# Gendaymtx, proper energy balance

Dear all

I’m running a series of 3PM daylight studies and 2PM façade radiation studies, in the same fashion as presented in: https://www.radiance-online.org/learning/tutorials/matrix-based-methods

Hence for illuminance based simulations I run:

gendaymtx -O0 xxx.wea > xxx.smx

… (rfluxmtx, rfluxmtx, dctimestep)

rmtxop -fa -c 47.4 119.9 11.6 xxx.rgb > xxx.ill

And for the irradiance based simulations I run:

gendaymtx -O1 xxx.wea > xxx.smx

… (rfluxmtx, dctimestep)

rmtxop -fa -c 0.265 0.670 0.065 xxx.rgb > xxx.wm2

Since I’m only interested in illuminance and irradiance, color information can be neglected. Post processing in only one channel enables me to speed up the dctimestep- rmtxop-daylightmetrics computations, due to the smaller matrix/vector sizes e.g. making a CUDA based implementation.

The default settings of the gendaymtx sky color is: “-c 0.960 1.004 1.118”. There is an example with “–c 1 1 1” yielding an uncolored sky, but what is the constraints on the “-c” settings in gendaymtx when it should yield a proper energy balance? And subsequently how is “-c 0.960 1.004 1.118” derived?

Any help understanding this is highly appreciated.

Best regards Tobias

The numbers in `-c 47.4 119.9 11.6` and `-c 0.265 0.670 0.065` relate to the weighting applied to the R, G and B (respectively) channels to account for the V-Lambda function (Wikipedia link, which I think does an okay job here).
I believe the sky color `-c 0.960 1.004 1.118` relates to a blue sky as the blue channel is slightly higher than green and red. Multiplying those numbers with the individual weighting factors for the V-Lambda function will yield 1 or 179.

``````0.265*0.960+1.004*0.67+1.118*0.065=0.99975
47.4*0.96+119.9*1.004+11.6*1.118=178.852
``````

For illuminance calculations as long as you still get a value of 1 or 179 with the above coefficients, I think you’d be fine with regards to energy balance. I guess in the case of irradiance calculations, the photopic efficiency part isn’t really relevant, so your coefficients of `-c 1 1 1` should be fine.

Regards,
Sarith

PS: The number 179 relates to the luminous efficacy of equal energy white light when integrated from 380nm to 780nm. Luminous efficacy is defined as per 683lumens/W at 555nm (green). I tried to do the math and derive that 179 for myself using spectral data for V-Lambda at 5nm intervals. I got around 180.21, which I guess is close enough (see cell 88C in https://www.dropbox.com/s/02n5kz928yud7b6/RadianceLumEff.xls?dl=0).

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