In the early days of high altitude research balloons many ballooons failed as they reached their intended float altitude. This is the level at which a gas balloon becomes fully inflated. The US Air Force Cambridge Reasearch Laboratories commissioned General Mills INC to research the problem.
The research culminated in 3 research papers, 2 of which I was able to obtain copies of in the early 1980's. I was never able to locate a source of the first paper.
Scientific Report #2 developed a series of tables to define the shape profile for zero superpressure balloons. The Sigma Zero shape that was developed as part of this project is used by many manufacturers as the basis of their balloons. Click the link to download a scanned version of Report #2 - Zero Superpressure balloons.
Scientific Report #3 developed shape profile tables for balloons that employed superpressure or subpressure. These are rarely used for sporting balloons but superpressure balloons are used frequently in upper atmosphere research applications where the float altitude needs to be stabilised throughout the day / night cycle. Click the link to download a scanned version of Report #3 - Balloons with superpressure, sub-pressure and circumferential stress.