Ignition of paper using lenses??

[Merlin66]

OK, we've all heard about the dead ants resulting from youthful use of magnifying glasses....
My issue at the moment (!) is trying to determine when paper when subjected to a focused solar beam (i.e. from a telescope objective) will burst into flames.

As you probably know I build and use solar telescopes...some solar observers are keen to mention that various telescopes/ filters can cause paper held at the focus to smoulder (never seems to burst into flame though??!).
Seeing this sort of thing happen puts doubt in their mind as to the safety of solar telescopes.

There's a critical ignition temperature for paper -around 246 deg C - at this temperature the paper will ignite.
Knowing the solar irradiation is 1000W/m^2 - what sized objective (this determines the input power - solar irradiation * area of the objective), what focal length (this determines the solar image area = 1/100 the focal length)
would give sufficient Heat Flux to ignite paper, and how long would it take??
Any ERF filters etc would reduce the power throughput...

I found the only "auto ignition" formula was based on work done on the ignition of wood products :
https://www.researchgate.net/publication/317041329_A_review_on_ignition_of_c ellulose_materials_under_external_h eat_flux

and the formula on page 38 gets bandied around as the one to use..
Unfortunately it doesn't work!!
(According to this formula a piece of paper lying in sunshine will burst into flames after 54 min!!!! -Obviously not true)
Has anyone got any creditable information/ knowledge/ documentation on the ignition of paper in a focused solar beam???

The attached spreadsheet image shows some of the factors I've been looking at.

[inline_online]

While I can't assist with quantitative analyses, I can give personal feedback.

Many years ago, I had a 10" Meade Starfinder with a Thousand oaks full aperture solar filter. During a solar observing session I got curious as to what would happen to corrugated cardboard if I took off the filter and held the cardboard in front of the eyepiece.

Within a few seconds the cardboard was black and smouldering and within a few more, it was on fire.

That hit home more than any warning in a book about not looking through an unfiltered scope at the Sun.

[Merlin66]

Yeah,
I’d think a 10” f5 would give a Heat Flux at focus to ignite paper...
Be thankful the secondary withstood the energy loading
Ken

[Wavytone]

From personal tests many many years ago when seeing up an 8" for solar a solar eclipse...
A 4" f/6 will ignite paper easily. In an 8" f/6.7, a filing card explodes into flame with an audible pop.

Never mind a 10" !

Be very careful with large scopes near the sun for several reasons:

The concentrated beam from a primary mirror will inevitably strike internal surfaces such as the secondary mirror cell, vanes, the interior of the tube wall, and the focuser. If you are careless this is quite capable of charring paint, melting plastic and igniting flammable parts - wood, epoxy (carbon fibre tubes) and cardboard (sonotube) will be charred or ignited. Metal parts will survive, but black paint will not. If the vanes of the spider were soldered, its quite likely the solder will melt in the beam.

Attempting to put that amount of energy through eyepieces can damage the coatings permanently. Eyepieces with cemented elements should not be used - the cement may boil, causing the lenses to come apart or worse, split. Secondly the glass will get very hot and expand - make sure they are quite loose in the cells because if tight, differential expansion between the glass and cell may well cause the glass elements to fracture.

For the eclipse I made a big oversize Ramsden eyepiece (two elements airspaced) to project the sun from the 8" onto a screen so many could watch the partial phase of the eclipse safely. The big scope provided a very nice big bright image.

[bojan]

From pure feeling I would say f/ number is prime factor here, because it determines the energy flux (or brightness) of the Sun's image.

Size of the hot spot (focal length) is also important, because for flame to be self-sustainable there must be enough smoke to burn. Air temperature will be tertiary factor....

[Merlin66]

Ok, guys I accept there is plenty of anecdotal evidence ...by how do I quantify the parameters????

[bojan]

I would use temperature controlled soldering iron to determine the ignition temperature.
Then I would use thermometer to gauge the temperature of the Sun's disk.. on black paper.

Perhaps this is can help you to correlate the actual measurements with theory?

[Wavytone]

Bojan solar furnaces routinely exceed 2,200 degrees so to be honest I'd be careful putting any thermometer in the image from a sizeable mirror.

Ken - a significant aspect is the total energy focussed in the spot. An all-reflecting system with aluminium first surface mirrors will focus everything from the far IR into the UV. Lenses on the other hand don't transmit so well in UV or IR and the chromatic issues mean the heat isn't all that well focussed as it is in a reflector.

Bojan is right in that f/ratio plays a role, but a simpler view is this:

- calculate the total incoming energy (entering the scope primary aperture) in watts, full spectrum;
- calculate the size of the solar image;
- calculate the energy density at the image (in watts per square cm).
- allow for thermal losses and inefficiencies, probably 50%.

[sheeny]

One critical factor you are missing, Ken, is the emissivity of the paper. Actually, it's more complex than that, you need to apply the absorption spectra for the paper to the solar spectra ex the scope to calculate the power absorbed by the paper.


Keep in mind that most glasses don't transmit IR too well (the basis of a glass type green house) and white paper by definition should reflect a large portion of the visible spectra.


White paper is largely coloured by kaolin clay (along with bleaching) if that's any help determining the spectra to use. Different colour papers will ignite at the same temperature but will achieve that temperature are different rates due to their absorption spectrum.


It should be right up your alley! ;)


Al.

[Merlin66]

Guys,
Thanks for the comments...

The ignition temperature is well established, no debate there.
I’ve already taken into account the UV / visual/ IR distribution of the input energy.
We know the input power, as per the example, 18W...
We know the size of the solar image, hence the Heat Flux at the focus.
What we need to know is the interaction of this Heat Flux with paper, and how long it takes to raise the temperature to 246 deg C.

[Wavytone]

Ok...

Let's assume paper density is 100g per square metre.
Image area = 0.000177 sq.m
Mass of paper in the solar image 0.0177g, ie 0.0000177 kg
Specific heat of paper 1336 J/kg/C
Temperature rise required dT = 226 degrees
Joules required therefore J = 5.3 Joules
Heat flux over the solar image H = 17.7 W

A Joule is a watt-second so the time to reach ignition temp = J/H = 0.3 seconds, which I suspect is optimistic (ie too quick) from what I saw with 4" and 8" mirrors producing much smaller images.

Beyond what Al suggested there are more issues -
- paper isn’t opaque - a fair bit of the energy will escape out the back;
- atmospheric losses (there is huge difference between solar noon on a clear midsummer day, vs the crap sky we have at the moment - which is struggling to warm a black metal surface),
- moisture content of the paper (it takes a lot of heat to drive off water), and also
- the transition from white paper through charring to ignition. Once that change begins it becomes carbon and absorbs the energy quickly.

I have a magnifying glass, a 70mm f/6.7 refractor, 6" f/15 Maksutov, and 10" f/12 Mak and Mental has a 10"f/5 newtonian... these could make an interesting experiment over the Xmas hols next week - assuming we get some sun (still overcast with smoke here). Assuming they are sufficient for ignition, it would then be neat to stop them down so the ignition is slow enough to time with a watch.

Might even try a couple of hand grenade eyepieces.

[Merlin66]

Yeah,
That's very similar to what the formula gives, but it's very very optimistic.

OK what about getting members to carry out the following experiment:

1. Using a telescope suitable for a Herschel wedge i.e. a refractor, not Mak or SCT etc. with no diagonal, eyepiece, just the OTA.. Measure objective diameter and record f ratio or focal length.
2. Pointed at the Sun close to noon, preferably on an EQ mount.
3. Using piece of white copy paper placed at focus.
4. Record the time (nearest second) to:
4a Show light smoke
4b Charring/ smouldering
4c visible flame -ignition. Take safety precautions, please!!
5. Submit the above data for analysis.

(A magnifying glass (aperture/ distance to paper recorded) would also work)
Caution: It's always dangerous observing the Sun - take special care.

[Wavytone]

ISure.

I’d also suggest stopping the scope down with a smaller aperture to start with then increasing that until it does ignite. Image quality is irrelevant so a non-circular aperture (square ?) or the secondary mirror don’t matter.

Need to know what sort of paper was used ie. new sheet of 80gsm photocopy paper, card or cardboard etc. and what colour if not white.

Pretty sure magnifying glasses will show a significant loss.

Good one to engage kids, too.

[Merlin66]

For "standardisation" I'd suggest 80 gms white copy paper.

If we can collect data from a few members with different sized lenses/ refractors is should be possible to solve this one!

If nothing happens ( no smoke/ smouldering/ flames) say within 30 sec, then just record the data with "no result" - a negative result is just as important as a positive one.

[sharkbite]

....probably wait for fire season to be over before beginning any experiments?

If not purely for safety, perhaps out of sympathy for the fireys?

[Merlin66]

I understand your sentiments .....

Don't do this experiment on a day of Total Fire Ban.

[JA]

Hi M66,

Also knowing the location latitude would be of benefit in any model in terms of factoring the radiant energy received by the paper according to the cosine of the latitude. This would not be insignificant in Australia where the latitude can range from -10 degrees way up in North Queensland to -44 degrees in The Huon Valley of Tasmania and account for a difference of perhaps 20-30% depending on time of year.

If it's of acute interest you could perhaps Use/acquire a thermocouple or infra red thermometer so as to study the effect more closely.

Best
JA

[Merlin66]

JA,
I agree, but at this stage I believe in KISS (Keep it simple, sunshine!)

If the results justify the addition data/ input then we can move in that direction.

Bear in mind, the topic was based on subjective assessments of "solar danger"

[sharkbite]

Or do it at night/indoors so you don't get caught

[julianh72]

I’m joining this conversation quite late, but here’s my $0.02 worth:

The temperature that the paper will reach as a function of time is a non-linear relationship between heat-in (from the concentrated sunlight) and heat-out, from conduction, convection, and radiation, together with the thermal properties of the paper (thickness, density, specific heat, and conductivity).

Typical thermal properties of 80 gsm white paper might be around:
• Thickness: 0.1 mm (a 500-sheet ream is about 50 mm thick)
• Density: 800 kg/m3
• Specific Heat: 1400 J/kg.K
• Conductivity: 0.05 W/m.K

Heat-in can be calculated fairly simply by starting with the assumed solar irradiation of 1,000 W/m2, multiplying by the concentration factor of the lens, and then allowing for losses. For the example given, we arrive at something like 100,000 W/m2 over a 15 mm disc, or 17.7 watts total (without losses), as an upper bound.

Conduction will be very small, as paper is a good thermal insulator – but it can be allowed for in the thermal analysis.

Radiation is a function of the temperature of the paper above ambient, and the nature of the surface – we can assume it is a classical black-body (on both faces) as a first approximation. The hotter the paper gets, the more heat it re-radiates (from both faces), reducing the rate of temperature rise, as the net heat gain (W/m2) falls as the temperature rises.

Convection is the biggest unknown, as it is very dependent upon the air temperature, airflow conditions, and the orientation of the paper.

If the paper is held vertically, natural convection cells will allow free convection to take heat away from both faces. If it is horizontal, the convective heat transfer from the bottom face will be very low (the buoyant hot air “bubble” will be held up against the bottom face of the paper), and for the top face, the heat transfer will be less efficient than when in the vertical orientation.

The presence of any air drafts can change the convection coefficient dramatically – typical values can be as follows:
• Free convection – vertical face in still air: 5 W/m2.K
• Forced convection - Low speed of air over a flat surface: 10 W/m2.K
• Moderate air speed over a flat surface: 100 W/m2.K
• Moderate air speed over a curved surface: 200 W/m2.K
That’s a 20-fold increase (or more) of heat transfer from convection to air, depending on the ambient conditions!
Ref: https://www.engineersedge.com/heat_transfer/convective_heat_transfer_coefficien ts__13378.htm

When I run some basic transient heat analysis, assuming 17.7 W over a 15 mm disc, and allowing for conduction, radiation and convection, I get the following indicative times for the paper temperature to reach 600 K (which should be enough to cause ignition):
• Convection Coefficient < 20 W/m2.K: 0.4 seconds
• Convection Coefficient 100 W/m2.K: 0.65 seconds
• Convection Coefficient 125 W/m2.K: 0.9 seconds
• Convection Coefficient 150 W/m2.K: Not applicable – the convective heat transfer is sufficient to keep the temperature below 600 K

If I repeat the analysis, but limit the heat input to say 10 watts total (~ 40% losses), I get the following indicative results:
• Convection Coefficient < 20 W/m2.K: 0.75 seconds
• Convection Coefficient 50 W/m2.K: 1.0 seconds
• Convection Coefficient 100 W/m2.K: Not applicable – the convective heat transfer is sufficient to keep the temperature below 600 K

It seems therefore that a 150 mm f10 OTA is indeed capable of igniting a piece of paper in about 1 second or so – but it can also be prevented from igniting depending on air conditions, losses, etc.

As I said – it’s a very non-linear relationship, and the efficiency of convective heat exchange from paper to air will be a critical factor in determining whether the paper will ignite.

[Merlin66]

Julian,
Appreciate your input....

I attach the spreadsheet I built using the original Auto Ignition Equation given in the text. There is discussion of convection losses in the paper.....

You can see it uses similar data.
The ignition temperature of paper is 247 deg C
The solar image in other configurations can be much less than the example, hence the Heat Flux is amplified.

It would be of great interest to see how "real life" experiments correlate to these mathematical models.

[julianh72]

Ken,

I can't really comment on the applicability of the model in the paper by Shen, Fang & Chow, but I suspect that your examples are pushing the limits of their theoretical model. A couple of critical differences between paper and wood occur to me:

. Paper is much thinner than even a small piece of kindling, so it heats up through its thickness very quickly, even when heated from only one face. Conversely, even though paper is a good thermal insulator, there is enough conductivity through such a thin film to ensure the convection / radiation on the unheated face plays a significant role in the overall heat transfer. (E.g. if you put a paper cup filled with water over a naked flame, it won't catch fire; a wooden cup will certainly char on the bottom face, if not burst into flame, in such a test.)

. Radiation and convection from BOTH faces is important for paper, less so for a "solid" piece of wood, for which the far side will stay much cooler than the heated side.

. For radiant heating of a substantial piece of wood, the radiant heat will also heat the air on the heated face, so the convective cooling effect will be limited - you will be drawing in hot air rather than ambient air. For our example (a converging light beam to a very small disc), there is an "infinite" source of ambient-temperature air to replenish the convective cooling mechanism.

. The surface area to mass ratio is MUCH higher for a piece of paper than kindling, let alone a plank of wood. This means that there is a much higher reaction area available to initiate combustion.

In practical terms - if you take a piece of paper, a twig, a dowel, and a plank, and hold them up close to a heat source, the paper ignites MUCH faster than the kindling, dowel or plank.

If I run my thermal analysis using heat input of 156 W/m2 over the 15 mm disc (to simulate the losses in the solar scope components), I find that the "hot spot" reaches an ambient temperature of about 8 degrees warmer than ambient, after about 20 seconds of heating. From then on, there is no net heating, as the radiant heat is in thermal equilibrium with the convective and radiative losses.

[Merlin66]

Julian,
Once again appreciate the input.

What are your thoughts on the concept of a "Critical Heat Flux" as a possible threshold "rule of thumb"??

With a OTA containing no filters etc the Heat Flux at the solar image can get up to 100KW/m^2 (150mm f10) and even a common ED80 (80mm f7.5) can give 178 KW/m^2 flux.
These are pretty big numbers.....
Even my magnifying glass (75mm, 130mm fl) gives 3,300 KW/m^2:eyepop:

[julianh72]

Ken,

There are so many variables, some of which are very sensitive, and / or can vary over a wide range of plausible values, so I would be cautious about using the following other than as a very indicative guide.

However, for what it's worth, if I assume a "worst-case" convection coefficient of 5 W/m2.K on both sides of the paper (representing still air), my thermal analysis suggests the 15 mm hot-spot will reach an equilibrium temperature of 550K (277 Celsius) with an input heat flux of 13,300 W/m2, and about 600K (327 Celsius) with a heat flux of about 16,600 W/m2.

In practical terms - less than about 10,000 W/m2 (10 kW/m2) applied to a small area of paper SHOULD be low enough to avoid ignition; anything over about 12 kW/m2 would run the risk of ignition.

Take this all with a generous handful of salt - it will be interesting to see how these predictions stack up against some actual testing!

[julianh72]

Ken,

On the subject of ignition temperature of paper - surely it is "Fahrenheit 451" (233 Celsius)?

[Merlin66]

Ray Bradbury was burning books!;)

yes, the literature quotes from 218 to 246 deg C
https://en.wikipedia.org/wiki/Autoignition_temperature

[gaseous]

lol

[Merlin66]

Brightening sky today, but also Total Fire Ban - no paper ignition trials today....

[Wavytone]

LOL Ken... In Sydney it will be weeks if not months before we see air clear enough to try this properly.

I'd say most of us in Sydney are glued to the media waiting to see if the heart of the Blue Mountains will be burned - there are major fires in progress in the Megalong, Burragorang and Grose valleys and its only a matter of time before these reach the Jamison Valley and the townships along the highway from Mt Victoria right down to Glenbrook.

Right now the wind is ENE putting Mt Victoria & Blackheath in the immediate path this afternoon; the wind is expected to swing west which means the rest of the towns to the east will be at risk.

[Merlin66]

I feel for you guys up there in NSW/ Q’land....
Stay safe.
It’s 46 deg down here and PowerCor have pulled the plug...no power...promise (!!) it should be on sometime after six pm.

[bgilbert]

The surface temperature of the sun is approx. 5700 deg C, the diameter is approx. 1.4 million km, the earth sun distance is approx. 150 million km. The highest temperature that you can achieve on earth by any known optical means is something a bit less than 5700 deg. C. the size of the image that you can focus on earth is the diameter of the sun divided the ratio the two focal distances at play here. The, a bit lessedness than 5700 deg. C is the efficiency of the lens over the f ratio of the lens. (I think?)
1.4*10^6/150*10^6= 9.4 mm
for 1m focal length @ f10 the temperature would be approx. 80 percent of 570 degrees
0.8*5700/10=456deg. C.
For .1m focal length @f1 the spot will be .94mm at a temp. of 4,569 deg. C.
For 1m @f1, the spot = 9.4mm at 4,569 deg. C
I think I may have stuffed up somewhere on the role of the f factor, but you can see my line of reasoning for at least the spot size and temperature part of the problem.

[Merlin66]

Barry,
The formula given earlier is more accurate than your method.

[Wavytone]

Barry countless magnifying glasses show it doesn’t work that way.

[bgilbert]

Wavytone,
Pray tell, give me some numbers, so I too, will be erudite.

[bgilbert]

Merlin66,
True, I left out the attenuation through the atmosphere. I considered It trivial In the context of the discussion, a dB or so, also the glass lens would attenuate the infra red, which Is about half the total energy. That avoids having to mention the CO2 in the atmosphere, boy, that could cause trouble.

If this not what you meant, give me the correct formula please.

[Merlin66]

Barry,
Look at messages #21, #11 and #1 below. The formula is given, and the attached spreadsheet gives the input data.
The discussions so far indicate that this is not a perfect solution...hence the practical experiment.

[Wavytone]

Barry all that remains is to do the experiment - and I definitely will when we have a clear day - but for the past few weeks we’re lucky to even see the sun dimly through the smoke.

[julianh72]

Barry,

I think it is incorrect to assume you can "focus" the temperature of a remote object through an optical system. The temperature of an object is a measure of the energy of the atoms, molecules and sub-atomic particles that make up that object; what we perceive as radiant energy is carried only by photons emitted by the object, not by the excited atoms and molecules themselves. The frequency / wavelength / energy of the emitted photons is a function of the temperature of the object (among other things), but the photons do not have "temperature" in the same way that the atmosphere of a star does.

What we can do is measure the Sun's radiant power (W/m2) and focus this into a smaller area to increase the energy flux. We can then try to work out what that focussed energy does - by way of heating the target and surrounding air, and being re-emitted by reflection, radiation, and convection. That is what merlin66's cited paper and spreadsheet attempt, and my thermal analysis tries to better allow for the thermal properties of paper vs wood (on which the cited paper is based).