We investigate the extension of self-injecting laser wakefield experiments to the regime that will be accessible with the next generation of petawatt-class ultrashort pulse laser systems. Using nonlinear scalings, current experimental trends, and numerical simulations, we determine the optimal laser and target parameters, i.e., focusing geometry, plasma density, and target length, that are required to increase the electron beam energy (to > 1 GeV) without the use of external guiding structures.