A novel shape generation algorithm for the envelope of lighter-than-air systems

The envelope geometry of a lighter-than-air (LTA) system governs its aerodynamic drag, buoyant volume, and structural behavior. Several low-drag envelope profiles are available in the literature and are widely used as design benchmarks, viz., NPL, GNVR, Wang, LOTTE, and ZHIYUAN-1. However, each of these profiles is defined by a different mathematical form, which makes the design space discontinuous and limits the use of gradient-based and multidisciplinary design optimization (MDO). Moreover, almost all of these profiles are restricted to axisymmetric bodies of revolution, and hence do not allow a systematic study of asymmetric, lift-generating envelopes. This paper presents a unified shape generation algorithm for LTA envelopes. The main feature of the algorithm is the generation of fully three-dimensional asymmetric envelopes, while the classical axisymmetric profiles are recovered as a special case of the same formulation. The envelope surface is built from three constraint-driven polynomial profiles along three orthogonal directions. Each profile is controlled by a small set of physically meaningful variables, viz., the location of maximum diameter, the nose and tail radii, and the prismatic coefficient. The lateral, upper, and lower profiles are controlled independently to produce asymmetric and hybrid lifting-body shapes, and the conventional body of revolution is obtained when the three profiles are made identical. The algorithm is implemented in Python and coupled with OpenMDAO. Using a gradient-based optimizer, the three-dimensional generator recovers a prescribed asymmetric ellipsoid with a surface root mean square error of about 0.03 mm in less than 40 iterations and a few seconds. The independent control of the three profiles also allows the buoyancy distribution to be adjusted; for example, deepening the lower keel lowers the center of buoyancy. The same algorithm reproduces all the standard benchmark envelopes within a single parametric space. For nine benchmark profiles covering fineness ratios from 1.0 to 6.56, the volume and wetted area match the target values to better than 1%, and the prismatic coefficient to within about 2.5%; the profile-specific fitting objective is reduced by at least 98.7% for the seven analytical profiles, with convergence in 10 to 20 iterations and at most 0.22 s per case in the recorded runs. A fineness-ratio drag correlation gives differences below 0.4% between six targets and their fits, and earlier RANS studies of envelopes generated by the same parameterization reproduce the wind-tunnel and computed surface pressures of the GNVR and ZHIYUAN-1 benchmarks; these comparisons are at zero incidence. Since every generated shape satisfies the defining geometric constraints by construction and exact analytic shape sensitivities are available, the formulation is numerically stable and computationally efficient. It provides a single, extensible basis for the design optimization of both conventional and asymmetric LTA envelopes and lets the optimizer decide whether the optimal shape is two- or three-dimensional, rather than fixing it in advance.