Speaking of science. I am sure you have tested the cold air kits as well as the oem box to determine the actual air temperature of the air inside the intake tube at the throttle body. I am sure we all would love to see the outcome of your own personal research. Please post the numbers so we all can be as educated so we all can make well informed decisions based on research.
I was simply posting my own personal observation with my install. I felt useful firsthand experience may benefit someone who was considering installing this kit.
If you need "proof" the warmer air inside your engine bay is not as dense as the cooler air outside your fender, there is a chance the proof is beyond your grasp anyway. I know some people don't have any faith in science, and choose to disregard sound data.
I don't need to do copious amounts of research to know the warmer air trapped under your hood next to your engine is not as dense (efficient) as the cooler air outside your fender. The reason I don't need to is because every modern auto manufacture has done exactly that, and come to exactly that conclusion.
But if you want numbers. Here you go.
ρ = 1.325 pin Hg / TR
= 2.7 ppsia / TR
= 2.7 (ppsig + 14.7) / (TF + 459.7) (1)
So at 0psi, and an ambient air temperature of 60 degrees at sea level (not to blow your mind, but elevation also changes the density of air) you have an air density of .076 lb/ft cubed.
Inside you engine compartment, with an ambient air temperature of 150 degrees (conservatively) also at sea level and 0 psi. You end up with an air density of .065 lb/ft cubed.
In conclusion, based on magic and sorcery, you get an approximate 15 percent decrease in air density when comparing inside vs. outside the engine compartment.
I won't even address the tubular metal air heater you added to your intake.
But none of the math and science mumbo-jumbo can compare to what you "feel".
All jokes aside, air intakes and performance filters can decrease the restriction of air flow. So if you do in fact feel a gain from the system you used, it is likely due to the volume of air being sucked in. So imagine how much you would feel if you got a good system that pulled in cooler air.... Something to consider.