GPS

[Fuji Abound]

Its a 400 mile journey with a front in the middle, as you cross the front the wind changes direction by 180 degrees from a cross wind to the right to a cross wind to the left. Which is more efficent, following the magenta line, or some other way?

[Genghis the Engineer]

In 2D, the great circle route - in other words the magenta line, should always be most efficient.

In 3D however, I'd be looking at the winds at different altitudes on a leg like that to see where I can take some advantage by minimising the head/cross wind components.

G

[what next]

Hello!

Intuitively, I would say: Fly the constant heading computed for zero wind condition all the time (assuming that the cross winds are of equal strength and change direction in the middle). The first half of your journey, you will drift in one direction, the second half, the drift will be reversed and you will arrive exactly at your destination. Your velocity vector will point in the direction of your destination all the way and you will not lose effective speed compensating for the crosswind.

max

[BackPacker]

In 2D, the great circle route - in other words the magenta line, should always be most efficient.

Don't agree. If the front is in the middle, and perpendicular to your 400 mile journey, and the crosswind component from the right before passing the front is as strong as the crosswind component from the left after the front, it's better to simply let yourself blow away to the left first, as this will be perfectly compensated later on.

When sailing at sea, you do the same thing. Let yourself wash one way with the tide, and the other way six hours later. Trying to compensate for the tide only costs in distance traveled.

However, practically speaking:
- Winds aloft forecasts are notoriously unreliable. (Tidal flow is much more predictable.)
- The perfect situation as above will almost never appear, which makes the calculation on how much to compensate much harder. It's far easier to follow the magenta line, or calculate your plog so that it follows the imaginary magenta line.
- Airspace, intersections, reporting points, placement of navigation beacons and general predictability of your (filed) route will usually be more important than saving a few liters of fuel.

[Fuji Abound]

Bp for the sake of discussion it is the perfect situation you describe and they really do reverse midway on the course equal cross wind from the right to an equal cross wind from the left.

Its an air race point to point and who gets there first wins -oh and yes theoretically speaking same two aircraft, same performance, airspace and weather not a consideration, but you cant change level, cant change the crosswind, you can only change how you navigate.

- yes and I know not very real world!

[dublinpilot]

Damn it's a tough question! I keep changing my mind!

Sounds like a piece of paper and a calculator is called for!

[peterh337]

The fact is that any crosswind component means you fly a longer distance, unless there is a tailwind component to it which is sufficient to compensate. So even a perfect 90 degree crosswind means you have to fly further than the GC route.

It thus follows that if you get a perfect 90 deg c/w from the right and then get a perfect 90 deg c/w from the left, you end up flying a longer distance to get there.

I don't know the answer, and I am too lazy to try some trig, but I think just following the magenta line (and thus crabbing the wind) will be most efficient because the aircraft is flying the shortest route and thus the wind has the least opportunity to "work" on it.

WN's suggestion of a constant zero-wind heading looks tempting and could well be right, but I feel that the aircraft will be subjected to the effect of the wind for longer.

[IanSeager]

There's a bell ringing somewhere in my head and it is saying something about 'pressure pattern navigation'

I can't recall the exact details, but I'm pretty sure it was about this kind of thing.

Ian

[Torque Tonight]

Fly a constant heading (equal to the track from the start to the end point) and accept the resultant drift. If you correct heading for drift to maintain the track line, you will have a permanent headwind component and get there slower.

[fujii]

Magenta line

This is a GPS question and has nothing to do with drift. The magenta line is your track over the ground. It's that simple. The heading on the compass/DG will change as you pass through the front but provided you stay on the line, your track remains the same. It's a good idea to always keep an eye on the compass/DG heading so if the GPS dies, you have a reference to maintain track.

[peterh337]

If you correct heading for drift to maintain the track line, you will have a permanent headwind component and get there slower.

That's true, but if you fly a constant heading all the way you will end up flying for longer, because the wind blows you increasingly off track on the first leg, and the second leg does not compensate for that; it merely puts you back where you should be, after having spent more time in the air.

The answer to this puzzle will be interesting.

A google finds e.g. this which makes sense but I am not sure it is applicable to the question as originally posted, which is a different scenario. It is obvious that if you are crossing a high or a low then flying to one side of it will help pick up a bit of tailwind.

[IanSeager]

That's what I was thinking of Peter.

Ian

[peterh337]

I would put a tenner on the two methods (constant zero-wind heading, and flying the GC track) being exactly the same

I reckon both hang on the small angle approximation (sin(x)=x).

[Morrisman1]

the way I see it is we are essentially asking the question:

Is the ground speed advantage by allowing the wind to push us off course sufficient to offset the extra distance we will travel across the ground?

I dont doubt for a second that we wont have a faster ground speed by not accounting for drift, in the end when we account for drift we are flying with more of a headwind (or less of a tailwind) than what we would if we just flew the heading. If we think about the wind triangle, it takes us the same time to travel the adjacent line as it would the hypotenuse. By choosing to stay on track we fly the adjacent line, if we let ourselves drift then we will fly the hypotenuse but the time spent is the same. Hypotenuse is longer and that reflects the extra groundspeed we will have from experiencing less headwind. The second half of the journey mathmatically is exactly the same as the first, just mirrored the situation.

I think that we will end up at the same place in the same time.

[seat 0A]

Very similar to sailing.
As you sail from Holland to England, you encounter drift from the flood- and ebstreams. The direction of the stream changes every 6 hours or so.
The fastest way is not to correct for the drift. Just let the wind (or stream) set you off track. It will blow you back on track during the second half.
Saves you beating into the wind on both sides of the front.

[bookworm]

I would put a tenner on the two methods (constant zero-wind heading, and flying the GC track) being exactly the same

I thought the same for a while but having done the trig I'm now with the sailors!

Constant zero-wind heading gets you there in the zero-wind time (the wind component just cancels). Flying the GC track takes a factor of 1/cos(drift) longer (that's the factor by which your groundspeed is reduced). That means of course that the result is second order in the drift (i.e. if the drift is 0.1 or 6 degrees, the difference is only 1%).

In the real atmosphere of course, nothing is predictable enough to make this a sensible strategy. But a fun question, Fuji, thanks.

[Fuji Abound]

Bookworm thank you - anyone want to hazard the difference in arrival times with say a 20 knot x wind component, cruising at 160 knots for the entire course - It is very surprising.

[Torque Tonight]

Although flying the straight ground track gives you the shortest ground distance, flying the heading and accepting drift gives you the fewest air miles. Think about your movement relative to the two airmasses.

Fuji, at a guess I'd say it would be about 5 minutes slower to follow the magenta line. If I have nothing more important to do l'll do the maths later.

[Whopity]

Which is more efficent

How do you define efficiency? In the RAF when confronted with Wind problems, typically crossing the Atlantic, we would look at Specific Fuel Consumption in pounds per mile. Quite often the longer distance at a higher speed gave a better figure however; at the end of the day it depends upon the relative wind speed which is not given. The sailors solution is based upon largely known and predictable conditions.

[Mark1234]

My take: While it's very tempting to concern ones self with ground distance, it's irrelevant. Aeroplanes fly in air, not ground! It's all about frames of reference.

Consider your track through the body of air in which you fly. If you just pick a heading and go, it's a straight line.Conveniently the body moves left and right sufficiently to put you back where you need to be at the end of the line.

If you crab and fly the magenta line, your groundspeed decreases, you fly a longer, squiggly path with reference to the body of air (which is the bit that matters).