AGL Lamp Life Formulas

AGL lamp life formulas: a power law fitted to two lamp life readings, the life at another circuit current and the lamp replacements a circuit needs each year.

The formulas

Lamp life rises steeply as the circuit current falls. Two readings from the lamp data sheet, (I1, T1) and (I2, T2), fix a power law, and the life at a third current I3 follows from it. n is the number of fittings and H the hours a year at I3. Rated life is an average, so some lamps fail earlier. The curve is exact only at the two readings: between them it is a fair estimate, and beyond them it is an extrapolation that should be treated as indicative. The readings below are examples and not data for any lamp, so use the readings for your own lamp, or the manufacturer's curve if there is one.

Worked example: 1,000 h at 6.6 A and 2,000 h at 6.1 A, evaluated at 6.3 A

The circuit has 60 fittings that run for 4,380 hours a year.

1. m = ln(2,000 / 1,000) / ln(6.6 / 6.1) = 8.798
2. T3 = 1,000 × (6.3 / 6.6)^(−8.798) = 1,506 h
3. T3 / T1 = 1.506 times the first reading
4. Replacements = 60 × 4,380 / 1,506 = 174.5 a year

Beyond the readings: 5.2 A

1. T3 = 1,000 × (5.2 / 6.6)^(−8.798) = 8,147 h, which is below the lower reading, so it is an extrapolation
2. Replacements = 60 × 4,380 / 8,147 = 32.26 a year

Life from the same two readings

Frequently asked questions

Why does a small drop in current extend the life so much?

The filament runs cooler, and the life of a filament rises very steeply as its temperature falls. The exponent m shows how steep the curve is for your lamp.

Can I use two readings that are far apart?

It gives a rough curve. Readings that are close to the current you want give a better estimate than readings far from it.

Why is the result an average?

The rated life is the average of many lamps. Some fail earlier and some later, so keep spare lamps and plan the replacements on the average.

What does the warning about the order of readings mean?

If the life rises with the current, m is negative, which is the wrong way round. Check that each current is paired with its own life.

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