How Far does a Jumper Fall After Pulling?
by Jan Meyer
The laws of physics govern how parachutes open and how jumpers under these parachutes move. These laws can be expressed in the form of equations. The equations can be manipulated to solve for specific quantities. Quantities of interest include distance, speeds and forces. Usually these quantities are expressed in terms of time and displayed in graphs.
Newton's Second Law, F=ma, is applied to a parachute-jumper system from the start of deployment to full parachute inflation. A second case is run for a cutaway. The weight of the jumper, including his gear, is assumed to be 160 pounds. At the start of deployment he is moving at 120 mph (176 ft/sec) straight down. For the cutaway situation the initial speed is 13 ft/sec. The distance measured from the top of the pilot chute to the three rings is 26 ft, see Fig. 1. The system has a 13 ft/sec descent rate after full opening. The time from pulling to full inflation is 3 seconds.
These numbers are used in a numerical integration scheme to calculate distance, speed and force of the jumper-parachute system. The results are plotted in Fig. 2-4 for a deployment from terminal velocity and in Fig. 5-7 for a deployment from a cutaway.
Fig 1: Line Stretch
The results show for a deployment from terminal velocity that the jumper-parachute system falls about 150 feet during the 3 seconds required for deployment. The system speed is nearly constant as the bridle line, suspension lines and parachute get stretched out. The speed rapidly drops off after line stretch. The force represents the force on the entire system and goes up to nearly 10 g's. It is NOT the force in the risers that the jumper feels. Internal system forces are not calculated by this analysis.
Fig 2: Distance fallen during deployment.
Fig 3: Downward speed during deployment versus time.
Fig 4: Jumper-Parachute acceleration, in g's, during deployment. This is NOT the forces in the risers.
The results show for a deployment after a cutaway that the jumper-parachute system falls about 125 ft during the 3 seconds required for deployment. Altitude loss during the first second is only 25 ft and is 50 feet for each of the next two seconds of deployment. The system's downward speed increases to about 75 ft/sec until line stretch and then rapidly slows to 13 ft/sec as the parachute inflates. The maximum force on the entire system is just over 4 g's.
Fig 5: Distance fallen during deployment versus time.
Fig 6: Downward speed during deployment versus time.
Fig 7: Jumper-Parachute acceleration, in g's, during deployment. This is NOT the forces in the risers.
The analysis can be applied to many scenarios, including tandem deployments, round parachute openings and BASE jumps. Jumpers can now find out if claims by manufacturers are valid. The analysis can be done for specific parachute systems under various conditions. Compatibility between jumper and system can be analyzed before equipment purchase.
Originally published in Sport Parachutist's Safety Journal, V2
#3 Jan/Feb. 1990.
Dedicated to enhancing sport parachuting safety by disseminating information about equipment, environments and human factors.