Collision Course
by Jan MeyerEditor's Note On July 14, 1990, Eric Hedges and Bob Nuckolls came over to my office for a swim on a hot summer day. We joked around and played in the pool for awhile. We talked about some programs I was working on. Eric saw all these equations written on sheets and sheets of paper. He was glad to realize that people use the stuff he was learning in school for realworld problems. We talked about skydiving, about how to fly, how to do transitions and blind exits. We talked about how to get other people to learn about the things we know about jumping. I mentioned that I tried perpetuating information through SPSJ and The Peregrine. I told Eric that my major motivation for starting Sport Parachutist's Safety Journal was that I was tired of seeing my friends get hurt or die from the same stupid reasons. If these guys only knew, they could be alive today. If they had more information, they might have dealt with the emergency better. I never thought I would have to write about Eric in the Safety Journal. I must pass on information about Eric's death so that others may avoid the hazard. Eric found a new way to die in this sport. He didn't die from doing something stupid. He was innovating and got snatched by something no one could foresee. To be true to Eric and to Sport Parachutist's Safety Journal, this article explains the hows and whys of Eric's death, how to avoid the hazard and how often it might occur. Somehow, I believe Eric is glad to see the equations used for a real problem.JM IntroductionMany skydivers believe that hitting the tail of an aircraft on exit is next to impossible. Every once and awhile, some skydiver may graze the underside of the horizontal stabilizer. Never has anyone smacked it so hard as to knock himself unconscious or hit so hard as to break his neck. Never until July 14, 1990. How did a skydiver hit the tail? What did he do differently? Can someone else do it just as easily? How does a skydiver's weight and height effect the chances of hitting the tail? Does it matter what body position a skydiver is in? Can this happen on other planes? A trajectory analysis of an aircraft and jumper was developed to study these questions and find some answers. The analysis, applied to a scenario similar to the actual incident, indicates that a skydiver must "jump up" in order to hit the horizontal stabilizer. The distance of the "jump up" depends on aircraft geometry and airspeed, location of a skydiver on exit and height and weight of a skydiver. AnalysisThe motion of a skydiver and a plane are governed by Newton's Second Law of Motion. It says that the sum of all of the forces on an object are equal to the mass times the acceleration of the object. The aircraft has no acceleration. The sum of the gravitational, lift, thrust and drag forces are equal to zero. The aircraft is assumed to be flying at a constant airspeed either in straight and level or a straight and climbing flight. The trajectory of the aircraft is simply calculated by multiplying its speed by the amount of time that has elapsed from exit. The forces on a skydiver at the instant he releases the aircraft arise from two sources. Gravity exerts a force on a skydiver exactly equal to his weight in a direction straight down. Aerodynamic forces are generated from the relative motion between the air and a skydiver. Aerodynamic forces are separated into two forces that act in directions perpendicular to each other. The aerodynamic force that acts in the opposite direction to the velocity direction is the drag force. Lift is the aerodynamic force that acts perpendicular to the velocity direction. For this analysis, the lift force is assumed to be zero. The equations of motion are solved numerically and the trajectories are calculated for the aircraft and skydiver. The technical details are beyond the scope of Sport Parachutist's Safety Journal, but may be made available to interested persons. The separation distance between a skydiver's center of gravity and the leading edge of the horizontal stabilizer, as shown in Fig. 1, is the determining criteria as to whether or not contact between a skydiver and the aircraft is possible. Safe exits occur when the separation distance is sufficiently large. Unsafe exits occur when the separation distance becomes too small. The separation distance is calculated from the trajectories of the aircraft and skydiver at each instant of time.
Results
A scenario must be mathematically described to model the initial
positions and velocities of the aircraft and jumper. Several cases
are studied and listed below, along with plots of the separation
distance as a function of time.
In all cases the aircraft's attitude is assumed to be level. The position of the leading edge of the horizonal stabilizer, relative to the aft and lower corner of the door, are taken from measurements of a King Air. The jumper's center of gravity position is even with the aft edge of the door and 2.875 feet above the lower edge of the door. This position is the most forward rear floater position. The jumper's weight is 145 lbs. The cases listed in Table 1 were run with a nominal fall rate of 109 mph and again with a 120 mph fall rate.
DiscussionThe criteria used to determine whether or not an exit is safe is the separation distance between a jumper's center of gravity and the leading edge of the horizontal stabilizer (Fig. 1). The separation distance decreases after exit until a jumper passes the stabilizer and then increases again. Safe exits occur whenever the minimum separation distance exceeds 3 feet. There is a chance of a jumper grazing the aircraft with extended arms, head or the upper torso anytime the separation distance becomes less than 3 feet. When the separation distance is between 1 and 2 feet, a jumper can strike the aircraft with his head, upper torso or midsection. Separation distances less than 1 foot indicate that a jumper is very likely to contact the aircraft in his midabdominal area. Whether or not actual contact is made depends on a jumper's orientation and height. A "cut, level and release" type exit (Case 1) is what normally occurs. Normally, a jumper's center of gravity clears the horizontal stabilizer by at least 5 feet. The difference between "cut, level, release" and "nocut, level, release" exits can be seen by comparing case 1 (cut) to case 3 (nocut). The nocut curve shows that the minimum separation distance becomes smaller than the cut case, but only by about 6 inches. Comparison with the "nocut, climbing, release" exit (Case 5) shows that the minimum separation distance again decreases, but not by more than 6 inches. In fact, the "nocut, climbing, release" (Case 5) minimum separation distance is greater (safer) than the "nocut, level, release" (Case 3). All exits are safe as long as a jumper releases the aircraft. It does not matter whether or not the aircraft has slowed or is still climbing. The most striking conclusion, from the results plotted in Figs 2 and 3, is that the separation distance is strongly dependent upon the relative vertical speeds between a jumper and the aircraft. This is illustrated by the two welldefined groupings of curves. The upper group represents Cases 1, 3 and 5. These are the cases when a jumper releases the aircraft on exit. The lower group of curves represent Cases 2, 4 and 6. These are the cases when a jumper jumps up 1 foot on exit. There is also a shift in when the minimum separation distance occurs. Jumpers who release the aircraft on exit pass under the tail sooner than jumpers who jump up on exit. The upward jump gives a jumper an initial upward speed. The extra upward speed tends to be observed from inside the aircraft as "floating" on exit. The additional time spent in the proximity of the plane allows the plane to catchup to a jumper increasing the chance of contact. Another observable trend is shown by comparing the "cut, level, release" exits at the two different nominal fall rates. Compare Case 1 in Fig. 2 to Case 1 in Fig. 3. Notice that as the fall rate increases, the minimum separation distance increases. This means that jumpers who "get big" or "catch air" on exit will pass closer to the tail. Most jumpers know this already from experience. Confidence in the analysis is gained when experiment (real jumps) and theory (computer results) agree. The exits with a "jumpup" are represented by the lower group of curves. A "cut, level, jump up" exit (Case 2) exhibits the largest separation distance of the jumpup cases. However, the minimum separation distance is about 2.5 feet with a 109 mph fall rate. This distance increases to 3 feet at the 120 mph fall rate. Any jumper taller than 5 feet and vertically oriented would hit the tail of a King Air. The "nocut, level, jumpup" (Case 4) and "nocut, climbing, jumpup" (Case 6) exits reduce the minimum separation distance to 2 feet or less at the 109 mph fall rate. At the 120 mph fall rate, the minimum separation distance is close to 2.5 feet. In these instances, jumpers over 5 feet tall have a very good chance of striking the horizontal stabilizer. The critical element of the exit is the "jumpup". All exits without a jumpup are safe. Nocut exits are safe. Climbing, nocut exits are safe, too. These results agree with what jumpers have been doing for quite sometime. Exits with a "jumpup" are unsafe. Exactly how far upward an individual jumper needs to jump for a given aircraft geometry, airspeed, attitude and climb rate in order to hit the stabilizer is immaterial at this time. The point is "Don't jump up on exit." What difference is one more foot of altitude going to make when you're already at 12,500 feet? Why would anyone want to "jumpup" on exit? Freestyle is very popular. A jumper may try to present himself to the relative wind in unique ways. A strong launch and pirouette may be easier and more natural to execute with some vertical motion. Practice exits on the ground. Launch and jump sideways. Eliminate as much upward jump as possible.
Originally published in Sport Parachutist's Safety Journal V2, #4 Jul. 1990.
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