|Another Look at Descent Kinematics|
The Fundamentals of Separation and Spotting
World Freefall Convention at Quincy August 6, 1999
Speaker: Winsor Naugler III and John Kallend
Seminar Notes by Tamara Koyn
DISCLAIMER: THE AUTHOR(S) MAKE NO WARRANTIES OR REPRESENTATIONS AND ASSUMES NO LIABILITY CONCERNING THE VALIDITY OF ANY ADVICE, OPINION, OR RECOMMENDATION EXPRESSED IN THE MATERIAL. ALL INDIVIDUALS RELYING UPON THE MATERIAL DO SO AT THEIR OWN RISK.
The following material is taken from the handout that Winsor Naugler provided during his seminar and is modified with additional information from the seminar. If you have any questions regarding this material, you should write to Winsor. Thank you.
Winsor intends to provide an overview of fundamentals of planning and conducting parachute jump operations. Methods are shown to best ensure separation between groups and enable safe landing at the desired location.
The goal is to be able to evaluate what will result from particular differences in exit order, skydiving discipline, and the jump run. Winsor also wanted to provide a means of planning cooperation between separate groups of jumpers on a particular load and communicating with the pilot. Considerations for avoiding potential collision after exit are also covered. We want to avoid having two jumpers occupying the same space in the air at the same time.
You want to organize the exit order of the groups to achieve the best horizontal separation. Winsor prefers Skydive Arizona's policy on exit order. Freeflyers exit after relative work groups. However, you should remember that no method provides complete safety because skydivers move horizontally in freefall. For example, relative work formations with one side heavy actually slide across the sky and can cover a lot of ground.
You will find that both airspeed and ground speed matter.
Topics included in this seminar are: Exit Trajectory, Tracking and Sliding, Fall Rate Differences, Optimum Spot, Frames of References ("Airspeed vs. Groundspeed"), Exit Order, Jumprun, and Potential Hazards.
|Introduction to Spotting|
The art of spotting has fallen victim to evolving technology in recent years.
Improvements in navigational aids have made it generally more effective for the pilot to find the desired exit point, so the burden of finding the ideal place in the sky to begin the skydive falls more and more on the pilot. There is a decreasing likelihood that jumpers will perform more than a perfunctory check of the proximity of the airport and the absence of traffic below (if that much).
Turbine aircraft routinely provide altitude that was previously unheard of outside of special events. This increase in time spent in freefall also increases the amount of wind drift experienced prior to deployment. In addition, the view of the planet is rather different from 3,500 feet than it is from 2 1/2 miles up. At the higher altitudes, it is much easier to be influenced by aircraft deck angle or other optical illusions. Thus, there are now more parameters with which to contend in obtaining a satisfactory spot than had been in the past.
In years past, four jumpers going out of a Cessna 182 at 9,500 feet had plenty of time watching the ground from the air during the 20 minutes getting to altitude. In addition, there was a 25% likelihood that any particular jumper would spot. Now, 20 jumpers packed into a Twin Otter are at 13,500 in around 12 minutes and climb out when the green light comes on - or simply chase the base when it exits.
For a number of reasons, many otherwise knowledgeable sources tend to ignore horizontal wind drift in freefall. This may be because terminal seems fast enough that horizontal wind drift is comparatively insignificant. Also, in the bad old days of rounds and piston aircraft, a greater portion of every skydive was spent under canopy and wind drift in freefall was fudged into the equation as climbout time after the "optimum" spot was reached.
Nowadays the 3:1 or better glide ratios of available canopies make it possible to open at 2,000 feet and land 6,000 feet from where a round would have deposited you. This is greater than a mile of leeway! No wonder so many jumpers of the current generation are at a loss when spotting.
Having heard many Old Wives Tales regarding characteristics of the optimum spot, another look at the kinematics involved seems advisable.
Kinematics: n.pl.: The branch of mechanics that deals with motion in the abstract, without reference to the force or mass.
While taking an engineering approach, we will review specific examples with specific conditions. We are analyzing movement which takes place in a three dimensional space. Technically, because we are studying movement, we are really analyzing a four dimensional medium.
The picture we shall use to illustrate the mechanisms at work consists of several key elements.
Time lapse photographs, taken from a stationary camera, of moving point sources of light showing trails along the route they follow. For example, pictures of autos moving at night are common. The taillights provide streaks in the picture which mark their passage.
Strobe photography shows an instant frozen in time, such as a clear picture of a bullet in flight or a hummingbird in mid-flap. A multiple exposure stroboscopic photograph can show successive positions of an object in motion, such as a ball bouncing.
We are all familiar with the idea of a smoke trail left by an object in flight. This could be a skywriting airplane, contrails of an aircraft flying at high altitude, or smoke canisters carried by demo jumpers.
For our examples here, we will depict jumpers with a light and a smoke canister. The time lapse trail made by the light and the smoke trail are captured by the strobe photography from a stationary camera. It is useful for our understanding to see a visual line of their pathway through the air. When the air is not moving, the light trail and smoke trail will be the same.
Exiting From A Moving Aircraft With No Winds
For experienced jumpers it should be apparent that a jumper exiting a moving aircraft will experience two basic regimes of freefall -- transition and terminal. During transition, "the hill," the jumper starts with the horizontal speed of the aircraft, but no vertical speed, and reaches terminal, where there is vertical, but no horizontal speed. In other words, each jumper experiences a forward through from the forward motion of the aircraft. At terminal, vertical speed is constant, and horizontal speed is absent -- unless supplied by the jumper -- an issue to which we will address later.
Assuming that there is no prevailing wind, the horizontal speed noted above is both airspeed and groundspeed. (Later, we will review examples which involve a substantial breeze that remains constant with altitude. Because upper winds are normally stronger than surface winds, we will also review examples of that as well.)
In this illustration, the jumpers start their smoke canisters prior to exiting the aircraft in flight. We observe that the smoke trail is horizontal prior to exiting. Once each jumper exits, the smoke trail from each jumper transitions to vertical at terminal. Due to the no wind conditions, the smoke trails coincide with the light trails.
We can observe that by providing a certain amount of time in between each exit, we give horizontal spacing between each jumper (or group). Horizontal distance between jumpers is very important. A jumper may accidentally be deployed at any altitude for any reason. Vertical separation would be a fatal solution.
Exiting From A Stationary Aircraft With Strong Winds
Some believe that ground speed determines everything in planning the timing between each exit. However, this is not true. In this next example, we show what effect airspeed at the time of exit has!
Skydivers exit from a tethered balloon on a breezy day. We'll use the US Customs Balloon! In this example, the prevailing wind is a constant 50 knot wind from the surface up to our 14,000 foot high exit platform. (Note: The magnitude is for illustration and computational simplicity, a 1:2 descent profile, rather than recreational purposes.)
The light trail and smoke trail for each jumper (or group) is different.
The light trail left by the jumper is almost constant in slope. When the jumper exits, he accelerates downward and horizontally from his initial speed of zero. After this exit and acceleration, the jumper is moving horizontally at the prevailing wind speed and downward at a constant speed, i.e., terminal velocity. When the jumper deploys, the slope of the light trail becomes shallower because the rate of descent decreases by approximately 90%. Assuming that the jumpers are using non-steerable rounds with no forward speed (so as to eliminates the effect of a canopy's forward drive from our study), the slope changes from 1:2 to 5:1. We will not consider the effect of canopy drive here.
The shape of the smoke trail is similar to that for a jumper exiting from a moving aircraft with no prevailing winds. The smoke trail is being blown downwind at the speed of the prevailing wind. In this example, that's 50 knots. Observe that the shape of the smoke trails in both terminal freefall and under canopy are completely vertical. Remember that we are assuming that the jumpers are falling straight down within their air column. (We will review tracking and backsliding issues later.)
Successive strobe images (on a single frame of film) of the progress of the jumper looks pretty much the same as a single exposure of successive jumpers. In other words, if we have 3 jumpers exit in 2 second intervals and take one picture at the 6th second, we will have the same photograph as we would if one jumper exits and we expose the same picture frame 3 times, once at the 2nd second, 4th second, and 6th second.
Horizontal separation between the smoke trails is the product of the prevailing windspeed multiplied by the delay between exits for each successive jumper.
Assuming each jumper opens at the same altitude and has the same descent rate both in freefall and under canopy, all jumpers leaving the tethered balloon under the prevailing conditions arrive at the same landing point. Successive jumpers have and maintain constant horizontal separation for the duration of the jump, as shown by their smoke trails. In this case, horizontal separation between the jumpers remains constant, regardless of the order in which the canopies open. That's because their rate of horizontal motion does not change (neglecting the fact that the open canopy actually does have more drag). Only the rate of vertical motion changes and that's why the slope of the light trail changes.
If the first jumper opens immediately, he is blown downwind before the next jumper exits.
Actually, in the real world, a prevailing wind would increase with height and a jumper's light trail would actually appear as illustrated below. The curved light trail reflects the jumper's drift in the stronger winds aloft and the weaker winds lower to the ground.
Exiting From A Free Balloon With Strong Winds
Case 1 involved a condition where the airspeed and the ground speed were equal. In Case 2, we studied a condition where the ground speed was zero and the airspeed at exit was that of the prevailing upper winds. In Case 3, we will study a condition in which the airspeed is initially zero but we do have a ground speed. For this, we will have the jumpers exit from a free balloon which is travailing over the ground with the prevailing upper winds.
In this example, we, again, assume that the jumpers are using a non-steerable round parachute. We also assume that the prevailing wind is the same from the surface all the way up to the jump height.
Again, each jumper (or group) leaves behind a light trail and a smoke trail when he or she exits the free balloon. The light trail and smoke trail for each jumper is different.
The light trail shows the constant horizontal speed caused by the drift in the prevailing winds. The jumper's vertical speed is zero at the time of exit and accelerates to some constant speed, i.e., terminal velocity. The light trail has a downward slope at an angle.
The smoke trail is completely vertical. Assuming that the prevailing winds are constant from the exit height all the way to the ground, all successive jumpers follow a common smoke trail. As the jumpers exit successively, each will have the balloon directly above him and the preceding jumper directly below him for the entire trip to the ground.
Observe that the light trails of successive jumpers lead to different landing points. The smoke column is traveling horizontally and is at a different location when each jumper touches down.
As long as none of the jumpers (except for the last jumper) decides to deploy high, providing a certain amount of time between each exit will provide horizontal separation. If the first jumper to exit the balloon opens high, his light trail will become flatter as he drifts more with the prevailing winds. This will put the first jumper on collision course with the second jumper in freefall. The freefalling jumper, blinded by the smoke, will collide with the first jumper's canopy. This problem is illustrated below.
Sliding Horizontally Across the Sky
In all of the previous examples, we have assumed that the jumpers were freefalling perfectly straight down and were using non-steerable round parachutes with no forward drive. We will now consider the effect of sliding around in freefall, tracking, or even flying an open ram air canopy (or ParaCommander, for that matter...).
We have all heard anecdotes of waiting a "safe" delay after a group exits only to find the earlier group directly below at breakoff. Anybody who has shot camera of freefall formations can tell you that this is likely the result of horizontal movement of one group or another, or of both, in freefall. Having a badly balanced formation can cover a lot of sky in a hurry.
Let's look at some numbers. Let's say that the exit speed is 80 knots and we give a solid 10 seconds between exits. If we are in freefall for 80 seconds, each group only has to drift toward the other at a rate of 5 knots to reduce the 1,200 foot horizontal separation to zero. Five knots is walking speed. A skydiver backsliding with their feet tucked to their butt can move fast enough horizontally to get a speeding ticket.
To put it in another perspective, one knot for 80 seconds gives the same results as one second at 80 knots. Thus, a group with an unstable base sliding at 30 knots horizontally (which is more realistic than might be imagined) can be right below a group exiting half a minute later by breakoff. That would be a half a mile (2,400 feet) on the other side of a group if the delay between exits was 10 seconds.
Let's examine the amount of sliding around that we may tolerate, without the possibility of interference between groups at breakoff. Winsor will tell you right now that it isn't much!
Ignoring the subterminal regime for simplicity, let's consider two jumpers who exit from separate aircraft in formation at 13,500 feet and can track together at an average of 35 knots each. A 35 knot track is easily obtainable by anyone qualified for an A-license. A particularly competent skydiver can track well over double that with no problem. (Tamara Koyn discovered that she covers about 2,500 feet of horizontal distance for 5,000 feet of descent during a lazy track.) With a closing speed of 70 knots and a terminal velocity of 100 knots, the jumpers lose 700 feet of separation for every 1,000 feet of freefall. Our jumpers here could collide by 3,500 feet after exiting from aircraft flying some 7,000 feet apart. This is illustrated below.
A jumper may break away from a RW formation and track up the jumprun. This is particularly a problem if that jumper leaves his dive early. At Quincy, where we have two parallel jumpruns that may be simultaneously used, that jumper may be tracking into the range of the other jumprun.
Maintaining a mile and a half between groups which is around 61 seconds at 80 knots is simply not a practical solution. The bottom line is that we must settle for what separation we can get.
If you think your 10 second delay is any guarantee of separation, in and of itself, think again.
The Shape of the Optimum Exit Point
Let's examine jump run from the standpoint of the jumpship.
Firstly, we assume that our acceptable landing area is a designated circle on the ground that is 2,000 feet in diameter.
For easier visualization, consider a thin stratus layer of cloud at jump altitude that has a hole which, by remarkable coincidence, is open only below the aircraft when the spot is acceptable for exit.
With no winds, the opening in the cloud will be the same shape as the area on the ground and would be positioned straight up from the landing area on the ground. This area is illustrated in Case 5, Figure 1 shown above. This round area is 2,000 feet in diameter like the landing area on the ground. If we put each group out, maintaining a distance of 1,000 feet between each group, we are able to put out 3 groups over the optimum spot area.
When there are prevailing winds aloft, the exit area is displaced upwind by a certain distance depending on the speed of the prevailing winds.
In the animated illustration above, Case 5, Figure 2, the airplanes start emitting a smoke trail at the beginning of the optimum spot area and cease emitting smoke at the end of the optimum spot area. Observe how the smoke trails blow downwind and elongate. In other words, if the upper winds are around 80 knots and the ground winds are around 10 knots, you can put out more than 3 groups over the optimum spot area.
With a headwind or tailwind, the shape of the hole in the cloud (compared to the shape of the landing area on the ground) is stretched or compressed, respectively. Because the airplane is flying in a moving medium, it partially resembles a tethered balloon scenario and the characteristics of Case 2 begin to arise. In other words, horizontal separation is also induced by the prevailing winds.
Notice that the above animated illustration shows five airplanes flying in formation across the optimum spot. Normally, we have only one airplane flying on the jumprun. However, by viewing the five airplanes in the animation, we can see that if the airplane is flying to the left or to the right of the optimum centerline for the jumprun, the length of the optimum spot area is shortened.
The elongated shapes in Case 5, Figure 3 are marked with the value of the headwind (at jump altitude):exit speed (of the aircraft) ratio.
Notice that when the ratio of the headwind to exit speed is 1 (in other words the headwind equals the exit speed), the hole becomes a "slot." The aircraft is stationary over the ground and jumpers can exit at any time after the aircraft positions itself with the same spot. This very much resembles our tethered balloon scenario!
With a downwind jumprun, the hole becomes more compressed.
A crosswind jumprun has the same opening as a no - wind day. Thus a crosswind fails to take advantage of the benefits of a headwind, but a downwind jumprun should be used only to get out of the airplane in an emergency.
Using a 3:1 glide ratio for our ram air canopies, with a 2,000 foot opening altitude, we have a 6,000 foot gliding radius to the target. This gives us 12,000 feet over the ground for an optimal "centerline" jumprun. Again, we assume that the jumpers are falling straight down the tube with no horizontal sliding nor tracking. (Note that anyone tracking away from the target in this model may be hosed). Figuring a nautical mile as 6,000 feet, we have a 2 nm jumprun over the ground. With a headwind, the aircraft will take longer to cross the optimum area for exiting. With an exit speed of 90 knots and no wind, we have 80 seconds of working time. A 30 knot headwind at altitude increases our window of opportunity to 120 seconds, and 45 knot headwind allows 160 seconds. In the case of our tethered balloon in CASE 2, the spot does not change and jumping can proceed until there are no more jumpers.
Reducing the exit airspeed increases the duration of the window similarly.
Due to the increased ground speed while flying jumprun with a tailwind, the aircraft will take yet less time to cross the optimum area for exiting.
In general, remember that, in the real world, the winds aloft do change with altitude. This must be considered when making spotting decisions.
Basic Rules of Thumb for Spotting|
If we break all of this down to a few basic rules of thumb for spotting, we will arrive at the following:
1) Determine the optimum spot from prevailing winds on the ground and at altitude.
2) Determine the window of opportunity, both before and after the optimum spot, both distance and time. This should include allowances for climbout time of the first group, and horizontal throw after exit.
3) Use landmarks and known distances (e.g. runway lengths and directions) for reference, to check the climbout point.
4) Look straight down when picking the climbout point.
5) Make a scan of the "cone of opportunity" for other aircraft before climbout.
6) Be aware of the intentions and makeup of the groups preceding and following you and adapt your scan accordingly. 8 jumpers with around 100 jumps each trying to get their Eagle awards (for whatever license it is that requires it) are more likely to have unexpected results than is a World Champion 8 way team banging out 23 points on a practice jump.
7) Stay heads-up, since the possibility of closure between groups exists unless you are the only group in the air. No rules of thumb will guarantee safety.
|Freefall Simulation Software|
John Kallend presents his freefall simulation software. The computer modeling does not include "human behaviors" such as tracking, funneling, or other way of failing to fall straight down the tube.
Visit: http://www.iit.edu/~kallend/skydive.html to download a copy so you can experiment yourself.
The purpose of the Freefall simulation software is to determine the most likely trajectories of (groups of) skydivers with different fall rates, given the fall rate, airplane speed, and winds. The software assumes an ICAO standard atmosphere, that the diver maintains a constant attitude with respect to relative wind, that the exit altitude is 14,000 feet, that the opening altitude is 3,000 feet, that one jumper/group takes 65 seconds to reach opening altitude and that the other jumper/group takes 50 seconds to reach opening altitude. The software allows the user to select different wind speeds at exit and opening altitudes, the altitude of wind speed change, the true airspeed of the airplane, the exit order and the delay between exits. All distances are specified in feet, all times in seconds, and all speeds in fps.
Do your own modeling! The software accepts the following parameters...
1) Plane Velocity (fps):
2) Upper Level Windspeed (fps):
3) Lower Level Windspeed (fps):
4) Altitude of Wind Change:
5) Delay Between Exits:
6) Which Jumper is the Fast Faller (1 or 2):
The software assumes that the head-down freeflyers fall from 14,000 feet to 3,000 feet in 50 seconds and that flat relative workers fall from 14,000 feet to 3,000 feet in 65 seconds. The drag co-efficient for head-down flyers and belly flyers from the forward throw of the aircraft to terminal is assumed to be the same. The flat relative workers slow quicker than the head-down freeflyers. The flat relative worker takes 3,000 feet to finish exit transition. Forward throw is less for slower exit speeds but if the freeflyer exits first, they still overlap at pull time.
Determine for yourself who should exit first. Head-down freeflyers or the flat relative work fliers?
Check also Tim Wagner's comments and Bryan Burke's Essay on Exit Order.