Hotwire Math

From CPFWiki

See Output Measurements for MSCP to Lumens conversion.

The formula for halogen lumens re-rating is as follows:

Lr = (Va/Vd)^3.5*Ld, where Lr is re-rated lumens, and Ld is design lumens, and Vd is design voltage and Va is applied voltage.

The formula for halogen lamp life re-rating is as follows:

Lr = (Vd/Va)^12*Ld, where Lr is re-rated life, and Ld is design life, and Vd is design voltage and Va is applied voltage.

The formula for halogen current re-rating is as follows:

Ar = (Va/Vd)^0.55*Ad, where Ar is re-rated current, and Ad is design current, and Vd is design voltage and Va is applied voltage.

The formula for halogen CCT re-rating is as follows:

CCTr = (Va/Vd)^0.317*CCTd, where CCTr is re-rated CCT, and CCTd is design CCT, and Vd is design voltage and Va is applied voltage.

[[1]]

To find voltage sag:

Va = (Aa/Ad)^1.818*Vd, where Aa is applied current, and Ad is design current, and Vd is design voltage and Va is applied voltage.

To find applied voltage from lamp life:

Va = Vd/((Lr/Ld)^(1/12)), where Lr is re-rated life, and Ld is design life, and Vd is design voltage and Va is applied voltage.

To find applied voltage from lumens:

Va = (Lr/Ld)^(1/3.5)*Vd, where Lr is re-rated lumens, and Ld is design lumens, and Vd is design voltage and Va is applied voltage.

Added 3-15-06 Incandescent lamps have a predictable change in behavior with the change of input voltage.

These formulas are applicable for a wide range of lamps in the range of 90-110% of rated voltage.

All of these formulas use the rated value as reference.

Life = v^-13(I'm not kidding, thirteenth power) (Interpretation. Let's say the lamp is rated for 10v 1000 hours life. If 11v is applied, the predicted life is 11v, the life can be predicted by (11/10)^-13 =0.2896. This means that predicted life at 29% of rated life)

Lumen output = v^3.4

Power draw= v^1.6

CCT(in kelvins) v^0.42

All of these formulas came from a lighting engineering reference book.

Ok, now lets look at real example. 4.8v 1.04A 5W Xenon bulb rated at 100 lumens output, 100 hour life.

Most 4 cell lights uses a 4.8v bulb, because alkaline batteries quickly drops to 1.2v/cell. When it is driven at 6v such as with fresh alkaline batteries, the aforementioned bulb:

lasts 5.5 hours makes 214 lumens uses 7.15 watt 53% gain in efficacy

An astonishing output that is over twice the rated lumens, but the bulb life is reduced by 95%. This is how manufacturers get you jaw dropping lumen figures. This also explains the very sharp drop on the graphs on flashlightreview.com site.

Of course, it isn't long before battery voltage is reduced to ~1.2v per cell, so the lamp get an acceptable life. if you were to do a mod like 5 x NiMH to try to maintain 6V, the lamp would likely only last through one charge.

Looking at the graph from the book that covers from 40 to 140% rated voltage, let's see what happens when the

voltage drops to 80% the rated(this is when battery voltage drops to 1V per cell(4v total), giving approximately 83% voltage to 4.8v rated lamp)

45% output 70% power consumption

65% the rated (0.8v per cell, 3.2v to 4.8v bulb)

20% output 50% power consumption