[The following is an excerpt from a letter to Allen Meece]

[Updated 4 September 2002]

I've been trying to think of ways to get the platform past the increased drag at intermediate altitudes and into the stratosphere without increasing the weight of the tether beyond what's reasonable. I think the prospects are good mainly because of how early in the platform's ascent the peak stable tension usually occurs.

The graph of wind speeds shows two peaks: one at lower altitudes and one at near the VBP platform's target altitude. The amplitude and exact position of the peaks vary, but this general wind distribution is typical. The wind peak at lower altitudes causes considerable tension in a stable platform at that altitude. It can occassionally rise high enough to break the tether. However, the air pressure (and density) drops exponentially as altitude increases, so that by the time the second wind peak is encountered the air is too thin to produce much drag. The highest wind drag invariably occurs below the 150mb level.

The cross section of the tether passing through the midlevel altitudes -- in fact, the cross section of the entire tether, fully extended -- is small enough that drag on the tether is small compared to wind drag on the balloon. While we can't ignore it, changing the tether diameter by a few millimeters doesn't have a major effect on the line tension. The most effective way to decrease tension is to decrease drag on the balloon.

The best way to decrease drag on the platform is by decreasing its cross section. We can do this by lengthening and streamlining it. Also, the cross section of a zero pressure balloon is naturally decreased at lower altitudes because the gas inside is compressed to a smaller volume. However, this also means that zero pressure lift cells don't have enough surface tension at lower altitudes to resist being blown back and forth by the wind, which at the intensities involved can set up oscillations in the platform capable of quite handily tearing thin balloon fabric apart. In short, at the point where the platform's cross section is small enough to make an appreciable difference in wind drag, the balloons are too underinflated to keep their shape and strength in the wind.

There are two solutions to this. We can simply keep all the platform lift cells pressurized all the way up, so that they will have most of their structural strength during the entire ascent. Since all of the cells are fully inflated all the time, this allows no reduction in cross section. Or we can include pressurized structures in the platform that will help the lift cells retain their strength during the ascent, even when the lift cells are not fully pressurized themselves.

A central tier of inflated cells can provide the necessary strength if unpressurized tiers of outer cells can be pulled relatively flat against them so that the uninflated cells do not wave in the wind. The balloon fabric itself can't be made to take such a strain but the platform's shround can. The force necessary to pull the deflated cells into shape can be provided by attaching the shroud to the tether. Additional strength can be provided by cells of air (rather like a carnival spacewalk, only hopefully with fewer leaks). During the ascent, the gas in the central tier of lift cells will ultimately expand almost 20 times, requiring most of it to be vented. I see no reason that a portion of this vented gas cannot be vented to the uninflated cells, pressurizing them as well.

To safely pass the 300mb level, the balloon needs as small a cross section as we can give it and still have it lift the platform. This means that venting to the unpressurized cells should be kept to a minimum before this point, giving them enough lift gas to hold them in position and no more. However, at 300mb, the platform still has enough lift gas to pressurize four or five more tiers of balloons to 50mb.

If the balloon's volume is only large enough to lift its payload to a given height, then expanding its volume x times should give it the lift to ascend to where the air pressure is x times less. The ratio of volume to final air pressure isn't quite 1:1 because of the lower temperature and added weight of the extra tether required, but if we wait long enough for full inflation the difference will be small enough to be easily compensated for. The higher we wait to start expanding, the closer the ratio will be.

I think we can get away with a three-fold or even five-fold expansion in volume by waiting until higher altitudes to fully pressurize the platform lift cells. This represents a reduction in balloon drag by the same factor. The cross section can be kept almost as small using such a scheme as using an unreinforced zero pressure balloon, without sacrificing structural strength.

A zero pressure balloon has a very small cross section at liftoff, four times smaller than the best we can hope for by waiting until the 300mb level or higher to fully pressurize. During the ascent, its volume and cross section will expand exponentially, but still not fast enough to exceed the cross section of a platform that starts out with a central tier of pressurized cells until after passing the 300mb level. If we could just use zero pressure balloons during the entire ascent, it would cut the peak drag by at least a factor of three. It is desirable to approach the cross section of a zero pressure balloon as closely as possible during the ascent.

It will undoubtedly prove necessary to pressurize some of the lift cells during the ascent to give the VBP the proper endurance. However, compressed air can provide just as much structural support as compressed lift gas. Alternately, we could use some sort of tie down or other lift cell restraint which can be released at higher altitude. There are other ways to do this than using a central tier of fully pressurized cells. I'll look into it and see if I can find which one is the best compromise.

On a related subject, I am having some difficulty in optimizing the circumferential surface tension for the individual lift cells. Most of the possible layouts I came up with using pressurized cells put the most tension exactly where the cells are least able to take it. I think we're going to be looking at some sort of internal reinforcement (e.g., Spectra twine or plastic straps) to redistribute the loads within the fabric of each lift cell. This has implications for our ability to replace lift cells during flight.