The song was also a rare nod to Realpolitik. It was de rigueur in the Cold War for snarky pop culture commentary to be directed exclusively at America, the MTV generation not comprehending it takes two to saber rattle. However, Nena guitarist Carlo Karges claims the idea for 99 Luftballons came to him after watching balloons released during a Rolling Stones concert drift over the Berlin Wall toward the Soviet sector. While the US certainly deserves its share of blame for nuclear brinksmanship, go ask Arthur Koestler or Andrei Sakharov about the innocence of the USSR. When you protested outside SAC you got on the cover of Newsweek. When you protested outside of RVSN RF you got sent to the gulag.
The Russians Love Their Children Too
For those of you joining us today who weren't alive in the 80s, perhaps I should pause and provide a back then. Back then the eastern half of present-day Germany was a communist satellite known as the DDR and chocked full o' Soviet missiles aimed at the imperialist dogs running on the other side of the Berlin Wall. These were kept on a short leash, ready to launch at the first sign of an incoming threat, including signs of the mistaken kind. As such, Karges had every reason to fret. To add insult to injury, any DDR launch sites would have certainly been included in NATO targeting packages, American architects of its first strike capability being nothing if not thorough. The only way to win is not to play, etc.
It ultimately took a Soviet to break the Soviet stalemate. Mikhail Gorbachev stepped up to end the fifty-year arms race begun by Stalin and Klaus Fuchs and accidentally dissolved the USSR in the process. The Berlin Wall came down, the nuclear doomsday clock got pushed back a few minutes, and a country once run by a corrupt and untouchable Politburo is now run by corrupt and untouchable Russian mobsters. Score one for capitalism.
Technically, only the English lyrics of 99 Luftballons imply nuclear war, something which does not feature in the original German version. Wikipedia informs me these were penned by British musician Kevin McAlea. Willypete also says Nena were not pleased with the results and refuse to perform the English-language version to this day. Presumably, McAlea was just taking his lead from contemporaries like Sting, Jesus Jones, the Scorpions, and Asia, all of whom tried to make Armageddon danceable. A mouse-half-not-eaten kind of cat, to coin a phrase. Anyway, it's unclear who is clamoring for Nena to perform these days, if anyone, and I felt bad about that little cheap shot until I remembered they probably made more money off their ditty than I will see in my entire life with four university degrees. (Also, they mock Captain Kirk in the song. That alone demanded some kind of a response.)
Right Here, Right Now
Today on Drink and Derive, let's have a look at what physics has to say about 99 Luftballons. In honor of our topic, I have switched from my usual whiskey to vodka. Still, there are difficulties. The capabilities of Soviet early warning radar aren't exactly something you can request from Kremlin.gov, glasnos not being the all-access pass one might hope. Hello, I am a random Internet doorknob. Please provide the technical specifications of your EWS so I can make mirth on my website blog. Not that it matters. Tell me your PAVE PAWS delivers 100 kW of radiant energy per steradian and I wouldn't know what to do with that tidbit. I think it goes into Maxwell's equations, then some kind of voodoo involving spherical harmonics happens and you get a return signal and the RMS gives you an SNR. Or something. I gave up trying to understand Maxwell's equations a long time ago. I'm not proud of that, but I have made my peace with it.
As such, we need to find some other angle of attack. A Fermi number, as Enrico Fermi called his approach to estimating the number of piano tuners in Chicago when you can't just look them up in the Yellow Pages and count. What to do?
Soviet radar on the other side of the Berlin Wall would have been watching for American Pershing II missiles. I know this because every West German exchange student attending my school at the time was rather cross about Reagan putting them there (you don't know heartbreak until your prom date dumps you over the INF). So, here's our plan: We compute the radar cross section of a Pershing II. We then compute the radar cross section of 99 balloons. The circumstances under which the latter approximates the former gives us some indication of the plausibility of the Rolling Stones starting WW-III. Easy peasy.
By a strange cosmic coincidence, it turns out LabKitty once worked at the aerospace firm that designed and built the Pershing. (Okay, it was more like an internship but anything to fluff the resume counts in this economy.) I could call in a few favors and obtain the radar cross section via industrial espionage, or, assuming I don't want to spend the next 40 years in Gitmo taking falafel smoothies up my butt, I could just use whatever the Internet has to say about it.
Willypete says the Pershing II is 10.6 m long and 1.1 m in diameter. This gives a nominal radar cross section of 1.1 • 10.6 = 11.6 m^2. We might reduce that by throwing in a direction cosine to account for the orientation of the missile relative to the radar wavefront, but I'm doing that thing they taught us to do in engineering school which is you assume every variable in your problem assumes the worst possible value. Or, as you discover it's called in the real world: Tuesday.
Next up: Balloons. Nena is rather vague on the nature of the balloons, save to say there are 99 of them. I will assume these are standard issue helium-filled latex, the mylar technology that would one day put minions in every conceivable public space not yet a thing in 1983. Clearly, latex has different E&M reflective properties than the rolled titanium outer hull of a Pershing, but that's one of those things you learn to overlook in a first approximation.
Footnote: I can neither confirm nor deny the Pershing outer hull is constructed of rolled titanium.
We assume the 99 balloons are released as a point source at t = 0. They ascend and diffuse, and at some later time their collective cross section will approximate that of a Pershing II. At that moment, and for some moments after, the 99 balloons are capable of triggering the Soviet EWS. However, further diffusion results in the disruption of a coherent return signal, upon which the balloons no longer pose a threat (to humans, that is -- I would imagine there's more than a few arctic terns somewhere choked to death on a scrap of latex silkscreened with Mick Jagger's lips). Let's see what kind of imaging window this implies.
Each balloon is subject to a constant vertical buoyant force. Plugging a constant F into F = ma and integrating twice, we find balloon altitude is proportional to time-squared.
The diffusion of the 99 balloons is described by the diffusion equation. If you look up the solution of the 2D diffusion equation, it will tell you the collective area of the balloon herd increases linearly in time.
Combining these, we discover the radar cross section (A) goes like the square root of altitude (a), or A = c √a for some constant c (which depends, among other things, upon the mass of the balloons and a diffusion constant -- we'll return to these momentarily). If the balloons do not approximate the radar cross section of a Pershing II whilst appearing on radar, we can call Nena busted. However, establishing this requires some numbers.
Winds of Change
Radar is not omniscient. There is a laundry list of imaging problems making life difficult for the would-be EWS, chief among them being ground clutter. If you've ever listened to ATC while on a commercial flight, and who hasn't, you probably noticed Departure doesn't pick you up on radar until you get up above a thousand feet or so. This is because at lower altitudes the echo from your aircraft gets swamped in the chaff produced by the terrain and buildings and flocks of suicide geese and whatnot. Similarly, Soviet EWS can't see the Luftballons below some minimum altitude.
Fortunately, with the collapse of the USSR a few details of their military hardware have seeped onto the net. The nice folks at fas.org provide some specs for the ZRK-SD Kub 3M9 mobile surface-to-air missile system, which seems like a reasonable stand-in for the listening post tech of the DDR. FAS lists a minimum altitude for radar engagement of the 3M9 equal to 100 meters. Make a note.
For balloons we go to fastballon.com, who offer a 12" latex in assorted colors with custom silkscreening and next day shipping (fastballon.com: When you need balloons fast!). These are $75/100, so we get a bulk discount and get to keep one balloon as a Drink and Derive memento.
The density of helium (at STP) is 0.18 kg/m^3. The density of normal air is 1.3 kg/m^3. A 12" helium balloon has a radius of 0.15 m, a volume of 0.014 m^3, and so a mass of (0.18 kg/m^3 • 0.014 m^3) + 0.005 kg = 0.0075 kg (I'm assuming the balloon weighs 5g uninflated). Chasing around the Archimedes, we find the balloon has an unbalanced buoyant force of [ (1.3 – 0.18) 0.014 – 0.005 ] 9.8 = 0.105 N. Plugging this into F = ma, we find a = ~14 or v = 14t or z = 7t^2. This gets the balloons to an altitude of 100 meters in about 4 seconds. If we plug t = 4 into the solution of the diffusion equation, it will give us the collective size of the balloon herd at 100 meters, that is, when they first appear on Soviet radar.
The final missing piece of the puzzle is the appropriate diffusion constant, D. The experiment is simple. Release two balloons and track their separation distance as a function of time. Fit a curve D√t to the data and extract D (diffusion area is linear in time; distance goes like square root). Repeat during various atmospheric conditions. Report your findings so that Internet wiseasses can overanalyze Cold War protest songs on their website blog.
Alas, nobody has carried out this experiment as far as Google is concerned.
This is a problem. Without a diffusion constant, we can't solve the diffusion equation, and without a solution we can't quantify the cross section of the balloons. Our choices are getting a Kickstarter started and coming back later once D is in hand or changing tacks now and getting more creative with our parameter estimation. Seeing as I currently still have some vodka left, let's go with the latter.
What Google will happily locate for me is a gazillion articles on smokestack dispersion. These model the concentration of a pollutant released as a point source from the stack which disperses into a cone shaped volume over time with a cross section described by the bivariate Gaussian distribution (i.e., the solution of the 2D diffusion equation). Airborne pollutants are not balloons, but our working assumption will be air motion dominates the dispersion process. The size of what's getting tossed around is irrelevant so long as it's buoyant.
The good news is we can simply read off the vertical and horizontal plume dimensions (standard deviations thereof, actually) as a function of distance using one of the many Pasquill-Gifford curves this material includes. The bad news is there's a fundamental difference between the behavior of stack effluents and the behavior of helium balloons. Once gas exits the stack it cools, and once a gas cools it no longer rises. From then on the pollution moves horizontally as determined by the wind. From the looks of various representative example photos, this transition occurs almost immediately, which I guess is why smokestacks need to be tall, lest your hot rising pollution becomes cool horizontally-moving pollution that visits the elementary school next door.
As such, the Pasquill-Gifford curves give the plume dimensions (standard deviations thereof, actually) in terms of downwind distance x, not vertical distance z. So, here's the plan. We assume dispersion is more a question of flight distance and less a question of whether the distance is horizontal or vertical. So while we really want the value of the standard deviation at z = 100, we will use the value given by the Pasquill-Gifford plot at x = 100. Capisce?
The other input required to use a P-G plot is the Stability Category, which is a qualitative description of the prevailing atmospheric conditions, specified as a letter grade: A (very unstable) through F (stable). I picked the middle value (C: slightly unstable) which seems appropriate for an outdoor concert. This results in values for sigma-z (vertical standard deviation) and sigma-y (horizontal) of about 10 meters. According to the usual bivariate Gaussian rules, 95% of the balloons would be contained within ±1.96σ, a circular area of π • (1.96•10)^2 or about 1200 m^2.
By the time they reach an altitude of 100m, the balloons would have dispersed across an area of more than a thousand square meters. This compared to the previously calculated Pershing II radar cross section of 11.6 m^2.
Alas, 99 Luftballons look nothing like a missile. What do they look like? A 12" sphere is about the size of a duck. Radar is routinely used to track migratory birds (something I did not know before beginning our strange journey today) and ornithology-grade radar can image individual birds (ibid). It seems reasonable to assume military-grade radar has at least as good a resolution, the priorities of national security commanding concomitantly more advanced technological resources than bird watching.
A balloon is not a duck, but a duck is even less a Pershing II. What the DDR monitoring sites on the other side of the Berlin Wall are going to see rising from the Rolling Stones concert is a flock of ducks. Slow-moving, ever-ascending, oddly-spherical ducks, but ducks nonetheless.
Not even the reddest Red was willing to start WW-III over ducks.
Or were they?
The Final Countdown
You and I in a little toy shop
Buy a bag of balloons with the money we've got
Set them free at the break of dawn
'Til one by one they were gone
Back at base bugs in the software
Flash the message "something's out there!"
Floating in the summer sky
Ninety-nine red balloons go by
Buy a bag of balloons with the money we've got
Set them free at the break of dawn
'Til one by one they were gone
Back at base bugs in the software
Flash the message "something's out there!"
Floating in the summer sky
Ninety-nine red balloons go by
It occurs to me I never showed you the song lyrics, so those of you not familiar with 99 Luftballons probably have no idea what I'm ranting about. Presumably you are capable of tracking these down on your own, but I find every lyrics site on the web to be a wretched hive of popup ads and crippled back buttons. (What's up with that by the way? Just because I want to know if Pat Benetar is singing hit me with your pet shark doesn't mean I owe somebody money.) I promise you will never find pop up ads or crippled back buttons on Labkitty, mostly because I don't know how to do that.
Ninety-nine red balloons
Floating in the summer sky
Panic bells, it's red alert
There's something here from somewhere else
The war machine springs to life
Opens up one eager eye
Focusing it on the sky
Where ninety-nine red balloons go by
Floating in the summer sky
Panic bells, it's red alert
There's something here from somewhere else
The war machine springs to life
Opens up one eager eye
Focusing it on the sky
Where ninety-nine red balloons go by
Instead, I will close by reminding you of a real-life 99 Luftballons. On September 26, 1983, the Soviet early warning "Oko" system was mistakenly triggered, not by balloons but by unusual atmospheric conditions. Had the incident been reported up the chain of command as was standard procedure, it's possible -- some analysts say likely -- the Soviets would have launched a nuclear strike. At the time, relations with the West had deteriorated to a new low, leaving the Soviets paranoid and twitchy, none of which was being helped by Reagan's cowboy posturing. Not to mention the Soviet command and control structure was riddled with equipment and administrative glitches. Just a few weeks earlier their air defense had shot down a civilian airliner.
Ninety-nine decision street
Ninety-nine ministers meet
To worry, worry, super scurry
Call the troops out in a hurry
This is what we've waited for
This is it, boys, this is war
The president is on the line
As ninety-nine red balloons go by
Ninety-nine ministers meet
To worry, worry, super scurry
Call the troops out in a hurry
This is what we've waited for
This is it, boys, this is war
The president is on the line
As ninety-nine red balloons go by
If even one Soviet ICBM cleared the silo that day (unlike the one that exploded during a test firing and killed the commander of their Strategic Rocket Forces) it would have been a bad day for everyone. SAC had like a billion nukes on constant alert ready for a counterstrike, and people like Curtis Lemay had been itching to poke the launch button since Cuba. The Soviets had every reason to fear American capabilities. That being said, I never understood Soviet fears about American intentions. What, was the West lusting after Trabants and combine technology? After 40 years of the most ferocious prosperity in the history of humankind, were the Americans suddenly going to trade all that for Fallout just to prove a point? Our eastern comrades seem to have not understood the Berlin Wall was keeping people in, not out.
Ninety-nine knights of the air
Ride super high-tech jet fighters
Everyone's a super hero
Everyone's a captain Kirk
With orders to identify
To clarify and classify
Scramble in the summer sky
Ninety-nine red balloons go by
Ride super high-tech jet fighters
Everyone's a super hero
Everyone's a captain Kirk
With orders to identify
To clarify and classify
Scramble in the summer sky
Ninety-nine red balloons go by
Fortunately, cooler heads prevailed. One in particular: Stanislav Petrov, the 34 year old duty officer manning the radar that day (or night). Believing the alert to be a system error, Petrov simply chose not to report it. That's it. That may well be the only reason you are sitting here reading my charming Internet wiseassery and not out somewhere battling Quiverfull crazies and horse-sized ducks in a post-apocalyptic wasteland.
Ninety-nine dreams I have had
In every one a red balloon
It's all over and I'm standing pretty
In this dust that was a city
If I could find a souvenir
Just to prove the world was here
And here is a red balloon
I think of you, and let it go
In every one a red balloon
It's all over and I'm standing pretty
In this dust that was a city
If I could find a souvenir
Just to prove the world was here
And here is a red balloon
I think of you, and let it go
Petrov received recognition for his actions, including two World Citizen Awards and a Dresden Prize, although not the Nobel. (Petrov does not have a Nobel Peace Prize and Barack Obama does. Chew on that for a moment.) He got interviewed by Walter Cronkite for 60 Minutes and by Danish filmmaker Peter Anthony for the documentary The Man who Saved the World, none of which would have happened had the USSR not dissolved and the incident been brought to light.
For their part, the Politburo commended Petrov for averting global thermonuclear war and reprimanded him for not filling out the proper paperwork, which I guess is about par for the Politburo.
Sometimes everyone is a Captain Kirk.
CREDITS: Song lyrics of 99 Luftballons (c) 1983 CBS Schallplatten GmbH and claimed here as fair use as they serve to illustrate a scholarly article discussing the work in question and do not in a reasonable person's mind prevent the owner of the copyrighted work from receiving compensation.
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