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Skydiving Coordinate System Part 3

Words by Niklas Daniel

Fig 15, High lift track For "body flight theory" article
Fig 15, High lift track — Image by Niklas Daniel

Body-flight Theory

Skydiving Coordinate System

This is the third of four episodes about defining a skydiving coordinate system. 

Previous Episodes

1 – The Axis system and Frames of reference

2 – Six directions of movement, Orientation borders and Range of motion

Fig 16, Carving For "body flight theory" article
Fig 16, Carving — Image by Steve Curtis

Move Combinations

Any maneuver that simultaneously combines translational and or rotational movements, results in a “super-positioning-move”. These will generally change a flyer’s location, orientation, and/or heading simultaneously. Examples include flying a circular path or an arc.

Some of these moves have their own names such as “high lift track” (Fig. 15, top of page), where the goal is to translate forward on the X-AXIS while simultaneously floating ‘up’ on the Z-AXIS. Another super-positioning example is “carving” (Fig. 16, above), which refers to a flyer translating around a target in a circular path (like an orbit) on the horizontal plane. This is accomplished by translating on the X-AXIS just off to the side of the target, while simultaneously adding some rotation on the Z-AXIS to adjust heading.

Transitions

A transition is an AXIS-shift between the six orientations. Because the wind-AXIS system is defined by the relative wind, a transition involves a change in the body’s primary flight surface (e.g. belly to another, such as head-up). In order for a body-pilot to transition from one orientation to another, rotation on either the pitch or roll AXIS are required. Therefore these two will be highlighted in the secondary colors green for pitch, and purple for roll.

A skilled body-pilot can rotate his or her body to various degrees of yaw, pitch, and roll. Rotations of more than 90 degrees around the X-AXIS or Y-AXIS result in an orientation change or “AXIS-shift”. For example, a pitch alteration of 90 degrees or greater is called a flip, whereas roll of 90 degrees or greater is referred to either as a barrel roll when horizontal or a cartwheel when vertical. Rotations on the Z-AXIS, however, cannot provide a flyer with an orientation change, as it only changes the jumper’s heading. Although the body can move in a countless number of ways through space, for practical purposes there are only 48 possible transitions using the six neutral orientations: 24 transitions involve pitch, rotating around the Y-AXIS (red) and 24 involve roll, rotating around the X-AXIS (yellow). There are no transitions involving the Z-AXIS (yaw) (because Z can only affect heading).

Each of the six body-flight orientations belongs to one of the three above listed planes. As such, each plane has an excluded maneuver – by name only. For example, a flyer is not able to perform a barrel roll while oriented vertically, because a vertical roll maneuver is called a cartwheel. The same principal applies for the other body-planes and their excluded maneuvers.

Table 5: Orientations and excluded transitions
Table 5: Orientations and excluded transitions

The three planes highlight the different orientations a person can fly in. However, what appears to be a single flying skill on one plane may require significant contributions from the other two planes. For example, head-up flying is a byproduct of belly and back-flying skills, and the pitch transition over the legs that connects the two. The lateral plane, and therefore edge-flying is often neglected in most training programs, and should be recognized as a true orientation of its own.

Edge-flying and “Wormhole” transitions

The X and Z-AXES of the Wind-AXIS system change location on the body when transitioning between horizontal and vertical flight modes through pitch. Similarly, transitions between the vertical and lateral flight mode causes the Y and Z-AXES to shift locations on the body during a roll maneuver. When transitioning between a horizontal and lateral flight mode however, an issue arises. Although one uses a ¼ barrel roll to transition between these two planes, they do not share the same final heading. The act of rolling, no matter the bank angle, is supposed to maintain heading. When an aircraft has its own propulsion system, it is typically in line with the longitudinal AXIS of the body. This creates very defined roll characteristics. When propulsion is absent, such as the case of a skydiver who only has gravity as a driving force, a rolling maneuver has the ability to change heading.

Edge-flying

Fig 17a, Slow flight mode For "body flight theory" article
Fig 17a, Slow flight mode — Image by Brianne Thompson
Fig 17b, Fast flight mode
Fig 17b, Fast flight mode — Image by Brianne Thompson

Edge-flying can be performed in a wide spectrum of wind speeds. The slow and fast flight versions differ slightly in appearance. A slow fall rate (Fig. 17a) requires more surface area to be exposed to the relative wind. Therefore the legs are generally further apart (oriented horizontally), and the arm leading into the relative wind is stretched out past the head for added surface area. The fast flying version (Fig. 17b) involves the legs to be vertically oriented, while the leading arm rests under the torso.

Although flying on the side of the body is by definition a horizontal flight mode, edge-flying exhibits the flight characteristics of a vertically oriented one. This is because the vertical and lateral orientations are both aligned parallel to the relative wind. Since the names barrel roll and cartwheel are synonymous with roll, it would appear that edge-flying orientations have two possible roll AXES - a “roll duality”. As heading is perpendicular to vertically aligned planes, the X-AXIS and therefore heading conforms to that of the vertical orientations. This allows for a cartwheel to take place on both parallel planes without heading being compromised throughout the maneuver. The pitch transition (flip) while flying on the side of the body is still referred to as a barrel roll. However, this creates a problem for maintaining heading when transitioning between the horizontal to the lateral planes. This is because a quarter barrel roll from the horizontal to the lateral falls into the roll category, but when performed in reverse should be considered a flip. A 90degree heading change is created when transitioning between the two planes. I have chosen to call this observation a wormhole transition (coined by my wife Brianne Thompson), since a roll maneuver is not supposed to transport your heading elsewhere. This counterintuitive characteristic does not go away by making the edge-flying roll-AXIS conform to that of the horizontal plane. This highlights the importance of recognizing a person’s starting and ending orientation for proper motion tracking.

Transitions involving a rotation of 180 degrees start and end on the same plane, but always end on the opposing side: 24 possibilities. Transitions involving a rotation of 90 degrees start and end in planes that are perpendicular to one another: 24 possibilities. Transitions that rotate beyond 180 degrees (270 degrees, 360 degrees, etc.) are a combination of 90 degree and 180 degree transitions. Therefore, becoming proficient at these higher- degree transitions is merely a task of combining the foundational elements of 90’s and 180’s. The chart below is an inventory of all foundational maneuvers a jumper can perform in the air.

AXIS directions of travel defined (+/-)

Fig 18, Right hand rule for bodyflight theory article
Fig 18, Right hand rule — Image by Niklas Daniel

In order to define the directions of angular rotation the right hand rule will be applied. This helps in understanding orientation conversions for vectors in three dimensions.

Since falling towards earth is a jumper’s direction of travel, we will establish “into the wind” as the positive direction, no matter the flying orientation. With the thumb of the right hand pointing in the positive direction of the Z-AXIS, the fingers of the hand represent the positive direction of the Z-AXIS torque as you curl them.

Z-AXIS

Z-AXIS: the path going into the relative wind is indicated to be positive, so we lose altitude in the positive direction of travel. In freefall a jumper can only travel in the negative direction relative to another jumper. When flying in the tunnel, the jumper can actually travel in the negative direction and fly away from the ground to go up.

X-AXIS

X-AXIS: The positive direction of the X-AXIS always lies ahead of the jumper – the person’s heading. Therefore a forward drive is positive, where as a backward drive is negative. A clockwise roll is positive, whereas a counterclockwise rotation is negative. To find X, turn the thumb of the right hand towards the direction of your heading. The positive X direction always lies ahead of the flyer, and the positive torque direction is clockwise as seen from the flyers perspective. Counter clockwise barrel rolls or cartwheels are rotations in the negative direction.

Y-AXIS

Y-AXIS: The positive direction is to the left of the flyer. This means a side slide to the left is positive, whereas a slide to the right is negative. This also means that a front flip is positive, whereas a back flip is negative. To find Y, look at the back of your hand (knuckles) with your fingers pointing towards your heading and your right thumb pointing to your left.

Note: To conserve space, the six flying orientations will be abbreviated thusly: BE = Belly, BA = Back-fly, HU = Head-up, HD = Head-down, EL = Edge-left, ER = Edge-right. Wormhole transitions will be indicated with **.

AXIS Shift Matrices

90-degree Transitions (12 categories)

Table 6: 90-degree Transitions
Table 6: 90-degree Transitions

180-degree Transitions (3 Categories)

Table 7: 180-degree Transitions
Table 7: 180-degree Transitions

Multi-AXIS combinations (twists)

There are two versions of twist maneuvers called horizontal-twist and vertical-twist. What determines which category is being executed depends on the performer’s spinal alignment throughout the maneuver:

A horizontal twist involves the performer starting the maneuver with his or her torso aligned perpendicular to the airflow (belly, back, or edges. S/he then has to turn (yaw), while simultaneously barrel rolling (roll) throughout the maneuver. This means that two AXES of rotations are being implemented simultaneously. An example of this is the half breaker in the dynamic dive pool, which in most cases will also have a translational movement coupled into it.

Fig 19, Three AXES of rotation and three planes of movement For "body flight theory" article
Fig 19, Three AXES of rotation and three planes of movement — Image by Niklas Daniel

A vertical twist involves the performer starting the maneuver with his or her torso aligned parallel to the relative wind (head-up or head-down). S/he then has to flip (pitch), while simultaneously inducing a rotation about the body’s longitudinal body-AXIS. Depending on the spines alignment with the Wind-AXIS during the flip, the twisting motion will alternate between rolling and turning. This is because the flyer is effectively rotating on all three AXES simultaneously. This is why this maneuver is considered to be very difficult to perform.

As there are many degrees of twists (quarter, half, full, double, triple, etc. that can be incorporated into any transition) they were excluded from the transition matrix above. Just as an artist can create millions of colors by combining three primary colors, a skilled body pilot can combine fundamental flying techniques to create more complex ones. This strongly suggests that all forms of flight complement one another and that no single orientation is superior to another.

In the image to the left, the figurine moves independently and throughout. The planes are not body planes, but planes of movement! The orange plane is always perpendicular to the relative wind and therefore represents the body’s cross sectional area pertinent to body flight.

Skydiving Coordinate System

That concludes Episode 3 – below the series content is summarised. Final episode 4 to follow next week

Episode 1 – The Axis system and Frames of reference

Episode 2 – Six directions of movement, Orientation borders and Range of motion

Episode 3 – Move combinations, including Multi-axis combinations

Episode 4 – Terminators, Real world applications and Conclusion

Download pdf of entire Coordinate System paper (4 Episodes) 

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

Nik invites comments,in order to advance the theoretical knowledge of body-flight (articles-at-AXISflightschool.com)

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