Rotation of the VBP about an axis, however, requires applying torque directly to the platform. We can apply a counter-torque to prevent rotation. Preferably, this counter-torque should be applied passively, as a consequence of torques inherent in the design rather than through any intervention of ours. The VBP already has tremendous advantages for stability. It's vast surface area means the damping force due to air friction alone is enormous, which damps out any motion without a continuous torque to sustain it. The platform has a large moment of inertia, which means that a torque has to be very large to cause much motion to begin with. It also has the tether, which will add a restoring torque that varies with its stability.

It's also important to note that the platform will not rotate about its center of mass. It tends to rotate about its center of pressure instead. The benefit of this is that the axis of rotation is very far removed from the surface of the balloon, closer to the geometric center. Since the forces that spin the balloon are applied on its outer surface, the leverage arm of the resulting torque is very large. So, force applied by the weight of the "gondola" (the beam, keel, and all the structures on the bottom of the platform) acts at a greater radius from the axis of rotation, which means more torque for the same force.

Unless T.tether = -W.gondola, with the tension pulling exactly opposite the weight, the torque is only zero where the two cross products are zero, and they are only zero where the two vector factors are parallel. The equilibrium position is found where the forces are in the same direction as the lever arm. Since the line tension, weight, and leverage arm are so large, their product quickly becomes large at very small angles, forcing the platform back toward equilibrium.

Platform yaw (spinning left and right) is unaffected by gondola weight or tether tension. To correct this requires adding another restoring torque. The best way to do this is to add fins, vanes, or some other structure to take advantage of the force due to wind drag. (Think of a rocket or derigible.) In this case the equilibrium position is facing into the wind. That means every time the wind changes -- such as entering a new wind layer during ascent -- the platform spins around to face into the new wind. However, such weathercocking is a good thing, because it means the platform is yawing about to a position which will minimize drag on the balloon. If we've done our design work properly, motion due to weathercocking should be transitory, quickly damping out.

We have a lot more leeway with controlling yaw. In theory, anything that will catch the wind can do it. The only trouble is, we're looking at adding on structure to the VBP platform, either by adding non-bouyant extensions or extending the bouyant section of the platform. This affects the center of mass and center of pressure. It alters the gondola weight distribution and moment of inertia, too.

The effect of a wind catching structure on the center of mass, weight, and moment of inertia can be limited by simply making it as light as possible. Sails or inflatable fins will do, but we'd have to have something to secure them to. I suggest a streamer, windsock, or some other kite-like tail instead. It would have to be as large as fins, but could be thinner, lighter fabric than inflated fins. It can be secured anywhere on the rear of the platform because, unlike fins, compressive & torsion forces are not a factor. And unlike sails, it would require no rigid structures. A streamer need only resist the wind enough to avoid being torn off the platform. Though the force acting on a streamer is smaller than that on rigid fins, it can trail the platform at a distance, giving it a very long lever arm. I don't recommend requiring it to fight the wind, but some ability for active guidance can be gained by including adjustable panels in the streamer design, as with some parachutes.

There is one more factor to consider. Just as the leverage arm determines restoring torque we can apply, it also determines the centripetal acceleration due to rotations we can't eliminate. There will doubtless be some. The further a point on the platform is from the axis of rotation, the more centrifugal force it experiences due to that rotation. Now, the sources of restoring torque described should be sufficient to keep the platform from constantly oscillating. However, they will not eliminate sudden jolts, which can be exaggerated by increasing the leverage arm involved. The effect will be most pronounced near the fornt and rear of the platform, where the radius of motion is greatest. This has implications for distributing the payload. The crew cabin, for example, should not only be as close to the axis of rotation as possible but as radially compact as possible to keep people from getting slung about inside by cetrifugal force.