface of sensor 412 but remains in thermal contact with window 400 by 
virtue of the low thermal resistance of the sensor 412 metal. Mathematical 
model equations are modified to take account of the change in position of 
the thermocouple relative to the thermal resistance of the heat flux 
sensor, see positions T'.sub.b and T'.sub.w in FIG. 8. In FIG. 6C 
thermocouple 410 is provided into a hole drilled into the heat flux sensor 
412 so that it is exposed to a temperature in the interior of sensor 412 
and is shielded from radiation 405. 
FIGS. 7A, 7B, and 7C depict alternative wiring details of the thermocouple 
and heat flux sensor pairs. In FIG. 7A thermocouple 410 has a separate 
constantan-copper lead pair 420 from lead pair (copper-copper) 422 from 
heat flux sensor 412. The input terminals of an A/D converter are shielded 
from 60 cycle AC hum pickup on lead pairs such as 422 by insertion of an 
RC hum filter having 22 mfd capacitor 424 and 1000 ohm resistor 426. 
In FIG. 7B, the need of four wires in FIG. 7A is obviated as in FIG. 2 by 
using a common 438 between thermocouple 430 and heat flux sensor 432. 
Thermocouple 430 is regarded as a junction of a single constantan lead 437 
itself to one of the copper leads 438,439 from the heat flux sensor 432. 
Division at point 441 into wire pairs 440 and 442 for the thermocouple 430 
and the heat flux sensor 432 respectively is made as desired. 
In FIG. 7C the thermocouple junction is made in the approximate physical 
center of heat flux sensor 452 for more accurate correspondence between 
the transducer placement and mathematical model assumptions. Heat flux 
sensor wires 458 and 459 emanating from the top edge of the heat flux 
sensor are folded down for presentation of wire 458 to the constantan lead 
457 of the thermocouple 450. Division at point 461 into wire pairs 460 and 
462 for the thermocouple 450 and heat flux sensor 452 respectively is made 
as desired. 
Mathematical Modelling 
FIG. 8 is a thermal circuit diagram of a steady-state 
radiation-convection-conduction mathematical model of the heat transfer 
processes occurring in window 500 having exterior glazing 501 and interior 
glazing 502. 
The thermal circuit diagram shows thermal processes in electric circuit 
form. The ambient temperatures T.sub.2 and T.sub.1 are modelled as voltage 
sources, and the flow of heat is modelled as an electrical current passing 
through thermal resistances R.sub.1, R.sub.g, and R.sub.2 according to a 
thermal analog of Ohm's Law wherein temperature drop is equal to the 
product of a thermal resistance times the heat flow, or flux. Solar 
radiation S.sub.1 passing toward region having temperature T.sub.1 is 
absorbed in glazing 501 and is modelled as a current source S.sub.1 
a.sub.1, the product of radiation S.sub.1 times glazing 501 absorptivity 
a.sub.1. Similar absorption occurs in glazing 502 as current source 
S.sub.1 a.sub.2, and in the white and black heat flux sensors 24 and 22 as 
current sources S.sub.1 a.sub.w and S.sub.1 a.sub.b respectively. 
Reradiation S.sub.2 passing toward the region having temperature T.sub.2 
is absorbed in the white and black sensors as current sources S.sub.2 
a.sub.w and S.sub.2 a.sub.b respectively. Each heat flux sensor presents 
a thermal resistance R.sub.s which is assumed the same in each sensor. In 
the presently-described one-dimensional modelling, the heat flux has 
dimensions of watts per square meter, the temperature differences or drops 
have dimensions of Celsius degrees, and the thermal resistances have 
dimensions of Celsius degrees times square meters per watt. All 
absorptivities a.sub.1, a.sub.2, a.sub.w, and a.sub.b are assumed to be 
knowns. The radiations S.sub.1 and S.sub.2 and heat flows (except for 
Q.sub.w and Q.sub.b measured by the sensors) are unknowns. All 
temperatures, except for temperatures T.sub.2,T.sub.1,T.sub.w, and T.sub.b 
are unknowns. The window thermal resistance R.sub.g is taken as a known 
function of window temperature drop .DELTA.T.sub.g, or as a known 
constant, or as unknown depending upon the mathematical model used. The 
thermal resistances of the regions on each side of the window R.sub.1 and 
R.sub.2 are unknowns. Each heat flux sensor is respectively assumed to be 
painted to have absorptivities of front and back be equal, although a more 
complex analysis suitably accounts for different front and back 
absorptivities. 
The uninstrumented part of window 500 is modelled by equivalent circuit 
510. Shortwave radiations S.sub.1 and S.sub.2 pass in opposite directions 
and a heat flux, such as a thermal loss, Q flows by convection, longwave 
radiation and conduction processes from the region having temperature 
T.sub.1, such as the inside of a building, to window 500. Manifestly, the 
net heat transfer NET from the T.sub.2 region to the T.sub.1 region is 
given by: 
EQU NET=S.sub.1 -S.sub.2 -Q (1) 
In order to permit the determination of the unknown components of the 
mathematical model, the window 500 is instrumented with at least white and 
black heat flux sensors and associated thermocouples. Because the 
absorption of radiation S.sub.1 and S.sub.2 by the white and black heat 
flux sensors warms them differently, they not only cause their thermal 
circuits 511 and 512 to have different temperatures T.sub.w and T.sub.b 
and different sensed heat fluxes Q.sub.w and Q.sub.b but also these 
temperatures and heat fluxes are not the same as the inside glazing 
temperature and heat flux Q of the uninstrumented window section 510. 
Thus, the sensors of the invention do not "measure" window circuit 510 in 
one sense of the word; instead they create two distinct circuits 511 and 
512 providing information by which the operation of window circuit 510 can 
be sorted out and deduced therefrom, mathematically. 
Window Model Assuming Resistance R.sub.g Known 
If the window resistance is known, only the sensor assemblies on the window 
in circuits 511 and 512 are needed, together with the T.sub.2 and T.sub.1 
measurements, in order to provide the computer with the data needed to 
permit solution for net energy transfer NET. 
The following temperature-drop equation can be written from inspection of 
uninstrumented window circuit 510: 
EQU T.sub.1 -QR.sub.1 -(Q+S.sub.1 a.sub.2)R.sub.g -(Q+S.sub.1 (a.sub.1 
+a.sub.2))R.sub.2 =T.sub.2 (2) 
This Equation (2) presents unknowns Q and S.sub.1 found in NET Equation (1) 
as well as the unknown resistances R.sub.1 and R.sub.2. Evidently, four 
more equations are needed together with Equation (2) in order to solve not 
only for Q, S.sub.1, R.sub.1, and R.sub.2, but also for the unknown 
S.sub.2 in the NET Equation (1). The additional four equations are 
provided by inspection of the circuits 511 and 512 having the white and 
black sensors. For the white sensor circuit 511 the following circuit 
equation holds for the leftward section of circuit 511 between 
temperatures T.sub.w and T.sub.2 : 
EQU T.sub.w -(Q.sub.w +S.sub.1 (a.sub.2 +a.sub.w))R.sub.g -(Q.sub.w +S.sub.1 
(a.sub.1 +a.sub.2 +a.sub.w))R.sub.2 =T.sub.2 (3) 
Also in white sensor circuit 511 the following circuit equation holds for 
the rightward section of circuit 511 between temperatures T.sub.w and 
T.sub.1 : 
EQU T.sub.w +Q.sub.w R.sub.s +(Q.sub.w -S.sub.2 a.sub.w)R.sub.1 =T.sub.1 (4) 
For the black sensor circuit 512 the following circuit equation holds for 
the leftward section of circuit 512 between temperatures T.sub.b and 
T.sub.2 : 
EQU T.sub.b -(Q.sub.b +S.sub.1 (a.sub.2 +a.sub.b))R.sub.g -(Q.sub.b +S.sub.1 
(a.sub.1 +a.sub.2 +a.sub.b))R.sub.2 =T.sub.2 (5) 
Also in black sensor circuit 512 the following circuit equation holds for 
the rightward section of circuit 512 between temperatures T.sub.b and 
T.sub.1 : 
EQU T.sub.b +Q.sub.b R.sub.s +(Q.sub.b -S.sub.2 a.sub.b)R.sub.1 =T.sub.1 (6) 
Omitting many tedious but straightforward manipulations, the unknowns 
S.sub.1, S.sub.2, and Q of the net heat transfer NET Equation (1) are 
derived from the five equations (2), (3),(4),(5), and (6) with results as 
follows: 
Solving Equation (6) for R.sub.1 and substituting into Equation (4) and 
solving for S.sub.2 yields the leftgoing radiative loss 
##EQU1## 
Solving Equation (5) for R.sub.2 and substituting into Equation (3) and 
solving for S.sub.1 yields the following quadratic equation in the 
rightgoing solar radiation 
EQU AS.sub.1.sup.2 +BS.sub.1 +C=0 (8A) 
where 
EQU A=a.sub.1 (a.sub.b -a.sub.w)R.sub.g (8B) 
EQU B=a.sub.1 R.sub.g (Q.sub.b -Q.sub.w)+(T.sub.w -T.sub.2)(a.sub.1 +a.sub.2 
+a.sub.b)-(T.sub.b -T.sub.2)(a.sub.1 +a.sub.2 +a.sub.w) (8C) 
EQU C=Q.sub.b (T.sub.w -T.sub.2)-Q.sub.w (T.sub.b -T.sub.2). (8D) 
Because the solar radiation cannot be negative by definition, quadratic 
equation (8A) is solved by the quadratic formula with the nonnegative root 
selected, wherein the quadratic formula is: 
##EQU2## 
Solving Equation (2) for heat loss Q yields 
##EQU3## 
where (from Equation (5)) 
##EQU4## 
and where (substituting S.sub.2 Equations (7A) and (7B) into Equation (6)) 
##EQU5## 
What has been done so far is to obtain formulas for the solar radiation 
S.sub.1, the radiative loss S.sub.2, and the thermal convective, longwave 
radiative and conductive loss Q in terms of knowns. The net energy 
transfer is computed by subtracting the losses S.sub.2 and Q from the 
solar radiation S.sub.1, according to Equation (1). These formulas, 
together with the knowns, are readily programmed into computer 34 so that 
the net energy transfer is continually computed and provided as an output 
from the computer. 
Computer System and Programming 
A computer system is suitably provided in the practice of the invention 
wherein analog-to-digital converters provide digital representations of 
the analog quantities presented by the heat flux sensors and 
thermocouples, or other temperature sensors, of the instrumented window or 
windows. The digital representations are stored in a memory of the 
computer system. The central processing unit of the system (CPU) performs 
the programmed instructions for computing net energy transfer, with the 
output being provided in serial digital form or in analog form for 
interfacing to a printer, CRT, or other recording device. Where one or 
more windows will be operated as in FIG. 2 with movable insulation, the 
output is provided to the appropriate window controller 172 and 182. A 
keyboard 35 is provided for occasional system control and initial system 
startup. 
An example of suitable commercially available hardware and system 
software/compiler is the MACSYM 2 system of Analog Devices, Inc., 
Instruments and Systems Division, Norwood, Mass. In addition to the CPU 
and memory, the system includes analog-to-digital input hardware cards 
(ADIO Cards) and Asynchronous Communications Cards for interfacing the 
computer output with terminals, printers, plotters, and intelligent 
instruments. A form of the well-known BASIC computer language is available 
in the MACSYM 2. A Perkin-Elmer Model 550 CRT and keyboard terminal is 
suitably used, the unit being available from the Perkin-Elmer Terminals 
Division, Randolph, N.J. 
The calculations in a suitable form of software for use in the practice of 
the invention are to be repeated over and over long periods of time as the 
temperatures and heat fluxes to be measured slowly change in response to 
meteorological and other factors. Accordingly, the computer burden is 
relatively low, permitting the practice of the invention with inexpensive 
minicomputers and microprocessors. The software dedicated to the invention 
is also suitably stored with unrelated programs and its execution 
time-shared with the other programs, thereby spreading the cost of the 
computing to other uses as well. 
FIG. 9 shows a flowchart of the programming suitable for the practice of 
the invention. The program starts at point 600 and proceeds to store known 
constants at point 610. For example, in the instrumentation the 
absorptivities were a.sub.1 =a.sub.2 =0.05; a.sub.b =0.6; a.sub.w =0.3; 
and flux sensor resistance R.sub.s =0.04 and window resistance R.sub.g 
=0.111. 
At step 620 the analog inputs from the heat flux sensors and thermocouples 
are read by the computer and stored in memory. Because the thermocouples 
are differentially connected to the computer, respective temperature 
differences are being provided in analog form. Where resistance 
thermometers or other types of temperature sensors are used, the analog 
input alternatively corresponds to temperature itself. 
At step 630 the analog input data previously read is conditioned to make it 
ready for use in succeeding calculations. For instance, the actual 
quantities for heat flux sensor output for the instrumentation were 
multiplied by calibration factors of -3510 and -3600 watts per meter.sup.2 
per volt, for the white and black heat flux sensors respectively. The 
differential thermocouple outputs as read by the computer were multiplied 
by 25,000 Celsius degrees per volt to obtain temperature differences. No 
further conditioning is employed for adequate operation of the invention. 
However, it is contemplated in further refinement of the practice of the 
invention that additional conditioning is provided for filtering out 
measurement errors (noise) and adjusting for transients when the system 
model is of steady-state type as in FIG. 8. Such additional conditioning 
utilizes data from previous measurements from the sensors and 
thermocouples in any suitable conditioning algorithm selected by the 
skilled worker. 
In another aspect of conditioning the inputs, it is to be understood that 
the analog-to-digital converters provide outputs corresponding to the 
manner of hardwiring the instrumentation to them. For instance, the black 
heat flux sensor wire pair connected to the A/D converter can produce an 
output proportional to +Q.sub.b, but when the wire pair is oppositely 
connected to the converter, the converter produces an output proportional 
to -Q.sub.b. This sign error can be corrected, of course, merely by 
multiplying by -1 in the signal conditioning step. The same consideration 
applies to the differentially connected thermocouples, with a further 
complication. Where there are four temperatures T.sub.2, T.sub.1, T.sub.b, 
and T.sub.w, wire pairs can be selected for the temperature differences 
T.sub.1 -T.sub.2 ; T.sub.1 -T.sub.b ; T.sub.1 -T.sub.w ; T.sub.2 -T.sub.b 
; T.sub.2 -T.sub.w ; and T.sub.b -T.sub.w (and their negatives). 
Fortunately, only three of the six foregoing quantities are needed as 
inputs to permit computation of any of the rest at the conditioning step 
630. For example, if (T.sub.b -T.sub.2) is needed, but only (T.sub.1 
-T.sub.2) and (T.sub.1 -T.sub.b) are available, it suffices to perform the 
subtraction (T.sub.1 -T.sub.2)-(T.sub.1 -T.sub.b) in the conditioning. 
At step 640 the net energy transfer NET and other system unknowns are 
calculated according to the mathematical model utilized. An approximate 
technique was employed for calculating the solar radiation S.sub.1 and the 
following programming was used to implement the step 640 mathematics: 
______________________________________ 
Line Instruction 
______________________________________ 
240 H2=(Q1/(A2+A4)-Q2/(A2+A3))/((T1-Q1/U1)/ 
(A2+A4)-(T2-Q2/U1)/(A2+A3)) 
260 T5=T2/(H2/U1+1) 
270 S0=(H2*T5-Q2)/(A2+A3) 
280 Q3=S0*A1 
290 H0=(Q1/(A1+A2+A4)-Q2/(A1+A2+A3)) 
300 H0=H0/((T1+(Q3-Q1)/U1)/(A1+A2+A4)-(T2+ 
(Q3-Q2)/U1)/(A1+A2+A3)) 
310 T6=(U1*(T2-T5)+Q3)/H0 
320 S1=(H0*T6-Q2)/(A1+A2+A3) 
330 H1=(Q1*A3/A4-Q2)/((T3-Q1/U2)*A3/A4- 
(T4-Q2/U2)) 
340 S2=(Q2-H1*(T4-Q2/U2))/A3 
350 IF S2&lt;0 THEN S2=0 
360 T7=(S1*(A1+A2+A4)+Q1)/H0 
370 Q4=H0*T7-S1*(A1+A2) 
380 Q5=S1-S2-Q4 
______________________________________ 
In terms of the previously-defined mathematicial model quantities, Q1 is 
Q.sub.w ; Q2 is Q.sub.b ; T1 is T.sub.w -T.sub.2 ; T2 is T.sub.b -T.sub.2 
; T3 is T.sub.1 -T.sub.w ; T4 is T.sub.1 -T.sub.b ; A1 is a.sub.1 ; A2 is 
a.sub.2 ; A3 is a.sub.b ; A4 is a.sub.w ; U1 is 1/R.sub.g ; U2 is 
1/R.sub.s ; and Q5 is net heat transfer NET. 
Calculations for a single-glazed window proceed the same way, except that 
a.sub.1 =0 and the thermal resistance R.sub.g is that of the window glass. 
At step 650 the computer is instructed to provide an electrical output 
signal corresponding to NET in those cases where a window controller is 
employed or for a recording device. 
Where more than one window is under automatic control as in FIG. 2, the 
computer is programmed to execute step 640 for the input data and 
constants corresponding to each window respectively, compute NET-101 for 
the first window, NET-102 for the second window, and net heat transfer for 
each window under automatic control, and then in step 650 direct the 
electrical signals corresponding to each window NET to the window 
controllers respectively. 
In step 660, upon request from the terminal keyboard the computer displays 
the input data and computed value of NET on the terminal CRT screen. 
In step 670, program execution is returned to starting point 600 to begin 
the program over again for a new set of input data unless a keyboard 
request or system interrupt causes execution of the program to end at END 
690. 
The program is executed at regular intervals, such as every 30 seconds, and 
the NET results for each window are stored in memory for at least 15 
minutes resulting in 30 NET values. The arithmetic mean of the 30 values 
is suitably calculated and output as NET-101 and NET-102, providing an 
advantageous averaging at step 650 and smoother operation of the window 
insulation control units. 
In all cases it is to be understood that the hereinabove-described 
preferred embodiments, arrangements, apparatus, methods, and systems are 
merely illustrative of a small number of the many possible specific 
embodiments and methods which can represent applications of the principles 
of the invention. Numerous and varied other arrangements, embodiments, 
apparatus, methods, and systems can readily be devised in accordance with 
these principles by those skilled in the art without departing from the 
spirit and scope of the invention and so that the utility of the invention 
can be fully realized.