# Steam Heating and Ventilation/Chapter V

Chapter V.—Design of Radiation.
Heat loss in buildings.—There have been considered in previous chapters the various kinds of radiators in use and the amount of heat given off by them under different conditions; and the subject now approaches a study of the particular way in which the heat is utilized. The object of any heating system is, of course, to maintain a uniform temperature in the building in question, and to do this it is necessary: First, to replace the heat lost by convection and radiation from the windows and walls of the building to the colder surroundings outside; second, to heat to the required temperature any air that may be intentionally admitted for ventilation; and third, to heat also the air that may be admitted unintentionally through cracks of window frames and porous walls and opening doors. The amount of heat required for this last cause is much greater than is generally supposed.
The amount of air that will pass through the walls of an apparently tight room is incredible to those who are not familiar with it by actual experiment. The author knows of no experimental data on the subject, but Dr. John S. Billings, in his valuable work on "Ventilation and Heating," describes a simple and interesting experiment that may be undertaken by any one. Take a room of average proportions, heated by a hot-air furnace or indirect radiation, and the air will, on a fairly cold day, be coming through the register with a very considerable velocity. If now this velocity be measured by an anemometer, or other means, and all doors and windows be closed and the measure be again taken, it will generally be found that there is scarcely an appreciable reduction in this velocity. If now all the cracks of the doors and windows be carefully stopped up with cloth or paper, the reduction in the velocity of the incoming air will still be but very little reduced. Some of the air in such cases escapes directly through the plastered and papered walls, but more through floors and into the outside air through brick walls, between the floors, and at such points as are not plastered and papered. In cold weather it will generally ​be noticed that with all windows and doors closed, there is a decided current of air flowing through any building, in the same direction as the wind out of doors, and this is always most noticeable at the floors.
It may be stated in general that brick buildings are much tighter than wooden; and fireproof buildings which have wooden flooring laid on some kind of a concrete filling are much tighter than the ordinary brick buildings. It is perhaps a valuable thing that the walls of buildings are not less porous than they are, for in far too many cases there is no ventilation in winter, except what is obtained in this way. It is, however, much better to make the walls tight and provide some proper inlet for ventilation, especially as from a sanitary standpoint the floor is the worst place to let cold air into an otherwise warm room. An ordinary brick building can be much improved in this respect, if, during construction, the walls around the joists and for some inches above and below be painted with a heavy coat of asphalt paint. It is for these reasons mainly that all rules for proportioning radiation surface are very largely empirical.
The heat required for a definite amount of ventilation can be very accurately calculated. A cubic foot of ordinary air, at 60 or 70 degrees Fahr., weighs about 0.0745 pound, or there are 13.4 cubic feet per pound; and the specific heat is about 0.24, so that one British thermal unit will heat 55.8 cubic feet of air 1 degree Fahr. This factor is, however, subject to considerable variation according to the final temperature considered and the degree of moisture, and is usually taken at 55.
The heat lost by radiation and convection from the walls of buildings has been variously calculated by different authorities, from Péclet down, and a great variety of results have been given. It is unquestionably very difficult to determine it experimentally, because of the fact that the loss of heat from walls, etc., depends first upon the construction of the walls, but more especially upon the condition of the air outside, the loss of heat being very greatly increased by a slight wind blowing against the exposed surface. The loss of heat is greatest from the glass surface of windows. Mr. W. J. Baldwin, in his book on "Steam Heating for Buildings," which has for some years been a standard, publishes a table of the relative "heat-transmitting power of various building substances," which is given here.
Baldwin's Table of Heat-Transmitting Power of Building Substances. :
| Window glass | ... | 1,000 |
| Hardwood sheathing on walls | ... | 66 to 100 |
| White pine and pitch pine | ... | 80 to 100 |
| Lath and plaster, good | ... | 75 to 100 |
| " " " common | ... | 100 to 150 |
| Common brick, rough | ... | 150 |
| " " hard finish | ... | 200 |
| " " hollow walls, hard finish | ... | 150 |
| Sheet iron | ... | 1,100 to 1,200 |
Mr. Baldwin further implies that the coefficient representing the amount of heat given off by glass surface per square foot per hour per degree difference in temperature between one side of the glass and the other is about the same as the similar coefficient for radiation, which may be taken at about 1.8 British thermal units.
The German Government made an investigation into this subject, and the results of its work have been translated into English measures by Mr. Alfred E. Wolff (Journal Franklin Institute, Vol. 134); and Prof. R. C. Carpenter has translated the results of Péclet's original investigations. The factors given differ very decidedly, as may be seen by the accompanying table, in which are given the coefficients of heat transmission for different surfaces:
Table of Coefficients of Heat Transmission. (British thermal units transmitted per hour per square foot of surface per degree difference of temperature.) :
| | | Baldwin. | Peclet. (Carpenter.) | German Gov. (Wolff.) |
| Single skylight | ... | ... | ... | 1.12 |
| Double skylight | ... | ... | ... | 0.62 |
| Single window | ... | 1.8 | .91 to .98 | 1.03 |
| Double window | ... | ... | .60 to .66 | .52 |
| 4-inch brick wall. | ${\Bigg \}$ ${\Bigg \$ | .27 | .43 | .68 |
| 8-inch brick wall. | ${\Bigg \}$ ${\Bigg \$ | to | .27 | .46 |
| 13-inch brick wall. | ${\Bigg \}$ ${\Bigg \$ | .36 | .32 | .32 |
| 17-inch brick wall | ... | ... | .26 | .24 |
| Wooden beams planked over as flooring | Wooden beams planked over as flooring | Wooden beams planked over as flooring | ... | 0.083 |
| Wooden beams planked over as ceiling | Wooden beams planked over as ceiling | Wooden beams planked over as ceiling | ... | 0.104 |
| Fireproof construction as flooring | Fireproof construction as flooring | Fireproof construction as flooring | ... | 124 |
| Fireproof construction as ceiling | Fireproof construction as ceiling | Fireproof construction as ceiling | ... | 145 |
| Wooden door | ... | ... | ... | 414 |
Mr. John J. Hogan gives 1.57 British thermal units as the coefficient for glass. Mr. Charles Hood, the English authority, states that one square foot of glass will cool 1.279 cubic feet of air one degree per minute per degree difference in temperature. This is equivalent to a coefficient of heat transmission of about 1.40 British thermal units per hour. Mr. Hood adds that this was determined in still air and that it is very greatly increased by the ​effect of wind. He states, however, that it is well known that in extremely cold weather there is invariably but little wind, so that he considers this a safe coefficient to use.
Mr. Wolff has constructed a diagram of heat transmission from buildings, which embodies the German coefficients with some slight modifications based on his own very extended practice. He states that he has used this diagram in the calculations of heating surface for buildings, during the past six years, with the most satisfactory results. This is a valuable recommendation, and the author takes much satisfaction in presenting the diagram herewith.
In using his diagram for proportioning radiation surface, Mr. Wolff calculates by it the number of heat units lost from the exposed wall and glass surfaces and further makes allowance for the direction of winds on the outside exposure, as shown on the small diagram on page 65 facing the main one. As indicated 5 to 25 per cent. is added to the calculated amount of heat dissipated in transmission through the actual wall surface and 10 per cent. for reheating the air constantly leaking in. An allowance is also advised, to the amount of 10 per cent., for the transmission of heat through floors, ceilings, etc. Where the rooms are not large, one calculation is made for all these factors by adding to the heat transmission as obtained by means of the main diagram, the percentage given in the small circle.
For "wooden floors" in cheaply constructed buildings, the author would recommend even more allowance than Mr. Wolff gives, since where such floors are used a great loss of heat comes from a large amount of cold air, which, even with a light wind blowing, will work through the brick walls where the joists are set in and where the walls are unsealed by lathing or plaster, and find its way into the rooms. This is a common source of heat loss in cheaply constructed brick houses and apartment buildings, and is the usual cause of the cold floors which are noticeable in many buildings in cold weather. In fireproof structures, on the contrary, the construction of the walls and floors is much more substantial and offers but little opportunity for air to blow in between the floor and ceiling.
Alfred R. Wolff's Diagram of Transmission of Heat in Buildings.
A, vault light; E, single window; C, single skylight; D, 4-inch brick wall; E, double window; F, double skylight; G, 8-inch brick wall; H, 1-inch pine board door; I, 12-inch brick wall; J, concrete floor on earth; K, fireproof partition; L, 2-inch pine board heavy door; M. 16-inch brick wall; N, 20-inch brick wall; O, concrete floor on brick arch; P, 24-inch brick wall; Q, 28-inch brick wall; R, 32-inch brick wall; S, wood floor on brick arch; T, 36-inch brick wall; U, 40-inch brick wall; V, wood floor, double. ​In the early days of steam heating, radiating surface was generally figured by various rule-of-thumb methods, based chiefly upon the cubic contents of the room to be heated. These varied all the way from one square foot of radiation for 30 cubic feet of space, up to one square foot to 100 cubic feet, according to the building considered. Mr. Baldwin, in the earlier editions of the work mentioned, gives a rule which only takes into account the exposed surface of the building. According to this rule it is first necessary to figure what may be called the "glass equivalent surface." This is the actual glass surface in a room added to the wall surface reduced to its equivalent in glass. Mr. Baldwin refers to his table of relative heat transmitting powers, previously given, and his rule is as follows:
Exposure Diagram.
"In figuring wall surface, etc., multiply the superficial [exposed] area of the wall in square feet by the number opposite to the substance in the table, and divide by 1,000 (the value of glass), the product is the equivalent of so many square feet of glass in cooling power, and may be added to the window surface." Mr. Baldwin then gives a rule for finding the number of square feet of radiating surface for each square foot of glass, or the equivalent of other building substances in glass, which may be expressed by the following formula:
$R=(t-t_{1})\div (T-t)xE\,$
where $t\,$ is the required temperature of the room, $t_{1}\,$ is the temperature of the outside air, $T\,$ the temperature of steam in the radiator, $R\,$ the radiation surface, and $E\,$, the glass equivalent surface.
With an outside temperature of -5 degrees, an inside temperature of 70 and steam at temperature of 220, this formula would allow ½ square foot of radiating surface for each square foot of glass or its equivalent. Mr. Baldwin further adds: "It must be distinctly understood that [this] . . . offsets only the windows and other cooling surfaces it is figured against and does not provide for cold air admitted around loose windows, or [through walls] of poorly constructed . . . houses. These latter conditions, when they exist, must be provided for separately, and usually require as much as 50 per cent. additional; a good ​common rule for ordinary purposes being three-fourths of a square foot of heating surface to each square foot of glass, or its equivalent." He further states that he has used this rule in preference to any other for several years and found it very satisfactory. Following in Mr. Baldwin's footsteps, the writer has used this method of calculating surface in the design of a large number of heating systems, chiefly for large office buildings in Chicago and elsewhere. He has found, however, for low-pressure systems in office buildings that from 60 to 70 per cent. of the glass-equivalent surface in figuring radiation gives ample and satisfactory results. For such buildings he has counted each square foot of wall surface as being equivalent to one-tenth of a square foot of glass. For brick houses or apartment buildings of ordinary construction it is better to take the wall surface as 15 or 20 per cent. of the glass. For office buildings 65 per cent. of the glass-equivalent surface in radiating surface is ample in most cases, and it may average rather less. It should be greatest on the sides of the building which are exposed to the severest winds in winter, and may be less on the southern exposures.
Mills' rule for direct radiation.—Mr. Baldwin's method of calculating radiation surface calls for the exercise of careful judgment on the part of engineers using his rule, and many authorities have devised rules which are more specific. Most of these take into account the glass surface, the wall surface, and also the cubic contents of the room. The rule recommended by Mr. Mills in his work is
$R=0.50G+0.05W+0.005C\,$
in which $R\,$ is the number of square feet of radiating surface; $G\,$, the square feet of glass surface; $W\,$, the square feet of wall surface (exclusive of windows); and $C\,$, the contents in cubic feet. This rule is recommended where the rooms are to be heated to a temperature of 70 degrees with an outside temperature of 10 to 15 degrees Fahr. If the outside temperature is less or greater, the result should be multiplied by the proportionate factor. This is a very good rule and perfectly safe. The writer knows of a contractor who has had a very wide experience in steam heating who uses this rule universally, except that he multiplies the cubic contents by 0.004.
Willett's rule for direct radiation.—Mr. Jas. R. Willett, an architect of wide experience, who has given much study to heating ​and ventilation, formulated, several years ago, a very valuable rule for proportioning direct radiation, which is expressed by the following formula:
$R=0.9(t-t_{1})(0.60G+0.10W+0.0025C)FJ\div t\,$
where $F\,$ is a factor depending on the method of heating (0.8 for low-pressure steam) and $J\,$, a factor depending on the exposure, which Mr. Willetts puts as 1.0 for ordinary south and east exposures and 1.4 for north and west. The other letters in the formula have the same reference as in the formulas previously given, but Mr. Willett states that $t\,$ should be taken 10 degrees higher than the lowest recorded temperature of the locality in question. With $t_{1}\,$ taken at minus 8 degrees; $t\,$, 70 degrees; $F\,$, 0.8; and $J\,$, 1, Mr. Willett's formula becomes:
$R=0.48G+0.08W+0.002C\,$.
This equation compares very closely with Mills, though less allowance is made for the cubic contents and more for the wall surface. The writer considers that if $J\,$, in Mr. Willett's formula, be taken as 1. for south and east exposures, it is sufficient in most cases to take it as 1.2 for north exposures. For such exposures, therefore, the same formula can be used as for south and east rooms and the radiation increased one-fifth.
Carpenter's rule for direct radiation.—Prof. Carpenter, in his work on heating and ventilation, has devised a formula which is very carefully derived. He first calculates the amount of heat lost from the room in question and then the amount of radiating surface necessary to offset this heat, using coefficients for heat transmission which he substitutes in his formula. According to Prof. Carpenter's method, the heat in British thermal units lost from a room for every degree difference in temperature between the inside and outside air is $h=nC\div 55+G+(W\div 4)\,$, in which $G\,$, $C\,$, and $W\,$ represent the quantities previously assigned them, and $n\,$ is the number of times the air of the room is to be changed per hour. Prof. Carpenter states that for direct radiation it is necessary to take $n=2\,$ for ground-floor rooms and $n=1\,$ for others, to allow for leakage of air. The quantity, $nC\div 55\,$ gives the number of heat units necessary to raise $nC\,$ cubic feet of air 1 degree in temperature. Prof. Carpenter states that the radiating surfact should be equal to $R=[(t-t_{1})\div (T-t)a]h\,$ in which $t\,$ is the required temperature of the room, $t_{1}\,$ the outside temperature, $T\,$ the temperature of the steam in the radiator, and $a\,$ ​is a coefficient of heat transmission from a radiator which varies from 1.7 for low-pressure steam heating to 1.9 for steam pressure of 40 pounds and 2.4 for steam pressure of 100 pounds. Taking the usual conditions of $t=70\,$ degrees and $t_{1}=-10\,$ degrees and with low-pressure steam heating, the factor, $[(t-t_{1})\div (T-t)a]\,$ becomes 0.324, so that with $n=1\,$ the equation for radiation surface becomes:
$R=0.324G+0.08W+0.006C\,$.
This formula differs very considerably, in the factors used, from those already cited, and it will be seen that it is based upon the coefficient of heat transmission for glass of 1 British thermal unit per square foot per degree difference in temperature, and the radiation surface due to the glass area is consequently much less than in the other formulas. The difference is more than made up, however, by the larger allowance for the cubic contents. In the opinion of the author, Prof. Carpenter's coefficient for glass is considerably too small, and his equation gives results which are too large for rooms having large cubic contents with comparatively small window surface, and results which are too small when the proportions are reversed.
Monroe's rule for direct radiation.—The author has recently deduced a formula which is a combination of Willett's and Carpenter's, and is as follows:
$R=(1.3G+0.25W+0.008C)J(t-t_{1})\div (T-t)a\,$.
In this the letters stand for the quantities previously assigned, $J\,$ being a coefficient depending upon the exposure (being unity in ordinary cases) and for the usual conditions as assumed in previous cases, this formula becomes
$R=0.42G+0.08W+0.0026C\,$.
In the following table are given the proportions of four representative rooms of an office building for which the writer was engaged to design the heating system, and for which the heating surface has been figured out according to Mills', Willett's, Carpenter's and the author's formulas, and also according to Mr. Baldwin's formula taking 65 per cent. of the glass equivalent surface.
Table of Coefficients of Heat Transmission. (British thermal units transmitted per hour per square foot of surface per degree difference of temperature.) :
| | | | | | Radiation Surface by | Radiation Surface by | Radiation Surface by | Radiation Surface by | Radiation Surface by | |
| Room | Exposure | G | W | C | Mills | Willett | Carp'ter | Monroe | Baldwin | Radiation Installed |
| 1. | West | 59 | 160 | 3360 | 54.5 | 47 | 51 | 44 | 49 | 46 |
| 2. | N. & W. | 118 | 312 | 2150 | 85 | 86 | 76 | 81 | 97 | 84 |
| 3. | NE. & E. | 88.5 | 420 | 4070 | 85 | 84 | 87 | 82 | 85 | 80 |
| 4. | NE. | 59 | 129 | 1730 | 44.5 | 42.5 | 40 | 46 | 47 | 40 |
$W\,$
It might be stated that in using the formula given, $t_{1}\,$ is to be taken 10 degrees above the lowest recorded temperature, and the factor, $J\,$, should be taken from 1.05 to 1.15 for severe exposures, and may also be increased 0.1 for ordinary brick buildings with wooden floor joists, and 0.2 for wooden buildings. The factor $a\,$ is to be taken at 1.7 for ordinary conditions of exhaust-steam heating. It may be increased somewhat for heating at higher pressures and for buildings with low-pressure heating and no power, in which steam pressure of 10 or 15 pounds may be carried, it may be made equal to 1.8. In such cases, also, the temperature, $T\,$, may be taken at 235 degrees. The factor a should be decreased where the radiators are of an unfavorable pattern or are unfavorably located, according to their relative heat-giving power, under such conditions as has been pointed out in Chapter III. The last part of the formula need be calculated but once for each building. The factor a may be taken as high as 2.8 in some greenhouses and in some factories in which wrought-iron pipe coils are used, which are quite an effective type of surface. Unless the coils are especially favorably located, however, the factor should be somewhat less than 2.8.
In the general application of the formula given above it will be noted that the expression $(t-t_{1})(1.3G+0.25W+0.008C)\,$ represents the total heat given off by the room, and it is equal to $R(T-t)a\,$, which is the heat given off by the radiation surface.
Mr. Wolff in his practice calculates the heat lost per hour from each room according to his diagrams previously given, with the allowance for exposure as shown thereon. He then (divides this amount by the number of British thermal units given off per ​square foot of radiator per hour, which he takes as 250 for a two-column radiator (bronzed) set under the window, but this factor varies within wide limits, as before described, according to the kind of surface used and the nature of the setting.
Indirect radiation.—With indirect radiation the heat lost from the glass and wall surface must be made up by the heated air coming in from the indirect radiator, and to accomplish this the entering air must, in cold weather, have a temperature considerably above the mean temperature desired in the room. The total heat lost by the room is $(t-t_{1})h\,$ where $h\,$ is the expression $(1.3G+0.25W+0.008C)\,$ and the volume of air required in cubic feet per hour is $V=(t-t_{1})hX58\div (T-t)\,$ where $T\,$ is the temperature of the air leaving the radiator. Now it is necessary for the indirect radiator to heat all of this air from the outside temperature to the temperature $T\,$, and the total heat required to be given off by the radiator is
$U=V(T-t_{1})\div 58=(t-t_{1})(T-t_{1})h\div (T-t)\,$
It will be seen that both $U\,$ and $V\,$ vary rapidly with a change in $T$, decreasing as $T\,$ is increased. If $t=70\,$ degrees and $t_{1}=-10\,$ degrees for extreme conditions, and if $T=150\,$, $V\,$ will be one-half and $U\,$ two-thirds of what they would be if $T\,$ were taken at 110. It is this fact that makes the indirect radiator quite a flexible device, for in extreme weather it is possible, by partially shutting off the air supply, to maintain easily the required inside temperature at the sacrifice of a small amount of ventilation. If $T=120\,$, $U=208h\,$, and $V=93h\,$; and with $T130\,$, $U=186h\,$, and $V=77h\,$. As a rule, it is safe to assume from 450 to 500 British thermal units per hour per square foot of surface for an indirect radiator, as will be seen by reference to the tests as described in the last chapter, and taking the former figure, with $T=120\,$, $R=0.46h\,$, and with $T=130\,$, $R=0.415h\,$.
Inasmuch as it has been found that for the same conditions of inside and outside temperatures $R\,$ for direct radiation $=0.325h\,$, it will be seen that according to this calculation from 28 to 40 per cent. more heating surface is required for indirect heating than for direct. The author has in his practice used these proportions for indirect radiators, usually installing about 30 per cent, more than for direct; although in some cases, where an exceptional degree of ventilation is desired and the room has a comparatively ​large amount of glass surface, more radiating surface is necessary. In such cases, and especially where a large amount of ventilation is desired, it is necessary to see that the quantity $V\,$, as obtained above, is equal to the amount of air required for ventilation. It will be found sufficient in all ordinary cases to change the air four times per hour, which is generally satisfactory for private houses; but where much entertaining is to be allowed for, six times per hour is better. In designing indirect radiators it is necessary to be very careful in the proportion of flues, but such details of construction will be considered in the next chapter.
In proportioning direct-indirect radiators the same rules apply as for the indirect type, although their action as direct radiators may be counted on to some extent. Where this kind of radiator is used in connection with an exhaust ventilating system very good results are obtained by using the author's formula for direct radiators, with an addition to the $0.008C\,$ of $2/3K\div 55\,$, where $K\,$ is the cubic feet of air per hour required for ventilation. This gives additional surface necessary to heat $2/3K\,$ cubic feet of air from the outside temperature to that of the room. The author figures on $2/3K\,$ (in some cases ¾), as in extreme weather the degree of ventilation may be somewhat reduced. For these radiators also, the factor $a\,$ in the formula may be taken as 1.9 or 2.