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Skydiving Coordinate System

Words by Niklas Daniel

Arsenal in action
Flying in all orientations defies traditional descriptions. VFS team, Arizona Arsenal — Image by Niklas Daniel

Body-flight Theory

Humans have built bridges longer than recorded history without complex engineering knowledge. But with a greater theoretical understanding, we have been able to create engineering marvels the world over. Similarly, you don't have to be an expert at theory to excel at bodyflight, but a deeper understanding should elevate the sport and your own flying to a new level. 

Now we have learned to fly in many different orientations, using all the surfaces of our body, then our traditional terminology for bodyflight has become inadequate. Orientation terms (such as head-up and head-down) are open to interpretation – they should be used to refer to the angle on the relative wind, not the ground. This makes newer disciplines such as MFS (Mixed formation skydiving) hard to judge because of the subjectivity. This series of four articles is aimed at establishing a more elegant, convenient way to visualize body-flight movement with the purpose of creating order by introducing AXIS systems. 

The Iron Man Example

A popular comic book character can help us better understand the conundrum. If Iron Man were to hover using only his rocket boots, then he is relying on only thrust and therefore is not actually flying. Flight requires airflow to pass over a flying surface. If Tony now powers up his rocket boots and flies straight up into the sky, then although he is in a head-up orientation with respect to the ground, he is actually flying head-down in the relative wind interacting with his body. His flight performance and body’s handling characteristics are that of a head-down flyer. If he now shuts off the engines and falls back to earth, he is in the head-up orientation, with respect to both the ground and the relative wind, it is making contact with his body from feet to head.

If iron man flies straight up into the sky, he is actually flying head down because of how the relative wind is interacting with his body. His flight performance and body’s handling characteristics are that of a head down flyer. If he now shuts off the engines and falls back to earth, he is in the head-up orientation, as the wind is making contact with his body from feet to head.
If Iron Man flies straight up he's in a head-down orientation with the relative wind. — Image by Film Kartun

A skydiving coordinate system

The system presented here is a type of bookkeeping that will outline the different ways a skydiver or tunnel flyer can move in the air. The language developed here and its use is meant to best represent the activity, and lay a theoretical concept or knowledge foundation.

An AXIS coordinate system is an arbitrary reference frame imposed upon physical phenomena to simplify our observations and analysis. Thus I am going use the one that is most appropriate for skydiving and tunnel flying, called the Wind-AXIS (relative wind). In future installments, we will use this system/language to examine the physics of body flight, as well as other noteworthy discoveries that pertain to body-flight performance.

Terminology

There are three words frequently used by skydivers interchangeably with respect to body-flight, which can cause some confusion: (body)-position, (body)-posture, and (body)-orientation.

Position will be used to define a flyer’s location in space, i.e. relative to another person, a particular location in a wind tunnel, or within a formation.

Posture will specifically refer to a jumper’s body-shape or anatomical-position. Different body-postures offer various functions depending on a flyers needs. Some qualities can include: “being neutral”, “aerodynamically stable/unstable”, “drive-inducing”, “symmetrical”, “asymmetrical”, etc. A change in a person’s geometric shape or posture can be referred to as morphing (think of the F-14 Tomcat with its unique feature called a variable-sweep wing), which is done to increase aerodynamic performance. This allows a proficient body-pilot to take part in various freefall disciplines, and even alter flying orientation – something unachievable by aircraft. Even when the engines stop, an aircraft has an inherent built-in stability and ability to glide. Humans on the other hand have no built in stability, and must find control in the relative wind by properly shaping their body to facilitate stability and mobility.

Orientation is a mechanical alignment between a flyer’s torso and the oncoming relative wind. A body-pilot is able to fly in two modes using six fundamental body-flight orientations:

 Fig 1a, Belly Fly For "Body flight theory" article
Fig 1a, Belly Fly
 Fig 1b, Backfly
Fig 1b, Backfly
Fig 1c, Right Edge For "body flight theory" article
Fig 1c, Right Edge
Fig 1d, Left Edge For "body flight theory" article
Fig 1d, Left Edge
Fig 2a, Head-Up For "body flight theory" article
Fig 2a, Head-Up
Fig 2b, Head-down For "body flight theory" article
Fig 2b, Head-down

Alignment of the body’s spine in relation to the Wind-AXIS (relative wind) determines whether a person is horizontal or vertical. A perpendicular alignment equals a horizontal flying orientation, whereas a parallel alignment equals a vertical one. Since a jumper’s spine is rarely perfectly straight, an imaginary line connecting the Coccyx (tailbone) with the Thoracic (T1) vertebrae is compared to the relative wind to determine Orientation. This imaginary line will be referred to as the Mean Spine Position or MSP. Leaving the head out of the equation allows for movement of the skull and cervical spine to not affect the MSP. Each body-flight orientation has to be maintained by the jumper with a specific range of postures. The spine’s alignment to the relative wind is nothing like a chord line on a fixed wing, and therefore angle of attack does not come in to play here. But the principle will be discussed at length at a later time.

Fig 3, Mean Spine Position (MSP) For "body flight theory" article
Fig 3, Mean Spine Position (MSP)

Certain disciplines such as MFS (mixed formation skydiving) and VFS (vertical formation skydiving), have formations in their dive pools that dictate specific orientations the performers must present in order to score a point. Though these disciplines have been around for years, the word ‘orientation’ has still not yet been properly defined. This causes an issue within the judging community, as orientation is currently subjective and open to interpretation. In an objective discipline like formation skydiving, there is no room for subjectivity. A possible solution to this problem will be explored later through the implementation of an orientation wheel (Fig 8, in next article).

AXIS System

Unlike a rigid airfoil, body-pilots are shape shifters that morph their cross-sectional geometry to utilize their entire body as a reconfigurable structure to fly in multiple orientations and speeds. To illustrate the six functional flying orientations, we need to implement a coordinate system that can highlight the different ways and directions the body can travel through the relative wind. To describe a body’s movement in three-dimensional space, we use three imaginary lines of reference. Each imaginary line that passes through the body is called an AXIS, and it represents the directions around which the body can either rotate or move along. We the reader/observer are located next to the jumper, like a freefall camera-flyer, remaining in an upright orientation relative to the Wind-AXIS.

It is important to note that the classical coordinate system of an aircraft cannot be successfully applied to a body-pilot. The ability to completely alter our body shape and flight surfaces can result in some unusual and unexpected conclusions. Therefore any letter, number, or symbols used throughout this paper may be considered arbitrary.

Frames of Reference

An individual AXIS-system can be applied to multiple frames of reference, such as the body in relation to itself, the body in relation to earth (gravity), and finally the body in relation to the relative wind. Since our goal is to make observations about skydivers/tunnel flyers falling through the air, a jumper’s relationship with the relative-wind will become our main point of interest. But first, let us isolate these three separate systems and then see later how they interact with one another:

Fig 4a, Longitudinal Axis (LA) – Height – from top to bottom For "body flight theory" article
Fig 4a, Longitudinal Axis – Height – from top to bottom

1) Body-fixed system (local coordinate system)

A person’s body has height, width, and depth. An outside reference frame like the floor is not required to know how to measure a person’s height. Regardless if a person is standing up or lying down, you would know to measure your subject from head to toe. Likewise, if you were to measure a person’s width, you would know to measure them from side to side (ex. arm-span). You could also measure a person from front to back, belly button straight through the body to the spine.

Thusly, a jumper’s body will be divided into these three properties by individual reference-lines, abbreviated by dual letters. Each one of these imaginary lines is called an AXIS. The body-AXES will be referred to by their medical names.

Fig 4b, Lateral Axis – Width – from side to side For "body flight theory" article
Fig 4b, Lateral Axis – Width – from side to side
Fig 4c: Anteroposterior (AP) Axis – Depth – from front to back For "body flight theory" article
Fig 4c: Anteroposterior Axis – Depth – front to back
Fig 5a, Coronal Plane. Longitudinal & Lateral AXES. Parallel to the spine, It divides the body into front/back For "body flight theory" article
Fig 5a, Coronal Plane. Longitudinal & Lateral AXES. It divides the body into front/back

Center of gravity is an important concept to consider when discussing flight because of its impact on balance and stability. This hypothetical point is where the force of gravity acts upon. Indicated in the images below by a black sphere near the waist, the CG is located where all three AXES intersect and is essentially the average location of the person’s weight. Since jumpers rarely stay perfectly still the CG is not fixed, but the precise location changes with every new body posture, and with the addition of equipment.

Body-planes are a combination of any two body-AXES used to create a two-dimensional surface (like a sheet of paper) representing a collection of body parts exposed to the relative wind. These parts of the body become the ‘flying surfaces’. There are three such planes, which are fixed to the person. It is possible to fly on either of the two surfaces defined by each plane, which gives us a total of six surfaces to fly on (think of a 6-sided die). These six surfaces make up the body-flight-orientations mentioned earlier. The body-planes will be referred to by their medical names.

The cross-sectional geometry around the flyer's center of gravity on the plane that is aligned perpendicularly to the relative wind will greatly affect the jumper’s fall rate, stability, and direction.

Fig 5b, Transverse Plane, Lateral & Anteroposterior AXES. Perpendicular to the spine, It divides the body into top/bottom sections For "body flight theory" article
Fig 5b, Transverse Plane, Lateral & Anteroposterior AXES. Divides body into top/bottom
Fig 5c, Sagittal Plane, Longitudinal & Anteroposterior AXES. Parallel to the spine, It divides the body into left/right sections For "body flight theory" article
Fig 5c, Sagittal Plane,Longitudinal & Anteroposterior AXES. Divides body into left/right
Body-planes with the AXES combination that defines them, their locations & applications
Body-planes with the AXES combination that defines them, their locations & applications

2) Earth-fixed system

Gravity, or our body’s relentless acceleration towards earth, is a skydiver’s power source. This drives our bodies through the air, and as a byproduct produces the relative wind we feel on our bodies. The gravitational force is represented by a straight line, which starts at the jumper’s CG, at the center of the body-fixed coordinate system, and then connects to the center of the planet. Inexperienced skydivers will use the horizon/ground as their primary frame of reference (visually) for their flight performance, because they instinctively know that the gravitational force acts on their body in a constant downward direction. But aerodynamic forces, not gravity, dominate our movements in freefall. A good example is the body-flight orientation “head-down”. Though gravity tells us which direction down is, this is a bit misleading, as one should think of it as head in to the wind, not necessarily head towards earth. Since airflow is not always aligned with gravity, particularly when exiting an aircraft, we cannot use the ground or horizon as a reliable reference for body-flight movement analysis.

3) Wind-fixed system

The definitions for maneuvers performed in skydiving/tunnel-flying are determined by the relative wind. What differentiates a roll from a turn is which orientation we are flying in (our presentation to the relative wind). In the introduction, we established that orientation is the jumper’s body-alignment compared to the relative wind. The relative wind emanates from the oncoming airflow opposite to our trajectory. Therefore, a wind-fixed system is the most relevant AXIS-system to skydiving, and is most easily visualized in a vertical wind tunnel where the wind and earth-fixed frames overlap. In the figures below, the Wind-AXIS is represented by a blue line called ‘Z’, which is always in-line or parallel with the relative wind.

Note: In the event a skydiver jumps from an aircraft with an initial forward velocity, the Wind-AXIS shifts relative to the earth-AXIS system. Every jumper needs to adjust for the shift in origin of the relative wind on exit, and must continue to adjust for it as the jumper’s path begins to move in the earthward direction. The jumper’s trajectory-change from horizontal to vertical is a phenomenon skydivers call “the hill”.

Fig 6a, Mixed vertical formation For "body flight theory" article
Fig 6a, Mixed vertical formation

In both images one jumper appears to be head-up and the other head-down when taking the horizon into account. But the relative wind determines orientation, not the ground; therefore in Fig 6a (above) the performers are in a mixed vertical formation, where indeed one jumper is head-down and the other head-up. In Fig 6b (below) however, which depicts an exit situation, the performers are both in a belly-oriented formation where neither of them is vertical with respect to the Wind-AXIS. (Remember Iron Man?!)

Fig 6b, Belly oriented formation For "body flight theory" article
Fig 6b, Belly oriented formation

Skydiving Coordinate System

That concludes Episode 1; The Axis system and Frames of reference. To follow..

  • Episode 3 – Move combinations, including Multi-axis combinations
  • Episode 4 – Terminators, Real world applications and Conclusion

Bodyflight Theory

Episode 4 will complete part 1 of this BodyFlight Theory paper, the Skydiving Coordinate System. Other parts will be subsequently added to cover theory and application for all human flight disciplines, through understanding the principles of human flight.

Article, Drawings and Images by Niklas Daniel of Axis Flight School unless otherwise stated

Nik invites comments, contributions and critique in order to advance the theoretical knowledge of the sport of body-flight (please send to articles-at-AXISflightschool.com)

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