The characteristic velocity of a DEM particle is the impact velocity of the particle with a surface and is also known as the drop velocity. The vertical impact velocity is the gravitational potential energy converted to kinetic energy at the instant just pre-impact.

The gravitational potential energy is a function of the particle’s mass and the height from the impact surface as follows:

Where m, g, and h represent the mass of the particle, the height of impact, and gravity respectively. The kinetic energy just prior to impact is given by the velocity pre-impact as:

Equating the particle’s initial energy state to the energy state prior to impact will provide the vertical impact velocity (assuming no energy dissipation such as drag)

Most dynamic textbooks provide collision and projectile problems for practice.