So you have your awesome giant Jaeger and you want to use it to fight the mean Kaiju that are destroying your city. But there is a problem. Your Jaeger is here and the Kaiju are there. How do you get from here to there? Clearly, you need to fly. Well, not really fly. No, instead you will just get some helicopters to carry you over there.
Don’t act surprised. You know what is going to happen. I am going to make some estimations to see if you could do this. Yes, I know it’s just a movie. Really, I do.
What do we know about these Jaegers? Really, no one states the mass. However, they do give the height. Here is an example Jaeger. A height of about 250 feet seems reasonable – or about 40 times the height of a human.
Does this mean the mass would be 40 times the mass of a human? No. Really, this is another great example of how things don’t scale up the way we sometimes expect. For a short moment, let’s just pretend that both the Jaeger and a human are cylinders. Yes, I know that’s not true – but it isn’t crazy either. Here is a cylinder human of height h.
If I know the height and radius of this cylinder, I can find the volume. Now, what if I increase the height by some factor, say s? If the larger cylinder “looks” the same as the smaller one, the radius would also have to increase by the same factor s. This would make the volume:
If you double the height of the person, you increase the volume by a factor of 8. The common sense answer (which is wrong) is that if you double the size, you double the volume. Wrong.
If a Jaeger is 40 times taller than a human and with a similar shape, it would have 403 = 64,000 times the volume. Actually no one really cares about the volume. However, if you know the volume and the density you can find the mass. Let me call the mass of a human mh and the mass of a Jaeger mj (and densities ρh and ρj). I can get the mass of the Jaeger in terms of mass of the human (assuming it is 40 times taller).
Now all I need to do is to estimate the mass of a human (let’s say 75 kg) and the ratio of densities. I have no idea what a Jaeger is made of, but I suspect the density is higher than a human. If the Jaeger density is twice that of a human, then the jaeger mass would be about 9.6 x 106 kg. See. That wasn’t so bad.
You know I love helicopters, right? In the Pacific Rim trailer, it looks like each Jaeger is being carried by 8 Boeing CH-47 Chinooks. According to Wikipedia, the CH-47D variant can carry a payload of 26,000 pounds (11,793 kg). Let’s say that you strip out any unnecessary stuff and maybe you increase the payload capacity to 15,000 kg. That would mean that 8 of these helicopters could carry 1.2 x 105 kg – assuming an ideal situation. Well, that is less than the 9.6 x 106kg.
Fine. Then how many? Well, if I need to carry 9.6 x 106 kg and each CH-47 carries 15,000 kg, that would mean you need:
You would actually need more than 64 helicopters. Why? Let me just draw a sketch showing many helicopters carrying a jaeger.
If you consider the tension in the cable from the far helicopters, they won’t pull vertically. Assume that each helicopter could pull with a tension of (15,000 kg)(9.8 N/kg). Then as the cable angle gets closer to horizontal, only a component of this tension will go towards lifting the Jaeger. Just as an example, suppose a helicopter made cable with an angle of 60° with the horizon. This helicopter would only be able to give a vertical lift of 86% compared to a helicopter pulling straight up.
But what would this look like if at least 64 helicopters were carrying a Jaeger? Suppose that the helicopters are arranged in a square grid pattern (because it will be easier to calculate. How big would each square grid have to be to give the helicopter enough space? Well, if I make a quick measurement from the trailer, the CH-47s have about 24 meters between adjacent aircraft. This would give each helicopter a square flying space of about 48 x 48 meters (just a guess). I would suspect that real helicopters would need to be even farther apart.
For 64 helicopters, the grid would have 8 helicopters by 8 helicopters. This would be a giant helicopter filled square that is 384 m by 384 m. Well, actually it would be just 336 x 336 m since you don’t need spacing on the outer helicopters. Let’s sketch this.
Of course this just shows the front row of helicopters. But what about the angle of the cable? I will mention that in the homework questions below.
If we make the assumption that each of these helicopters supports 1/8th of the Jaeger load, then it would need a thrust force of about 12 million Newtons (including the mass of the helicopter – which is small compared to the load). I also know the rotor area for this helicopter is about 526 m2 (it has two rotors).
It just so happens that I recently looked at the power needed for a helicopter device to fly (in this case a hover bike). First, let’s calculate the thrust speed for the air coming off the rotors.
Using my value of the thrust for mg, I get a thrust speed of 195 m/s (436 mph). That’s pretty fast considering that most real helicopters produce a thrust around 25-30 m/s. Now, what about the power? (if you want a derivation of these expressions, check out my post of the S.H.I.E.L.D. Helicarrier).
Again, putting in the values for the case of eight helicopters the power for each helicopter would be 1.17 x 109Watts or 1.56 million horsepower. The listed engine for the CH-47 is around 7 x 106 watts. In order for 8 CH-47 helicopters to carry a Jaeger, they would need an engine about 1000 times more powerful.
Why do I have to suck the fun out of these cool movies? It’s just what I do.
Here are some extra questions for you.
- Suppose only 8 normal CH-47s carry a Jaeger. Using this, calculate the mass and estimate the density of a Jaeger.
- For the case of 64 CH-47s carrying a Jaeger (as I estimated). What kind of cable would you need to use?
- Also for the 64 helicopters. Suppose you arrange them in a square grid. How high above the Jaeger would they have to fly so that the cable angle on the outer helicopters is no more than 20 degrees from vertical?
- For the above question, estimate the total mass of the cable needed.
- What if you wanted to carry a Jaeger with rockets? Could the Saturn V rocket lift a Jaeger? If you like, you can just use the first stage of the rocket. Don’t forget to include the mass of fuel.
- Suppose a Jaeger was able to fly with its own large rotor. If the thrust speed from the rotor was 40 m/s, how large would the rotor need to be? What kind of power would this require?