Approximations for spatial separation

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Approximations for spatial separation

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Ser TIT]-N21t2 no. 231 e , 2 BI,DG

NATIONAL RESEARCH COUNCIL CANADA

CONSEIL NATIONAL DE RECHERCHES

Spatial Separation

Approximations

fo,

by G. Williams-Leir A N A L Y Z E D Reprinted from

sfeq

Fire Technology, Vol. 2, No. 2 May 1966, pp. 136-145

Technical Paper No. 231 of the

Division of Building Research

OTTAWA August 1966

B U I L D I N G R E S E A I C H

- L I B R A R Y

;1;p rz 1970

litATroNAL *r*.\.an _{couNcr L}

NRC 9161 Price 25 cents

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CALCUL APPROXIMATIF DES DISTANCES DEVANT SEPARER LES BATIMENTS

par G. Williams-Leir

SOMMAIRE

Le calcul pr6cis des distances devant s6parer les biitiments en vue de pr6venir la propagation des incendies par la chaleur qu'6met un bdtiment en feu est assez laborieux. Le pr6sent expos6 donne des m6thodes de calcul rapide des distances ap-proximatives.

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REPRIIVIED FROM

FIRE TECHNOLOGY

V o l . 2 N o . 2 M A Y 1 9 6 6

copyrishr t965 NAT|ONAL FtnE PROTECITON AssoctATtoN

60 BATTTRYMARCH ST., BOSTON, MASS. O21IO

Approximations fo, Spatial

PRICE 90 CENTS EACH; Discounts on Quantily

Separation

G. WILLIAMS-LEIR

Diuision of Building Research National Research Council (Canada\

Strict application of the theory governing ignition by radiation would demand tedious calculations to determine distances be-tween buildings sufficient to prevent fire spread. The author pro-poses simple formulae that can be used with relative ease to esti-mate safe separation distances.

NLIKE some other problems in fire, the principles underlying the calculation of distances between buildings sufficient to prevent fire spread by radiation from window openings are thoroughly understood. They have been explained, for instance, by Bevan and Webster;l the equation appropriate to the situation to be discussed has been provided by Hamilton and Morgan2 and McGuire;s and Miss Lawa has explained its application.

M E T H O D S F O R D E T E R M I N I N G S E P A R A T I O N D I S T A N C E S

Given the equation, it should not be a difficult task to calculate what the permissible window area should be for a building in a given situation. If, instead, the windows are predetermined and the acceptable separation distances are sought, the equations can be solved only by graphical or iterative techniques. To solve the equation to any accuracy by hand would be laborious. Simplified formulae yielding an approximate solution could be of great assistance to an engineer or architect approaching this task conscientiously. There are several possible remedies.

INrr,unNcp Cnenr

The influence chart method may provide the simplest way of taking into account the combined effects of more than one separate radiating

Norr: This paper is a contribution of the Division of Building ReseSrch, National Research Counciil,^Canada, and is published with the approval of the Dfuector of the Division.

FT.14

136

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Spatial Separation 137 area. However, it will not be discussed further here. Readers are referred to the original description.s

Gnepnrcar- PnnsnNrantoN

A graphical presentation may take the form of Miss Law's Figures 6, 9, and 10, or of Figure 1 of this paper. For some purposes, these methods are satisfactory, provided that a reasonably large-scale graph and suffi-cient interpolation skill are available. For building code use, they leave something to be desired. The fact that it is necessary to legislate on build-ing separations at all implies that intelligent self-interest is not sufficient to ensure that they are adequate. Where litigation may be necessary for enforcement, methods depending on graphical interpolation may be con-sidered undesirable by some administrations. If a graph is desired, how-ever, Figure 1 is considered an improvement on any published to date. TeeuLAn PnnsprvrarroN

Spatial separations in the National Building Code of Canada have hitherto been expressed in tabular form. Such tables are open to objec-tions. Either the tables are very bulky, or the steps are wide and create injustices where the variable considered is on the unfavorable side of the step. It is difficult to see the underlying unity of the material presented. Painstaking proofreading is required if errors are to be avoided. If tables are to be used, Table L is more concise and more precise than those given in the National Building Code of Canada, 1965 edition.

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In view of the objections to the use of tables, interest has been shown in other modes of presentation. This interest has resulted in the develop-ment of simple formulae that provide approximate solutions to the equa-tion.

S I M P L E F O R M U L A E

It is hardly feasible to make provisions in a building code for every possible relationship of one building to another. It will be assumed that the important case is the straightforward one where the exposing building has a rectangular facade and the exposed building is parallel and opposite to the center of this facade. Windows are treated as a large number of in-dividually small openings uniformly distributed over the part of the facade considered. Certain less favorable window distributions can also be pro-vided for.

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Little need be said here regarding the principles that determine safe separations. Fire can. spread by radiation only when the radiator and the irradiated surface are in such a relationship to one another that a quantity

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a

Spatial Separation 139

known as the configwation factor - calculable from the geometry of the situation alone - exceeds a critical value. This critical configuration factor is the ratio of the radiant intensity for pilot ignition of the materials of the exposed building to the expected effective radiant intensity at the windows of the exposing building. The adjective "effective" implies that an intensity higher than the actual intensity at the windows may be taken in order to compensate for the effect of flames beyond the window frarne, a procedure first suggested by J. H. McGuire.G

The numerical value thirt should be assigned to the critical configura-tion factor is still, to some extent, a matter for judgment, but it is not the purpose of this paper to participate in a debate on this subject. If, at any time, new information should lead to a revision of this number, all tables depending on it must be recalculated, and new ones printed. On the other hand, we can continue to use the formulae or the graph (Figure 1) in the sarme way as before.

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The form of the configuration factor equation appropriate to the geometry described above 2,3 is

F _ u A S A

s + 4

(2) (3a) (4)

AR :99

_, 7f-approaches zero, as follows: AS A S + 4

+

arctan A s A for A

this equation reduces to a form that can be solved

where,

and

("

*l)

2

It was found by trial that this agrees well with the exact ( 2 - A P ; z : 4 ( r - q )

rRF

q : -_{' u}

(3b) equation for values of q less than 0.75.

As S approaches infinity, the equation reduces to the form

and this is found to agree well with the exact equation for values of g greater than 3.6.

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140 Fire Technology For the range in which q is greater than 0.75 but less than 3.6, an empirical equation has been fitted.

AR : (sr)'

Figure 2 shows the accuracy of these three equations in relation to the independent variables S rrra4. It is expressed in terms of the percentage deviation of a calculated separation distance, d, from the correct value.

It wiii be seen that where large separations are needed - *h""" 4 i" u small - the formulae are very accurate. For instance, over the range in which { i" l"r, than 0.05 and S is less than 8, the deviations are less than

u

F 1 per cent. They continue to be quite acceptable un to

7 : 0.4. Above this level, there are errors of 10 per cent or more, always on the safe side. This is not regarded as a drawback to the system for reasons that will be discussed.

For the convenience of the users, the equations have been rearranged and expressed in terms of

B : d : A - + {hw

A P P R O X I M A T I O N S A N D S M A L L W I N D O W A R E A S

Are the approximations too conservative for small window areas? As remarked earlier, the approximate formulae are conservative in the range

F

where _ i" greater than 0.4, by comparison to Equation 1. Two points_u should be noted regarding this.

. The range is one for which relatively small separations are needed. Thus, in most cases, the absolute deviation from the exact equation will only be a short distance - rarely more than 5 ft.

. The exact solution assumes that the windows are uniformly dis-tributed over the facade, and all other window distributions will be more unfavorable. In the range under discussion, the proportion of windows is low, and it is increasingly unlikely that they will be uniformly distributed.

For example, consider the case in which F : 0.15, u : 0.25, and F

- :0.6. With windows distributed uniforunly over a facade 20 ft by 125 u

ft, a separation of 72.5fbwould be sufficient, but the approximation calls

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Spatial Separation l4l for 16 ft. However, 16 ft is the appropriate separation for a single window

12.5 ft square; therefore, to justify a smaller separation, the windows must either be much smaller than this or be smaller and spaced about 30 ft apart. A strip window 5 ft high across the entire frontage would demand L7 ft. It is hard to imagine a plausible window arrangement that would need much less than 16 ft.

V A L I D I T Y O F " D I S T R I B U T E D " W I N D O W S F

It has been shown that, so long as : is less than 0.35, no serious error arises through treating windows that are actually finite in number

B o t o t 2 5 o 1 6 o . 2 0 5 o 4 o.6 3 o . 8 F /, , / v t ^ . z o o 3 2 s

Figqre 7. Parameter B for colculating sep-arat.ions needed to preuent ftre spread by

rdd.ratlon-P E R C E N T A G E E R R O R

L O W H G B

0 5 0 5 l o u p

refWri.l

Figure 2. Accuracy of approxintations.

and size as though they were uniformly distributed over the facade.6 While the fact is not of the highest importance, there must be a region where the use of the distributed window concept introduces errors on the wrong side. In this region, the errors of the approximation will tend to compensate and perhaps overcompensate somewhat.

Where doubt arises on this point and it is still desired to avoid the labor of exact calculation, the separation for the largest window alone should be calculated. This sets a lower limit to the separation for the entire facade. In extreme cases where, for exampL, ! isgreaterthan 1'5

u

responding to windows separated from one another by more than twice the distance between buildings - the effect of other windows may be disregarded,4 and this separation adopted for the entire facade.

One might think that an upper limit could be set by combining the areas of all the windows into one square opening and calculating the

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142 Fire Technology separation for that opening. No case, however, has yet been found in which this would lead to separations less than the approximations provide. Where the proportion of window area is so small that the distributed concept breaks down, the approximations still provide a reasonable solu-tion. For example, if tr'is 0.07 and there are 7 per cent *iodo*", 4 i" unity; and Equation 1 would permit openings in contact with the radiator-a situradiator-ation in which even smradiator-all windows would permit ignition. For this case, the approximations would demand a separation of 17 ft for a 50-ft square facade. This would safely allow for four S-ft square windows spaced 34 ft apart, or a larger number of smaller windows.

H O W T O D E T E R M I N E S E P A R A T I O N D I S T A N C E S

The first step is to find the parameter B, using any one of the three methods described below - Approximate Forrnulae, Graphical Deter-mination, or Tabular Determination. Once B is known, the rest of the calculation is as follows. If the facade area, hu), is given and the minimum permissible separation distance, d, is sought, substitute values for B, h,

and w in the equation

d : Bfnr'u. (7)

If, however, a separation distance is given and the maximum permissible facade area, hw, is sought, use the equation

n* : (!l'.

_{\ a / '}

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Lot line separation is one-half of the building separation or d/2.

The area of the largest permissible single window in the facade may be found by treating it as a facade of any desired shape for which z equals 1. Once the largest window is known, it may be subdivided into smaller ones without restriction. This provides a conservative preliminary estimate of how much window area there may be in a facade. Facade for this purpose means the smallest rectangle on the face of the building that encompasses all the windows.

After applying the procedure described to the facade, a series of smaller rectangles should be drawn within the facade so as to increase the propor-tion of windows by including as much window area and as little wall area as possible. The procedure should be repeated for each of these rectangles until it is clear that no smaller area demands a greater separation. The greatest separation found is the safe one.

Where, for legal purposes, separation from the lot line is required, it should be half the safe building separation distance. This rule is discussed in references 4 and 6.

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Spatial Separation f43 AppnoxrrvrerE FoRMUT,AE

In using the approxqnate formulae, first calculate .E and g from the expressions given in the list of nomenclature at the end of the article. If q is less than 0.75, use Equation 9 to calculate B.

B :

A rough preliminary approximation of this is B : 0.52{u/F. If q is greater than 0.75 but less than 3.6, use Equation 10 to calculate B. One way to obtain the fourth root used in Equation 10 is to take the square root of the square root.

(e)

i l-"'

n : o.t+ll

,*-I

Finally, if q is greater than 3.6, use Equation 11.

B : --!: FJEN

Gnepnrcal DnrnnMrNatror.t

To use the graphical method, first divide F by u and calculate S (see nomenclature list). Note the point at which these values intersect on the graph and estimate the approximate value of B on the third scale.

Taeur-ln DnrnnurNanroN

To use Table 1, first calculate the width to height ratio of the expos-ing facade. Then, measure the area of windows or other unprotected openings, and express this as a percentage of the facade area. Assess whether the exposing building represents a low or a high hazard. Locate the percentage of windows in the appropriate hazards column, and read B in the column that corresponds to the width to height ratio.

The figures in the table are based on configuration factors, ,F', of 0.035 for high hazards and 0.07 for low hazards. These values are those adopted on the recommendation of J. H. McGuireo for the National Building Code of Canada, Subsection 3.2.4, 1965 edition. If a different configuration factor value were to be adopted, the table would have to be recalculated. A computer prograrn, which renders this a simple task, is on file at the National Research Council Fire Laboratory. Authorities requiring such a table are invited to consult the author.

A more concise table could readily be prepared by omitting alternate values of each argument, for example. The user might have to pay a small price in additional interpolation. The function is given to greater precision than is ever likely to be necessary in building regulations. and it would rarely make appreciable difference in practice if the tabular values were

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n ( 1 + { t - n )

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144 Fire Technology rounded off to three significant figures when the first is 1, and to two sig-nificant figures in other cases. The table is calculated at exact,logarithmic

intervals of S, but the column headings are rounded. C O N C L U S I O N

The separation distance necessary to prevent fire spread by heat radi-ated from a burning building can be obtained by solving Equation 1, but this presents some difficulties. This paper derives forrnulae - Equations 9, 10, and 11 - that are simple to apply and are approximately equal to the exact equation. Figure 2 shows their accuracy. Where eaorsi would arise from applying the equation to facades in which windows are not evenly distributed, the formulae tend to compensate for these errors.

Solutions of the exact equation can also be presented graphically or in tabular form.

Any one of the three presentations is suitable for use in building codes. Each can stand alone as a possible method for deriving safe separation

distances.

N O M E N C L A T U R E

d

: :, a p€fameter

\/ nw

: Safe separation distance

: Critical configuration factor according to occupancy and hazard (to be specified in the bylaw, e.9., 0.035 for high hazards or 0.07 for low hazards) : Height of building rRF : -, a parameter u R : _{, R shape factor} A : h w d2 B d F h w + -w h 2 h w

- " or;, whichever is greater w n

: Unprotected openings as a fraction of facade area;

. Der cent windows

I A _'

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Spatial Separation 145 ru : Width of building

r -- 3.L4

Nors: ft, w, and d must be in the same units. Other quantities are dimensionless.

R E F E R E N C E S

r "Radiation from Building Fires," R. C. Bevan and C. T. Webster, National Building Studies Technical Paper No. 5 (H.M. Stationery Office, London), 1950.

2 "Radiant Interchange Configuration Factors," D. C. Hamilton and W. R. Morgan, U.S. National Advisory Committee for Aeronautics Technical Note No. 2836, De-cember 1952.

3 "Heat Transfer by Radiation," J. H. McGuire, Fire Research Special Report No. 2 (H.M. Stationery Office, London), 1953.

a "Heat Radiation from Fires and Building Separation," M. Law, Fire Research Technical Paper No. 5 (H.M. Stationery Ofrce, London), 1963.

6 "fnfluence Charts for Configuration Factors," C. H. Jones, CIB 64/31 (C.A.) (Commonwealth Experimental Building Station, Sydney, N.S.W.), August' 1962.

-6 "Frle and the Spatial Separation of Buildings," J. H. McGuire, Fire Technology, Vol. 1, No. 4 (November 1965), p 278.