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<strong>the</strong> same incandescent lamp at <strong>the</strong> same<br />

d<strong>is</strong>tances as above, but in <strong>the</strong> absence of <strong>the</strong><br />

SunPipe, and <strong>the</strong> amplification factor AF of<br />

<strong>the</strong> SunPipe:<br />

Horizontal illuminance generated <strong>by</strong> <strong>the</strong><br />

75 W incandescent lamp<br />

L, cm l, cm Eh,l,il, lx AF<br />

23 0 5600 5.63<br />

33 10 2250 13.13<br />

43 20 1380 20.63<br />

53 30 950 29.19<br />

63 40 730 35.39<br />

73 50 520 46.79<br />

The light amplification factor AF <strong>is</strong><br />

given <strong>by</strong> Eh,l/Eh,l,il.<br />

For <strong>the</strong> measured values, <strong>the</strong><br />

CurveExpert 1.3 software generated <strong>the</strong><br />

recurrence functions using <strong>the</strong> Levenberg-<br />

Marquardt method of nonlinear regression<br />

for 23 regression models.<br />

The most accurately found form for <strong>the</strong><br />

horizontal illuminance function was:<br />

() ( ) c<br />

ϕ l = a l − b<br />

(7)<br />

if using <strong>the</strong> shifted power fit, with 0.9919<br />

correlation coefficient, where:<br />

a=39.358572<br />

b=-10.332781<br />

c=1.2648536<br />

The most accurately found form for <strong>the</strong><br />

vertical illuminance function was:<br />

() ( ) c<br />

−1<br />

ψ l = a + bl<br />

(8)<br />

if using <strong>the</strong> Bleasdale model of regression,<br />

with 0.8927 correlation coefficient, where:<br />

a=0.80990555<br />

b=-5.5413364e -005<br />

c=0.021229594<br />

Approach on numerical modelling<br />

Afterwards, <strong>the</strong> branched SunPipe<br />

system was supplied with daylight from <strong>the</strong><br />

diamond dome light collecting unit. The<br />

horizontal branch was located at three<br />

metres from <strong>the</strong> roof level and two<br />

situations were assessed:<br />

A – branch without mirror<br />

B – branch equipped with mirror<br />

The mirror was made of <strong>the</strong> same<br />

material as <strong>the</strong> SunPipe (Super Silver<br />

mirrored aluminium) and was installed at<br />

<strong>the</strong> entrance of <strong>the</strong> branch at 45 degrees<br />

rotation relative to <strong>the</strong> horizontal (see<br />

Figure 4).<br />

SunPipe main duct<br />

SunPipe branch<br />

Super Silver<br />

aluminium mirror<br />

Figure 4 Mirror-supplied SunPipe branch.<br />

The mean values of <strong>the</strong> illuminance<br />

measured within <strong>the</strong> ax<strong>is</strong> of <strong>the</strong> branch for<br />

<strong>the</strong> two situations, at <strong>the</strong> same level of<br />

external horizontal illuminance at roof level<br />

of 85,000, are shown in <strong>the</strong> table below.<br />

Branch illuminance, lx<br />

δ, cm without mirror with mirror<br />

0 8600 13,000<br />

17 8400 13,300<br />

27 9100 14,800<br />

37 8900 13,700<br />

For <strong>the</strong> branch supplied with light<br />

directly from <strong>the</strong> main light-pipe, without a<br />

mirror, <strong>the</strong> most accurate form for <strong>the</strong><br />

INGINERIA ILUMINATULUI 18-2006 43

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