I so enjoy the experts in the AvWeb comments. “I can do math.” But can you do physics?
Your calculations are correct, but useless.
The fact that CO2 is .04 of the atmosphere doesn’t mean that it is insignificant when it comes to the physics of radiative transfer. Now it doesn’t compete with water vapor or methane, but it is an effective molecule when it comes to absorbing energy in a few different wavelengths. It’s biggest absorption region is around 15 micrometers (down at the infrared end of the spectrum), and another around between 4 and 5 micrometers.
Now the catch is that these work with atmospheric “windows” where the energy from the sun (relatively short wavelength, blackbody spectra ~5780K) passes through. This is good because that means the shorter wavelengths from the sun aren’t absorbed much and give us everything we enjoy from warmth day light, to photosynthesis and color. On the other hand, the longer wavelength radiation reradiated by the earth (absorbed from sun, then radiated at a different wavelength depending on the surface, blackbody spectra ~255K) does not coincide with one of these windows found in the absorption spectra of CO2, water and methane.
This longer wavelength energy emitted by the earth is why you can have frost on the ground (or windshield) when it’s only 35F or 36F overnight. Or why sleeping under a tree will keep dew from forming on your sleeping bag during a fall camping trip.
Unfortunately these molecules which have relatively strong electric dipole moments absorb radiation much more strongly in these longer wavelengths than they do the sun’s shorter wavelengths. That means that the energy radiating from the surface of the earth does not all escape into space. Interestingly it is why you only get that windshield frost on clear nights when more does escape into space and isn’t absorbed and reradiated by a cloud layer that consists of that pesky greenhouse gas H20. Instead that longer wavelength radiation is absorbed by CO2, water and other dipole molecules and is again reradiated in the atmosphere. This is of course a source of energy in the atmosphere and gives us a habitable planet. But as Venus shows, too much of a good thing is a bad thing.
I recommend chapter 4 of Atmospheric Science by Wallace and Hobbs for a good primer on the blackbody physics, Rayleigh and Mie scattering (good rainbow and sunset info), Schwarzschild’s equation, Wien’s displacement law, and Stefan-Boltzmann law and a bunch more. There’s nothing worse than high school calculus, so should be well within your expertise in math.
Oh, and a side note…you seem to think .04 percent of the atmosphere makes C02 insignificant. A typical flight in my 340 I’m at around 5500 pounds. If I removed .04 percent of the weight it might not mean anything. But it’s useless to simply do some multiplication and say that this is the case. 220 pounds of seats, heck even some old instruments and wiring wouldn’t make a difference. 220 pounds of rivets or wing ribs or the tail surfaces on the other hand…
Math is good, but physics is a bit more important. Know the context of your math calculations before you make yourself look foolish again next time.