10.9: Natural coordinates are better horizontal coordinates.
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Understanding the results of a balance of forces can often be easier if we choose a horizontal coordinate system that is aligned naturally with the air flow, and not just set up in Cartesian coordinates x and y or spherical coordinates λand φ. We can choose one direction—let’s call it s—so that it is aligned with the streamline (and is thus always parallel with the flow) and increases in the direction of the flow (i.e, downwind). The second direction—let’s call it n for normal—increases to the left of the flow. An interesting an noteworthy feature of natural coordinates is that the wind velocity is always positive because, by the definition of natural coordinates, the velocity vector is always pointed in the positive s direction.
For the horizontal momentum equation without friction: