2014, 7-30 , 星期三


Physics of the New SHIELD Helicarrier

Rhett Allain 於 2013 年10月29日

There it is. The new and upgraded S.H.I.E.L.D. Helicarrier from the new Captain America movie: The Winter Soldier. You can check out the trailer here on YouTube.


Maybe you notice that this is a little different than the Helicarrier in The Avengers. For one, the thrust stuff coming out of the propeller blades looks more like a jet engine than a helicopter. Why? I would like to think that the writers for Captain America 2 read my previous post on a flying SHIELD Helicarrier. In that post, I estimated that the speed of the air coming out of these helicopter-like blades would have to be over 650 m/s (the speed of sound at sea level is about 340 m/s). So, clearly the writers want to emphasize the massive speed of air thrust by making it look like a jet engine.


I guess these writers owe me a beer or something. At the very least, I should appear somewhere in the movie credits.


Modeling Thrust


How do you even calculate something like the thrust of a Helicarrier? You do we what we always do in science – make a model. It doesn’t have to be a perfect model, it just has to sort of work.


Imagine you have one of those ping pong ball shooting guns. These work in different ways, but imagine one that has a rubber-band powered launcher. When the ball is being shot, the the rubber band has to push on the ball.


Since forces are always an interaction between two objects, the gun pushes on the ball and the ball pushes back on the gun. This force on the gun will cause a change in momentum for the gun – that’s recoil. Of course a ping pong ball won’t do too much in terms of kick-back, but still.


Now suppose you shoot this ping pong ball straight down. Could you shoot it fast enough to push you up in the air? Well, that doesn’t seem very likely. But what if you shot a whole bunch of ping pong balls straight down? Or what if you didn’t even shoot ping pong balls at all? What if you shot tiny balls of air? Would that work? Yes. That’s essentially what a helicopter does.


If the helicopter is going to hover in place, the force it pushes on these tiny air balls will have to be equal to the weight of the helicopter. There are two things that you could change to change this thrust force. You could change the speed that these balls move down, or you could increase the number of balls.


You can either have larger rotors with slower moving air or smaller rotors with faster moving air. Once you set the rotor size, you pretty much have determined the thrust air speed (if you know the mass of the helicopter).


I’ll skip the details (check out the original post for the details). In short, there are two interesting things. This model says the thrust speed depends on the mass and rotor size (and the density of air).



The second thing is about the power needed to make this vehicle hover. The faster you have to throw these air balls down, the greater the power needed. This is why the human powered helicopters are so large- they require less power. This gives the following expression for helicopter power.


P=1/(4√ρA) 〖(2mg)〗^(3⁄2)

Is it clear that I am using the letter ρ for the density of air? I hope so.


Here is the best part. Maybe this model is BOGUS, right? I accept that possibility. But what if I look up data on real actual flying helicopters? I can look up the rotor size and the weight. From this I can calculate the estimated required power. If I also look up the engine power, I can compare my computed power with reported power. This is what that looks like:


I love that graph. Nice and linear which indicates the model works with these vehicles. Oh, and if you use the same thrust model with real helicopter data you would find that the thrust air speed for these real helicopters is in the 18 – 30 m/s range (not over 600 m/s).

我喜愛這張圖。完美的線性顯示這個模型適用於這些飛行器。喔,如果你將真實的直升機數據用於相同的推力模型,將發現真正直升機的空氣推進速度落在18 – 30公尺/秒範圍(不超過600公尺/秒)。

What about the Helicarrier?
If you just make some estimates for the mass of the Helicarrier and rotor size, you can get both the thrust speed (640 m/s) and the power required (3 x 1011 watts). Assuming the new Helicarrier has the same size rotors and mass, these values would be the same.


如果你預估天空母艦的重量及旋翼大小,可得到推進速度(640公尺/秒)及所需動力(3 x 10^11瓦)。假設新天空母艦擁有相同的旋翼大小及重量,這些數值將會相同。

What thrust speed does this new Helicarrier look like it would have? If it looks like the thrust from a jet, let’s estimate the jet’s thrust speed. I can use the same idea even though jets take air in front of them and throw them behind. Yes, it’s more complicated than that, but it will give an estimate.


Let’s look at an F-15. According to Wikipedia, this plane has a thrust of 63.38 kN or 105.78 kN with after burners (for each engine). What about the area of the thrust nozzles? Based on this image, I am going to estimate each nozzle to have a radius of about 0.6 meters (although I think that estimate is a bit large).


If I just look at the thrust force based on the air (yes, there are some assumptions and estimations here), I get:


F_(air=) (ρAυ^2)/2

Using this, I get the following two thrust air speeds:

˙Dry Thrust: Air speed = 305 m/s.
․After Burner: Air speed = 394 m/s.


˙淨推力:空氣速度= 305公尺/秒。
˙經燃燒室後:空氣速度= 394公尺/秒。

Ok, since I took some liberties in my calculations (like assuming incompressible air and dumb stuff like that), I don’t think these are too far off. I think that this new Helicarrier is much more realistic. Yes. I actually just wrote that.


There is still one problem. Quite a large problem, actually. What if these Helicarriers are more like jet engines than helicopters? On top of that, here is an image of a plane with afterburners on.


That sort of looks like the stuff from the Helicarrier, doesn’t it? I think you could technically run a turbofan on electricity (from a nuclear power plant or something more exotic). However, that isn’t true for afterburners. When a jet uses afterburners, it adds fuel to the exhaust. This increases the temperature and pressure of the gas leaving the plane and increases thrust. Unfortunately, it also increases fuel consumption and you can’t do this with just electricity. You actually need fuel. I have a feeling that this Helicarrier would take MASSIVE amounts of fuel to fly. Especially if it is to fly for extended periods on time.


I guess that’s something the writers can fix with the next appearance of the Helicarrier – maybe in The Avengers 2.




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