PPRuNe Forums - View Single Post - Wind Triangle Vectors & Curved Trajectories
Old 1st Sep 2010, 06:29
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PBL
 
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The answer to "do wind vector calculations work for curved tracks?" is: it depends on the calculation.

The straight answer to your question
Plane 1 attempts to fly from point A to point B, but drifts laterally "X" feet due to crosswind by the time it was to have reached point B.

Plane 2 then attempts to fly an RF leg from point A to point B that would reach point B under zero crosswind, but experiences the same crosswind as Plane 1. Does Plane 2 drift laterally by the same distance as Plane 1?
The crucial parameter is the time taken, not the position of A and B. If Plane 2 aims to fly its RF leg in exactly the same time as Plane 1, the drift will be the same. If not, the drift will be different.

Basic analytic geometry, of the sort needed for basic calculus, yields the following.

Suppose your position at time t in zero wind is given as <x(t),y(t)> in rectilinear coordinates, i.e. for a flat plane, not lat/long.

Suppose the wind is coming at w kts from z°N, where z for simplicity is between 0 and 90. Then the position at which you need to aim in this wind condition in order to fly the track <x(t),y(t)> is given by <x1(t),y1(t)>, where

x1(t) = x(t) + t.w.sin(z)
y1(t) = y(t) + t.w.cos(z)

If you've done basic calculus, which often includes trajectory calculations, then this is simply a reminder. If you haven't done basic calculus, then this might look like mumbo-jumbo, but I can assure you it's the math you need.

It follows from this that at time t1, your aimed position <x1,y1> is displaced from your desired position <x,y> by <t.w.sin(z),t.w.cos(z)>, which is, expressed in vectors, just

desired position = aimed position + wind-vector.t.

In that sense the wind-vector calculation "works" for a curved track.

PBL

Last edited by PBL; 1st Sep 2010 at 11:05.
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