# How hot is my dragon?

Little side project on fantasy story with dragons (or wyverns to be exact, but they're equivalent for the purpose).

I have dragons roaming the country side, laying waste and ruin in their wake. As most known draconids, those creatures are able to breath fire to devastating effect. They breathe in massive amounts of air in their dragon lungs (this will be important later) and then expel it while their throats ooze a substance that catches fire when exposed to air. Now, this amazing hunting and defense mechanism has a big drawback, as it creates a lot of heat the dragon has to get rid of. So much heat, in fact, the dragon radiates it, and nearby vegetation tends to catch fire, making it really dangerous to fight one in a forest.

Wandering on the stack, I found some great unrelated answers, mentioning interesting ways to do what is stated above. What I've come to is an alternative breathing system.

Most of the time, a dragon breathes in and out through mouth and nose alone. When it has to breathe fire, it fills its lungs through the biggest air opening it has, namely the mouth, block, then exhale. During exhalation, cooling "vents" open, that are direct pipes to the lungs. They help chase the air and reduce the heat build-up. Next inspiration, the dragon now takes an even deeper inhalation, and simultaneously chase air through the vents, creating hyper-heated jets of air, biologically jettisoning air to cool down.

(For a visual representation, take a look at the fire drakes from Warcraft. Shorter and stubbier than full dragons, with rows of larges scales from head to end of the tail, with spikes protruding from said rows. For this question, the spikes are hollow, and are tubes used as cooling vent.)

Now my question is how hot those air jets have to be for surrounding vegetation to reach autoignition temperature?

• We're in common "Western-European" medieval forest, not Australia, so the average tree is not eucalyptus. More the vegetation you expect in north of France, Germany and South of Great Britain.
• I don't need the whole vegetation to catch fire on the spot, but the leaves with lower than average autoignition temperature in the area have to. Consequence being fires starting spontaneously around the dragon.
• I suppose the answer differs a lot depending of the humidity around. The forest has to catch fire only during dry periods of summer, with at least a week without rain.
• Handwave everything happening "inside" the dragon, even if it should cook itself, it is able to withstand the temperature the time it needs to cool down.
• The cooling process takes the time the dragon empties its massive lungs, so the air venting lasts in average 7-8 seconds depending on the size of the dragon.
• The dragon will expel around 150 L of air during the cooling process.

I'm asking to know what else would catch fire and picture what it would looks like from an external point of view to describe it. Wikipedia has an article about auto-ignition, with the equation and some examples, but I have been unable to locate any data regarding trees and leaves (from the concerned regions) autoignition temperature and lack the theoretical knowledge to deduce the answer.

This question asks for hard science. All answers to this question should be backed up by equations, empirical evidence, scientific papers, other citations, etc. Answers that do not satisfy this requirement might be removed. See the tag description for more information.

• Does the dragon compress air in its lungs? Compressing air would heat it up, and this heat could be evacuated by lung blood toward the wings. then, when releasing the air, decompression cools it down, and it can better cool the throat region down - like in a refrigerator. And the dragon can store significantly more air in its lungs. – Eth Feb 20 at 18:06
• The way the title is phrased suggests you should ask a dragon of the opposite gender. – M. A. Golding Feb 22 at 15:44
• @M.A.Golding Completely intentional pun. I regret nothing. – Nyakouai Feb 22 at 16:16

Your dragon seems to be very similar to a chainsaw. Luckily for you, there was an investigation regarding safe chainsaw temperatures. Link

It appears that safe chain saw operation would result if the muffler with a screen-type spark arrester on the chain saw had a shell temperature that did not exceed 260C° (500° F) and a gaseous exhaust temperature that did not exceed 232° C (450° F). This is based on the data, plotted in figure 5.

If your chainsaw (dragon) is constantly moving, it can have a higher temperature - see chart at the bottom.

I know this answer is probably only suitable as a starting point.

The dragon exhale hot air at temperature $$T_{air}$$ and that air increases the temperature of the leaves from environment temperature $$T_{env}$$ to the ignition temperature $$T_{ign}$$, while cooling to the same temperature. The energy lost by the air is, in first approximation, entirely absorbed by the leaves.

With formulas

$$H_{air}=m_{air}\cdot c_{air} \cdot (T_{air}-T_{ign})=H_{leaves}=m_{leaves}\cdot c_{leaves} \cdot (T_{ign}-T_{env})$$

Let's approximate the dry leaves with paper. The ignition temperature of paper is 246 C.

150 liters of air (at room temperature) weight about 0.2 kg. Air specific heat is $$c_{air}=0.718 \ kJ/kg\cdot K$$, while for paper it is $$c_{paper}=1.336 \ kJ/kg\cdot K$$.

This gives the relationship

$$T_{air}=T_{ign}+(T_{ign}-T_{env})\cdot{m_{leaves}\cdot c_{leaves}\over {m_{air}\cdot c_{air}}}$$

Since you don't specify the mass of leaves, I have computed the equation for some values of it.

To ignite 0.1 kg of leaves you only need the air to be at 447 degrees, while for half a kilo the air need to be at 1250 degree.

• Just to be sure I understand. If the air temperature in the heat stream behind the dragon is about 450°, around 0.1 kg of leaves will ignite - total? As in "uniformly" (or whatever the distribution would look like in the terrain) in the heat zone? Or having a dense foliage is a higher mass for your calculation and thus better able to dissipate the heat? (-> no leaves will catch fire, cause the total mass is over 0.1 kg) – Nyakouai Feb 21 at 9:27
• @Nyakouai, the above calculation is made under the assumption that heat is uniformly transferred and without taking time into account. – L.Dutch - Reinstate Monica Feb 21 at 9:42