## Sunday, December 30, 2012

### Reindeerpower

While watching football today I saw a commercial for the Chevy Silverado featuring the Santa Salesman. Here's a Youtube clip:

Santa is poised to calculate the reindeerpower of the Silverado, but sadly the commercial ends before he can give us an answer. Thus we are left to speculate the magnitude of 1 reindeerpower.

How would we go about doing that? We need to start off by setting a few ground rules. Santa and his reindeer are clearly capable of time travel and/or superluminal speeds, which makes estimating their power output somewhat troublesome from a theoretical perspective. Like good scientists, we have to limit ourselves to the reindeers' documented behavior.

The most authoritative eyewitness account makes the claim that:
More rapid than eagles his coursers they came...
Although the authorship of this account is apparently in dispute, the two possibilities are both American. We can assume that the author was most familiar with the American Bald Eagle, which Wikipedia says can fly at about 17 m/s. Let's estimate that Santa's reindeer can achieve something on the order of 20 m/s.

Now, the record here provides us with another useful tidbit as well:
As dry leaves that before the wild hurricane fly,
When they meet with an obstacle, mount to the sky.
So up to the house-top the coursers they flew,
With the sleigh full of Toys, and St Nicholas too.
We learn from this that the reindeer are ascending while traveling faster than eagles. This gives us a very easy way to calculate their power output.

But before we go any further, we have to figure out just what power is from a physics standpoint. Most of us encounter power in two forms: the horsepower of our cars, and the wattage of our electrical items. Both measure the same thing, just in different units. Power is the rate at which energy is transferred -- the standard unit being Joules/second, the watt. 1 hp is 746 W.

So how do we measure the rate of energy transfer? Well, we know that Santa's reindeer can ascend at 20 m/s, which means they can create 20 meters worth of gravitational potential energy in just 1 second. Gravitational potential energy, as we recall, is mass * gravity's acceleration * height. Gravity's acceleration is a constant and our height is 20 meters, which just leaves us with mass as an unknown.

There are about 2 billion Christians in the world. If every one of them receives an iPad or a Kindle for Christmas, we can estimate that (with packaging) this amounts to 2 billion kg worth of presents. We can safely assume that Santa, the sleigh, and even the reindeer add nothing significant to this estimate. All that's left to do is plug in the numbers, then.

The power output for the entire sleigh comes to about 400 gigawatts. (This is an encouraging result, because it's over 300 times the power needed by the DeLorean to travel through time. And as previously discussed, Santa must rely on time travel to deliver all his presents in a single night.)

If we assume that Santa derives all his motive power from the reindeer, and that there are only 8 reindeer (Rudolph, being a mutant, likely delivers all his power to his red nose and provides no motive contribution), then each reindeer is worth 50 gigawatts. In terms of horsepower, this is 67 megahorsepower. The Chevy Silverado talked about above delivers a pitiful 315 hp, which comes out to 4.8 &#181rp (microreindeerpower).

I must reiterate that this is only an estimate. Santa clearly knows the proper conversion himself, so any confirmation on his part would be swell.

Happy holidays everybody.