Today, for the finale of this 5-blog-series on dragon flame, we do things the old-fashioned way – experimentally.
No, I don’t have a full-size dragon, or a shield, or a knight… but I do have a kitchen torch, some pieces of sheet metal, and a Lego guy that my son tearfully sacrificed in the name of science. With some non-dimensionalization and slow-motion videoing, we can get a pretty good idea of whether all the mathing in the last post got us anywhere close to the right answer.
No, I don’t have a full-size dragon, or a shield, or a knight… but I do have a kitchen torch, some pieces of sheet metal, and a Lego guy that my son tearfully sacrificed in the name of science. With some non-dimensionalization and slow-motion videoing, we can get a pretty good idea of whether all the mathing in the last post got us anywhere close to the right answer.
My first thought was to somehow use aluminum foil (my wife refuses to stock steel foil in our kitchen for some reason). Aluminum foil is typically 0.0005” thick (0.0127mm), which is about 157x thinner than the 2mm shield we gave our knight. So I started with a 1:157 scale model:
I then c̶a̶r̶e̶f̶u̶l̶l̶y̶ ̶s̶i̶m̶u̶l̶a̶t̶e̶d̶ ̶t̶h̶e̶ ̶a̶p̶p̶l̶i̶c̶a̶t̶i̶o̶n̶ ̶o̶f̶ ̶d̶r̶a̶g̶o̶n̶ ̶f̶l̶a̶m̶e̶ ̶t̶o̶ ̶t̶h̶e̶ ̶g̶e̶o̶m̶e̶t̶r̶i̶c̶a̶l̶l̶y̶ ̶s̶c̶a̶l̶e̶d̶ ̶m̶o̶d̶e̶l̶ blasted it with a butane kitchen torch. It did not fare well.
The foil shield basically melted instantly… not at all what I’d predicted with all the convection and radiation calculations. I’d fallen victim to one of the classic blunders (right up there with getting involved in a land war in Asia and going against Sicilian when death is on the line) – I’d confused geometric similarity with heat-transfer similarity.
Engineers have been building scale models of things for a long time. The thing is, you can’t just build a 1:100th scale model of an airplane and expect it to fly in a wind-tunnel the same way it would fly at full scale (turns out you’d have to increase your wind speed by almost 22x to get the scaled model to fly the same way, and the forces on the model plane would still be 3.4x smaller than those on the real plane).
There’s a whole procedure for determining exactly how things scale (it involves differential equations re-written in terms of non-dimensional parameters). By adjusting the way you scale, the materials you use (testing a model submarine in oil instead of water, for example), and the way you interpret the results, you can indeed use a small model to get real answers about a full-size system.
So how do I scale my shield? Starting with the basic equation for heating something up (see Part 3), assuming that I can scale my flame size to the shield size (and that the shield won’t heat up enough to change the rate of heat transfer significantly), and making sure to keep the material the same, it turns out that I should keep the thickness constant while adjusting the shield’s area to whatever size I need:
Engineers have been building scale models of things for a long time. The thing is, you can’t just build a 1:100th scale model of an airplane and expect it to fly in a wind-tunnel the same way it would fly at full scale (turns out you’d have to increase your wind speed by almost 22x to get the scaled model to fly the same way, and the forces on the model plane would still be 3.4x smaller than those on the real plane).
There’s a whole procedure for determining exactly how things scale (it involves differential equations re-written in terms of non-dimensional parameters). By adjusting the way you scale, the materials you use (testing a model submarine in oil instead of water, for example), and the way you interpret the results, you can indeed use a small model to get real answers about a full-size system.
So how do I scale my shield? Starting with the basic equation for heating something up (see Part 3), assuming that I can scale my flame size to the shield size (and that the shield won’t heat up enough to change the rate of heat transfer significantly), and making sure to keep the material the same, it turns out that I should keep the thickness constant while adjusting the shield’s area to whatever size I need:
After hunting through my garage with a pair of calipers for about half an hour, I found a piece of steel 2mm thick and turned into a Lego-guy sized shield. My son picked his least-valued Lego guy (I couldn’t guarantee that it would survive). I now had an experimental setup.
I used hot glue to attach the shield. Hot glue melts at about 175F (link), which is about when your skin starts burning (skin temperatures above 140F cause 3rd-degree burns, which happens after brief contact with metal at 160F, link). This means that hot glue works well as a timer – when it starts melting, my knight’s skin would be starting to burn.
In five experiments, melting the hot glue took 0.8s, 1.0s, 1.4s, 1.2, and 1.2s, for an average of 1.1s.
1.1 seconds!
This matches our analysis ridiculously well. We predicted a temperature rise of 70F/s, and we experimentally got about 90F/s… in spite of not having a spherical fireball, or a polished shield, or a gasoline flame, or 5m/s uniform flow. This experiment was definitely in the ballpark enough to lend confidence to the complicated math and hand-wavy assumptions we made along the way.
So there you have it! After five blog posts, we finally have the takeaway:
In five experiments, melting the hot glue took 0.8s, 1.0s, 1.4s, 1.2, and 1.2s, for an average of 1.1s.
1.1 seconds!
This matches our analysis ridiculously well. We predicted a temperature rise of 70F/s, and we experimentally got about 90F/s… in spite of not having a spherical fireball, or a polished shield, or a gasoline flame, or 5m/s uniform flow. This experiment was definitely in the ballpark enough to lend confidence to the complicated math and hand-wavy assumptions we made along the way.
So there you have it! After five blog posts, we finally have the takeaway:
Take a giant metal shield to a dragon fight, but don’t hang around for long
To see a 6-minute summary of all 5 parts of this blog series (and some cool videos of fire), check out the video here:
Leave a comment or connect to let me know what fantasy scenario I should apply the all-seeing eye of engineering to next.