神盾局天空母艦原理！

Physics of the New SHIELD Helicarrier
BY RHETT ALLAIN 10.29.13

新神盾局天空母艦物理原理
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.

這是《美國隊長2：酷寒戰士》中的新神盾局天空母艦。你可前往YouTube觀看預告。

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.

也許你注意到，它與《復仇者聯盟》的天空母艦稍有不同。第一，螺旋槳葉片組成的推進器較像噴射機，而非直升機。為什麼？我認為《美國隊長2》的編劇看過我之前關於神盾局天空母艦的文章。在那篇文章中，我估計這些直升機式葉片產生的氣流速度必須超過650公尺/秒（海平面音速約為340公尺/秒）。因此，顯然編劇想藉由使它看起來像噴射引擎，突顯空氣推進的高速。

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

我想這些編劇欠我一罐啤酒什麼的。至少我應該出現在影片感謝貢獻者名單中。

Modeling Thrust

推力模型

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.

如何計算天空母艦的推力？藉由一般科學研究方式－製作模型。不必是完美的模型，只要能用即可。

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.

想像如果你有一把乒乓球槍。它們以不同方式運作，但想像一下這種擁有橡皮筋動力發射裝置的槍。當球被射出時，橡皮筋必須提供推力。

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.

因為力一向是兩個物體間的交互作用，槍施予球推力，球施予槍反作用力。施予槍的力將導致槍的動量改變－這就是後座力。當然，乒乓球不會產生太大的後座力，但還是會有。

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.

現在假設你將乒乓球垂直向下射擊。你是否能以足夠以將你推向空中的速度射擊？好，似乎不太可能。但如果將一大堆乒乓球垂直向下射擊呢？或者，如果並非射擊乒乓球？如果你射擊空氣微粒？這是否可行？是的。基本上這就是直升機的原理。

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.

如果想使直升機懸停於某處，這些空氣微粒的推力必須相當於直升機重量。有兩種方式可改變這個推力。你可改變這些粒子向下移動的速度，或增加粒子數量。

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).

你可使用較大旋翼、較小空氣速度，或較小旋翼、較大空氣速度。一旦旋翼大小固定，幾乎決定了空氣推進速度（如果你知道直升機重量）。

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).

我將跳過細節（詳情請看原始文章）。總之其中有兩點令人感興趣之處。這個模型顯示推進速度取決於質量及旋翼大小（和空氣密度）。

υ=√(□(2mg/ρA))

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.

第二點是使飛行器懸停所需的動力。這些空氣微粒向下噴出的速度越快，需要越大的動力。這就是為何人類使直升機擁有如此大的動力－它們不需要這麼大的動力。這產生以下的直升機動力方程式。

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.

我用ρ代表空氣密度是否相當明顯？希望如此。

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:

這是最精彩的部分。也許這個模型是假設性虛構的，對嗎？我接受這個可能性。但如果我查閱真正直升機的資料？我可以查閱旋翼大小及重量。我可藉此計算所需的動力估計值。如果我也查閱引擎動力，我可將計算出的動力與資料顯示的動力比較。這是兩者的比較圖：

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.

天空母艦如何？

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.

如果擁有這樣的推進速度，新天空母艦會是什麼模樣？如果它的推力看似來自噴射引擎，我們不妨估計一下噴射機的推進速度。我可使用相同想法，即使噴射機從前方吸入空氣、從後方排出。是的，它比這更複雜，但將產生一個估計值。

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).

我們以F-15為例。根據維基百科，這種飛機的推力為63.38千牛頓，或經過燃燒室後，（每個引擎）推力為105.78千牛頓。噴嘴面積是多少？根據這張圖，我估計每個噴嘴的半徑約0.6公尺（雖然我認為估計值稍微大了點）。

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

如果我只觀察空氣推力（是的，其中包含一些假設和估計），我得到：

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.

藉由這個方程式，我得到以下兩種空氣推進速度：

˙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.

好，雖然我的計算有些不嚴謹的部分（例如假設空氣不可壓縮及類似的非實際情況），我不認為這與事實相距甚遠。我認為新天空母艦更接近真實情況。是的。我剛剛確實寫過了。

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.

還有一個問題。事實上是相當大的問題。如果這些天空母艦較類似噴射機，而非直升機？最重要的是，這是裝設後燃器的飛機圖像。

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.

這類似天空母艦上的東西，不是嗎？我認為理論上你可藉由電力使渦輪風扇運轉（來自核電廠或某種更新奇的能源）。然而，這並非後燃器實際運作的方式。當飛機使用後燃器，將使燃料加入噴出的氣流中。這增加了氣流施予飛機的溫度與壓力，增加了推力。不幸的是，這也增加了油耗，你無法僅靠電力做到這一點。你確實需要燃料。我認為這種天空母艦需要相當大量的燃料。尤其是如果它需要長時間飛行。

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

我想這是編劇可對下一部天空母艦外觀進行的修改－也許在《復仇者聯盟2》中。

原文：https://www.wired.com/2013/10/physics-of-the-new-shield-helicarrier/