# Difference between revisions of "620: Wings"

 Wings Title text: Please do not try any of this and die or get arrested.

## Explanation

Titan is the largest moon of Saturn. Icarus was a character in Greek mythology who is most famous for the fatal end of his flight, when the wax holding the wings together melted and he fell to his death in what became known as the Icarian Sea. In the original, this was because Icarus flew too close to the Sun; in this comic, Black Hat is bringing an artificial "sun" (the heat lamp) to "Icarus" to recreate the tragedy.

## Transcript

Man: Titan's gravity is 14% of Earth's, and its atmosphere 50% denser.
Man: So if you can generate 9% of your body weight in lift, you can fly on Titan.
Man: With wings, a stage harness, a cable, and 91% of my bodyweight in in bricks, I want to test this.
[There is a heap of materials on the ground. The man is holding a stage harness.]
[Large diagram of a bridge. A rope leads through pulleys tied to the bridge. One end goes to the man, one end to a pile of bricks.]
[The man is standing with wings attached to his arms.]
[The man flaps the wings, and appears to be floating.]
[The man glides.]
Man: It works!
Woman: Except you have two problems.
Man: What?
Woman: You used hot glue on your wing joints and you have friends into Greek mythology.
Man: Huh?
[Black Hat Guy is standing on the bridge, with a large lamp labeled 'heat lamp' attached to a battery.]
[The wing segments fall off the man and he tumbles downward.]

# Discussion

Cueball's physics has a mistake on this one (or at least assumes we've managed to heat the atmosphere of Titan to Earth's temperature). The temperature of Titan is roughly 1/3 the temperature of Earth on an absolute scale. Starting with the Ideal Gas Law, PV = NkT (k is Boltzmann's constant, N is # of molecules, P is pressure, V is volume, T is temperature), its easy to define the density of a gas, ρ as:

ρ = m/V = (m P)/(N k T) = P (m/N) / (k T)

Titan's atmosphere is 98.4% molecular nitrogen (N2) and on Earth only 78.1% molecular nitrogen (by volume), but for simplicity we'll assume 100% for both. The weight of one molecule of Nitrogen is (m/N) ~ 2 × 14 × 1.67x10-27 (kg/molecule) (there are 28 nucleons per molecule with a mass of about 1.67x10^-27 kg.

The pressure on Titan is PTitan=146.7 kPa, and TTitan = 93.7 K, while on Earth PEarth=101.3 kPa and TEarth = 287 K.

Plugging in numbers, we get ρTitan = 5.3 kg/m3 and ρEarth = 1.2 kg/m3 (note the measured surface density of air on Earth is 1.2 kg/m3 at Earth's mean temperature even without the simplifying assumption of 100% N2).

Hence Titan's atmosphere is 4.4 = (5.3/1.2) times denser than Earth's (or 340% denser); not 50% denser as stated in the comic.

You will get the 50% denser if you assume the same planetary temperature on Titan as on Earth. Titan at 287 K would have a density of ρTitan at 287K ~ 1.73 kg/m3 which is about 50% greater than Earth's.

For the second calculation (panel 2), note lift is proportional to the density of air. If your action on Earth creates a lift of L0 and you weigh W0, on Titan you'd have a lift of 4.4 L0 (Cueball calculated 1.5 L0) due to the greater air density. Your weight would only be 0.14 W0, due to Titan's lower surface gravity. If lift balances weight, you would be able to fly on Titan, that is if 4.4 L0 = 0.14 W0. That means to fly on Titan you need a lift on Earth of L0 = 0.03 W0, that is 3% of your Earth weight. Substituting Cueball's Titan density you would get the critical value from the comic: L0 = 0.14 W0/(1.5) = 9% W0.

PS: I largely adapted this my writeup on xkcd forums from 2009 when the comic was made. Jimbob (talk) 05:44, 8 June 2013 (UTC)

That was the whole point of Blackhat's presence. He was there to make sure Rob (AKA Cueball) wasn't hurt.
Fortunately, Blackhat couldn't care less about the outcome. So he's got that going for him, which is nice.

I used Google News BEFORE it was clickbait (talk) 01:21, 29 January 2015 (UTC)

Why is this not a thing you can do in amusement parks or places like that?141.101.104.44 17:00, 8 September 2016 (UTC)