General tendency of a homogeneous floating balloon in a wind current

[jeremyjr]

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.

 

[jeremyjr]

Let me add here that this tendency of an object floating to present to the current a section of maximal drag have been seen by anybody seating in a boat navigating through a smooth water current: if the boat is left unattended for just a moment it will start to "drift" laterally presenting a section of maximal drag to the current.

This problem indirectly try to make precise the meaning of being "adrift".

 

[jeremyjr]

Let me give here a solution for an idealized case of a planar fluid moving at a non zero speed and a segment floating on the fluid.

Assume that the fluid and the segment are moving at the same speed.

Now consider the case when the segment is perpendicular to the fluid speed direction. Imagine that the segment deviate a "small" angle from that perpendicular position. The tip of the segment moving opposite to the fluid speed direction will have now an effective positive speed in an static fluid and then a "drag" force will oppose that movement, the same will happens to the tip of the segment moving in the direction of the fluid speed. So this perpendicular position is one of stable equilibrium.

If the segment is aligned to the fluid speed direction and the segment deviate a "small" angle from that position, the segment's tips will have speed components perpendicular to the fluid speed direction and then the drag generated by that movement will be effectively zero. This is not an stable equilibrium position.

This argument explains why people trying to "align" a boat in a water current have to exert a force to be able to do it.

 

[jeremyjr]

Let me add here, to maybe make this a little more interesting, that this "problem" is the result of a dispute, of a challenge from very professional people, also let me point that there is plenty of evidence backing the claim, including indirectly the mentioned drifting boat situation. But we are looking for a "formal" confirmation and debate, or some published results that give more clarity to the claim.

Also Let me add here, for completeness sake, that this statement apply only to planar air fluid patterns, or more generically when any speed gradient perpendicular to the air flow direction is "small" and its magnitude variation is irrelevant compared to the object length. In the case of a tubular-like air flow pattern, like the one inside of a pipe, and where the diameter of the pipe is comparable to the object length then any elongated object will align itself with the flow because on these conditions that will be the position of minimal drag.

 

[jeremyjr]

This problem general claim is an extension of one more simple claim, that the professional people mentioned before were denying and I then "extended" to a more general case. This is the more restricted claim:

An elongated homogeneous axially symmetric balloon will never float in a wind current consistently pointing its axis in the direction of the wind speed.

This is clearly a particular case of the more general problem claim, because a section of maximal drag for such elongated balloon will be a position with its axis perpendicular to the wind flow. There is plenty of evidence supporting this more restricted claim, you just have to observe balloons in fly to realize that. But these professional people were forcefully denying that, even on the face of evidence. I want to confirm, even in more restricted conditions the general case on this problem main claim. Of course I wan to prove, by using an impartial arbiter, that all these people are wrong or that I am wrong.

Let me add here that even when this statement looks very simple and innocuous it have very important implications, for example in surveillance and that was actually the genesis of this "dispute", if these people that are claiming the opposing view are in charge of the security of a very sensitive installation and they see an elongated balloon above or close to the installation moving consistently along its axis these people will dismiss it as a "normal" balloon, but if my claim holds, and I believe that it will, these people should be fired from their position as security consultants for their lack of physical intuition and insight.