Reviewer Three: Response to LeBeouf et. al. (2008) Indiana Jones and the Kingdom of the Crystal Skull.
Research Summary: In previous works, the authors established and characterized a novel model system, COL. H. WALTON “INDIANA” JONES, PH.D. (hereafter, “Indiana,” “Indy,” “Dr. Jones” &c.), which functions as commentary on a more innocent time in popular culture, Hollywood’s so-called “Golden Age.” His adventures remind us of an overly romanticized world still deeply connected to its social roots, ruled by simplistic moral factions of “good” and “evil” and untainted by the scars of American post-war militarism. Dr. Jones is himself a sort of retro pre-superhero: alternately a tweedy professor everyman and a leather-clad rogue adventurer. Yet, each of his personae fight to maintain our connection to the past, in so doing often unearthing primeval magics that bind humankind (if not Christianity in particular) to the spiritual realm.
In the current work, the authors abandon all of this context and characterization, instead presenting a story in which Indy has to rescue some lucite trinkets before they’re devoured by cavernous holes in the plot.
Review: This reviewer finds the present work to be utterly unpublishable, for reasons enumerated below. Strictly speaking, however, most of the film would hold together nicely, were it not for two flawed points:
- The sequence in which a human being survives a close-range atomic detonation by enclosing himself in a lead-lined refrigerator, and
- Every other scene in the movie.
As reviewers One and Two have previously expounded upon the second point in great detail, we shall limit our critique to the first issue. To recap, please observe the following:
Now, a work of adventure fantasy is expected, perhaps required, to incorporate elements beyond the commonly plausible. In the act of “Fridge Nuking,” however, the authors have overstepped the comfortable realm of suspension of disbelief, a storytelling tenet second perhaps only to the need for a protagonist. True, while many–such as the soldiers in this clip–have witnessed a nearby nuclear blast and survived to tell (or rather, to be debriefed of) the tale, all were either encased below the blast site in reinforced bunkers, or were stationed far enough from the ground zero that the bomb’s shock wave had been reduced to a moderate gust by the time it reached them. Riding a nuke’s shock wave to safety is, simply put, a laughably absurd concept. To prove this to the authors, this reviewer shall illustrate the myriad lethal effects that a nearby atomic blast would have on a person, even when enclosed in the very finest of kitchen appliances.
Preliminary Assumptions and Calculations.
It will be difficult to calculate the magnitude of forces, temperatures, ionizing flux, etc… without knowing (1) the power of the bomb detonated and (2) its distance from the ‘fridge-clad Dr. Jones. Addressing issue (1): given the year and location–1957 and the Nevada desert, respectively–and the surreally macabre pseduo-city from which Dr. Jones makes his unconventional escape, we can assume that the atomic test was a part of the U.S. Military’s Operation Plumbbob. Since this particular test is a “tower drop,” one of eight performed that year, the weapon’s power must lie somewhere between 10 and 44 kilotons (i.e. equivalent to instantaneously detonating between 20,000,000 and 88,000,000 pounds of TNT [thanks for correcting our type-o, Jon.-Ed]).
Addressing point (2) is a bit trickier, but through back-calculations and the available data, we might be able to make some inferences. Dr. Jones and his ice box appear to co-migrate with the expanding edge of the bomb’s shock wave, which delivers its concussive force in a single burst. Let us therefore model the ‘fridge as undergoing rapid, uniform acceleration to a constant final velocity (before returning to the ground, cavorting with gophers and ~2 more hours of inexplicable drivel). Given this assertion, we’ll calculate the force that would be required to accelerate Dr. Jones and his ice box to their final apparent speed, and from that infer the distance he’d have to be relative to a 10–44 kt detonation to receive such a force.
Let us assume that the refrigerator has approximately the dimensions listed here, and hence weighs approximately 71 kg. Indy’s clocking it at (We’re just guessing here) 99 kg, for a combined mass of 170 kg. Of course, initially they’re at rest, but what is the maximal velocity they achieve?
As is standard scientific practice, let us approximate Dr. Jones’ Soviet captors’ vehicle as a 1950 Studebaker Commander, with a length of ~2.3 meters. Traveling in his makeshift TARDIS, Indy overtakes the Studebaker (by our watch) in ~0.9 seconds. Assuming the Soviets are attempting to escape the advancing plume at their vehicle’s maximum speed (~80 mph, or ~35.76 m/s), we estimate Indy’s horizontal velocity to have a total magnitude of approximately (2.3 m/0.9 s + 35.76 m/s) = 38.32 m/s. Note that he’s also been accelerated vertically, but as the magnitude of his displacement is difficult to gauge we’ll not incorporate it into our initial calculations; all forces etc… calculated can therefore be considered as lower estimates.
Ignoring the effects of drag and wind resistance (which are tricky under standard conditions, but nigh-impossible within the mixture of soot, aerosolized concrete and atomically-catalyzed oxidizing nitrogenous smog through which he’s travelling), we calculate that Dr. Frigidaire has undergone a net change in momentum (mass*Δvelocity) with a minimal magnitude of (170 kg)*(38.32 m/s) = 6514.4 kg•m/s. Physicists term this quantity the “Impulse,” roughly thought of as the force imparted to a body multiplied by the time spent imparting it: I = F•Δt. Therefore, if we knew how long it took to accelerate the ‘fridge, we could calculate the force imparted to it.
Now, the bombs deployed at Hiroshima and Nagasaki prouced blast winds approaching 620 mph (= 277 m/s) as far as one mile from their detonation centers. A comparably powered blast would overtake Dr. Jones’ refrigerator (depth = 0.7 m) in 0.7 (m)/277 (m/s) = 2.5 millisconds. This means that the force exerted on him–the impulse divided by the time–would be a whopping 6514.4 (kg•m/s)/0.0025 (s) = 2,605,760 Newtons. To put this in perspective, on Earth’s surface Pete Fenzel weighs ~801 N. SO, having this much force put on you would be like having 3253.13 Pete Fenzels simultaneously sitting on you [Or, as Wrather calls it, “The Perfect Weekend.” – Ed.].
Were the bomb’s blast winds to hit the rear of the refrigerator with a force perfectly normal to the ‘fridge’s back plane, they’d be delivering a 2.605 MegaNewton force onto an area of 1.46 x 0.6 meters = 0.876 m². Hence, the pressure exerted on the ‘fridge at the point of impact would be (2,605,760 N/0.876 m²) = 2,974,611.87 Pascals (= 430 psi, almost certainly a drastic understatement). Consulting this table, derived from Dolan’s Capabilities of Nuclear Weapons, Part 1, we can estimate that Indy must have been initially placed far less that 0.6 km (~660 yards) from the detonation of a 10–44 kT atomic weapon.
This is a deeply problematic result, since a nuclear explosion delivers not only a tremendous concussive force but also intense heat and radiation. Which is to say, in order for an archeologist-stuffed Frigidaire to be accelerated by an atomic blast to the speeds observed in this sequence, it would need to be placed so close to the bomb as to be surely obliterated by the blast’s other myriad effects. Of course, for the authors’ benefit the full extent of these effects might require some elaboration…
It’s not scientifically relevant, and he may hate me for it, but I just want to point out that today is David Shechner’s birthday.
Excellent post. While many complain about the implausibility and downright stupidity of the set pieces in Indiana Jones IV, none I know have gone so far as to write a (quasi)scientific peer review.
Now just do the same with Die Hard 4.0 and I can stop sending death threats to Len Wiseman.
Uh, it’s a movie………….
So what you’re saying is that he’s treating something that’s obviously not real as if it were real and criticizing him for it?
This article makes me want to invent an internet version of the “slow clap.” Like, I will post a comment that says “clap,” and 15 minutes later someone could post another one. Then another one 14 minutes after that, and so on, closer and closer together, until the comment thread is overflowing with claps.
I like the article, is what I’m saying.
*clap*
Clap
*clap*
Clap.
Clap
*clap*
Clap
Clap
Clap!
clap
*clap*
Love the article, and completely agree with the implausibility of survival. However, I take exception with the calculated distance of 0.6km from ground zero.
Short of intentionally manipulative perspective, the shot that shows us the tower-based bomb establishes a distance far greater than ~660 yards. Moreover, from flash to the cloud of debris overtaking and destroying the house in which the fridge is found, it’s a good 8-9 seconds. Even obscenely underestimating the average speed of the blast from ground zero to house at 800 feet/sec, yields 6400 ft, or 1.2 miles or 1.9km.
It is not unreasonable to conclude that Indiana was at least 2km away from ground zero, where he would still have almost no chance of survival but where the effects would have been slightly less harrowing. If my naive watching of the film were true, that is, Indy was about 2 miles (3.2km) removed from ground zero, then surviving the event is somewhat near the realm of plausible–albeit far from any scenario where he emerges unscathed.
I think the bigger pill to swallow is the remarkably intact fridge overtaking the car, the gentle bouncing than the survival itself. The far likelier scenario is that given a 2 mi distance from ground zero and a 20kT blast, he would have been buried in the rubble of the house hosting the Frigidaire, and would have clawed his way out with second degree burns, a nasty exposure to ionizing radiation, significant injuries and a questionable prognosis.
@PJ – Yeah, this is a great point! I actually wrestled with this problem a bit. There is that one early shot where we see the nuke, with the mock city framed in the background. But, since it’s difficult to gauge from that shot the precise distance between foreground and background, it’d be hard to continue the calculation from that starting point. We could–-as you mentioned–time the interval between detonation and the shockwave hitting the city, but translating this to a distance is tricky. The blast wind’s speed isn’t constant (it slows down over time), and modeling it would require making assumptions about the air pressure, temperature and humidity, the vertical distance the bomb is raised above the city, and the shape of the valley through which it travels…
Either way, though, the point you make is logically related to the conclusion I reach at the bottom of page 2. Namely, that in order for Indy to receive a concussive force that’s sufficient to lift him off the ground, he’d have to be so close to the nuke that all the other effects would become lethal. We could follow my calculation, which has the caveat that the apparent distance in the establishing Nuke/City shot is some trick of parallax. Or we could follow your calculation, which has the caveat that the actual force of the nuke greatly exceeds 10-44 kT. In either scenario, the local outcome is the same.
Thanks for reading, and thanks for the great comment!
I have to agree with PJ. The claimed point of your article is the probability of his survival, not the probability of his fridge bypassing the car. I’m quite willing to suspend my disbelief on that one, especially given that, for him to bypass the car, as show, he would have to be accelerated past the wavefront of the blast — That’s where you could use the second law of thermodynamics.
In short, I’m willing to concede that point, which leaves us at the question of how far he was from the blast — because the question we’re dealing with is the probability of him surviving the blast where he is, not the probability of him being thrown ahead of the blast wave (through the walls of the house, no less).
Being thrown ahead of a supersonic blast wave is a near impossibility, and I’m just going to throw that one down to good old FX fun. The question of surviving the blast in a fridge, is actually a more interesting one and, unfortunately one that you didn’t really address in your article.
Never mind the reviewers, I can’t believe this made it past the editor. It’s so weird that this came out of Spielberg’s group, he usually does pretty good work.
Fantastic article (as a fellow scientist, this really amused me). One quibble: you mentioned the First Law of Thermodynamics, when I think you mean Conservation of Energy. The first law is generally only invoked for temperature-specific energy conservation.
Thanks, Carrie!
Oof, you got me there. Though, we typically treat the solar system as energetically closed, but that doesn’t exactly save my butt (especially since mass and energy are being actively converted only a short distance from Indy’s perspective). Alas, this is what you get when you send a biochemist to do an engineer’s job.
Incidentally, I encourage anyone who’s into *truly* macabre amusement to check out:
http://www.nucleardarkness.org/nuclear/nuclearexplosionsimulator/
…in which I learned exactly *how* large a nuke I’d need to set off in my house, given certain weather conditions, to ensure Harvard’s immediate destruction. SCIENCE!
Yeah, I couldn’t resist a “well, actually” opportunity :)
That simulator is fascinating, although it’s a bit disheartening to see that it would only take a 100 kt bomb centered on the National Mall to also wipe out my apartment.
This (awesome) article assumes that the acceleration of the fridge is accurately depicted and builds out from there, coming to the conclusion that this is incomptible with Lucas’ claim that riding the fridge left Indy with a 50% chance of surviving. I wonder what would happen if we assume that Lucas’ claim is accurate, and build out from there? Wikipedia says that the 50% mortality rate dose of radiation is something like 6 Gy. (That’s with modern medical care, mind you, but I couldn’t find figures for effects without treatment.) The questions, then, are these:
1) How far would you need to be from a blast of that kind to receive a 6 Gy dose through a centimeter of lead? (We’ll call it a centimeter to make the math easier.)
2) What kinds of mechanical and thermal stresses would Indy be subjected to at that distance?
Work backwards to determine how small the bomb would have to be in order to produce these results? Great idea. What we really need is a 3D version of Crystal Skull to help us see the exact distance of the bomb from the fridge, and the exact distance the fridge moves in the explosion.
But no matter how small the bomb might have been, I don’t think Indy would have survived the force necessary to carry a fridge that high and far, any better than our peer reviewer’s eggs in a Pringles can dropped from a roof.
I’m picturing the similar idea of an elevator cable that snaps, causing you to plummet 50 floors to the bottom, but kids would think maybe you’ll be okay if you jump at the last minute. There’s a kind of Wile E. Coyote cartoon logic that makes it seem like it would work.
Fraid I am not going to give you any calculations and figures, but a long time ago I was working on an aircraft project where we were trying to determine how close the aircraft could be to a Tactical Nuke (i.e. a small one) for the aircraft to survive the blast (i.e. not have the wings ripped off.
We gave up when it was pointed out that (discounting all other affects) the pilot would have received a radiation dose which would have killed him long before the could have flown the aircraft back to landing field.
Great review! Of course you are arguing against George Lucas armed with mere facts, so I am sure that no matter how concise and elaborate your analysis is, you are still going to be wrong and Lucas is going to be right in the eyes of the unwashed masses.
One minor point – you delve greatly into musings about neck injury due to acceleration. As a physician I can tell you that the #1 cause of fatal injury due to acceleration is aortic rupture thanks to the Ligamentum arteriosum that is anatomically just sitting there waiting for the opportunity to slice into the pulmonary arteries and rip open the aorta under the weight of the heart it’s attached to. This happens at far less g-force than neck injury. Then you can consider ventricular contusion as the left ventricle is pushed and crushed against the person’s rib cage causing it to tear and bleed into the pericardial sack where if the person is “lucky enough” to survive without immediate cardiac arrest, the person dies of cardiac tamponade a minute or so later; and finally direct brain trauma as the brain bashes itself into the inside of the skull, followed by immediate hemorrage from all the ruptured emissary veins that drain the scalp and underlying bone tissue into the brain’s drainage system.
Oh, there are plenty of fatal g-force inuries that happen far, far more frequently than whiplash. Still it was an interesting read!
Thanks, Steven; that’s incredibly helpful! Acceleration-induced aortic rupture is… well, a new item to add to the growing list of my darkest nightmares.
FWIW, I’d also tried to track down relevant statistics on concussions and associated brain trauma, but just didn’t have the time to get independent confirmation on the things I was finding. In addition to my laziness, though, part of the reason why the medical sections are worded so vaguely is that making concrete conclusions requires making more elaborate assumptions about elements not seen in the film. For example, I’m told that a person can die from jugular/carotid rupture due to rapid neck motion at particular angles, but I’d have no way of knowing how to calculate the probabilities of such injuries in the present case, without making inferences regarding the pertinent torques, angles, etc…
Again, thanks for reading, and thanks for the assist!
While I certainly agree with the HIGH probability of Dr. Jones dying in his flying refrigerator, it is worth noting that in the Hiroshima bombing, there is a documented case of a bank worker surviving the blast from less than 330m from the hypocenter. Now granted, she was inside, at the back of a concrete bank building, but she DID survive, and was not fatally injured. Assuming the bomb was at the low edge of the kilotonnage listed (i.e. similar to the Hiroshima bomb), and assuming that the distance was as far as it appears in that one shot (i.e. much greater than 330m), I think Dr. Jones would have quite a reasonable chance of surviving provided the blast wave was NOT enough to propel his refrigerator through the air (and frankly, from the movie shown distance it seems unlikely). If instead George Lucas had chosen to have the fridge knocked over in a pile of burning rubble, I think Dr. Jones’s chance of survival, while not excellent, would be within the real of reasonable probability.
So because one person survived, you think Dr. Jones would have a “reasonable chance”? How many people died in and around the bank? Would you say 50%, or more than 50%?
While it’s always nice to see optimism, we must be aware that it can predispose us to make assumptions that are simply not true. The exception may prove the rule, but it is not the rule.
He doesn’t have to have a 50/50 shot of survival to ‘suspend disbelief’. Typically something like a 10% shot of survival is enough for most audiences. Obviously if he is flying 100ft through the air in a lead lined refrigerator at 90mph+ and then hits the ground (AFTER being exposed to the bomb itself), then the probability of survival is much, much lower than 10%. Before seatbelts and airbags (and even WITH them) most people won’t survive a 90mph head on crash into retaining wall, much less some guy in a fridge with none of those things.
If my estimates of someone surviving something is much below 5-10%, then I can’t suspend disbelief. But from ~1,000m+ (which is what the movie distance roughly looked like), percentages of people can and have survived nuclear explosions if sufficiently protected from the radiation, blast and thermal effects (like one might be inside a fridge).
Oh sure, a number of people survived the Hiroshima bombing (“Little Boy”) at a fairly close distance; the bank you mention had a concrete-lined vault that served as shelter for a number of such survivors, and this only a few hundred yards from the explosion. Given the power of the bomb, it’s not surprising that many structures survived the initial concussion wave. Moreover, a few feet of solid concrete will do well to shield you from the initial onslaught of radiation. But, what I find surprising is that these people managed to survive the heat of the explosive fireball, and the ensuing firestorm that initiated ~20 minutes after the initial detonation and lasted for hours thereafter.
There was actually a study done on the 18 people who–get this–survived the Hiroshima bombing (though from a much greater distance than the bank survivors), and in the aftermath travelled to Nagasaki where they later survived the subsequent attack, too. They had some not insignificant psychological damage. Also leukemia.
FWIW, I’ve been to the Hiroshima Peace Museum 3 times and stood on the spot directly below the hypocenter, as well as read several accounts (including some that you can only seem to find in Japan) of survivors of the bombing, and I think the reason many of those people survived the resulting firestorm is because of the river that runs by the hypocenter. Many people took shelter in the river to avoid the fires.
Also FWIW, note that I don’t say that Indiana would have had a nice, long life after this bombing. The odds of him getting leukemia or some other very nasty cancer, as well as near lethal dose of rads is also very high, but not something that would likely show up immediately (i.e. in the duration of the film).
Yes, I have read the stories of the of the few lucky/very unlucky folks who were in BOTH bombings like Tsutomo Yamaguchi. Very sad stories and amazingly lucky that he survived.
Minor error: you off by a factor of 1000 on the mass of TNT. 10 kt is 20,000,000 pounds, not 20,000. Nukes are nasty.
Yipe. That there’s a boneheaded error, that is. Thanks for the catch!
While the general conclusion (a predicted near-zero survival rate for archaeologists inside ballistic refrigerators accelerated by nuclear explosions) is entirely valid, your arguments run through some very rough patches.
The calculation of the mechanics of the fridge’s impact includes some rather basic mathematical errors (the square root is not a linear function, thus the height of apogee cannot be factored out of it). Nevertheless, the depicted reunion of the fridge with its home planet would be quite lethal for an enclosed human, based only on vertical speed implied by the time of flight.
The derivation of the conditions necessary for its initial launch may be suspect (the initial shock is followed by outflowing material for some time, which means that not all of the acceleration must occur during that shock). But this is of little consequence, as we clearly see that the refrigerator OUTRUNS the shock wave. Said shock wave initially travels far faster than the speed of sound (~4 km/s at the point of separation from the fireball), and gradually slows down to the speed of sound as its intensity lessens (which suggests a conflict between the timing data and blast effects, but we aren’t likely to resolve that here). Setting aside the inevitable question of how the refrigerator attained a velocity greater than the shock wave (to quote Venkman (1984), “Generally you don’t see that kind of behavior in a major appliance”), we may conclude that at least most of the refrigerator’s flight is thoroughly supersonic. Its brief time in the air affords little opportunity to decelerate; at best it might drop below the sound barrier and land at high subsonic speed. Such a landing would tear the fridge to pieces, and likewise its occupant.
The thermodynamics of a mostly-intact refrigerator inside a nuclear-initiated conflagration are actually quite favorable for the occupant, if we momentarily neglect the glaring kinetic issues. Thanks to the significant temperature tolerance of the (presumably steel) outer shell and the insulated, multi-layered structure inherent to refrigerators, it’s quite likely that internal temperatures would remain survivable for several minutes of exposure to an exterior inferno. Small leaks in the door seal would not be immediately injurious, as the intruding superheated air would quickly mix with the comfortably cool interior atmosphere, diluting the thermal impact. Not until such influx managed to heat the entire interior volume of air, the inner shell of the refrigerator, and the skin and clothes of the human would the temperature become problematic.
The calculation of the subject’s exposure to ionizing radiation is also flawed — shielding is exponential, not linear. If (for some suitable gamma spectrum) a 3.3cm layer of lead reduces the gamma flux by a factor of ten, each further 3.3cm layer tacks on another factor of ten; only 10cm or so is therefore necessary for a thousandfold reduction. This makes little difference in the conclusion, as no refrigerator capable of being supported on a conventional residential floor could possibly contain enough lead (or any other material, for that matter) to significantly protect its occupant against neutron or hard gamma radiation. The relevance of this depends very sensitively on the distance from the blast, since the atmosphere significantly attenuates ionizing radiation at kilometer-scale distances. Again, this is of purely academic interest when the mechanical stresses on the subject are considered.
There is one additional nail in dear Dr. Jones’ (flying, splintered, scorched, and irradiated) coffin, though, which seems to have been hitherto neglected: the effect of blast overpressure on the structure of the fridge. Since the door seal of a refrigerator is intended to be more or less air-tight, and external pressure would only improve that seal, we may assume that the pressure within the fridge remains near 1 atmosphere (at first, anyway). Apart from the other calculations of the subject’s distance from ground zero, we may make a rather optimistic estimate of the blast overpressure simply from the damage which occurs to the structures of the simulated town — better than 10 PSI would be required to cause the complete destruction depicted, and the estimate of proximity based on acceleration would predict a much, much larger figure. Given that refrigerators are not generally constructed to withstand large amounts of static pressure, the metal shell would rapidly implode. Despite humans’ tolerance for direct exposure to significant overpressures (40 PSI is claimed to be survivable), we are far less tolerant of being crushed within buckling steel and lead cans. Even before the refrigerator’s supersonic landing, it would have been reduced to something vaguely resembling a can of tomatoes run over by a tank.
To conclude, I concur with the reviewer that the published simulation of nuclear blast effects on a refrigerator-encased human is wildly unrealistic, and the interiors of major kitchen appliances near a nuclear blast should be considered very low-survivability environments.
Dr. Bunsen, I presume,
Thanks for reading, and for your thoughtful commentary! Indeed – as you and others have pointed out, I totally bonked the mgh ==> (1/2)mv^2 calculation. The conclusion I draw holds in spirit, even if the math is flawed: he’d be undergoing a pretty massive change in momentum upon impact, and hence an incredible impulse, force, &t.
Yipe – the shielding thing appears to have been a calculator typeo, another sad biproduct of my only writing after midnight. In retrospect, I don’t think we should treat basic physics calculations like we do gremlins. Though, it would explain, at least, why I never see physicists bathing or being exposed to direct sunlight.
For the rest of the audience, a brief explanation: while shielding strength is exponential, we quantify it with base two. My calculations are based on lead’s literature halving thickness (the thickness required to reduce–in this case–gamma flux by 50%) of ~0.4 in, 1 cm. SO: if F is the initial, outside flux, F’ is the final, internal Flux, and n is the distance in cm, we have F’ = F•(1/2)^n. Rearranging produces (in log base 10) n = (log(F’/F))/(log(1/2)), or n ~ -3.32•log(F’/F). SO, if F’ is 10% of the initial flux, n ~ 3.32 cm. I correctly managed to calculate that for the article. If F’ is 1% of the initial, n should be ~6.64 cm, way less than was quoted, but still probably far more shielding than Indy’s got going for him. Now, if you consider that one would probably want to receive far less than 1% of the gamma burst produced proximal to a nuclear blast, then he’d require a preponderance of shielding in excess of what anyone could possibly argue is found in that ‘fridge.
As for how the ‘Fridge possibly outpaces the supersonic nuclear blast – yeah, seems unlikely. If you imagine that the ‘Fridge is launched into the air by absorbing the linear momentum from a more massive object that’s co-migrating with the blast wave, then it’s theoretically possible. Still, in order to calculate that, we’d need to make all sorts of assumptions as to the speed and weight of this object, and justify why it itself hasn’t been pulverized/melted by the explosion. I’ll assert, however, that my construction of the system isn’t totally unreasonable. Since, after the initial shock wave, much of the force from an atomic explosion is directed inward (i.e. due to air flow towards the fireball), the force propelling the Fridge outward must have been delivered in a single short burst early on.
I’ll also note What I’m not factoring in: (a) the vertical component of his initial acceleration, and (b) the fact that–due to wind resistance–he must have slowed down between the point of initial impact and the time he overtakes the Studebaker. Both of these imply that the magnitude of the initial accelerating force was, in fact, substantially higher than calculated.
Again, thanks for your time and help! I hope you managed to enjoy the article, despite my boneheaded errors. :)
I absolutely *love* the article.
I think, however, that you made a mistake in “Crushed on reentry”. You state that “v = sqrt(2gh), approximately 4.43h”. This should be 4.43*sqrt(h). :)
From TFA: “given the year and location–1957 and the Nevada dessert, respectively…”
I haven’t tried that before, sounds tasty.
The problem here is that the Jones film is in the dead zone between fantasy and scifi. Vampire fiction requires no explanation, the audience is compliant. Space adventures generally attract a different, more critical audience. Jones seems to be aimed more at the fantasy crowd, and thus science takes a back seat.
I don’t anticipate a common ground between ‘romantic fantasists’ and ‘science geeks’ in my lifetime. Regardless of the technical difficulties with Jones’ heroic exploits, I’ll bet there are more available single women enjoying his movies.
“I don’t anticipate a common ground between ‘romantic fantasists’ and ‘science geeks’ in my lifetime.”
Firefly
One way to approach the analysis is to realize that 20 miles away you’d be perfectly safe, and at 0 miles away you’d be perfectly toasted to atoms. At some point along that line between 0 and 20 you could expect to find a survivable level of the various factors analyzed. For instance, you could survive the radiation at 3.4 miles, the heat at 4.0 miles, the blast front at 2 miles, etc. Then toss in a calculation of how much force it takes to launch a fridge, and see how far you’d have to be for that (although as you say, it’s pretty darn complicated).
Of course, it looks like the fridge dropped from a high point more than 2 stories up; Indy’s a goner.
For anyone interested, a the Nuclear Weapons Archive, hailing from the days of Usenet and still very informative, gives a thorough discussion on the effects of nuclear weapons from the three types of effects, for various weapon sizes and distances from the point of detonation, along with the amount of injury the inflict on a human body:
http://nuclearweaponarchive.org/Nwfaq/Nfaq5.html
Excellent article, and one can only hope that the burgeoning extreme sport of nuclear-fridge-death-riding looks back on this article as its birthplace.
I would suggest, however, that the reason that we find the Nuclear Fridge so annoying is not because of it’s impausability, but in fact the reverse; members of the audience unfamiliar with the forces involved may think this is perfectly reasonable, and that ignorance (or the assumption of viewer ignorance by Lucas et al) is what irritates.
We’re not maddened beyond all rational argument by Wily Coyote because everyone understands that running off the edge of a cliff and plummeting thousands of feet is not survivable, and the added jest of him ‘treading air’ for a few seconds reinforces the ridiculousness of the situation. It’s clearly and obviously a joke, and so pointing out that it’s not realistic is just exhibiting a sense of humour failure.
The same with Indy’s other escapades. They’re just about within the bounds of sanity but clearly ludicrous enough to not be ‘serious’. Except the Fridge of +4 Nuclear Blast Survival, which seems a reasonable response to the situation for people ignorant of nuclear science (in other words EVERYONE WHO READS NEWSPAPERS after Fukushima).
This is reinforced by Lucas clearly not getting his own joke and claiming a 50% survival rate. How can we be expected to know this was a Wily Coyote moment, if he clearly doesn’t?
A 2.3 m long Studebaker? Really? The page you link to lists the length of a 1950 Commander as 207.9 in, or 5.28 m. Not that this helps Mr. Lucas in any way…
Yeah, I was using the wheelbase length, since the 0.9 second figure corresponds to the time we see the ‘Fridge’s reflection over the dome of the car. Also, I’m in shocked disbelief that we used to make >17-foot long cars.
Hop in my Chrysler; it’s as big as a whale, and it’s about to set sail!
A 120 in wheelbase translates to 3.05 m.
And what’s so shocking about a 17 ft car? It’s not much longer than your average station wagon, and a good deal shorter than a Chevy Suburban.
Of course, every bit of evidence we have suggests that Dr Jones will always survive that which would kill anyone else. The films have him survive again and again in situations which would have polished off virtually anyone else – like a reverse Final Destination. In fact, it’s arguable that Indy has a degree of preternatural luck so profound that it can
only reasonably be attributed to the magic – perhaps as a result of the artifacts he’s surrounded himself with over the years. The nuke would have burned/poisoned/suffocated/crushed anyone else, but Indy’s survival is a not just a matter of science – it is a matter of established and pretty reliable magic.
There’s a cut scene in Temple of Doom which demonstrates this in a comically low-stakes manner (and is in the novelisation I cherished as a youth): Indy is asleep on the plane from Shanghai, and is going to be killed by the pilots via the time-honoured method of the braining upon the noggin with the heavy implement. As the dude creeps up to sleepy Indy, one of the chickens on the plane lays an egg. The egg rolls across the luggage and piles of crap, and to the horror of the pilot, seems about to fall onto Indy and wake him up. But Indy, completely asleep and with his hat pulled over his eyes, opens his palm and catches the egg. Indy remains asleep and the pilot is so freaked out that he daren’t cosh him. It’s magic.
I can’t agree with your analysis, I’m afraid, though I definitely appreciate the spirit of your inquiry! :-)
The tricky part is the interaction between the shock wave and the fridge, and just how that would accelerate the fridge. The key assumption you made is the acceleration time equal to the time for the shock wave to overtake the fridge. That is quite simply a vast oversimplification of the way that the impulse would be transferred, and I think it wildly underestimates how long it takes for the fridge to accelerate. It seems reasonable to me to think of it less like a baseball bat knocking the fridge out of the park, and more like a flow of turbulent gases carrying the fridge along like a river. This could easily mean that the fridge is set down relatively gently in the vertical direction, and then gradually loses its horizontal velocity as you see in the video clip. So: no big, body-crushing impact required.
I *really* like Mr. Picky’s approach, above:
“One way to approach the analysis is to realize that 20 miles away you’d be perfectly safe, and at 0 miles away you’d be perfectly toasted to atoms. At some point along that line between 0 and 20 you could expect to find a survivable level of the various factors analyzed. For instance, you could survive the radiation at 3.4 miles, the heat at 4.0 miles, the blast front at 2 miles, etc. Then toss in a calculation of how much force it takes to launch a fridge, and see how far you’d have to be for that (although as you say, it’s pretty darn complicated).”
Taking your table here:
http://en.wikipedia.org/wiki/Effects_of_nuclear_explosions#Summary_of_the_effects
it would appear that we are in the range of “Destruction of most civilian buildings (5 psi/34 kPa)”, which corresponds to a 20 kT blast. Since this matches your information of the sizes of above ground detonations in that time period, we’re in the right ballpark.
34 kPa is a wildly smaller number than your calculation of 2,975 kPa, which gives me some confidence to stand by my comments about how the impulse is transferred to the fridge, and over what time period. So, the pressures, forces, and accelerations involved are likely a factor of 88 smaller than your estimate.
That means your 1650 G’s of acceleration would now become 19 G’s — perpendicular to the spine and ‘eyeballs in’ — well within the range of acceleration withstood by test pilots and astronauts during their training.
http://en.wikipedia.org/wiki/High-G_training
From the article: “completely untrained individuals can withstand untrained humans were able to tolerate 17 g… for several minutes without loss of consciousness or apparent long-term harm harm”. And for a tough guy like Indy, no problem. ;-)
I don’t get your suffocation comment… he’s not in the fridge long enough to suffocate. And your negative pressure comment is also strange: there is a net positive pressure which is what is propelling him in the first place, so no negative pressures out on the edges of the blast (in the centre, sure, but that’s not where he is).
As for radiation effects, I don’t know enough about those topics to comment. But it seems clear to me that he could very plausibly survive, and in pretty good shape, when considering the purely mechanical and kinematic effects going on.
Best regards,
Scott
“I don’t get your suffocation comment… he’s not in the fridge long enough to suffocate.”
This claim in the article was a reference to a specific episode of Punky Brewster that aired when we were children about the terrible dangers of trapping ourselves inside refrigerators.
I’m pretty sure by now the design of refrigerators has changed enough that this isn’t actually a problem, but back in the day, it was a threat to our lives on about the same level as pot handles that weren’t turned inward toward the stove, taking candy from strangers, or the Soviet Union.
Hi, Scott!
Thanks for reading the article. I’m not sure how the mechanism by which the shock wave exerts force on the Fridge has much to do with the outcome, as you’ve written. True, it’s certainly not going to be of the simple-Newtonian-acceleration-on-a-frictionless-plane-type, but we know for certain that the following things are true:
(1) Initially, he’s at rest,
(2) Later, he’s going much faster than at rest (see the calculation in the article)
(3) The force required to accelerate him to his final velocity is delivered in a single impact.
Now, as you correctly point out, calculating the force from the Impulse required estimating the time this impact took. If the shock wave were travelling at half the speed, then the time would double, and the Force would be half of what was calculated. One tenth the speed would likewise mean one tenth the force, and so on. But, the slower the shock wave travels, the less overpressure it exerts on the objects it passes. Since the shock extends from Ground Zero in a (first approximation ) spherical fashion, the further away you are from it, the less power it delivers to you upon impact; the energy released by the bomb is being distributed over a volume that increased by r^3 as r increases. This is nicely illustrated by the nuclear test footage video I linked in the article: a few miles from the blast, all you get is a hot, gusty wind. And later, leukemia.
Again, the take home point is essentially the same as the conclusion I reached at the bottom of page two. Namely, in order for one to be close enough to a detonation to be accelerated as seen in the film, the other effects of the detonation would do you in.
The maximum survived G’s is 46.2 (not 42 as you state), not that it matters. From the link you provided:
he experienced a record-breaking 46.2 G’s
I know this is picky but I thought I’d post anyway. Have a good day, and thanks for this great article.
super.
now, can you please use the maths to debunk dorothy surviving a tornado, her house flying/landing in tact, and that clicking ruby slippers won’t send you back home? please use 1st and 3rd laws of thermodynamics…
ok, i understand the website is called “overthinkingit.com” but there is something for leaving stories to the wonders and imagination of children. if we only relied on the laws we know, how would we find breakthroughs like relativity or higgs-boson?
imagination is awesome, and 94% of the time, imagination violates at least three of the laws of thermodynamics, if not all 4 simultaneously…
Haters gonna hate.
I think you misunderstand why we do this kind of Overthinking: because it’s fun. Dave is a scientist. He enjoys thinking through problems and unpacking the implications of unusual situations. So Dave didn’t write this article just because he needs to prove that fridge-nuke survival is unlikely. He wrote it because he wanted to figure out WHY it’s unlikely.
From a simple movie-goer viewpoint, another issue is that Indy’s fridge is the ONLY fridge to apparently end up flying! Why are lighter fridges immune from flying?
Bravo. Excellent article.
Far, far be it from be to defend Mr. Lucas, but I think Spielberg is to blame for the fridge. Spielberg decided to rehash one of his old, unused plot devices. From the IMDB page for Back to the Future:
—
The time machine has been through several variations. In the first draft of the screenplay the time machine was a laser device that was housed in a room. At the end of the first draft the device was attached to a refrigerator and taken to an atomic bomb test. Robert Zemeckis said in an interview that the idea was scrapped because he and Steven Spielberg did not want children to start climbing into refrigerators and getting trapped inside. (See also Indiana Jones and the Kingdom of the Crystal Skull.) The Nevada desert bomb test was left out in order to reduce the budget. In the third draft of the film the time machine was a DeLorean, but in order to send Marty back to the future the vehicle had to drive the DeLorean into an atomic bomb test.
—
Great article. Although, I’d have taken a different tack. You chose to pin the flight as the factual point, and I’d have used the apparent distance or the apparent explosive force as the factual starting point. Using either of those “facts” would wind up declaring the fridge couldn’t possibly have been launched in the air like that. But even those two facts are in serious conflict. I’m so conflicted which fact do you start at?
I’d have gone with the statement 50/50 of surviving in a 57 lead lined fridge. The most favorable condition is as earlier stated a healthy 2 miles out. Given the house structures were ala Mythbusters quality stickframes, and a 2 mile distance. I’d say, without doing any math at all, it’s plausible to survive a 10Kt blast at 2 miles in a ’57 leadlined fridge, if you have a trick to open the fridge back up once stupidly sealing yourself up in one. So, 1 thumbs up for surviving the blast at 2 miles out, and two thumbs down for locking yourself in a fridge and dying of asphyxiation.
Of course the real kicker is how high above ground the bomb was exploded at. Hiroshima’s was mid-air, but the more powerful Nagasaki bomb was at ground level. Nagasaki resulted in far less damage than Hiroshima. BTW, those things at ground zero in Hiroshima didn’t burn, they were vaporized. Once you got further out you had burning. Big difference.
Lastly, the Indy watching the fireball, was actually quite a bit of authenticity. That was actually a not unusual thing at that time. There was that bomb test that happened while John Wayne was filming, and the crew did exactly that. Very authentic time-period nod. Chalk one up for George. Surprised you missed that. Guess I’m showing my age. No not that old.
I disagree entirely with your essay. Ask yourself, would Chuck Norris survive that blast? Of course, it would be more like a cool breeze for him. Hence, it’s entirely plausible to me that a half-Norris man like Indiana would be thrown away for some miles, without many scars. I’d also add that, following the principles of quantum mechanics, the Norris-degree of a man can alter the properties of any surrounding objects and environments, including fridges. I’m pretty sure that with the real deal on the bomb site (Norris Himself), the bomb wouldn’t even mind exploding.
Agreed. I’d even go so far as to say that Indiana could be as much as .75 Norris. I’m surprised the author didn’t cover this extremely important point.
Good, funny article, but I took exception to the word Nipponese and bamboo pagodas. The former is too close to being a slur and the latter a stupid stereotype. Surely someone as clearly intelligent and sophisticated as the author doesn’t need to resort to such cheap (and lame) tricks.
Hi, Pangolin,
Well, I certainly don’t mean to offend. FWIW, most of my Japanese friends prefer being called Nipponese, in the same way that my Iranian friends prefer to be called Persian. It’s probably not helping things that I’m currently reading Stephenson’s Cryptonomicon, too.
Atomic Shockwave Jamboree is definitely the name of my next band.
ANNOUNCEMENT:
I’ve made a few edits to the original text, in response to some of your incredibly helpful comments. These are all noted and cited, either in italics or mouse-overs. Thanks, everyone, and thanks for reading!
-Sheq, who notes that this draft/review/revise process eerily resembles the process of scientific peer review. :)
Just another little nitpick, probably about a typo:
According to this report, even a 0.16 second exposure to 450°C air can result in second degree burns to the skin; temperatures above 560°C will induce burns in under 0.6 seconds, faster than a human’s reflexive response time
If those numbers are correct, then it means you’d burn quite a bit faster at 450°C than at 560°C which seems strange. Also IIRC, reflexive response time is considerably faster than 0.6 seconds, closer to 0.1 seconds. Is it maybe supposed to be 0.06 s at 560°C ?
Ah! Good catch, Chuk. It should be 1.6 and 0.6 seconds, respectively. Thanks!
Time for a mind unhindered by Science to take a shot at this. Indy survives the fridge nuking. It bounces across the desert in the wake of increasing radiation (or whatever the radiation levels do). The way I see it, wouldn’t he be stuck in the fridge if it landed on it’s door?
“we observe that the air surrounding Indy becomes hot enough to cause spontaneous combustion of the mannequin test dolls, and infer that the air temperature[…]”
Err, no. That’s not hot air toasting mannequins, that’s just well lit mannequins.
When near a bright flash, (a) step into the shade, (b) use an umbrella, or at least (c) don’t wear black.
Somewhere on the interwebs, a careless observer of a conventional nuclear simulation test, recounts realizing afterward, that had he dressed darkly that day, his fashion faux pas would have been blisteringly critiqued.
I feel I must go on record, noting that my own complaint is that Indy, scrabbling out of his refrigerator life pod, was not crushed by or even have to dodge away from all those other flying refrigerators from the immediate vicinity of his takeoff point, which would be landing at about the same time.
They would only be slightly different in weight since they hadn’t been emptied of food, so the vicinity outside the blast area should already be littered with refrigerators.
I’m sticking with George’s original 50-50.
Either Indy will survive, or he won’t.
Two things strike me about the piece:
1) As far as surviving the Bomb, we are after all talking about a character who a few years before supped from the True Chalice, the cup of Christ that allowed a Templar Knight to survive for hundreds of years without food or sunshine with his mind intact. Anyone else, yes, that person in the fridge would be fallout, but for Indy after that experience, well maybe…
2) The point about our inability to handle jokes about the Bomb does ring very true to me. I also think there were other elements that got used in the film that audiences weren’t ready to deal with when it came out; I had discussions with people who had watched the film and were turned off by a lot of the Red Scare references, which were way more accurate than the Nevada test scene was, which makes me think that what contributed to the film’s rejection over and above the obvious was a setting that made audiences more nervous and uneasy. It would appear that movies about the Nazis and their obvious threat coming out during the 1980s (when the first three Indy films were released) were far more distant than one about sly duplicitous Commies being watched in a post-9/11 environment.
Yes, presumably his “life-force” was augmented by his experience with the holy grail.
Also, refrigerators of the time were insulated with fiberglass (this being before good plastic foams were available), and fiberglass has boron in it as a flux and boron is a good absorber of neutrons.
The refrigerator door is gasketed and would seal against external pressure which would tend to compress the seal and make it seal tighter.
I was actually thinking about the Holy Grail thing, too. The problem is that Dr. Jones Sr was mentioned as having passed away earlier, and he, too, partook of water from the Grail.
As nice as your article is, I feel you lacked some alternative approach to the ‘flying fridge’ issue.
let me trace a simple comparison with a block of foam floating on water. In open air, it takes some amount of energy (blowing) to cause the foam block to fly. But in water it just floats and can ‘ride a wave’.
If instead of being thrown by the sheer force of the explosion, the airborne dust increases the air density to make it somewhat easier for the fridge to ‘ride a dust wave’, how would that make it easier for the fridge to float?
Would the energy necessary to make the air+dust density increase to the point of flotation – or dense enough that a ‘gente push*’ can lift it – be much less or much more than the energy necessary to lift the fridge by a sheer shock wave?
*gentle push = a force which would not be enough to obliterate to smithereens the fridge and the malleable, soft subject contained in it
Hi, Joe,
It’s a great comment, but I think the comparison isn’t necessarily direct. The styrofoam block in your example is already less dense than water, and naturally floats above it, whereas the starting density difference between Indy+Fridge and his surrounding medium is substantially greater.
SO, a better question would be: how much of a “gentle push” would it take to propel a solid lead block off the bottom of a pool of water and thereafter propel it along the water’s surface? Answer: I’m not sure, but certainly a *lot* more energy than it takes to translate a foam block.
Thanks for reading!
-Sheq
The mind boggles at the sheer level of awesomness on display in this article…this makes every useless thing I’ve read on the internet worth it. And I thought you guys couldn’t get better…one thing though, it’s now clear to me that my Economics degree is essentially useless. Thank you for that…!
“After all, is it any less absurd that a man could survive being dragged for miles underwater by a Nazi U-Boat?”
This is wrong. World War 2-era submarines cruised on the surface. They submerged only to attack or to hide from attack. They had diesel engines that were faster and had greater range for use on the surface but couldn’t be used underwater because, being internal combustion engines, without a free supply of air they would soon consume all the oxygen in the ship and asphyxiate the crew. So subs also had electric motors that could be safely used underwater but were much slower. Since Raiders takes place during peace-time, there would have been no reason for the U-boat to submerge. It’s still a little ridiculous, but the ridiculity comes from the idea that he could ride along up there without anybody noticing him.
Actually, we’ve already addressed this mystery on the site:
http://www.overthinkingit.com/2008/11/19/the-mystery-of-indys-sub-ride-solved/
According to the original script, the sub dives, but Indy makes the trip lashed to the periscope, being dragged through the ocean.
And apparently, you can’t survive having your heart ripped out of your chest, either… And the likelihood of living through a drop from a plane on a life raft is also pretty low…
I see why this site is called “Overthinking It”.
Saying that George is used to working with “stupendous bombs” doesn’t really work as a pun since in box office terms a bomb is a movie that under-performed or didn’t even cover its budget; Episodes I,II and III made 924, 649 and 848 million dollars at the box office respectfully. Successful by all accounts…except critically :/
The maximum survived G’s is 46.2 (not 42 as you state), not that it matters. From the link you provided:
he experienced a record-breaking 46.2 G’s
I know this is picky but I thought I’d post anyway. Have a good day, and thanks for this great article.
(sorry there’s a missing post or something above so a reply button was sitting there, I accidentally used that the first time around)
If you hated the 2000 elections, you’re going to have a conniption after the 2012 elections.
You wrote “would become for we pop culture geeks what the 2000 elections were for we liberals”. This is a mistake that my first grade English teacher would not have tolerated. You set yourself up as arbiter of what is so stupid it requires lengthy denunciation and make such a bone-headed gaffe? Physician, heal thyself.
Well, as he had drunk from the Holy Grail in the last film, perhaps he was imbued with a Wolverine-like ‘healing factor’…
I should say only that its awesome! The blog is informational and always produce amazing things.
Watching that fridge fly and tumble is like watching the perils of Wile E. Coyote in his “Indestructo” steel ball late in the Road Runner cartoon “Wild About Hurry.”.
I know I’m late to this party but, as somebody used to dealing in metric measures, the assumed length of the Studebaker @ 2.3 meters struck me as unlikely. 203 inches are, in fact, 5.156 meters.
This article is fantastic – not only the science but the humor. Only took me 11 years to find it . Can’t wait to read more of the blog.