《那些古怪又讓人憂心的問題》第15期:機槍飛行揹包
MACHINE-GUN JETPACK
Q. Is it possible to build a jetpack using downward-firing machine guns?
Q．用一挺向下射擊的機槍能做出一個飛行揹包嗎？A. I WAS SORT OF surprised to find that the answer was yes! But to really do it right, you'll want to talk to the Russians. -
A．我很驚訝地發現，答案是肯定的！不過要真的想把它做出來，你還得去向俄國人討教一下。-羅布.B
The principle here is pretty simple. If you fire a bullet forward, the recoil pushes you back. So if you fire downward, the recoil should push you up.
這東西的原理相當簡單：如果你朝前方開槍，槍的後坐力會把你往後推。因而如果你向下開槍，那麼後坐力就會把你往天上推。The first question we have to answer is "can a gun even lift its own weight?" If a machine gun weighs 10 pounds but produces only 8 pounds of recoil when firing, it won't be able to lift itself off the ground, let alone lift itself plus a person.
那麼我們要弄清楚的第一個問題是：槍產生的後坐力能夠抵消自己的重量嗎？如果一把機槍重5千克，但只能產生摺合4千克的後坐力，那麼它就沒辦法把自己推離地面，更不用說再算上開槍的人了。In the engineering world, the ratio between a craft's thrust and the weight is called, appropriately, thrust-to-weight ratio. If it's less than 1, the vehicle can't lift off. The Saturn V had a takeoff thrust-to-weight ratio of about 1.5.
在工程領域裏，一個飛船的推力和自身重力的比值被稱爲推重比。如果這個比值小於1，那麼飛船就飛不起來。"土星五號"在起飛時的推重比約爲1.5。Despite growing up in the South, I'm not really a firearms expert, so to help answer this question, I got in touch with an acquaintance in Texas.
雖然我在南方長大，但對於槍支卻不怎麼了解，因而爲了回答這個問題，我找了一個在得克薩斯的熟人幫忙。Note: Please, PLEASE do not try this at home.
警告：請你千萬不要在家裏嘗試這麼做！As it turns out, the AK-47 has a thrust-to-weight ratio of around 2. This means if you stood it on end and somehow taped down the trigger, it would rise into the air while firing.
通過測試我發現AK-47步槍的推重比在2左右，換言之，如果你把槍口立在地上，然後拿膠帶把扳機纏住，那麼整支槍就能飛起來。This isn't true of all machine guns. The M60, for example, probably can't produce enough recoil to lift itself off the ground.
但並不是所有機槍都有大於1的推重比，比如M60機槍的後坐力大概就不足以把它自己推離地面。The amount of thrust created by a rocket (or firing machine gun) depends on (1) how much mass it's throwing out behind it, and (2) how fast it's throwing it. Thrust is the product of these two amounts:
火箭（或射擊中的機槍）所能產生的推力取決於：（1）它能向後拋射出多少質量；（2）拋射出東西的速度有多快。推力等於這兩個量的乘積。If an AK-47 fires ten 8-gram bullets per second at 715 meters per second, its thrust is:
如果AK-47能在一秒內以715米/秒的速度射出10發8克的子彈，那麼產生的推力爲：Since the AK-47 weighs only 10.5 pounds when loaded, it should be able to take off and accelerate upward.
推力＝拋射質量的效率×拋射物的速度In practice, the actual thrust would turn out to be up to around 30 percent higher. The reason for this is that the gun isn't spitting out just bullets-it's also spitting out hot gas and explosive debris. The amount of extra force this adds varies by gun and cartridge.
在實際情況中，產生的推力還會比計算值大30％左右。原因在於槍口發射出來的不只是子彈，還有熾熱的氣體和炸藥碎片。這些額外推力的大小取決於槍支和彈藥的種類。The overall efficiency also depends on whether you eject the shell casings out of the vehicle or carry them with you. I asked my Texan acquaintances if they could weigh some shell casings for my calculations. When they had trouble finding a scale, I helpfully suggested that given the size of their arsenal, really they just need to find someone else who owned a scale.
整體的推進效率還取決於彈殼是不是也隨着子彈發射一起拋出去了。我問我那位得克薩斯的哥們兒能不能幫我稱一下彈殼的重量，當我發現他家裏似乎沒有秤之後，我善意地提醒他，以他家裏的軍火庫規模，去找一個家裏有秤的人就好了。We can try using multiple guns. If you fire two guns at the ground, it creates twice the thrust. If each gun can lift 5 pounds more than its own weight, two can lift 10.
10子彈/秒×8克/子彈×715米/秒＝57.2牛≈6千克重力So what does all this mean for our jetpack?
那麼對我們的飛行揹包來說這意味着什麼呢？Well, the AK-47 could take off, but it doesn't have enough spare thrust to lift anything weighing much more than a squirrel.
而一把AK-47裝滿子彈的重量也不到5千克，因而它能夠飛起來並向上加速。At this point, it's clear where we're headed: You will not go to space today.
你今天去不了太空If we add enough rifles, the weight of the passenger becomes irrelevant; it's spread over so many guns that each one barely notices. As the number of rifles increases, since the contraption is effectively many individual rifles flying in parallel, the craft's thrust-to-weight ratio approaches that of a single, unburdened rifle:
如果我們能把足夠多的步槍綁在一起，那麼搭載的那個人的重量就無關緊要了，因爲他的體重已經分散到大量的槍身上去了。隨着步槍數量的增加，由於這個裝置本質上還是許多獨立的步槍的並聯，因而整體的推重比會漸漸趨近於一把不搭載負載的槍的推重比。But there's a problem: ammunition.
但還有一個問題：彈藥數量。An AK-47 magazine holds 30 rounds. At 10 rounds per second, this would provide a measly three seconds of acceleration.
一把AK-47步槍只能裝彈30發，以每秒10發的速度來算，這把槍只能提供3秒的加速度。We can improve this with a larger magazine-but only up to a point. It turns out there's no advantage to carrying more than about 250 rounds of ammunition. The reason for this is a fundamental and central problem in rocket science: Fuel makes you bullet weighs 8 grams, and the cartridge (the "whole bullet") weighs over 16 grams. If we added more than about 250 rounds, the AK-47 would be too heavy to take off.
我們可以通過攜帶更多的彈藥來克服這一缺點，但是這個方法有一個上限。你會發現當你攜帶超過250發子彈後，再繼續增加子彈數將不會再給你帶來任何好處，原因在於火箭科學中一個基礎卻重要的問題：燃料會增加你的重量。每枚彈丸質量8克，整顆子彈（彈丸、彈殼、火藥、底火……加起來）質量超過16克。如果你攜帶超過250發的彈藥，那麼你的AK-47就會因過重而無法飛起來。This suggests our optimal craft would comprise a large number of AK-47s (a minimum of 25 but ideally at least 300) carrying 250 rounds of ammunition each. The largest versions of this craft could accelerate upward to vertical speeds approaching 100 meters per second, climbing over half a kilometer into the air. So we've answered Rob's question. With enough machine guns, you could fly.
這意味着最佳配置是一大把（至少25把，最好超過300把）各攜帶250枚彈藥的AK-47步槍，這個配置能讓你的飛船加速至接近每秒100米的速度，你能飛上500多米的高空。所以至此，羅布的問題已經有了答案。只要你有足夠多的機槍，你是能夠飛起來的。But our AK-47 rig is clearly not a practical jetpack. Can we do better?
但我們的AK-47步槍顯然不是製作飛行揹包的理想武器，能不能再給力一點兒？My Texas friends suggested a series of machine guns, and I ran the numbers on each one. Some did pretty well; the MG-42, a heavier machine gun, had a marginally higher thrust-to-weight ratio than the AK-47.
我的朋友推薦了其他一些機槍，我也一一進行了計算。有些表現很好，比如重機槍MG-42，它的推重比要比AK-47更高一些。Then we went bigger.
接下來就輪到大傢伙了。The GAU-8 Avenger fires up to 60 1-pound bullets a second. It produces almost 5 tons of recoil force, which is crazy considering that it's mounted in a type of plane (the A-10 "Warthog") whose two engines produce only 4 tons of thrust each. If you put two of them in one aircraft, and fired both guns forward while opening up the throttle, the guns would win and you'd accelerate backward.
GAU-8復仇者多管機炮能在1秒內射出60枚0.5千克的炮彈，它產生的後坐力將近5噸。這個後坐力是相當恐怖的，因爲搭載它的A-10雷電攻擊機的2個引擎每臺只能產生4噸的推力。如果你在A-10上裝上2臺機炮，油門全開並同時向前開火，那麼機炮會贏過引擎，飛機將會向後加速。To put it another way: If I mounted a GAU-8 on my car, put the car in neutral, and started firing backward from a standstill, I would be breaking the interstate speed limit in less than three seconds.
換個角度，如果我把GAU-8裝在我的車上，車子掛空擋停着，然後開始向後開火，那麼我會在3秒之內超過美國州際公路的速度限制（約110千米/小時）。"Actually, what I'm confused about is how."
"其實我更想知道你要怎麼把我攔下來。"As good as this gun would be as a rocket pack engine, the Russians built one that would work even better. The Gryazev-Shipunov GSh-6-30 weighs half as much as the GAU-8 and has an even higher fire rate. Its thrust-to-weight ratio approaches 40, which means if you pointed one at the ground and fired, not only would it take off in a rapidly expanding spray of deadly metal fragments, but you would experience 40 gees of acceleration.
雖然這炮拿來做陣列火箭引擎會很不錯，但俄羅斯人還有更好的東西。格里亞澤夫－希普諾夫GSh-6-30加特林機炮的重量只有GAU-8的一半，但射速更高，它的推重比接近40。這意味着如果你朝地面開火的話，除了會有一股急速膨脹的致命金屬碎片雲，你還會以將近40倍重力加速度騰空而起。This is way too much. In fact, even when it was firmly mounted in an aircraft, the acceleration was a problem:
GSh-6-30的後坐力過於恐怖，即使是牢固地安裝在飛機上，後坐力產生的加速度仍然是個很大的問題。The recoil . . . still had a tendency to inflict damage on the aircraft. The rate of fire was reduced to 4,000 rounds a minute but it didn't help much. Landing lights almost always broke after firing . . . Firing more than about 30 rounds in a burst was asking for trouble from overheating . . .
後坐力……仍然容易對飛機造成損傷，即使把射速降低到每分鐘4000發也沒有多大改觀。在開火之後着陸燈幾乎每次都被毀了……連續發射超過30發就會因過熱而發生故障……But if you somehow braced the human rider, made the craft strong enough to survive the acceleration, wrapped the GSh-6-30 in an aerodynamic shell, and made sure it was adequately cooled . . .
但是如果你設法把人類乘客安置好，建造出一個強度足夠承受這麼大加速度的飛船，把GSh-6-30包裹在氣動外殼裏，然後確保它能妥善地冷卻……. . . you could jump mountains.
那麼你就能飛越重山啦。1 Judging by the amount of ammunition they had lying around their house ready to measure and weigh for me, Texas has apparently become some kind of Mad Max-esque post-apocalyptic war zone.
1． 從他堆在家裏用來給我測試的彈藥數量來看，得克薩斯很明顯已經變成某種程度上的"瘋狂的麥克斯"式的後末日戰爭區了。--格雷格.戈貝爾，2 Ideally someone with less ammo.
2． 最好是家裏沒這麼多軍火的。
