Estimating the Deployment Pressure in Pumpkin Balloons

Abstract

A vexing conundrum that has hindered the development of a high-altitude heavy-lift pumpkin balloon system is the system's ability to reliably deploy into the desired symmetric shape. With design strategies honed by empirical results from inflation tests in 2007 using 27-m-diam 200-gore pumpkin balloons, NASA's Balloon Program Office executed successful pumpkin deployments in 2008: Flight 586-NT, a 2 million cubic foot 200-gore design, and Flight 591-NT, a 6 million ft 3 200-gore design. Earlier stability analysis of strained symmetric float shapes yielded partial information regarding deployment. Balloons that were found to have a large number of unstable modes at float conditions were found also to have deployment problems. The question remained, what was the minimum pressure at which a pumpkin balloon would deploy into a cyclically symmetric shape (not necessarily the fully developed one)? Careful examination of a family of axisymmetric ascent shapes revealed a correlation between differential pressure and the number of unstable modes. In this paper, criteria that can be used to estimate the deployment pressure is presented. To bound the problem, fixed-, constrained-, and free-boundary conditions are considered for the top endplate fitting. It was found that the stability results using the fixed and constrained conditions are nearly identical, and so the strategy for estimating the deployment pressure, called the deployment pathway portrait, is as follows. The deployment pressure P Dep is defined as the smallest nadir pressure where the topfree boundary condition yields two unstable modes and the top-fixed boundary condition yields no unstable modes. The approach is validated by comparing analytical predictions of deployment pressures based on the deployment pathway portrait with the deployment pressures that were recorded during the inflation tests in 2007: Flight 586-NT and Flight 591-NT. Very good agreement between the observed deployment pressures and the analytical predictions was found. This is the first analytical-based approach for estimating the deployment pressure.

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“…They found H = 50.32 m and D = 82.11 m when the nadir differential pressure P 0 = 120 Pa. In Table I, below we present the dimensions when P 0 is between 19.9 and 120 Pa; H and D were not reported in [37].…”

“…In earlier designs, lobes would often remain folded over one another even in a fully inflated balloon, leading to distortion and unplanned stress in the balloon surface. However, in the most recent designs, this problem appears to have been solved through a new analytic method [37], and all recent SPB launches have deployed successfully.…”

“…Typical mean differential overpressure for the SPB tests to date are about 50-60 Pa, and variations of ±30 − 40% have been observed due to variations in the solar angle and float environment. Baginski & Brakke [37] considered the strained shape of the gore for the Flight 591-NT design, which also formed the basis for the 616NT designs as well. Let H be the height of the balloon (measured from nadir fitting to apex fitting) and D to be the diameter.…”

“…Super-pressure balloon height and diameter as a function of differential balloon pressure, as found in[37], for flight 591NT.P 0 (Pa) H(m) D(m) 120.500 50.325 82.115 99.256 50.326 82.021 77.991 50.355 81.920 56.867 50.444 81.804 36.522 50.674 81.654 19.902 51.248 81.416 maximum of 75 Pa (day) (see…”

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“…The first two authors developed an approach, called the deployment pathway portrait [5], to predict the differential pressure at which an ascending superpressure balloon is likely to deploy. This approach was adapted to the problem of estimating the torus collapse pressure of two tension-cone IADs ([6] Sec.…”