A carbon arc lamp produces light between two carbon electrodes. As their tips are consumed, regulating gear advances one or both holders to compensate for the growing gap. The animation shows this burn-and-feed cycle; the calculator finds the combined holder travel needed from the two entered consumption rates.
Arc Light Regulating Gear Interactive Calculator
Vary carbon consumption rates, gap and feed timing to calculate total closing travel per cycle. Electrical arc stability is not calculated.
Equation Used
The total closing motion of the holders compensates for recession of both tips. Over one feed cycle, required closing travel equals the combined consumption rate multiplied by cycle time.
- Positive and negative carbon burn rates are constant during one feed cycle.
- One feed action restores the total gap growth caused by both electrodes.
- The selected gap and smooth-step limit are inputs, not verified operating limits for a lamp.
Compensating for electrode consumption
With the holders stationary, each receding electrode tip contributes to an increase in the gap. Feeding the electrodes toward one another closes that extra distance. A regulating mechanism coordinates the motion so the light source can continue while usable carbon remains.
The Science Museum Group records a late nineteenth-century lamp whose electromagnet controls clockwork and the position of the upper carbon rod. Other lamps used different sensing and feed arrangements. The rack-and-pinion drawing here illustrates holder advance rather than identifying every part of one historical patent.
Parts in the animation
- Carbon electrodes: their tips recede at the separately entered rates.
- Holders: support and advance the rods.
- Gap: grows during the burn interval and is restored during the feed event.
- Feed mechanism: supplies the combined closing travel.
In a differential regulator, current-sensitive and voltage-sensitive magnetic effects can act on the feed mechanism. Predicting its response requires the actual circuit and mechanism. Neither those coil forces nor the arc’s electrical behavior are represented by the consumption calculation.
A historical lighting mechanism
Regulating gear let carbon-arc lighting compensate for consumable electrodes. Museum examples preserve different answers to the same mechanical problem: how to advance the carbons as their tips recede. The Science Museum Group’s clockwork lamp record describes use of the bright source for large outdoor areas.
Not every carbon arc lamp had automatic feed. The museum also holds a hand-regulated example. Comparing these arrangements helps explain the purpose of the regulator without assuming a universal electrode diameter, current, gap or feed interval.
For studying an existing lamp, use its own documentation to identify its electrical supply, carbon specification and feed arrangement. This calculator can compare stated consumption rates; it cannot establish restoration settings, wiring, ballast values or a lamp’s suitability for operation.
Feed travel from the two consumption rates
Let r_pos and r_neg be positive and negative electrode consumption in mm/min, t the interval in seconds, g0 the starting gap in mm and s_max the entered step limit in mm.
Feed Rate = r_pos + r_neg. Feed Step = (r_pos + r_neg)t/60. No-Feed Gap = g0 + Feed Step. Step Excess = max(0, Feed Step − s_max).
Feed Step is the sum of closing travel across both holders, not necessarily the travel of either holder alone. If both advance, their contributions add. No-Feed Gap is the gap reached after one interval with no compensation. Step Excess compares the travel against the chosen limit; zero excess does not prove stable light, adequate electrical protection or smooth mechanical feeding.
Changing g0 changes No-Feed Gap alone. Changing s_max changes Step Excess alone. Changing a consumption rate or cycle time changes travel and gap growth. The rates are entered directly: this model does not infer consumption from current, carbon composition or diameter.
Worked example: one feed cycle
At r_pos = 4 mm/min and r_neg = 2 mm/min, Feed Rate is 6.0 mm/min. Choose g0 = 5 mm, t = 6 seconds and s_max = 0.5 mm.
Feed Step = 6 × 6/60 = 0.60 mm. Without feed, the gap reaches 5.60 mm. Step Excess is 0.60 − 0.50 = 0.10 mm. Restoring the starting gap requires 0.60 mm of combined closing travel.
Reducing t to 3 seconds gives a 0.30 mm step, a 5.30 mm no-feed gap and zero excess. Increasing t to 12 seconds gives a 1.20 mm step, a 6.20 mm no-feed gap and 0.70 mm excess. These are comparisons at constant entered consumption, not recommended timing for a particular lamp.
The animation repeats a single illustrative cycle with fresh starting carbon lengths. It does not predict full electrode life or a projector’s running time between carbon changes.
What different feed arrangements change
| Arrangement | Mechanical distinction |
|---|---|
| Hand regulation | An operator adjusts electrode position. |
| Automatic carbon feed | A mechanism advances one or both holders in response to its regulating system. |
| Continuous feed | Closing motion can compensate gradually for consumption. |
| Intermittent feed | Gap growth accumulates between feed events, requiring a corresponding step. |
For the same constant rates, shorter intervals require smaller steps. That arithmetic alone does not compare real regulator stability, lamp output, maintenance cost or service life.
Carbon-feed calculation questions
No. It only means calculated travel is at or below the limit you entered. The model contains no electrical arc or feedback-response calculation.
Recession of either tip increases the separation. The combined closing movement must compensate for their sum.
No. Feed Step is total closing travel. If two holders move, their inward travel adds to that amount.
Consumption rates are independent inputs. The initial gap changes the calculated no-feed gap, but this model does not make consumption depend on gap or current.
No. Those depend on the particular lamp and circuit. The calculation gives no conversion or power-supply design.
Not from this model. It does not simulate sound, discharge behavior, coil condition or friction. A generic hiss or hum is not enough to identify a fault or declare operation safe.
No. Usable rod length and changing consumption conditions are not inputs. The repeating animation is a single feed cycle.
No. They illustrate the calculation. Use documented values for any particular lamp you are studying.
Historical examples
- Science Museum Group: arc lamp with electromagnet-controlled clockwork.
- Science Museum Group: hand-regulated carbon arc lamp.
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