# How badly could someone be injured by concentrated sunlight?

Recently-ish, I stumbled across an interesting short story (by way of Science Fiction & Fantasy Stack Exchange) where a soccer referee is apparently incinerated by concentrated sunlight.

Where the referee had been standing, there was a small, smoldering heap, from which a thin column of smoke curled up into the still air.

This is accomplished in-story by some 50 000 reflective tinfoil program covers, each about the size of a tabloid sheet.

What got me interested (physics is one of my peripheral interests) is the feasibility of this method in the real world. Wikipedia says a tabloid sheet is $279\;\mathrm{mm} \cdot 432\;\mathrm{mm} = 120528\;\mathrm{mm}^2 \approx 0.121\;\mathrm{m}^2$, giving fifty thousand people with a program each a total of $6026.4\;\mathrm{m}^2$ to work with. (Adjusting for less-than-perfect aim, I'd say closer to about $5000\;\mathrm{m}^2$.) If you could redirect that much sunlight at about a person's surface area, how much power would that be? What damage could you cause?

He couldn't have felt much; it was as if he had been dropped into a blast furnace...

Could that amount of power actually incinerate someone?

It occurs to me that the Wikipedia summary of the story (quoted on SciFi.SE) states only that the referee "collapsed and died". If incineration isn't possible, could the energy involved still be lethal by other means?

• Considering the amount of coordination required to get a ship to smoulder, it's unlikely the fans could accidentally aim all of their program covers on such a tight spot. Jun 24, 2014 at 13:25
• As a data point, the THEMIS power plant was using 11800 m^2 of mirrors and could produce about 2 MW of electricity. Of course there are some loss... with 1 MW, you need 21 seconds to heat up 80 litres of water from 37ºC to boiling point (100ºC). Since 75% or so of a human being is water, one can conclude that "vaporization" is a narrative exaggeration for dramatic effect -- but serious health consequences are a definite possibilities. Jun 24, 2014 at 14:15
• That said, we burn ants on the sidewalk with just a magnifying glass. It wouldn't vaporize him, but the ref could be set on fire.
– Jim
Jun 24, 2014 at 18:31
• The story says that it look "long seconds", which isn't precise but feels like more than a second and much less than a minute. Jun 24, 2014 at 20:15
• @Byte56 It's not accidental in the story - we're talking fifty thousand soldiers with prior training. They're all actively trying to injure the ref. Jun 24, 2014 at 21:47

At the radius of the earth, the solar irradiance is approximately $1.412\;\mathrm{kW/m^2}$, giving a total power hitting the foil sheet (assuming normal incidence) of $\sim7.06\;\mathrm{MW}$. The average human in America is around $1.7\;\mathrm{m}$ tall, and somewhere around $0.5\;\mathrm{m}$ wide, making his cross sectional area around $0.85\;\mathrm{m^2}$. This means that the human will have an irradiance of around $8.3\;\mathrm{MW/m^2}$ (again assuming normal incidence, increasing the angle of the foil with respect to the sun will decrease total power, and hitting the man from any angle will increase the power he feels locally). Now, this is where it gets tricky. The blackbody spectrum of the sun peaks in the visible, and is absorbed strongly by the atmosphere in the UV and decays in the infrared. Tissue ablation requires somewhere on the order of $2\;\mathrm{MW/m^2}$ for an infrared diode laser peaking at 1470nm (see "Optical Sealing and Cutting of Blood Vessels Using Near-Infrared Laser Radiation." by Sarah Rosenbury). Now, that is from all the power directed at an absorption peak of the water absorption spectrum. Thus, because the absorption of human tissue in the visible is predominantly due to melanin and blood (hemoglobin-Hb), scattering will occur before absorption (except in the hemoglobin and melanin molecules) and more power will be lost. Not to forget mentioning that the penetration depth (how deep the light goes) is at best a couple of millimeters. Thus, while you are likely to cause burns, light his clothing on fire, and be generally painful, the damage would only be skin deep. In order to penetrate more deeply one would need to use gamma rays (which is difficult due to atmospheric absorption) or something with a longer wavelength like microwaves (but they have very low energy per particle so it would require MUCH MUCH more). So as a final answer to your question, no. It is not possible to instantly vaporize someone under those conditions, let alone incinerate them.

• So much data to come up with the wrong answer. Jun 24, 2014 at 18:25
• A solar over can reach temperatures of 150C with about 2 sq m area. Focusing the sunlight from 5000 sq m into a 1 sq m could easily generate temperatures higher than 100C. On a good sunny day, this would be enough to vaporize someone. Jun 24, 2014 at 18:41
• There must be a typo in that last comment. Maybe a mild sunburn.
– DWin
Jun 25, 2014 at 1:04
• Would the melanin and hemoglobin still exist/have the same effect after you have charred away the skin? Yes the human body has a lot of mechanists to deal with sunlight, but i am not sure that they still work when your body is covered in severe burns. And after you have charend enough to light the fat, hair, and clothes on fire, you can get other energy sources added to the equation. Jun 25, 2014 at 3:36
• @JonathonWisnoski Once the skin is charred, the optical penetration depth drastically decreases, and it becomes far harder to ablate the charred area, thus the melanin and hemoglobin actually no longer really contribute to the absorptive effects, but would still contribute to thermal properties. If charring were actually obtained, its highly likely that the target would die, but given the fact that the skin is not predominantly water (actually its mostly collagen) and light has an average penetration depth of around 3 microns, I doubt he would be fatally injured before he moved out of the way. Jul 20, 2014 at 11:41

On your figures, it's going to depend on conditions, and also critically on what the referee was wearing; but in general it would certainly put the hapless referee in very dangerous position. It probably wouldn't be quite so dramatic as in the tale.

On a typical day, let's say the Sun delivers $750{\rm\;W\;m^{-2}}$ intensity when straight overhead. Scale it by $\cos(\pi/3)= 1/2$ for a typical latitude. Scale it again by $1/2$ to account for the fact that the foils must be tilted roughly 45 degrees to aim the light. And add a further factor for random losses, so we assume that a tenth of the sunlight reaches its target. You still have $500 \times 750{\rm\;W}$ reaching the hapless fellow: that's $350{\rm\;kW}$. Let's assume a body is mostly water: a 70kg body therefore has a heat capacity of $280{\rm\;kW\;K^{-1}}$. So that heat loading, if all absorbed by the fellow's body, would lead to a temperature rise of a couple of degrees celsius a second. That's not good. As you can see, if some of my scale factors were increased for more "favourable" (to the killers) values, we might get a third of the light trained on his body: six degree celsius rise per second. That would very swiftly be lethal.

Now we come to what the fellow were wearing. And also his skin colour. his will be critical. If he were clad in a highly reflective spacesuit, he might fare pretty well. If he were wearing white and were quick witted, he might have the time to duck down and crawl away. If what he were wearing were wool or fire retardant, even better.

You would need a bit more light than that arising from the conditions in the tale to get a dramatic "vapourisation", but it would not be good for the referee.

It's interesting to compare my answer and Chris's as I've just looked at heat loading whereas Chris is looking at more specific safety limits on optical intensity for skin. The two answers roughly agree in their conclusions, although I should think that "skin deep damage" to a large fraction of the body could well be lethal, as any clinician or nurse in a burns unit will tell you.

• Wikipedia just says the referee "collapsed and died" (now edited into the question). Given the apparent lethality of lots of heavy burns, it does seem plausible that he could have been knocked off this mortal coil - if not quite so dramatically as in the story. Jun 24, 2014 at 2:17
• Aren't you missing a factor the story says 50.000 foils. Jun 24, 2014 at 3:29
• @annav The calculations in the question present the total useful surface area as $5000\;\mathrm{m}^2$. Divide by ten as stipulated in the answer, and you have a factor of 500. Jun 24, 2014 at 3:59
• @annav I don't think so: I'm scaling the total foil surface area, calculated to be $5000{\rm m^2}$ by the OP for the 50 000 foils. This ends up with all the losses to be $500{\rm m^2}$ effective, which is what I multiply by the Sun's irradiance. $5000{\rm m^2}$ and 50 000 people is a co-incidence wrought by each foil's surface area Jun 24, 2014 at 4:03
• OK, my estimate from lens damage comes up same order of magnitude to your estimate , with losses. A factor of two could enter on all of my estimates. ( I do not know the focal point dimensions needed for a burn , must depend on the power of the lens of course ) Jun 24, 2014 at 5:15

A lens can burn badly at the focal point, one can easily start a fire and get a bad burn if one is stupid enough to focus for long on skin.

A $5 \ {\rm cm}$ diameter lens concentrates the power from about $2 \times 10^{-3}$ meter square. Taking the conservative $750 \ W/m^2$ (it can be $1200$ in my area) a power of $750\times (2 \times 10^{-3})$ on $2 \rm mm^2$, or $1.5 \ W$ on $2 \ \rm mm^2$ of skin or paper or wood, sets fire and burns flammables.

If the cross-section area of a man is $0.85 \ \rm m^2$ as Chris estimates, to burn with the power similar to a lens such an area , one should send $\sim 4.3\times 10^5$ watts on that area ($0.85/2\times 10^{-6}$).

So if megawatts were concentrated on the man, depending on the time, first his clothes would burn, then the skin would dry up and burn. Chris' solution gives megawatts (8.3) to cover this estimate, and I suspect the authors used the lens example to get at realistic numbers and needed 50,000 people in the stadium sun side..

About Archimedes setting ships on fire:

A test of the Archimedes heat ray was carried out in 1973 by the Greek scientist Ioannis Sakkas. The experiment took place at the Skaramagas naval base outside Athens. On this occasion 70 mirrors were used, each with a copper coating and a size of around five by three feet (1.5 by 1 m). The mirrors were pointed at a plywood mock-up of a Roman warship at a distance of around 160 feet (50 m). When the mirrors were focused accurately, the ship burst into flames within a few seconds. The plywood ship had a coating of tar paint, which may have aided combustion. A coating of tar would have been commonplace on ships in the classical era.

Did myth busters use tar coated ships? Tar was the only water resistant material known to the ancients for waterproofing boats and ships. In addition the Mediterranean has very dry sunny days most of the summer, the watts/metersquare can reach 1200, ( good for solar panels)

Moral: Do not believe whatever myth busters say uncritically.

• In Greece we often get summer forest fires blamed on broken bottle bottoms that act as lenses on dry weeds and start the fires. I have not tried it :) but if I find a broken bottle bottom this summer I might . Jun 24, 2014 at 5:04
• +1, especially for the Archimedes test. Myth busters (what little I've seen) seem to do very little history research: as you say, tar was one of the few waterproofing materials around at the time. I'm not a big fan, mainly because of their obsession with explosives and several family members of mine died messing with these (farmers who freely used explosives here in bygone years to remove treestumps and the like). I recall also reading a calculation many years ago by Theodore Stephanides grounded on assumptions of tar and mirrors of the era: he reached the same conclusion as Ioannis Sakkas. Jun 24, 2014 at 7:48
• @WetSavannaAnimalakaRodVance . Tar was still widely in use in Greece when I was growing up. On beaches where there were fishing boats one had to be wary of stepping on tar left over from patching the fishboats. Now they use a type of fiberglass. Jun 24, 2014 at 7:53
• Yes and although I like the idea that Mythbusters makes science more widely accessible (even though I don't personally like it), I think I would tend to believe someone as careful and widely learned as Stephanides more. There's one other factor Mythbusters didn't account for, and that's the motivation begotten by the threat of death. Archimedes was indeed slain, as you likely know, at the end of the siege of Syracuse. Jun 24, 2014 at 9:31
• I would find it far more plausible that mirrors were used to impair the vision of people on attacking boats, and that someone who was blinded by the light accidentally set his own boat on fire, than that the mirrors were able to achieve adequate focus to ignite boats directly. If a sun-blinded sailor set his own boat on fire (e.g. while preparing to launch a firebomb at the shore) observers in other boats who saw the sun focused on the boat and then saw the boat on fire could quite plausibly believe that the sunlight itself was the source of ignition, whether or not it was. Jun 24, 2014 at 17:26

There's a solar furnace in France that can melt steel. I don't know the collection area of it, but it's probably larger than 5000 m${}^2$. Tin foil tablets ... I don't know. But it sounds like the sci fi story is not outlandish.

• The ancient greeks considered a similar weapon and thought to use it to ignite ships, but it proved too difficult to build (and wouldn't effectively work, as it would require focusing on one spot on a ship, which is difficult for a moving ship). Mythbusters did a few tests on it and similar principals and showed it to be busted. Also, the furnace uses a parabolic mirror directing the light to a point that reaches those temperatures. Jun 24, 2014 at 2:00
• @Chris the amphitheater is parabolic approximately. That myth is why probably how the story started :). Jun 24, 2014 at 3:25
• @Chris: See anna v's answer. Said busting was busted by the (correct!) inclusion of tar. Jun 24, 2014 at 15:13
• The website says the Mega Watt Solar Furnace is "a 1830 m2 facetted truncated parabolic concentrator, focal length 18 m, illuminated by 63 heliostats, total area 2835m2". Jun 24, 2014 at 18:53
• Aha. Well this practical demonstration carries a lot of weight next to a theoretical back-of-the-envelope calculation. Jun 24, 2014 at 19:38

Read about a solar crematorium which shows what is possible with 4 sq m of concentrated sunlight.

http://www.solare-bruecke.org/infoartikel/Papers_%20from_SCI_Conference_2006/22_wolfgang_scheffler.pdf

• Excellent source. What it actually says about the 4m^2 reflector is "The complete burning of 4kg of goat meat took with 50 min a bit longer" [sic]. I think they mean it took 50 min. So more research necessary on whether that can be ramped up to 80kg instantly using more area. Jun 24, 2014 at 20:07