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## Homework Statement

Any floating homogeneous balloon in a planar uniform wind current will always "tend" to present to the wind flow a section of maximal drag.

**2. The attempt at a solution**

I have three possible solutions to this "problem":

1- Speed gradient justification:

When an object float in a fluid, the "natural" tendency is that the speed difference between the object and the fluid will tend to be zero, asymptotically, then we should ask ourselves the question: which is the object position respect to the flow that will tend to minimize faster the speed difference between the object and the fluid? If you think about that for a moment then the answer will be clear: it is the position of the object that offers maximal "resistance/drag" to the fluid when you try to move the object in the fluid, or equivalently it is the position of the object that offers maximal drag when the object is the one moving.

2- Minimizing drag argument:

Drag is defined as the forced exerted on each point of the object surface that have a component along the direction of the flow, it is the force that "tend" to move the object in the fluid direction, when the object is being "pushed" by the flow all areas on the object perpendicular to the flow will have zero component of the drag force, so to minimize drag on this conditions the object will have to position itself in such a way that the longitudinal component of the drag force is minimized and that is obtained when a "maximal face" is presented to the fluid. That will be a section of maximal drag.

3- Pressure gradient argument:

When an object is moving in a fluid a pressure difference is created between the "front" and the "back" of the object, there is a natural tendency for this pressure difference to be minimized as soon as possible, that difference will be minimized faster when the force exerted by this pressure difference is maximal, but that force is directly proportional to the "exposed" surface area, again a section of maximal drag.

I will be interested in any published paper or reference about this problem.

Thanks.