Optical trapping of light-absorbing particles in a gaseous environment is governed by a laser-induced photophoretic force, which can be orders of magnitude stronger than the force of radiation pressure induced by the same light intensity. In spite of many experimental studies, the exact theoretical background underlying the photophoretic force and the prediction of its influence on the particle motion is still in its infancy. Here, we report the results of a quantitative analysis of the photophoretic force and the stiffness of trapping achieved by levitating graphite and graphite-coated glass shells of calibrated sizes in an upright diverging hollow-core vortex beam, which we refer to as an “optical funnel”. The measurements of forces are conducted in air at various gas pressures in the range from 5 mbar to 2 bar. The results of these measurements lay the foundation for mapping the optically induced force to the intensity distribution in the trap. The mapping, in turn, provides the necessary information to model flight trajectories of particles of various sizes entering the beam at given initial speed and position relative to the beam axis. Finally, we determine the limits of the parameter space for the particle speed, size, and radial offset to the beam axis, all linked to the laser power and the particular laser-beam structure. These results establish the grounds for developing a touch-free optical system for precisely positioning submicrometer bioparticles at the focal spot of an x-ray free-electron laser, which will significantly enhance the efficiency of studying nanoscale morphology of proteins and biomolecules in femtosecond coherent diffractive imaging experiments.