What size magnifying glass is required to ignite a fire at sunrise?
September 23, 2019 12:26 PM   Subscribe

A component of an art installation I am planning involves igniting a signal fire at sunrise each morning using a magnifying glass. Short of conducting experiments with magnifying glasses large and small, is there a way to calculate how early in the morning one could achieve combustion and what size lens would be required to do so?

Obviously, the more direct the angle of sunlight, the hotter the beam, but there's got to be some formula somewhere that would allow me to precisely determine the earliest possible moment to achieve combustion with an appropriately sized lens.

Assumptions: environment will be VERY dry (less than 10% humidity). Material to be burned will be dry kindling, and will be enhanced with accelerants if necessary. Just need that one spark.

BONUS: I'm also interested in knowing the furthest distance away from the combustible material I can place the lens, and how high in the air it should be placed.
posted by piedrasyluz to Science & Nature (32 answers total) 5 users marked this as a favorite
The distance-from-combustible-material measurement you're looking for is the focal point. This page goes into some detail on how it's determined and it's going to be a function of the lens power. This site on solar ovens suggests that any time the sun is visible and you can capture light, you're good to go. The angle you're looking for then will be a function of your latitude, time of the year, and any obstructions between your installation and the sun (distant hills, trees, etc).
posted by jquinby at 12:42 PM on September 23, 2019 [1 favorite]

What do you mean by sunrise? If you're in a flat region, right after sunrise, the intensity will be relatively low because the light will have to travel through a lot of atmosphere. Within a short time - half hour or hour, I guess by looking at this model, with the toggle set to "perpendicular" - the intensity will be pretty much the same. (Note that the intensity on the ground peaks when the sun is high and is low when the sun is low in the sky, because the ground is flat, but you can adjust the angle of your magnifying glass to make it perpendicular to the sun.)
posted by Mr.Know-it-some at 12:49 PM on September 23, 2019 [1 favorite]

I'm looking for how soon after the sun begins to rise that combustion can be achieved. Within a half hour would be great, but shaving the time delay down as much as possible is the goal. Location is shielded by a small mountain range, but the installation terrain is perfectly flat.
posted by piedrasyluz at 12:58 PM on September 23, 2019

Is the installation adjustable, in real time? The sun rises in a different location every day of the year and is moves almost 2 degrees every 10 minutes. So the focus point is going to move day by day and minute by minute.
posted by JackFlash at 1:13 PM on September 23, 2019 [1 favorite]

Yes, it will be adjustable. We know the exact latitude and longitude, and the days on which we want to ignite the signal fires.
posted by piedrasyluz at 1:17 PM on September 23, 2019

You would need to figure out how much energy your lens is going to concentrate (like so), and feed it the figure(s) for sunlight intensity for your latitude, time of the year, and so on (much math here). Depending on how math-inclined you are, experimentation with a large, inexpensive fresnel lens may be faster. The calculations wouldn't necessarily take into account things like distant weather, haze, and so on, all of which could affect the received-and-focused energy a bit. Very curious to see the final installation - please post a pic at some point!
posted by jquinby at 1:17 PM on September 23, 2019 [2 favorites]

blargh, ignore that second link - it's for total sunlight over a 12 hour period, not for a moment in time.
posted by jquinby at 1:18 PM on September 23, 2019

This seems pretty much unanswerable other than by experiment. But here are some of the numbers you might need. Starting from the knowledge that the sun deposits about 1400W/sq m when it's directly above...

What is the angle above the true horizon that the sun makes when it is first visible (or when you begin)? (this is going to be greater than zero because apparently you're doing it near a mountain range. It's also going to depend strongly on the time of year.)

By what fraction does this angle reduce the energy density at the magnifying glass? (this is simple trigonometry)

By what fraction does the significant amount of atmopshere along the sun's line of sight near sunrise further reduce the energy density? (harder to estimate, but you can probably look up estimates)

The area of the magnifying glass? (assuming 100% of the energy it receives is focused to a single point on the fuel)

How much energy do you need to deposit on the fuel in order to ignite it? (depends on the fuel's composition, structure and the ambient temperature)

How accurate your answer is will depend on how accurately you estimate all these things, in some cases very strongly.
posted by caek at 1:21 PM on September 23, 2019

@caek absolutely expect that in the end it will involve experimentation toward the end, but I'm looking for arriving at a ballpark calculation here. For example, what effect does using a very large lens have, and how far away from the combustible material can it be? All of the solar ovens have a very short focal point (lens very close to what material to be heated). I want to have as much distance as possible, without making it impossible to ignite.
posted by piedrasyluz at 1:26 PM on September 23, 2019

A cloud passing at just the wrong time can make a big dent in the solar intensity. Similarly, overcast days happen, and those have far less light.

At true sunrise, only a tiny fraction of the sun's disc is visible. This further reduces the amount of energy available. You'll also need to take the low mountain range into account, as it will make local sunrise later. When I was a professional solar energy nerd, I had tools to calculate shadowing effect of terrain, but alas no more.

Seconding jquinby's suggestion on a big cheap plastic fresnel lens and much experimentation. Heating a matte black metal target filled with some kind of accelerant might guarantee reliable starting.
posted by scruss at 1:36 PM on September 23, 2019

Interesting Instructables experiment here.
posted by piedrasyluz at 1:40 PM on September 23, 2019

To first order:

1) the bigger the lens the better (basically, the area of the lens is going to determine how much light gets concentrated, so a lens with an area of 0.5 m^2 will capture twice the light of a lens with an area of 0.25 m^2)

2) Focal length shouldn't matter. A long focal length lens will focus the same amount of light as a short focal length lens.

Here are some back of the envelope calculations that may help:

The ignition temperature of wood varies, but lets assume 700℉ = 371℃.

The heat capacity of wood is 1.76 J/g℃.

So, let's assume that we can make the spot on the magnifying glass 1 cm^2. The density of wood is roughly 1 g/cm^3, so lets assume that you need to heat up 1 g of wood to get a fire going (this is probably the most uncertain part of the calculation).

We'd have to raise 1 gram of wood from ambient temperature at sunrise (in the desert, so let's assume 10℃) to 371℃. This would require about 635 Joules of energy.

Total solar irradiance is 1000 J/s m^2 at sea level. A lens that's a foot across would have an area of 0.073 m^2. So, that lens would have about 73 J/s being focused when the Sun is high in the sky. Assuming it takes about a minute for a piece of wood to cool off, there is clearly enough energy to light the wood when the Sun is high in the sky (it should light in ~10-15 seconds, depending on how fast the wood actually radiates energy away).

So, it (maybe) could still light if 20% of maximum solar irradiance hit the lens?
posted by Betelgeuse at 1:46 PM on September 23, 2019 [1 favorite]

A cloud passing at just the wrong time can make a big dent in the solar intensity. Similarly, overcast days happen, and those have far less light.

I came here to say the same thing. Your contingency calculation (or margin of safety if you want to call it that) should account for how much % of cloudcover you're ok with dealing with before you enter a no-go situation w/r/t the fire starting.

matte black metal target filled with some kind of accelerant

I immediately thought of charcloth possibly in addition to the bone-dry timber/kindling you plan on using.

big cheap plastic fresnel lens

Be aware that higher quality lenses (or better material like glass) will likely perform better for the same given physical size so you may not see as much of a valid comparison without going apples to apples in your test case.

One more thing I'm thinking of is that you'll have to have a clean lens because any sort of buildup of dirt, dust, or grime (it doesn't sound like you'll have dew problems) on the lens will cause issues as well.

Could you use a reflector aimed at the same focal point as well somehow to get double the energy from the same given solar output?

Just spitballing, please keep us informed with how this works out. Another keyterm you may want to search/familiarize yourself with when seraching these things/calculation is heilostat. You aren't quite building one but some of the math may well be the same or really helpful anyhow when it comes to making the linkages/adjustment settings you need, four bar linkages or what not being what they are or set screws if you're using that.

Good luck!
posted by RolandOfEld at 1:48 PM on September 23, 2019

OK. Here's a simpler way of thinking about it.

The distance of the combustible material depends entirely on the focal length of the lens. It can't be closer or further than this. Moving it closer won't make it ignite faster. So choose a lens with a focal length you like.

The bigger the lens, the sooner after the sun rises above the horizon this will work. So get the biggest lens you can afford/move/etc. with the focal length that works for you.

Now set it up and see what time it works.
posted by caek at 1:49 PM on September 23, 2019 [4 favorites]

Calculations are great, I don't blame you for wanting them, but you're really going to want to test this out empirically and practically before you start on any sort of final build.
posted by RolandOfEld at 1:50 PM on September 23, 2019

If you're shielded by a mountain, by the time the sun gets high enough to crest the range, a regular-size magnifying glass seems like it should work fine. You could use a larger-size handheld one to be safe, but it doesn't seem like a ridiculously large lens would be worth the trouble (unless you really WANT the deathray-style beam linked above).
posted by rikschell at 2:08 PM on September 23, 2019

Yes to Death Ray-style beam. Would like to be as far from the fire when it ignites. We may also be considering remote adjustment of the lens, but ideally, this wouldn't take more than a few minutes to ignite.
posted by piedrasyluz at 2:17 PM on September 23, 2019 [1 favorite]

Dryer lint is really good at catching fire. I am too lazy to make charcloth when I go camping and will just take a bag full of dryer lint instead (I'm just throwing it away otherwise). Catches a spark really well. Never tried it with a magnifying glass though.
posted by any portmanteau in a storm at 2:22 PM on September 23, 2019 [1 favorite]

Another thought is to aim the beam at a fuse instead of directly on the fuel source. I don't want to detonate the signal fire, but being a safe distance away is good. 50-100 feet would be ideal. Det cord would be an amazing effect.
posted by piedrasyluz at 2:27 PM on September 23, 2019

As a data point from my younger years, a cheap plastic fresnel lens approximately 8.9" x 6.1" (included as a page in the book) will cookburn/char a hotdog slice and can burn leaves with the afternoon sun. I don't recall if it would quite be enough to start a fire with dry kindling but it'll get pretty close. I expect it could handle det cord no problem with the full sun, early morning might need a touch more magnification.
posted by Nonsteroidal Anti-Inflammatory Drug at 2:39 PM on September 23, 2019

Right now first light around here is 6:30 a.m., and things are definitely "light" by 7. We have a small range of hills to the east, so it takes a while for actual sunlight to get through. The local meteorology says that 6:30 a.m. is a third of a watt per meter squared, 3.5 W at 7, and 25 by 7:30. A match head is supposedly about 1 BTU, which is about .3 watt hours. So I think if you got several letter-sized fresnel lenses, assuming a randomly chosen efficiency of about 50%, you would be able to light a match sometime after 7. But this is really going to depend on the specific conditions and how good a convergence you get from your lens. Water is hugely energy intensive to heat, so if your material is wet, which still happens overnight in the desert, it might take longer. "Sunrise" is really tough because the eye has million to one contrast sensitivity and, especially coming out of the night, any light looks bright. I'm curious to see what you get. As an upper bound, even a small magnifying glass with an area of .01 m^2 can light a match at 1000 W/m^2 (broad daylight), so 10 watts incident energy is definitely enough. A letter-size lens is .06 m^2, so you'd need 16 to get a m^2. That's my guess.
posted by wnissen at 2:45 PM on September 23, 2019

FYI, you can get square-meter fresnel lenses on Alibaba pretty darn cheaply so you can simply overpower things, but be warned in turn that a square-meter lens will be putting quite a lot of heat into your target area so it should be something like a cinder block since it'll still be pouring on the heat long after your signal fire has triggered and burned to ash.
posted by aramaic at 4:35 PM on September 23, 2019 [1 favorite]

The only think I was thinking was a fuse, and a small maybe automatic movement of the lens (due to the every morning bit). The sun rises at 15 degrees per hour and the further the lens from the ignition point the faster the focus point is going to keep moving. It will do you no good to get 'almost' and a minute later be focusing on a different bit of fuel and also getting to 'almost' and a few minutes later getting to a further distant bit of fuel and again hitting 'almost'. You're going to need some low temperature to ignition exothermic fuse material to use for the ignition source unless you want to put the lens on something like an astronomical following mount to keep the focus in the right place for long enough on the each and every day.

The trig is that the farther away the lens is, the less time it spends on the same spot that you're trying to ignite.
posted by zengargoyle at 5:34 PM on September 23, 2019

That's sorta in a way doing something like having long fuses so you can put the end close to the lens (and keep them from accidentally igniting each other) and letting the fuse fast burn down to the distant boom.

I totally want to see what you come up with. This sounds like so much fun.
posted by zengargoyle at 5:38 PM on September 23, 2019

You do not need a huge lens if the stuff you are igniting is suitably flammable.

A neighbor once had a little brass "salute cannon" with a 2in (or so) magnifying glass mounted on an armature above it, with the axis of rotation centered on the touch hole of the cannon, such that you could move the magnifying glass and have the sun fire the cannon at a particular time. It worked reasonably well as long as the glass was very clean and it was a bright, sunny day. We never tried firing it at dawn, though—the few times we played with it, usually we'd set it for local noon. I can't find anything like it online, but it seemed to be commercially manufactured.

He'd put Pyrodex pellets (modern black powder) in the tube and very fine-grained smokeless "flake" gunpowder in the touchhole. IIRC the autoignition temperature of smokeless gunpowder—which you can get at any decent gun shop or large sporting goods store, but is a royal pain to buy online for shipping reasons—is much lower than black powder. But you don't get a good "bang" out of smokeless, hence the black powder charge in the tube. You probably don't want a bang, you want something that burns, so use smokeless. I'd have the lens light some gunpowder, which then you could have light some match heads or the innards of a road flare, then kindling, then larger materials, until you have a proper fire going of whatever size you want.

There are chemicals with lower autoignition temperatures than smokeless gunpowder, of course—gasoline is only 550F or so—but I think the issue you'd run into is they're fairly volatile, and will boil off before the focal point of the lens gets to them and causes them to light. Might be worth a (careful) experiment, but I think a half-teaspoon of smokeless propellant would be safer and more reliable.
posted by Kadin2048 at 6:19 PM on September 23, 2019

If you want a long focal length, that may be hard to do cheaply. You could always use a photocell controlling a relay to hook a battery to a heating element. I am not sure what the point of the art project is, but you said you were okay with accelerants so I thought I’d offer the notion. Good luck.
posted by Gilgamesh's Chauffeur at 6:44 PM on September 23, 2019 [1 favorite]

I'm imagining Burning Man. And as primitive as possible.
posted by zengargoyle at 6:49 PM on September 23, 2019

I think I'd reverse it and build a big parabolic reflective surface on a rotating platform timed to match sunrise. And maybe individual small lenses at each site. Big death light beam tracks the sun every morning and the far away little bits with a lens and a fuse go boom. You just need a midnight party where you dance around and move the mirror to tomorrow. Whatever is at that spot gets toasted.
posted by zengargoyle at 7:04 PM on September 23, 2019

So, it (maybe) could still light if 20% of maximum solar irradiance hit the lens?

Here's some information about how much the solar irradiance is blocked by the atmosphere when the Sun is near the horizon. Roughly speaking, you get a little over 1/4 of the "average" solar power by the time the Sun is about 5° above the horizon. But right at sunrise, when the Sun is on the horizon, you'll only get something like 2% of the average solar power.
posted by Johnny Assay at 8:05 PM on September 23, 2019 [2 favorites]

People designing or learning to use solar ovens set the wrong thing on fire pretty often - the next dish, a fence, a roof. You set the solar part aside to stir, or when they’re done cooking, and... A single lens strong enough to start a fire at dawn will be really strong at noon. Careful.
posted by clew at 9:41 PM on September 23, 2019

Even fresnel lenses are fairly dangerous. Make sure to put it in a book or covered somewhere once you are done; leaving one leaning outside is a recipe for disaster.
posted by benzenedream at 10:57 PM on September 23, 2019

As you can see from https://en.wikipedia.org/wiki/Olympic_flame the olympic flame is lit from the suns rays using a small parabolic mirror, but in Greece and in the summer so you might need a bigger one. Personally I'd go more towards overkill than just right, but thats me.
posted by koolkat at 6:42 AM on September 24, 2019

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