This blog, by Richard Fellows, discusses historical questions concerning Paul's letters, his co-workers, Acts, and chronology. You can visit my web pages here, but note that they are not kept up-to-date.

Monday, December 28, 2009

Why did Eutychus fall asleep? The physics of heating and ventilation

Acts 20:8-9 (NRSV) reads: "[Paul] continued speaking until midnight. There were many lamps in the room upstairs where we were meeting. A young man named Eutychus, who was sitting in the window, began to sink off into a deep sleep while Paul talked still longer. Overcome by sleep, he fell to the ground three floors below..."

Why does Luke mention the lamps? Did they contribute to the accident in some way? Some have suggested that the lamps made the air 'heavy' and that this made Eutychus sleepy, but I am not aware of any scientific assessment. Larkin suggests that "the boy must have tried to catch the night air by sitting on a windowsill". Haenchen and F.F.Bruce assumed that the air would be freshest by the window. But if the air was freshest there, why did he fall asleep?

I will argue that the lamps would have made the room comfortably warm and may have caused a soporific concentration of carbon dioxide in the air. I will also argue that the air may well have been more sleep-inducing at the window than elsewhere in the room.

Lamps produced a lot of heat and relatively little light. In a scientific experiment an oil lamp produced 60W of heat and only 10 lumens of light. A modern incandescent 60W light bulb produces the same heat, but gives 870 lumens of light. Along with its 60W of heat, the oil lamp produces 0.0084 cubic meters of carbon dioxide per hour. This is the same amount of heat and carbon dioxide as a typical person (modern adults produce 75W of sensible heat).

From what I can gather, upper floor rooms in insulae (apartment blocks) were typically 4m by 5m. We can imagine there being 20 people in the room and 30 oil lamps (or equivalent). The lamps would give a third of the light of a modern 60W bulb, so the room would still be dimly lit by our standards. Now, the people would then emit 1.2kW of heat and the lamps would produce 1.8kW, making a total of 3kW. Now, the incident occurred at the end of April or the beginning of May. At this time of year in nearby Istanbul the average daytime maximum temperature is 18C, and the nighttime minimum is 10C. Now, we do not know whether the room in question was constructed of brick or wood, so let us consider each case in turn.

Brick construction
Brick has a high volumetric heat capacity so the building's temperature will have varied little between day and night. The room will therefore have been at about 14C before the arrival of the large number of people and lamps. I have performed a computer simulation to calculate how much the room would warm with 3kW of heat starting at dusk (8pm). The model predicts that by midnight the effective temperature in the room would be a cozy 23C. Therefore the people and lamps are sure to have made the room comfortably warm and this may have contributed to Eutychus's drowsiness.

It is reasonable to suppose that they would have kept the door(s) and window(s) closed (for privacy and to avoid disturbing the neighbors) until the room had warmed up. I do not have a good estimate of what the natural air infiltration rate would have been. Well sealed modern buildings can give as little as 0.4 air changes per hour. If the room in question had 2 air changes per hour, the 30 lamps would have created a carbon dioxide (CO2) concentration of 4800 parts per million (ppm). This much CO2 could well have contributed to Eutychus's sleep since complaints of drowsiness occur at concentrations as low as 1000-2500 ppm. Also, since warm air rises, we should expect the CO2 concentration to be higher for Eutychus at the window, than for the others, who would have been at a lower level. Thus, it seems plausible that CO2 was a factor in inducing Eutychus's sleep. CO2 buildup would be possible only if the window was closed, but Eutychus would still fall out if the shutters or window covering were not secured. The image above is of carbonized wooden shutters in Herculaneum.

Wood construction
If the room in question was made of wood it is likely to have started the evening at a temperature above 14C since it would have gained heat from the outside during the day. It would also have warmed up quickly after the people and lamps arrived. By midnight the occupants would have needed to open the window(s) and perhaps door(s) to induce a considerable amount of ventilation to prevent over-heating. This ventilation would prevent a CO2 problem, but the temperature distribution in the room would be an issue. The through-draught needed to prevent over-heating would make the room cool at the end of the room where the fresh air entered, and warm at the end where the air left. Someone sitting at the warm end of the room might well start to feel sleepy and move to the nearest open window in search of cool air. Unfortunately the air in that window would be warmer, not cooler. To find the cool, fresh air, Eutychus would have needed to cross to the other side of the room where the cool air entered. Now, by midnight the ambient temperature will have been lower than the temperature of the air in the building, so there would have been a tendency for air to enter the building on the ground floor and rise by buoyancy and exit through the window on the third floor where Eutychus sat. Therefore, Eutychus is unlikely to have found fresh air at the window.

If the room was crowded, the window may have been the only available spot for Eutychus to sit. Alternatively, when he started to feel sleepy he may well have moved to the window in search of fresh air. Like Haenchen and Bruce, he may not have thought through the physics of air movement in a three floor building, for the air was probably warmer and richer in carbon dioxide at the window than elsewhere in the room. The heat produced by the lamps, and perhaps the carbon dioxide, will have helped to induce Eutychus's sleep and this may be why Luke mentions them.

To do a more thorough study we really need someone with expertise in ancient building architecture to collaborate with someone who is expert in thermal modeling of buildings and computational fluid dynamics (CFD). Any volunteers?

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