How does humidity affect the path of a bullet?

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.

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?

• You have some problems here. You quote them as saying that humidity up = impact down, then you reinterpret that as humidity up = impact up, completely inverting what the quote says. Sep 30, 2013 at 14:40
• @Wutaz Oh, thank you for bringing this to my attention. I guess I was just so concentrated on my own thoughts and wrote what I thought to be correct. Now the question makes more sense, and the FM 23-10 is still wrong.
Sep 30, 2013 at 15:30
• Once scenario is the water vapor does not just displace the air. It adds to the air make it more dense. There is miles of air above and is not immediately moved (displaced). May 4, 2017 at 15:55

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.

• Thank you for your answer. The effect it small, but it's not insignificant at all. Having that said, I understand that the usual operating distance for a regular sniper doesn't exceed 500m in most cases. This would translate to about 2.5-3cm shift in the point of impact, which isn't that important at that distance. However, if you double that distance, now you're dealing with ~ 8cm. Stretch it to a mile (conventional long distance shooting), and you'll quickly start seeing more thank half a meter offset. I've personally seen a meter of offset purely due to 10 degrees temperature difference.
Nov 16, 2016 at 12:08

Today I have noticed that our humidity is extremely high compared to yesterday. The temp is about approx 5degrees F warmer today than yesterday. I just shot 30 rounds and noticed without any bias on this subject (no previous opinion) that my rounds were landing .125" higher than yesterdays 30 rounds. Hence why I am researching this subject of humidity and the impact on subsonic rounds. So for what it is worth, my experience has been humidity higher, POI higher. Then again, it could just be me.

• Were you aiming, or did you have a machine fire for you? Same location? How about windspeeds & direction, did they change between the two days? There are probably a lot more variables here than simply a single guy firing off a pair of boxes on different days. May 18, 2015 at 20:47
• While I think that your method is far from scientific, it's clear to me that my experience matches yours. Higher humidity has consistantly given me a higher POI
May 19, 2015 at 7:20

According to several sources, such as http://longrangebpcr.com/accuracy.htm , you are right: higher humidity - higher point of impact. But those sources also point out that humidity effect is small.

• Yes, I've noticed that usually at 1000m the maximum shift of POI (point of impact) caused by humidity cannot be more than about 3-5cm. Yeah, it's very small, but it's there. I do appreciate your answer, but could you please expand it a bit with some physics mojo? Thanks.
Sep 30, 2013 at 9:51
• I am afraid I cannot add much to what you wrote in your question ("air has higher molecular mass than water vapour.") Let me just note that the above is correct when we compare dry and humid air at the same pressure. Maybe the army manual referred to the effect for the same partial pressure of dry air. Sep 30, 2013 at 10:12
– user28737
Oct 2, 2013 at 11:55
• @Waqar Ahmad: Both in humid and in dry air, air viscosity causes deceleration of the bullet, which leads to the bullet going lower due to gravity. What is discussed here is whether this effect of air viscosity is greater in humid or dry air. Oct 3, 2013 at 6:39

I would expect the effect of density variations to be smaller than viscosity - yet not the one of water vapour rather that of the condensing water droplets. Remember that the manual says drastic humidity changes.

Apart from that, humidity changes usually don't come about on their own, they tend to be connected to changes in temperature (drops) and pressure - especially on time scales one would expect for a sniper waiting for a shot which, given the context, is in hours. Hence the question all other factors fixed doesn't fit the real situations expected by the manual (plus you'd have to specify what other factors you'd keep intact, since state equations bind some of them together, so you are not really free to change them arbitrarily).

Could be that the expanding gasses behind the projectile diminish faster as the outside air influenced the outcome ,herefore decreasing ramp time(bullet arc)wich lead to bullet drop on its intended path!pesonal experience in sub tempreatures using a 45acp had the same outcome at 15metres.2seprate 1911 pistols were fired and both litterally experienced bullet drop using the same reloaded ammo(185gr swc).normally we used the very same range and ammo when climate is humid_hot and bullets seemed to print on sight of aim or slightly higher 2-5cm.

Drier air creates more friction thus slowing the projectile. Slower feet per second, translates, to a lower point of impact.

All things being equal, I would tend to believe that water or vapor molecules are larger, tougher, and thus encountered more frequently thus slowing the bullet down.

• Have you any evidence to support this claim, or is it simply a belief? Feb 22, 2015 at 15:31
• Water molecules (H2O) are significantly smaller than nitrogen (N2) and oxygen (O2) molecules, which is what air is mainly made of. A water molecule consists of 3 atoms instead of 2 for nitrogen or oxygen, but 2 of those are hydrogen atoms and they are much much smaller than nitrogen or air atoms. Jul 27, 2015 at 12:23