Soft, growing inflated beam robots, also known as everting vine robots, have previously been shown to navigate confined spaces with ease. Less is known about their ability to navigate three-dimensional open spaces where they have the potential to collapse under their own weight as they attempt to move through a space. Previous work has studied collapse of inflated beams and vine robots due to purely transverse or purely axial external loads. Here, we extend previous models to predict the length at which straight vine robots will collapse under their own weight at arbitrary launch angle relative to gravity, inflated diameter, and internal pressure. Our model successfully predicts the general trends of collapse behavior of straight vine robots. We find that collapse length increases non-linearly with the robot's launch angle magnitude, linearly with the robot's diameter, and with the square root of the robot's internal pressure. We also demonstrate the use of our model to determine the robot parameters required to grow a vine robot across a gap in the floor. This work forms the foundation of an approach for modeling the collapse of vine robots and inflated beams in arbitrary shapes.