Sunshine is very cold! (Spoilers Ahead)

Sunshine was a movie made in 2007 by director Danny Boyle. Overall the science in this movie wasn't terrible. There was one scene, however, that made me cringe.

(begin minimal spoilers)

About 1 hour into the movie, several crew members get stuck on a second ship which has had the airlock blown out. There is only one space suit, and no other way to return to the main ship, or pressurize the airlock area once the seal has been breached. They come up with an idea to try to get as many crew as possible back to the other ship. They put one crew member in the suit and have the others wrap themselves up tightly in insulating fabric, then they tie themselves onto the suited member. Using the gas pressure from the damaged ship when the airlock is blown, they will rocket across to the other ships airlock and live. So far, this is very good. The gas would expel you across the gap pretty quickly, and it's possible that you could survive a very short exposure to hard vacuum. Further, the tight wrapped insulating material would help protect you from the vacuum to a certain extent.

The problems occur shortly before they launch from the airlock. The crew members who remained on the main ship inform them that they will have "20 meters to cover at -273 degrees Celsius". Although this temperature would be more accurate for deep space than this close to a star, since they are behind a solar shield and would be likely to round the temperature to the nearest whole number, -273 Celcius is a reasonable temperature. After wrapping themselves up in insulating material torn from the walls of the ship, they blow open the airlock and start to shoot across the gap. Oh no, one of the crew members got knocked off a strait trajectory and has drifted off into space unable to be rescued. At this point, due to the great cold of space, he quickly freezes into a astronaut-sicle. Wait, is that right? Freezing in about 1 minute is what you would expect in an atmosphere at that temperature, but what about space?

In space, temperature doesn't mean the same thing that it does on earth. When you are in an atmosphere, the temperature has to do with the thermal energy possessed by the air. It turns out that in air, Newton's law of cooling describes the rate at which things cool fairly accurately. The rate of change of thermal energy equals the heat transfer coefficient of your medium times the area of your object times the difference in temperatures. For air, the heat transfer coefficient is between 10 and 100 watts/meter^2 kelvin. So, for very large temperature differences, this will cause you to cool very quickly, linearly increasing as the difference decreases. In space, a much different process occurs. It turns out that radiative heat transfer is proportional to the difference between the 4th power of the temperatures (body^4 - ambient^4), which would be very fast, but the constants on the front are very tiny. Specifically, a given object with an identical temperature difference would cool 6 to 60 times faster, depending on atmospheric composition, in an atmosphere as compared to in a vacuum. That gap will widen very quickly, since in a vacuum the loss rate changes proportionally to the temperature to the 4th power. If you do the math, using the approximation that a human is a sphere with a surface area of 1.81 meters, an emissivity of 1, and a mass of 80kg of water, you get that after 1 minute the temperature of his body would only have dropped to 308K, from 310K, which is well above the freezing point of water. In fact, it would take more like 45 minutes to even reach freezing. So, that scene, although very dramatic and cool, was kind of silly. I admit though, the much more realistic thing to have happen would be some nasty things coming out of all your orifices, and it would be much more disgusting than what they chose to portray.

Go rent Sunshine though, it's a very pretty and thrilling movie!

Edit: New exciting information! It turns out that according to the FAA and NASA, you won't actually be able to stay conscious very long if exposed to hard vacuum like that. The amount of time that you retain useful consciousness in rapid decompression situations would be on the order of 5-10 seconds if you were breathing normal air before the decompression. What this means is that it is unlikely that the unsuited crew members would have been able to act in any way once exposed to space. Further, the damage taken would be so extreme that they would need immediate medical attention to survive and would in no way be active after exposure to space. This scene gets less plausible as I learn more.

Science advised?

Watch the video above, and then read below.

I have just watched the first 6:38 minutes of Vertical Limit. I was thinking that I would do this in a sort of narrative, where I explain what's happening in the movie, and then pause when they get something wrong, but they got too many things wrong. Since I found 24 things, I think I'll just list them one by one.

1. In the first scene of the movie, there is an eagle swooping around near a mesa. During one scene you can clearly see the eagles legs dangling down towards the ground. Now I'm no ornithologist, but I'm almost totally certain birds don't fly like that. The scene looks CG , and I think they may have missed a bit. Any ornithologists can email me, and I'll get up the correct information.

2. During the entire scene, you can clearly hear their voices echoing as if off the walls of a canyon. This seems reasonable on the surface, they are near a rock wall...echoes! But in reality this is a little bit odd. If they were climbing the wall of a canyon, you could expect to hear echoes, but on the face of a mesa like they were climbing on, there would be nothing to have the echo bounce off of. Probably, it would have sounded more like if you were standing next to the second story of a house in the middle of a big open field. One slight echo, and nothing else.

3. Another problem in this scene is the way they used anchoring. The first instance of this is the crack which the girl has placed three cams in. The only serious problem I see is that it appears the crack is increasing in size as it goes down, which would seem to cause some problems in the event that any force should be applied down on it. Overall, I think this was a bad protection setup.

4. This is a minor nitpick, and may have just been something that they did off screen because it wasn't considered important to the plot, but the girl never once secures her carabiner locks, or checks them for having locked. Bad practice if nothing else, but they have bigger problems.

5. Shortly after the scene with the three cams in the wall, the young male character is seen jumping up to one high section of the wall. Apparently they didn't build the sound stage to the same dimensions as the rock wall they used for filming, because although in one scene the climber is shown feet dangling, in the next he is easily bracing against the wall below him. Just sloppy really.

6. This was another thing that struck me as quite odd. The girl is clearly using cams in a crack in front of her as an anchor for her and her brother and father. Although this in and of itself isn't very odd, everywhere else on the wall they used pitons, a sort of nail system where you pound an iron spike into the rock that has a hole to put a carabiner through. These are effective, if usually illegal. I'm not really clear on why you'd use a more secure type of anchor everywhere but your main anchor.

7. If you carefully watch the girl on belay (belaying explained in number 18), you can see that she isn't backing up her automatic locking belay system with a strictly physical system. This is also a bad practice. Should the boy fall, and the automatic stop fail, he would likely plummet to his doom, almost a minute earlier than he would otherwise.

8. Just before the real insanity starts, there is a pack dropped from high above them. The pack falls past them with the rope trailing. Depending on what was in the pack, this might actually be reasonable. Climbing rope is fairly dense stuff, and would tend towards overcoming air resistance quite well, but the pack could be full of water, or cooking supplies, or lead weights. The bigger problem is that the pack seemed to be falling at terminal velocity. Although it's possible that it would have reached its max velocity in the time shown, it's very unlikely.

9. Right here is the first time that the physics of the situation gets really out of hand. One of the inexperienced climbers high up on the rock face slips and falls off of the rock. Normally this wouldn't be a big deal, but his piton anchor fails as he falls. But there's the problem: the anchor fails before he even puts weight on it. In a real situation, if his protection were to fail, it would be most likely to do so when he was at the bottom of his fall, where the tension was at the greatest, not when he was at the top, where there would have been no tension on it at all.

10. The next problem is another problem with anchor tension, but this time on the opposite side of the swing. The climber falls down, but has a second anchor which stops him from immediately falling to his doom. Since it's tied to the wall and to the second climber, he swings in a long arc, almost another climber further down the wall, and then swings back up to the level of his climbing partner. This is the point when the anchor fails. Not when it was under the maximum strain at the bottom of his arc, but afterward when it was once again under almost no stress at all. It's very odd that these climbing protections keep failing when there's no strain and holding when the strain is greatest.

11. One thing that I found a bit odd was the relative speeds of the falls, as mentioned earlier when a pack was dropped from the people higher up on the wall. The pack, when it falls past them, appears to be roughly in the steady state, with no acceleration, and the fall is quite fast. The two people who fall later however take almost 3 seconds to reach the height of the climber closest to them. Either the people are much less dense than the pack, which is possible if the pack was filled with lead weights as discussed, but not likely. Why they didn't just film packs being dropped off of a cliff, I have no idea.

12. Okay, this isn't a problem in and of itself, but it sets us up for some of the later problems. When the people fall off of the wall, they are accelerating at the earth standard of 9.8 m/s^2. With this acceleration, it takes them 3 seconds from when the 2 of them are off the wall, to when the father is pulled off of the wall. After 3 seconds of acceleration, they would be going 29.4 meters per second, or about 65 miles per hour. This certainly makes it reasonable that the lower climbers and most of their anchors would be pulled off of the wall, a person going 65 miles per hour has quite a bit off momentum!

13. At this point we see the falling climbers pull two more climbers and two more anchors off of the wall. This is reasonable since they are carrying quite a bit of momentum, but their fall is arrested by reaching the end of the trio of experienced climbers' ropes, and being wrapped around the father. How, though, did the last set of anchors hold when the first two were ripped out of the wall without even slowing them down? The breaking strain of a piton is on the order of 15000 newtons. Since these snapped quite fast, we can assume that these had much higher forces applied to them, but the cams which she used for the final anchor which held have an approximate breaking strain of 14000 newtons. If you assume that the climbers were in free fall until the end of the rope. reaching a speed of 50 meters per second, and that the rope stopped the fall in about .2 seconds, there should have been upwards of 40000 newtons being applied to the cams just from the first two climbers, not including the father and son, which would have broken them handily. This is the fist point at which everyone would have died.

14. The next problem we have is the problem of the father stopping the falling climbers with his midsection. Using the numbers from above, there were 40000 newtons being applied to his midsection. If we assume a climbing rope has a 1cm contact width and that his waist was about 45cm of contact length, he must have had a pressure on his waist of approximately 8 million pascals. Since the breaking pressure of muscle is on the order of 500,000 pascals, it's safe to assume that the rope would have, if not cutting him in half, at least have delivered fatal injuries to his internal organs and spine, making falling down a bit of a moot point.

15. After the impossible stop that would have ended all their lives, and the force which almost certainly would have killed the father, there was yet another force which would have ruined his, otherwise, perfectly good day. After several seconds of being calm and trying to keep things together, the father slips and the rope which was around his waist slips past his neck and off of him, killing the first two climbers. Your neck is not a free interface though, according to the internet, it takes on the order of several hundred newtons to break someones neck, and the climbers appeared to weight more like 1000 newtons. As the rope slid past his neck, he would have, at the very least, had his trachea crushed, making it impossible for him to talk or breath, and at the worst a broken neck. So, the father is now dead 3 times over.

16. After the people fall, there is some discussion about how the anchors don't have the strength to hold all three of them. This is odd as they survived a 40000+ newton fall, but now only have to hold something on the order of 1200 newtons static. Also, since these anchors are specifically designed to hold up to these forces it is unlikely that even one would fail after the initial fall, let alone all three that she placed.

17. Something interesting I noticed was the fact that they were hanging very far away from the wall. The girl was trying to reanchor them in, but couldn't reach. There was a shot earlier though that clearly showed the section of rock which was underneath them had a gentle slope, which is kind of the opposite of an overhang. If anything they should have just hit the wall quite hard.

18. Now that they are hanging free though, we see another large physics blunder. The climbing system basically works by having one person on belay, who serves as an anchor, and another person climbing. Ideally there is a top anchor which has a pulley so that if one person falls the other person's weight is used to stop them. Since there is a pulley at the top, a much lighter person could belay for someone. However, in this scene we see the small girl being a stable counter for 2 grown men. Even with the pulley, she wouldn't have enough weight to balance it, and should have been pulled up to the top of the belay system instead of hanging stably.

19. The next blunder is that after the girl is unable to reach the wall to anchor them back in, the father tells his son to cut to rope, thus reducing the weight and saving his kids. The son pulls out a strait bladed knife to try to cut the rope. This would be fine if he had quite a while, but this type of knife was not designed to cut ropes. It would have taken quite a while for him to cut it even after he decided too. Much more likely for a climber to be carrying would be a serrated edge, which would be much faster at cutting that type of tensioned rope. I'll post a video about this later!

20. The next problem would have occurred just after cutting the rope. Although it may not seem like it at casual glance, climbing rope is actually a very stiff spring. This give is what allows you to fall any distance without breaking anything when the rope stops you. If it wasn't springy like this, the stop from the rope would be just as bad as hitting the ground from the same height you fell from. Now the problem is what happens when you partially unload a spring? The spring begins to bounce. The oscillations will be quickly damped in a climbing rope, but they will be there, and the bounce would have easily been enough to pull the last anchor from the wall, in fact, much more likely to do it than the weight of a third person.

21. This last one is a bit speculative, and they likely did it to keep the rating down, but the end of this 6:38 seconds of pain is a shot of the fathers body hitting the ground. When a person would hit the ground at the speed he hit, landing on solid rock, it's more likely that he would splash than bounce. A person's body simply couldn't maintain structural integrity if it hit like that. Would have been quite gross, I suspect.

Okay, that's all I could find in the first 6:38 minutes of Vertical Limit. I guess it was actually quite a bit. Between all the breaking and falling, that was really quite bad. Now, I suspect you'll have noticed I didn't really suggest any changes, that's because this scene was a total loss from go, more or less. A much better scene might have been to film a real climbing scene with real climbers where a reasonable single piece of equipment fails(say a carabiner) for the kid to blame himself for. At least you wouldn't have to violate the laws of physics.

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