I'm going to try again, against my better judgement.
Sierra is contradictory on this point but they are not contradictory on acknowledging the error in 4.3.
The quote I provided is not from 4.3. It is from 5.3.2 If you believe you have a point, it's fair to raise it. Once it is categorically addressed, please don't raise it again as if it's a new point.
The error in 4.3 is not relevant to a quote from 5.3.2. So we're done with that, right? Furthermore, you then go on to quote from 4.3 after saying twice that 4.3 is in error. How does that make sense? Why wouldn't you quote, instead, from the article that claims to be correct?
There are a number of equations in that article that involve the difference (Vcrosswind - Vcrossrange), that is the difference in the crosswind velocity and the crossrange velocity of the bullet. That expression reduces to zero if the two are the same. Clearly they are not the same or all those equations would be fancy ways of writing 'zero'. Clearly the bullet is not moving at the same crossrange velocity as the crosswind velocity.
As far as contradictory goes, let's address this.
You say: "...
our .308 168 grain SMK bullet takes up an angle 47.6 MOA thru the air to strike that object on the ground 1.8 inches downwind from the target
while moving 25mph across the ground with the airmass."
I say: "...Which is to say that <the bullet> isn't moving at 25mph across the ground"
You respond with: "Nobody ever said it did..."
Somebody obviously did say that--in fact, it was you in the very quote I was addressing. If you say something, then don't deny saying it and then move on as if nothing happened.
Next.
Why does it have to move at the same velocity??
Because you said it did when you stated very clearly: "
our .308 168 grain SMK bullet takes up an angle 47.6 MOA thru the air to strike that object on the ground 1.8 inches downwind from the target
while moving 25mph across the ground with the airmass".
You say that the bullet is moving 25mph across the ground with the air mass which you stated was also moving 25mph earlier.
In fact, I was the one saying it was not moving at the same velocity while you were saying it was, but you ask me why it has to be moving at the same velocity as if that were an assertion I had made. If you don't mean that they are moving at the same velocity, then don't say it. And if someone calls you on it, admit it, don't pretend instead that they are the one who made the claim that you made.
Ok. Let's move on.
Nothing says that it does move at the same velocity but it must equalize those forces and therefore it will take on the velocity of the air mass it is traveling in.
Well, sorta.
1. The crosswind force acts on the bullet but the bullet counteracts it by "steering" into the wind and cancelling out much of the crosswind velocity. By doing so, it effectively "flies" in the upwind direction in the air mass instead of being carried along at the same velocity as the wind. This is easily verified by comparing the crossrange movement of the bullet during TOF to the crossrange movement of a hypothetical object moving at the crosswind velocity during the same timeframe and noting that the bullet will travel only a small fraction of the distance crossrange as the hypothetical object moving at crosswind velocity does.
2. Because of the nature of the interaction, a bullet will not ever achieve the full crosswind velocity because TOF is limited by practicality. Even at distances far exceeding a mile the crossrange velocity of a bullet will never take on the full velocity of the crosswind. That is what Sierra says and that is what Hornady's ballistic calculator says.
. Here we are all amateurs.