flight computer calculation

Hi,

I noted something very strange while I was "playing" with my flight
computer.

e.g. W/V: 340/60
TAS: 330 kts
True Course: 088°

I found a GS of 344 kts (so the TW-component is 14 kts (makes sense up
to now right?)

On the way back (the True course becomes 268° (088° + 180°)
I found a GS of 306 kts (so the HW-component is 24kts)

To be honest, I expected the HW-component to be 14kts...

What is happening here? Why is there a difference of 10 kts between
the 2 wind components?

Thanks,

Tim

"Tim" wrote in message
m...
I noted something very strange while I was "playing" with my flight
computer.

e.g. W/V: 340/60
TAS: 330 kts
True Course: 088°
I found a GS of 344 kts (so the TW-component is 14 kts (makes sense up
to now right?)
On the way back (the True course becomes 268° (088° + 180°)
I found a GS of 306 kts (so the HW-component is 24kts)
To be honest, I expected the HW-component to be 14kts...

OK. You have a wind component that is 108 degrees offset from your course.
So draw yourself a right-angled triangle whose hypoteneuse is 60 units long,
and one of whose angles is 72 degrees (180-108). The headwind/tailwind
component is 60 x cos(72), = 18.54 knots. (Obviously it's a tailwind if
you're flying 088 and a headwind if you're flying back the other way).

Okay, so this explains that your expectation is valid - namely that the
headwind component is the same as the tailwind component. So how do we
explain the difference?

Simple. Your whizz-wheel isn't showing you the headwind component as simply
as you think. The whizz-wheel's ground speed calculation is taking into
account not just the wind component BUT also the fact that because you're
pointing the nose into wind. So if the difference between the wind direction
and your direction is big, you're also losing a sizeable component of your
airspeed. A large chunk of your thrust is being lost in simply fighting
against the crosswind because you're pointing the nose off-course. Draw
yourself a cosine curve and you'll see that once the angle gets above about
30 degrees, every extra degree gives a massive change in the cosine of the
angle between your track and the wind direction, and hence you get a large
change in the loss due to the nose being pointed upwind. (Oh, and in order
for this to make sense, you need to note that the difference between track
and heading are different when flying at 088 or 268).

So both your answers are probably right. You would expect the headwind and
tailwind to be the same, and you're right to think this. But remember that
because your actual heading for the trips there and back aren't exactly 180
degrees different, so the difference between IAS and groundspeed will
differ.

D.