To shield, or not to shield, that is the question.
This is part 4 of a 5-blog series on dragon fire vs metal shield. Last time we looked at how much dragon fire would heat up our shield via convection (answer – not much). Today we look at radiation, and we get some much more exciting results.
This is part 4 of a 5-blog series on dragon fire vs metal shield. Last time we looked at how much dragon fire would heat up our shield via convection (answer – not much). Today we look at radiation, and we get some much more exciting results.
Radiation is heat moving through space in the form of light. As engineers, we often ignore it, because it’s usually pretty small in day-to-day problems (and it’s a bit harder to figure out).
For things that are really hot (the sun, dragon flames), radiation can be huge. Today, we’ll find that it's much bigger than convection in our knight's situation.
So how do we calculate it?
Well, radiation depends on several things:
To summarize:
For things that are really hot (the sun, dragon flames), radiation can be huge. Today, we’ll find that it's much bigger than convection in our knight's situation.
So how do we calculate it?
Well, radiation depends on several things:
- The temperatures of the objects in question. We’ve already decided that our shield / flame are at about 25C / 2150C (77F / 3900F).
- The emissivity of the objects in question. Emissivity is a measure of how effectively something shoots out heat as light (or absorbs heat as light). The highest emissivity possible is 1. A polished steel shield has a very low emissivity (0.07, link) while flames can have an emissivity of anywhere from 0.15 (for low-sooting fuels like alcohol) to 0.6 (for high-sooting fuels like hydrocarbons link, pg 5-3). We’ll go with 0.6 for dragon’s breath.
- The view factor of the objects (a measure of how much of the light leaving one object will hit the other object). For this, we’ll say our 1m dragon shield is touching the edge of a 2m spherical fireball of dragon fire. This means the view factor from the shield to the flame is 1 (all the shield “sees” is flame, link), while (by reciprocity) the view factor from the flame to the shield is 0.0796 (only a small amount of the fireball’s heat goes into the shield).
- The area of the objects (1 square meter for the shield, 12.56 square meters for the 2m fireball).
To summarize:
With these numbers, the heat transfer from object 1 (fireball) to object 2 (shield) can be calculated using this equation.
Online calculator here: make sure F12 < A2/A1 (0.079 instead of 0.08) or you'll get an error.
The answer?
The answer?
Radiation dumps 156,000 W into the knight’s shield.
This is 140 times bigger than convection. It will heat up the knight’s enormous 35 lb shield by 21C (70F) every second. In one second the shield will be 150F (hot enough to burn skin). In two seconds it will be 230F. The knight will be able to withstand one or two seconds of dragon fire (at best) before his arm begins to burn.
So what our conclusion? it’s not absolutely crazy to think a knight might stop a very brief gout of flame from a dragon with a giant steel shield. Still, with all the assumptions we’ve made, I wouldn’t send a knight charging into dragon battle (unless, of course, knight needed roasting as much as the dragon needed slaying). Engineers like to have a comfortable safety factor for this sort of thing, and with our slap-dash calculations and marginal results, I'd still say our knight has a good chance of being in grave peril.
Next time we’ll do a little experiment (Lego knight, meet kitchen torch). But for now, we’ve mathed our way to an uneasy conclusion.
(Side note – it may seem here like a lot depends on the size of the shield. It actually doesn’t – a shield that was half the area would get half the heat from the flame, but it would also have half the mass, so it would heat up at the same rate. A thicker shield (say 3mm instead of 2mm) would help, but would also get very heavy (35lb is already a lot for a shield).)
What fantasy or science-fiction analysis would you like to see next? Let me know in the comments.
So what our conclusion? it’s not absolutely crazy to think a knight might stop a very brief gout of flame from a dragon with a giant steel shield. Still, with all the assumptions we’ve made, I wouldn’t send a knight charging into dragon battle (unless, of course, knight needed roasting as much as the dragon needed slaying). Engineers like to have a comfortable safety factor for this sort of thing, and with our slap-dash calculations and marginal results, I'd still say our knight has a good chance of being in grave peril.
Next time we’ll do a little experiment (Lego knight, meet kitchen torch). But for now, we’ve mathed our way to an uneasy conclusion.
(Side note – it may seem here like a lot depends on the size of the shield. It actually doesn’t – a shield that was half the area would get half the heat from the flame, but it would also have half the mass, so it would heat up at the same rate. A thicker shield (say 3mm instead of 2mm) would help, but would also get very heavy (35lb is already a lot for a shield).)
What fantasy or science-fiction analysis would you like to see next? Let me know in the comments.