Friday, December 8, 2017

Reindeer Power

It's the most wonderful time of the year, and to spread some *physics* holiday cheer, today we will calculate the horsepower of Santa's reindeer.

Santa's sleigh weighs 75,000 gumdrops, can carry a payload of 60,000 tons of gifts and carries a passenger weighing 260 lbs according to the official NORAD Santa tracker sleigh technical data. The average gumdrop weighs 3.6 grams according to my research. Quick unit conversions yield that Santa's sleigh with payload and passenger weighs 60,000,388kg:

75000*3.6g*1kg/1000g = 270 kg
60000 (metric)tons*1000kg/ton = 60000000 kg
260 lbs*1kg/2.2lbs = 118 kg

Next, NORAD also tells us that the maximum sled speed is "faster than starlight." To approximate this, we will use the speed of light (c = 2.998*10^8 m/s). NORAD does not have any technical data on the acceleration of the sleigh, but we can make some assumptions. First, I will assume the length of Santa's runway, which I will arbitrarily assign as the length of one house roof. The average length of a house in the U.S. is 60 ft (18m). This means that Santa accelerates from 0 to c in 1.2*10^-7 s or 120 ns (nanoseconds).

Vf^2 = Vo^2 + 2ax                      Vf = Vo + a*t
a = 2.50*10^15 m/s^2                  t = 1.2*10^-7 s

Now we can determine the force, work and power exerted by the reindeer. To do so, we will consider the force of friction caused by snow to be negligible. F=m*a, which gives us a force of 1.5*10^23 N. We also know that W = F*d*cosø. For simplicity we will assume an angle of 0, and therefore the work done by the reindeer is 2.7*10^24 J. For comparison, the sun produces 3.8*10^26 J in one second. The power generated by the reindeer during takeoff is P = W/t. This yields 2.3*10^31 W (watts). Since horsepower is approximately 750 W, and there are 9 reindeer (Rudolph, Dasher, Dancer, Prancer, Vixen, Comet Cupid, Dundee, Blitzen) pulling the sleigh, each reindeer is generating 3.3*10^27 horsepower. That is 3*10^22 times more horsepower than the engine with the most in the world (Wärtsilä-Sulzer RTA96-C, for container ships, 109,390 Hp). Indeed, Santa and his reindeer are truly magical.

Happy Holidays everyone!


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