Thursday, May 26, 2022

Dragon Fire vs Shield – An Engineering Analysis

So you've been wondering as have i what actually happens to a knight's shield when it faces dragon's fire i've been doing uh some blog posts on that we've been going through some of the physics behind what happens today we're going to actually use a kitchen torch to do that .

Experimentally but first let's review how we've gotten here so our first blog post we kind of broke it down into a very simplified version of the problem where we have a shield at a constant temperature or a uniform temperature .

That has convection heat transfer and radiation heat transfer flowing into it in our second post we looked at convection heat transfer which is heat transfer from a fluid to a solid and vice versa so we kind of went through the math and decided that our convection heat transfer going into that shield isn't that much it's only about a .

Thousand watts which is about as much as your microwave puts into your food third post we looked at what would that actually do to a 35 pound shield we assumed we had a one meter shield for ease of math and also so that it might be big enough for a knight to hide behind well .

1124 watts only heats up that shield by about 0.27 degrees fahrenheit every second so take about 6 minutes for that shield to get too hot to hold so so far night seems in pretty good shape in the fourth post though we looked at radiation just a little bit harder to analyze made some more assumptions decided we had a .

Flame that was a fireball of one meter radius with a again the shield of one meter length went through all the math made assumptions on the emissivity of the flame for a flame a polished steel shield and uh ended up deciding that radiation would be putting 156 .

000 watts into that shield which would heat it up by 70 degrees fahrenheit every second so in one to two seconds that shield would be too hot to hold usually your skin starts burning in contact with metal at about 150 160 degrees fahrenheit so today i wanted to do some experiments and my first first thought for an .

Experiment was to use aluminum foil if you look at this pink outline here that's the size of a one meter shield it's pretty giant you can see why it would weigh 35 pounds even if it was only two millimeters thick like standard plate armor but aluminum foil is 157 times thinner so my first thought was let's make an .

Aluminum foil shield that's 157 times smaller so that's what we've got here we're going to hit it with a kitchen torch what happens to it not looking like good news for a night shield melted it pretty much instantly but i made a couple mistakes with that .

First i use aluminum instead of steel which has a lot less heat capacity than steel so that makes the shield melt faster i also geometrically scaled so i just said let's make 157 scale model of the shield which does not give you valid answers for heat transfer you may have heard of people doing .

Simulations of boats by putting them in oil or other fluids and dragging them through you actually have to be very careful about how you scale a problem so that your results are valid in our case we care about how fast the shield heats up you have to be very careful how you scale things so if you look over here the .

Basic heat equation for heat heating up a shield would be q the heat into the shield matches the mass and the heat capacity of the shield times the delta t of the shield so since we want to find the heat rate how fast that shield heats up we can turn that into a rate equation .

Turn it into density times volume cancel out the area and we end up finding as long as we keep the density and heat capacity the same which is keeping the material the same keeping it steel as long as we keep our heat flux per area the same which we're going to do by shrinking down our dragon flame to match the size of the shield .

Then we can get a valid d temperature d time by keeping the thickness of the shield constant so what we should really do in scaling is make this nice little shield that matches the thickness of the original shield it's two millimeters thick so if we we've hot glued that onto .

A lego guy hot glue melts at about 160 degrees fahrenheit which is conveniently about the same rate time or the same temperature that your skin gets damaged so we're going to hit that shield with the flame and when it falls off melts the hot glue and falls off that is when .

The knight's arm will be burned so about one or two seconds is what we predicted so that gives us a pretty valid experiment now we know if you're a knight facing a dragon with a giant steel shield you have maybe one or two seconds of dragon's fire before .

You're starting to burn your arm thanks you

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