Background
Last night, I was reading the FM 23-10 (The U.S. army official field manual for sniper training), and I've noticed that they're potentially teaching snipers incorrect information.
Generally speaking, when we say "impact goes up" it means that the bullet was either somehow made faster or its path was easier, therefore the curve in its ballistic trajectory is smoother. Thus, it will hit higher. When we say impact goes down, we mean the opposite.
For example, atmospheric heat will, loosely speaking, make the air "thinner" and therefore the impact will be higher. Cold weather will do the opposite. This part is correct.
What about humidity?
The sniper can encounter problems if drastic humidity changes occur in
his area of operation. Remember, if humidity goes up, impact goes
down; if humidity goes down, impact goes up.
They're basically saying that when humidity goes up, then the bullet's travel will be more difficult-> steeper trajectory curve -> lower point of impact.
However, as far as I know, dry air is denser than humid air because air has higher molecular mass than water vapour. In humid air water vapour replaces other gases, thus bringing the whole density down. So, the point of impact should be higher with higher humidity.
So my question is:
All other factors being equal, does humid air pose less resistance to the bullet making the point of impact higher than in dry air?
Best Answer
You are right. Field manual is wrong. Water has a lower molecular mass, which reduces air density.
But is the difference significant enough to notice?
Terminal velocity is the speed at which a falling body reaches a stable velocity when gravity and air resistance meet in a stable equilibrium. Let's assume the bullet travels close to terminal velocity so we can use its model.
Air density is part of the terminal velocity equation. Air density is inverse square-root proportional to terminal velocity. This means terminal velocity goes down, but only as a function of the square root of air density.
wiki - air density - humidity
Air density is charted above (credit to jaffer@MIT). You can see that in a hot climate of 30 deg C, air density has about a 3 percent from 0-100% humidity. But remember we have to take the square root of that difference - about 1.5%. So the most humidity can affect the speed of the bullet is 1.5%.
I don't know the math for how that affects a ballistic trajectory. Sorry.
It could be insignificant, which is why it they got it wrong. It's probably based on what people think intuitively, and backed up by confirmation bias. If it had a significant impact, you think they would know this by know. This scientific knowledge is not exactly new.
The field manual is wrong.