It's Not the Heat, It's the Humidity
What's with the flight instructors and density altitude? Sometimes it seems like all we every say is "Right rudder! Density altitude! Centerline!"
But our job is to remind everyone about the things that don't necessarily come up every day, like engine failures, flying by instruments, and unusual weather.
For the record, density altitude is the pressure altitude corrected for temperature in accordance with the International Standard Atmosphere (ISA), which converts between density and altitude in standard air. Heat changes the density of the air, so you calculate the density and use the ISA table backwards to interpret that density as an altitude. You learned this in pilot training, and maybe even saw a Koch Chart
Too much math for most folks.
I live in high desert country, 4500 feet above sea level and dry. Summertime high temperatures are usually over 90F, or about 32C, so the density altitude is often around 7500 feet. This is normal for us.
But density altitude is sneaky, as we discovered the other evening. We were flying in the evening because it was cooler. Cooler air means lower density altitude, so we should climb better at 7pm than we would have at noon, right? But the airplane barely climbed.
Earlier that afternoon I had gone for one of my usual runs. One of the pleasures of running in this climate is that perspiration evaporates almost immediately, but that day the sweat was pouring off my bald head and stinging my eyes. The dewpoint, which is usually around 0C, was 19C! This meant a relative humidity of about 70%.
And that's the problem: humidity. You'll notice that the Koch chart does not mention humidity! But my worst density altitude encounters have been due to humidity, not heat. The worst was in the lush part of New Jersey, in a Mooney. There was a deer on the runway, so I went around, but the Mooney wouldn't climb. This was at sea level, the temperature was probably near 85F/30C, but the humidity must have been around 95%. The Koch chart would say that the density altitude effect was small, especially compared to the effect of 30C at 5000 feet MSL. But that doesn't reflect the true density of the air. Koch may not have known this, but the Mooney did.
[All together now] It's not the heat, it's the humidity.
My student that night is a retired chemist, and he understood this right away. "The atmosphere is mostly Nitrogen," he said, "with molecular weight 28. But water has a molecular weight of 18. That's a big difference!"
Now for a little basic aerodynamics. You climb at a high angle of attack, where Newton's Law (every action has an equal and opposite reaction) dominates. In other words, air molecules hit the wing from below, so it goes up. Momentum is conserved, so an 18 unit mass transfers about 35% less momentum to the wing than a 28 unit mass transfers. In other words, if we flew in pure water vapor, the wing would produce 65% of the lift. This is the difference between 15,000 feet and 25,000 feet in ISA!
Wikipedia had complete nonsense about this in the "Density Altitude" article. I fixed it.
Just wait until winter, when I'll start in on cold temperature altimeter errors...