For those wanting to talk about flying, rather than physics, look away now.
Has anyone mentioned 'Momentum' yet..?
Consider two cases... Airplane flying North at ASI of 100 kts with 99 kt tailwind, and second Airplane flying North at 100 kts into a 99kt headwind.
This makes the ground speeds 199 kt and 1 kt, respectively.
The first has considerable Momentum (Mass x Velocity) the second has almost none.
So if they are both disturbed by a similar force (a gust of wind, or a control movement.) The first aircraft will be deflected from its course by one or two degrees, whereas the second will change its direction vector by a very large amount.
scifi, if that were correct then aircraft would be more agile when flying downwind than upwind.
And they aren't.
Hi Boss Eyed... No I think you have got it completely the wrong way round...
If you are going North downwind at GS = 199 kts a small control input could change your course by one degree... (your still effectively going North.)
But going into wind at Ground Speed =1 kt, the same control input could make your course change by 90 degrees (i.e. you fly west.)
In both cases your heading remains about the same, but the Course works out very differently.
For those not familiar with the Jargon, 'Course' is the track over the ground.
'Heading' is the way the front of the aircraft is pointing.
Scifi, Most of what you say is true, but your conclusions are wrong - at least if you're trying to imply that the two examples' agility are different.
In particular, the statement "The first aircraft will be deflected from its course by one or two degrees, whereas the second will change
its direction vector by a very large amount." is wrong.
You've used the term "direction vector". Difficult to know what you mean by that - but if it's velocity (which is a vector), then the change in it is the same for both aircraft. Similarly the change in momentum (which is just the velocity times the mass, and is also a vector) is the same for both aircraft. The course change (or track as I think we'd conventionally call it), changes dramatically, but that's just a direction and not a vector quantity, nor does any law of conservation apply to it.
That the momentum of your two examples is different is just a consequence of the frame of reference you are using - in that case that of the ground. In the air mass frame of reference, the momentums are the same.
And the fact that you've chosen a different frame of reference doesn't change the agility of the two aircraft. They are both equally agile - it's just that the ground is moving in respect of the airmass frame at 99 kts.
Paul