In recent days, many people have asked whether Santa Claus really exists. I believe it’s worth reflecting on this a bit, as physical calculations suggest that if he does exist and actually visits us, the consequences could be catastrophic.
More than two decades ago, Gyula Dávid (assistant professor at the ELTE Institute of Nuclear Physics) published an intriguing article in the December issue of Mafigyelő (the journal of the Association of Hungarian Physics Students). The piece was a translation of an American article that used scientific calculations and estimates to argue for the impossibility of the Santa Claus legend. Its conclusion was that if Santa ever attempted to deliver gifts to children, he would have died in the process. The event likely occurred on June 30, 1908, near the upper Tunguska River, and it is now known in the scientific literature as the Tunguska event. However, that article contained some inaccuracies, so it’s worth reconsidering the matter!
The article did not address the question of flying reindeer. That is fundamentally a zoological and evolutionary biological problem. Estimates vary widely among experts, but it is believed that 8–10 million animal species live on Earth. Of these, only about 1.9 million have been described and named by zoological taxonomy, and we know little or nothing about 95% of them. It’s said that fewer than 100,000 species are ones about which a specialist biologist could meaningfully speak, and only a few hundred species are well-known enough to warrant popular science books. While most unknown species are small (e.g., spiders, beetles), even recently, large animals have been discovered (e.g., the Lesula monkey in Congo, 2007, or the Vu Quang ox in Vietnam, 1992). So, we cannot exclude the possibility that somewhere in the far north, a small population of reindeer species capable of flight—known only to Santa—might exist.
The aforementioned article derived Santa’s average travel speed from the number of children living on Earth. Currently, the world population is 7.3 billion, and 26% of that—1.9 billion—are under 15 years old. The original study estimated the average distance between children and then calculated the travel speed necessary to visit them all. However, there are some major flaws in this logic. The article did not consider that Santa does not serve Muslim, Hindu, Buddhist, sun-worshipping, etc., children. It also ignored the fact that in Hungary, Santa comes not at Christmas but on December 6. Protestant (Evangelical) children don’t await Nikolaus on December 6 either, but instead their own gift-bringer “Pelzetmärtel” on St. Martin’s Day, November 11. In Russia, Ded Moroz brings gifts on New Year’s Day. Furthermore, the article makes the scientifically unsupported assumption that every household contains at least one good child. Finally, a major conceptual flaw is that it used 1980 world population data and concluded that Santa died at the start of the 20th century.
So, let’s look at the numbers from the early 20th century. In 1900, the global population was estimated at 1.65 billion, with Europe’s population at 408 million and North America’s at 82 million. As a pessimistic estimate, let’s limit ourselves to the Anglo-Saxon cultural sphere where Santa arrives at Christmas. That’s about 130 million people, of which 25%—30 million—were children. With an average of 3 children per family, that gives 10 million households spread across roughly 25 million square kilometers. The original article assumed Santa had 31 hours to visit all households due to Earth’s rotation and time zones. In our narrowed region, however, he would have only about 21 hours.
In a region of area A containing N points, the average point density is m = N/A. The distance to the nearest neighbor is approximately D = 1/(2√m) = 0.8 km. Let’s assume Santa finds the optimal traversal path! Even so, the path length must be greater than the average neighbor distance times the number of points: 8 million kilometers. Santa must cover at least this distance in 21 hours, which requires an average speed of 380,000 km/h (=106,000 m/s = 310 Mach). The original article estimated 1,046 km/s—ten times our result!
Our calculation is highly optimistic—not only because of the assumption of an optimal route, but also because it doesn’t consider that within the 7.5 milliseconds per household, Santa must not only travel to the house, but also:
- Find parking,
- Jump out of the sleigh,
- Slide down the chimney,
- Fill the stockings,
- Place remaining gifts under the tree,
- Eat the snacks left for him,
- Climb back up the chimney,
- Get back in the sleigh.
In apartment buildings, he might have slightly more time per household, but dealing with windows on the 10th floor, clinging to the wall—that’s no piece of cake either! Our neglect of these activities is partially offset by the continued assumption that every household includes at least one good child.
The calculated 106 km/s average speed is striking: the fastest man-made spacecraft (Ulysses probe) reached only 44 km/s. The fastest aircraft, the Lockheed SR–71 Blackbird, achieved a record of 0.98 km/s (=3,529.56 km/h = 2.88 Mach).
The Blackbird, just approaching three times the speed of sound, experienced dangerous heating due to air friction (its titanium body needed constant cooling, reaching over 300°C). In contrast, Santa moves at 300 times the speed of sound—more than 100 times faster than the Blackbird! That would clearly require extraordinary reindeer, since an ordinary one can manage only 24 km/h at most.
How much kinetic energy does the sleigh have? The original article estimated the total gift mass at 375,000 tons, and with Santa and the needed reindeer, a total of 435,000 tons. That’s clearly excessive—if an object of that mass entered the atmosphere at our calculated speed, the result would not resemble the Tunguska event but rather the Yucatán impact that nearly wiped out all terrestrial life.
A more reasonable approximation is to assume 1 kg of gifts per household, for a total of 10,000 tons. Santa appears quite portly in illustrations, but even the heaviest human ever was only about 0.6 tons—so Santa is slim compared to the sleigh; his weight is negligible. Given the super-reindeer implied by the speeds, we can also assume only 6–8 reindeer are needed (as shown in pictures). Thus, Santa and the reindeer’s weight is negligible compared to the gifts, and the total mass is about 10,000 tons. The average kinetic energy is W = ½·m·v² = 56 quadrillion joules, or 1.34 megatons of TNT—roughly 90 times the Hiroshima bomb. Bombs developed in the 1950s had comparable energy (by the 1960s, the USA tested 24 Mt, and the USSR 50 Mt bombs—but these were mainly for propaganda, not military utility).
We don’t know how Santa protects against the heat generated by atmospheric friction and adiabatic heating, but just as we accepted the existence of super-reindeer, we may assume the sleigh is protected by a special heat shield preventing instant vaporization. But we cannot ignore the fact that Santa must decelerate when reaching a household!
Each household affords him 7.5 milliseconds. Assuming he spends half of that time accelerating and half decelerating, he must decelerate from 310 Mach to zero in about 3 ms. All kinetic energy must be transformed—into heat, light, or something else—within that time. That’s an enormous energy release in an incredibly short period! What would this mean in practice?
Suppose Santa (Joulupukki) arrives in the main square of Vác and decelerates. Based on experience from the UK’s 1957 Grapple X test, the released energy would generate a 30,000°C fireball vaporizing everything within a 2.4 km radius—stretching from Szentmihály dűlő through Törökhegy to TESCO, and halfway down the road from Tahitótfalu to the ferry. The ~30,000 inhabitants in this zone would be “lucky”: their bodies would turn to ash faster than their brains could register what happened—they’d feel nothing.
Following the fireball, a shockwave would level everything within 10–12 km, from eastern Nagymaros to Alsógöd, through Vácrátót. Except for the strongest reinforced concrete structures, nothing would remain. The Naszály mountain might offer some protection to Ősagárd and Nőtincs, but Dunabogdány, Tahitótfalu, Leányfalu, and parts of Szentendre would vanish. About half the people in the blast zone would survive only to suffer agonizing injuries. Within 30 km, most injuries would be from flying debris and shattered windows.
Fragments of Santa, his sleigh, and gifts could scatter over an 80–100 km radius. Expect glowing horseshoes, bolts, LEGO sets, and bottles of syrup to rain down on an area from Komárom to Nyitra, covering Székesfehérvár, Dunaújváros, Kecskemét, Füzesabony, and Salgótarján.
This unimaginably destructive Santa would have only been capable of delivering gifts to all deserving children in the early 20th century. Today’s multiplied population would make his arrival even more disastrous. Perhaps it’s best if we skip this spectacular disaster-movie-level event. We might suggest to Santa alternative destinations: the Arctic, uninhabited parts of Siberia, or maybe… Mars. Santa to Mars!
Addendum
András Sümegi: After two and a half years, it occurred to me that my own calculation contains an error no one noticed: if Santa accelerates during the first half of the trip between two houses and decelerates in the second half, then his peak velocity (assuming linear acceleration) must be twice the average velocity. This means the kinetic energy—which is proportional to the square of the velocity—is four times higher. Since destructive forces typically follow an inverse square law with respect to epicentral distance, the radius of destruction doubles. So, Santa is even more dangerous than we thought.
