Lasers in SF, Part II: Why didn’t James get fried like a piece of meat?
I mentioned in my last post that my analysis of Goldfinger’s laser-cutting setup was a little over-simplified. Before I move on to my next topic (the Death Star!), I want to talk about this in a little more detail. Here are a few questions that came to mind as I wrote the post:
1) Does it matter that the table is gold rather than steel?
Yes. A laser may have a high power output, but that doesn’t mean that all of that energy goes directly into heating and melting the metal surface. Some of the laser light, and thus some of the energy that it carries, gets reflected from the surface. Exactly how much light is reflected depends on the metal.
Gold has a very high reflectivity. In the infrared part of the spectrum, which is where the light from a CO2 laser falls, gold has a reflectivity of about 97%. That means that at most 3% of the light (and energy) from the laser can be absorbed by the metal.
Steel, on the other hand, absorbs more of the laser’s energy. The reflectivity of steel depends on the type of steel, and I found references giving numbers from about 70% to about 95%. This is a wide range, but either way, steel reflects less (and absorbs more) of the energy from the laser light than gold does. This means that cutting steel requires less laser power than cutting gold, because more of the energy from the laser light actually goes into melting the metal.
Laser cutters capable of cutting gold do exist. However, they tend to use a different type of laser that puts out light at a shorter wavelength than the CO2 lasers used for cutting steel. Gold absorbs more of the laser light at these shorter wavelengths, making it easier to get enough energy into the metal to melt it. These lasers also usually produce short pulses of light rather than a continuous beam, which effectively helps pack all of the beam’s energy into a much faster punch.
Last but not least, gold also has a higher thermal conductivity than steel does. This means that when you’re cutting gold, heat energy can move away from the laser spot faster than it can when you’re cutting steel. As a result, you have to put in even more energy to get the metal directly under the laser hot enough to melt.
2) Wouldn’t the metal table heat up and fry Bond like a (particularly delicious 😉 piece of meat?
It seems like it would, doesn’t it? If we’re heating up part of the table to 1400 degrees Celsius (to melt steel) or 1064 degrees Celsius (to melt gold), it seems like the rest of the table must get pretty hot, too.
But it doesn’t. At least, not if you do it right.
One of the beautiful things about using a laser to heat the metal is that the laser can quickly deliver a lot of energy to a very small area. If the laser is powerful enough, it can melt the surface beneath it so rapidly that there is no time for the heat to diffuse into the rest of the metal. So, the metal gets hot enough to melt directly underneath the laser spot, but the temperature drops off very quickly as you move away from the laser spot.
Materials engineers care a lot about this, because even if the metal doesn’t melt, it can rearrange its internal structure if it gets hot enough. A lot of the time that weakens the metal or has other undesirable effects.
Usually, what engineers care about is the size of the “heat affected zone” (HAZ), or the area that gets hot enough to cause changes to the metal’s properties. You can find equations for calculating the size of the HAZ in books on laser processing of materials (like this one). However, we can use the same equations to calculate how far we have to move away from the laser spot before the table is just pleasantly warm rather than burning hot.
Here’s a temperature map for a thick piece of steel absorbing 1 kW of power from the laser, which is moving across the metal at 50 mm/s. This is in the ballpark of what you might get with an industrial laser cutter.
In this image, the laser’s position is marked by the white circle, and its path by the white line. All of the temperatures are given in degrees Celsius, and each contour line represents a jump of 100 degrees. The temperature drops to under 100 C, the boiling point of water, just 4 mm away from the laser’s path. So, until the laser beam gets really close to Bond’s crotch, he’s probably not going to notice the table heating up too much.
Gold’s higher thermal conductivity does affect things a bit. Here’s the same temperature map, but calculated using the heat transport properties of gold:
The temperature still reaches 100 C just 3.5 mm from the laser’s path. What you should also notice is that the temperature drops off more quickly, because the metal is better at moving heat away from the laser spot.
But of course, we calculated these temperature maps for something similar to an industrial laser cutter, and Goldfinger isn’t using an industrial laser cutter. His laser is at least a thousand times more powerful, his spot size is bigger, and he’s cutting the metal veeeeery slowly (probably to increase the suspense!). This changes the picture dramatically.
This is what I get when I use a cut speed of 5 mm/s and assume the metal is absorbing 0.5 MW of power. The key here is that the scale on the axes is different (thousands of mm rather than tens of mm) – so this graph shows that the metal is still more than 100 degrees a full foot (300 mm) away from the laser’s path! So it’s pretty unrealistic that Bond is lying on the table carrying on witty banter with Goldfinger rather than whimpering (or writhing) in pain.
3) Can lasers burn flesh?
In other words, would the laser actually burn Bond if it hit him? The answer is yes, absolutely. Lasers are most certainly capable of burning people. To give a real-world example, people have reported getting skin burns from the lasers used in laser hair removal (here are a few photos – warning: these images aren’t graphic, but still a little ick-inducing). I’ve also gotten a minor skin burn or two from the lasers in my lab.
Goldfinger’s laser is many, many times more powerful than these lasers. In fact, Class 4 lasers, which are listed as being capable of causing skin or eye damage, can have powers as low as 0.5 watts. This is 6 million times less power than the 3 MW we calculated Goldfinger would need. So, unfortunately, I think it’s safe to say that if Goldfinger’s laser reaches its target, Bond doesn’t stand a chance.
4) When the movie of Goldfinger was made in 1964, high-power lasers like this weren’t around, and it would have been too dangerous to use a real laser to film this scene anyway. So how exactly was this effect done in the movie?
According to Wikipedia, the “burning” effect in the movie was apparently made by aiming a blowtorch at the table from underneath. Cool! How’s that for a low-tech way to generate a high-tech effect?
Anyway, that’s it for James Bond. Next week, we’ll head off to space and start learning about the Death Star’s superlaser!