### The Nose Knows Physics

@neiltyson tweeted

According to the song, Rudolph’s nose is shiny, which means it reflects rather than emits light. Useless for navigating fog.

To which I responded

Nose also glows & bright. Since it’s red we could determine temperature if a thermal source & estimate Rudolph’s calorie needs

If Rudolph’s nose is a thermal source it will follow the Stefan-Boltzmann power law, which tells us the radiated power depends on the fourth power of temperature. Something red-hot will have a temperature of about 1000 K. Now this is an estimate and since it’s raised to the fourth power, will give us a large error bar on our answer. But let’s go with that because I don’t have a calculator handy. For the emitted power we multiply by the area, a few square centimeters (converted to square meters) and Stefan’s constant. Assuming I did the math correctly, we get about 10 Watts. The temperature should not be as large as 2000 K, which would give us and answer 16 times as large. (I am ignoring the “power absorbed” term in the equation, because at these temperatures it’s going to be small — 300K or less)

There’s also the emissivity. The nose is shiny, meaning the emissivity is not close to 1. So perhaps we double our guesstimate. Tens of Watts, maybe as large as 100 Watts as a probable value.

A thermal source has a maximum luminous efficacy of 95 lumens/Watt, at a temperature of around 6600 K but actual bulb filaments that give us white(ish) light are a lot closer to 10 lumens/Watt. So the nose probably emits around 1000 lumens at best — this is not even as bright as a traditional 100W light bulb, but is around what low-beam halogen headlights emit. However, those have reflectors on them to direct most of the light into a beam. Rudolph’s nose emits into a much larger area.

So perhaps the nose is not a thermal source (unless it’s much larger than I estimated) — the radiation is not because it is hot. We could check this if we knew the spectrum of the light being emitted. Perhaps it is some other type — does Rudolph have an LED nose?

1. bph on December 25th, 2011

The spouse was speculating that the harness carried the glycol for cooling (the refrigerator would be in the sleigh of course). But we settled on a LED as the source, cooler and more photons per Watt in the right part of the spectrum.

2. Uncle Al on December 25th, 2011

Perhaps Rudolph has major infestation of nose weevils glowing like fireflies: luciferin, luciferase, and oxygen. Perhaps the North Pole – given the Greenhouse Effect, er, Global Warming (we have always had Global Warming!), ah, Climate Change – has its seas suffer a major infestation of Aequorea victoria hydromedusae, and Rudolph is a gormand.

http://www.mazepath.com/uncleal/satax.htm
Perhaps Santa and the whole crew did a certain ectomycorrhizal symbiont that Santa is dressed to resemble.

Hallucinations; “agitation, ataxia, auditory and visual distortions, combativeness, stupor, euphoria, dizziness, hypotension, mood swings, nausea, seizures, tranquility, salivation, sweating, and muscle twitching.” Your mileage may vary.

3. Xittenn on December 25th, 2011

I think that would be an OLED nose; hilladious! : D

4. Emory K. on December 25th, 2011

Reindeer are mammals, so it’s a compact furescent.

5. rob on December 27th, 2011

Emory K. wins!