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Santa's reindeer are pretty awesome. They can stand on arbitrary planes (giving the illusion of flight, the reindeer are actually running on n-dimensional hills) and can dilate time in a bubble around Santa without tidal effects tearing holes in the universe. This lets Santa and the sleigh make as many trips to and from the North Pole as needed in order to deliver all the gifts (uncompressed) moving as the crow flies.

But for all their skills the reindeer still have to eat, and for them time passes as normal (though they're immortal, naturally).

The question then is how many calories must 9 reindeer consume in order to deliver presents worldwide, assuming the presents are located at the North Pole and the reindeer are otherwise normal reindeer.

For bonus Christmas sparkles: what is this in oats (dry weight)

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    $\begingroup$ If by "can dilate time in a bubble around Santa" and "make as many trips .. as needed .. to deliver all the gifts" time is manipulated to do all the deliveries, then the time in the bubble isn't dilated. Time dilation refers to the geometric representation of relativistic time in Lorentz diagrams. The closer to lightspeed the more dilated and apparently slower. The time in Santa's bubble will be contracted to allow time to pass faster, thus giving more time for deliveries. This is a common conceptual confusion about time dilation. Hope you hand out lots of Christmas sparkles. $\endgroup$ – a4android Dec 25 '16 at 12:28
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    $\begingroup$ @a4android It's common enough parlance that I think using it a shorthand for 'someone is messing about with general relativity I n order to make time flow more quickly here than there' is acceptable, and I think I'm going to have to find more Christmas sparkles!!! $\endgroup$ – Joe Bloggs Dec 26 '16 at 12:23
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An article on Oilprice.com estimates the amount of switchgrass Santa's reindeer would consume using analogs to biofuel production, which has some interesting data but I dislike their analysis.

Useful data from his oil article includes:

  1. Santa needs to travel around 226 million miles to deliver all of the presents to the world’s children.
  2. We do know that mules and oxen can go roughly 15-20 miles per day.
  3. We also know that a typical livestock animal might need to eat around 1.5 percent - 2 percent of its bodyweight in forage feed (depending on the nutritional content of that feed).
  4. We also know that a male reindeer weights 350-400 pounds.
  5. Santa’s reindeer are probably on the more muscular end of that scale, meaning that they’d need to eat about 2 percent of 400 pounds, or 8 pounds to be able to fly 15-20 miles.
  6. Update. My assumptions were wrong, so I've updated this answer below!

So, this is "forage feed," your hay and grasses. According to Dayville Hay and Grain, 8 pounds of Hay (a mix of Alfalfa Hay and Timothy Hay, because we're running up against a lot of assumptions and estimates here) runs up to 7,124 calories.

So, the "fuel economy" of a single reindeer, dashing up and down hills (average them out to flat) is about 407 calories/mile (7124 / 17.5). Santa has 9 reindeer, so his sled's "fuel economy" is 3,664 calories/mile.

828,012,342,857 calories in mixed Alfalfa and Timothy Hay. This doesn't include trips back and forth to the North Pole, because I don't know what the sled capacity is for toys, and therefore I cannot calculate how many north pole trips would be required. With the fuel economy figures provided, you can add on however many additional miles you deem necessary.

Using the same reference material above, Santa's reindeer would need to eat **662,409,874 lb (331,204.937 short tons) of premium feed oats. That comes up to 73,601,097 lb (36,801 short tons) each!

Bonus round: To grow that much oatage you would need 103,501.5 acres of land, assuming a decent harvest for silage source. To get that much, you'd need to plant an area at least half the size of Rhode Island in nothing but Oats, just for consumption this one night.

ALSO UPDATE. According to the San Diego Zoo, reindeer would actually eat about double the numbers above. The exact numbers depend on the specific animal and their workload, but we can give an estimate of 1,324,819,748 lb (662,409 short tons) of premium feed oats. This would require oat production across the entire state of Rhode Island to produce the food burned this one night.

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    $\begingroup$ The San Diego Zoo says 9 to 18 pounds or 4 to 8 kilograms of vegetation a day. This seems higher than your estimate. Perhaps reindeer use more calories than average. $\endgroup$ – Brythan Dec 26 '16 at 3:46
  • $\begingroup$ To be fair, @Brythan, my number was based on horses and other livestock, not Reindeer, because I didn't have your Google-Fu to find the info from the San Diego Zoo! I've updated my answer with your data. $\endgroup$ – Zoey Boles Dec 26 '16 at 9:12
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    $\begingroup$ I think Christmas sparkles are in order!!! $\endgroup$ – Joe Bloggs Dec 26 '16 at 12:24
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    $\begingroup$ they are going to leave one big pile of manure... $\endgroup$ – Mr Scapegrace Dec 27 '16 at 10:12
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With the exception of the "time dilated bubble", which makes the question quite meaningless in regards to energy calculations. You can get an idea of that actual cost of energy to move presents to all children in 24 hours.

Solving this with conservation of energy

Using the 226 million mile (360 million km) number for how much distance the presents need to go from Zoey's answer and assuming a 24 hour time for all presents to delivered. This averages to about 4 million m/s. Which is ~1.3% c.

Just using: $E_k = 1/2 mv^{2}$ then multiplying by 2 to get the acceleration and deceleration. Allowing Santa to pre-accelerate the sleigh for 24 hours before Christmas so he is at max speed the second Christmas starts.

Even ignoring the effects of relativity, that is ${2*10^{13} J}/ kg$ of energy needed to accelerate and then decelerate reindeer. That is about $5*10^{12} cal/kg$. So for 9 reindeer of ~200 kg each makes about 2000 kg.

So total reindeer takes about $1.0*10^{16} cal$. Which is about 12000x the amount in Zoey's answer. If you are using the area of rode island to farm the oats in Zoey's answer, you'd need about 12000x as much land, which is about 10 million $km^2$, the size of Canada. There isn't enough farmland in the world to do this.

Zoey expected a linear relationship between energy and speed which is not true. Kinetic energy rises to the square of the velocity. So all the accounting for how much energy a reindeer takes to go 10 miles would not work here.

If you expect each present to be about 1 kg and about 2 billion presents, you'd get a total energy of $10^{22} cal$ for the presents. This would is about a billion times the energy of just the reindeer. This is about 100x the energy consumption of the world per year.

Note: This is assuming a perfect engine and that there is no air resistance and that the sleigh only accelerate and decelerate 1 time. This also means presents are basically taking the whole 24 hours to slow down while being delivered. This is a minimal answer and probably underestimate the actual amount by a couple million order of magnitude if you want Santa to actually slow down at each house and personally deliver the presents.

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  • $\begingroup$ Note that the reindeer can dilate time, according to the question, so the reindeer don't need to travel quite so fast. For my question - and any question invoking the 24 limit - I think this answer is correct. $\endgroup$ – HDE 226868 Dec 21 '17 at 20:05
  • $\begingroup$ @HDE226868 I somehow missed that part. In that case, the reindeer would need no energy since they can literally move without taking any time to do it. It moves all the energy required for them to move to the ability to slow their own time down in relation to the world. They wouldn't even need to travel a distance as they would effectively be able to be in all places at once in all time. $\endgroup$ – A. C. A. C. Dec 21 '17 at 20:16

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