TWC = GS - TAS will only work if the wind is parallell to your direction of flight. More than that, and it is trig or vector calculations territory. Fortunately made easier to perform on the fly by advanced variations of the slide rule concept.
Some FMCs allow you to enter the predicted winds along the route to get more accurate predictions of fuel burn, top of descent etc.
Even when that is not an option, you should at least compare the actual times for each leg with the planned time, note any significant discrepancies and update your plan accordingly. If it is done, well... Iíll leave that to those who do it on a day to day basis.
But to calculate the said tailwind component (or headwind, for that matter, which would be a negative value from a TWC perspective) you need to take the cosine of the actual wind and the angle relative to your flightpath.
So the tailwind component of a 120/12 when you're heading (not bearing!) exactly 360 would be 12*COS(180-120), and equals 6 knots.
The EFIS indeed does this by calculating the difference between the TAS value from the ADC and the GS from the IRS/GPS. Looking at the difference between the plane's heading and bearing you can calculate the wind vector by reversing the trig function I posted earlier.
Is it not rather dangerous to pick a wind angle where the sine and cosine happen to be the same as is the case above. In fact for headwind and tailwind calculations the cosine of the angle should be used. The sine will give you the crosswind component.
All big EFIS planes that have an inertial reference system seem to have this kind of wind vector, the key is breakdown into two components that are parallel and perpendicular to the plane's trajectory: crosswind and head-/tailwind components.
I recall that in the Boeing FMC's last PROG page. (737, 747 and 777, and I imagine others as well) there is a breakdown for the head-/tailwind and crosswind components.
I haven't seen it in the Airbus MCDU, but like Boeings 'buses have a wind vector on the ND as well, as do the F100/F70s.
In the upper left corner of the ND you can see it, two perpendicular arrows with the respective indications for the values in knots below the TAS/GS readouts. As you can see it displays a 4-knot headwind.
In your example the wind vector is at right angles to the track but not the heading. Relative to the heading you certainly do have a headwind component. The effective TAS method can be used where you are using the track as reference and is used with calculators not having a sliding TAS/Drift capability.
But when the air is moving, I think you are forgetting one important fact: All movement has a direction as well as a speed.
Draw the ground speed as an arrow on a paper, with direction and length to represent the speed. Then draw another arrow, starting in the same point, to represent the TAS with the direction of the heading of the aircraft and the length to represent the TAS.
If you draw a third arrow from the tip of the TAS arrow to the tip of the GS arrow, this third arrow will be the wind.
These arrows are what you'd call vectors, and what you just did was in fact to subtract one vector from another. Subtract the GS vector from the TAS vector and you get a third vector representing the wind.
The tailwind component is something else though. It is the part of the wind which blows along the GS vector. The other part which blows perpendicular to the GS vector is the crosswind component.
Probably waaaay oversimplified, but there are probably a few people who are not as knowledgeable as those who post reading this.
As you so eloquently put it, the wind vector applied to the TAS vector results in the GS vector. And this wind vector is itself comprised of 2 vectors relative to the aircraft - a crosswind vector and a head/tail wind vector , ie tailwind component.
So my point is Fred, that of course wind has direction as well speed. But this discussion is not about drift. It is about tailwind. So the component of the wind vector that effects the speed over the ground is head/ tailwind vector ie the diff between the TAS and GS is head or tail wind component. The crosswind component results in drift - something else.