Parachute Research Group
The effects of unfolding are described by the motion of the transition region between folded and unfolded fabric (called "unfolding front"), a region which moves like a traveling pulse up the parachute's longitudinal axis. The particular tubular geometry of the unfolded portion of the parachute allows the use of an axi-symmetric version of the mass conservation and Euler/Navier-Stokes equations, which are modified to include fabric permeability effects and the force contribution of fabric unfolding near the sock's endcap.
An interesting prediction of the model is that for most cargo and personnel parachutes currently in use, the translational velocity of the unfolding front rapidly reaches a constant value - or terminal velocity - which may be significantly lower than the speed of the wind entering the parachute. A comparison with experimental data collected at the U.S. Army Yuma Proving Ground appears to confirm this and other predictions of the model.
This graphic file is a computer-generated picture of the pressure distribution inside a tube which has just finished unfolding. The picture shows a crosssection of the pressure excess in the tube (excess compared with the pressure outside the tube). The lines are isobars.