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Skydiving Coordinate System Part 2

Words by Niklas Daniel

Body-flight Theory

Fig 9a, frontal view For "body flight theory" article

Skydiving Coordinate System

This is the second of four episodes about defining a skydiving coordinate system. Last week saw Episode 1; The Axis system and Frames of reference, read this first if you haven’t already.

Six degrees of freedom (6DOF)

Jumpers can move in six distinct directions while in any of the six body-flight orientations. Half of these are called translation, while the other half are called rotation. Three X, Y and Z-AXES (which are fixed to the relative wind) are highlighted in the three primary colors, and pass through the body perpendicular from one another (aka orthogonal coordinate system).

Translation

Translation in its purest form involves any movement of the jumper in a straight line along a specific AXIS that maintains heading. Jumpers who move to a new location through space in this manner, are said to have translated into that particular direction. Translational movements are highlighted in the three primary colors: blue, red, and yellow.

Rotation

Rotation in its purest form involves a revolving movement around an AXIS. The terms Yaw, Pitch, and Roll clarify the type of rotation being executed. The body-plane about which a body moves is always perpendicular to its AXIS of rotation. Rotational movements are highlighted in secondary colors, i.e. a turn/yaw involves a rotation around the blue vertical AXIS. Therefore, the body is passing through the red Y-AXIS and yellow X-AXIS, creating the color orange – blue’s complementary color.

Fig 7, Six Degrees of Freedom For "body flight theory" article
Fig 7, Six Degrees of Freedom — Image by Niklas Daniel
Table 3: Wind-AXIS with their role in rotations or translations
Table 3: Wind-AXIS with their role in rotations or translations

If neither rotation nor translation is present within a flyer’s performance, the jumper is said to be ‘neutral’ in his or her current orientation. To be neutral, one does not have to hold a specific body posture; rather being neutral is the act of neutralizing any rotational and or translational movements all at once. Therefore various body postures can be considered neutral. A jumper can choose to be “passive” after an initial input, such as a high lift track. Letting your momentum come to rest naturally over time without any additional input is called “coasting”

Wind-AXES defined

The Z-AXIS

The Z-AXIS, shown in blue, is the “line of force” as it is always aligned with the relative wind. Yaw is the rotation to the left and right around the Z-AXIS and is solely responsible for heading and directional stability. Based on how the person’s torso (MSL) lines up with the Z-AXIS, the jumper can be either horizontally or vertically aligned, giving you his or her orientation. In the wind-tunnel scenario this Z-AXIS is always parallel to the walls of the flight chamber.

In order to define the other two AXES, let us first digress a little and talk about “heading”. The subject of heading presents a challenge in skydiving. Unlike an airplane that has a primary flight orientation, a skydiver can fall through the air in multiple orientations. A jumper’s orientation influences the concept of heading. Skydivers typically use the word “heading” like a sailor uses the term “relative bearing”, a direction that is always straight ahead. There is a difference between heading and flight path. A great example is a belly flyer who is engaged in a side slide. The heading and direction of travel are perpendicular from one another. In skydiving, heading is determined by examining a person’s MSP and then referencing the X-AXIS, of the Wind-AXIS system. With the ‘clock method’, the heading of the jumper is measured as if on a clock face perpendicular to the Z-AXIS (relative wind). An object, such as another jumper, the center of a formation, a tunnel wall or a fixed object on the horizon is said to be at ‘twelve o’clock’ when it is straight ahead. This means that heading is not line-of-sight. Turning your head to look around does not constitute a heading change, as you have not rotated your body on the Z-AXIS. The body plane of flight is always comprised of the X and Y-AXES. Heading is located on the body plane of the applied orientation in the forward/backward direction of the flyer. A jumper’s heading always lies in the forward direction of travel on the X-AXIS. When applied to an external reference point, a jumper is said to be in-facing when the target is in front of the flyer at the 12 o’clock position. If the target is behind the jumper, in the 6 o’clock position, s/he is now out-facing.

The X-AXIS

The X-AXIS, shown in yellow, lies on the body-plane in the forward/backward direction. Tilting the body side to side around the X-AXIS is called banking for small amounts and roll for larger ones. A jumper’s heading is determined by observing the positive (front of body) end of the X-AXIS as it rotates on Z. Heading is always perpendicular to the Z-AXIS. While rotating on the X-AXIS, the jumper maintains heading while either side-sliding or altering orientation (barrel roll or cartwheel), depending on the magnitude of the rolling action. In the wind-tunnel scenario this AXIS runs parallel to the net of the tunnel, in the direction of the jumper’s heading.

The Y-AXIS

The Y-AXIS, shown in red, also lies on the body-plane and is perpendicular to the X and Z-AXES. Tilting the body front to back (or nose up and down) around the Y-AXIS is called Pitch. Small changes in pitch cause the body to translate forwards or backwards, while larger changes in pitch can alter orientation (flipping). In the wind-tunnel scenario, the Y-AXIS is always parallel to the net of the tunnel, and perpendicular to the X-AXIS (flyer’s heading).

Wind-AXES applied to orientations

Start by locating the Z-AXIS as it is always fixed to the relative wind on the vertical plane. Next, locate the X-AXIS, which is perpendicular to the Z-AXIS, and is in line with a jumper’s heading. Lastly the Y-AXIS is always perpendicular to the X and Z-AXES but on the same plane as the X-AXIS.

Table 4: Wind-AXES applied to orientations
Table 4: Wind-AXES applied to orientations

Table 4 (above) highlights the various flight characteristics the different flying orientations have. As one progresses though the chart, greater flying skill is required in order to maintain control over one’s body in freefall. Therefore the chart also highlights the most logical learning approach.

Orientation Borders

Using an orientation wheel (Fig. 8), we can establish imaginary boundary lines called ‘Orientation Borders’ (OB) that divide the space around a jumper into six sections.

Fig 8, Orientation Wheel For "body flight theory" article
Fig 8, Orientation Wheel — Image by Niklas Daniel

This wheel can be implemented looking at a jumper either from the front or side. The Z-AXIS, indicated in blue, and the center of gravity ball in the middle of the wheel (black), help orient the wheel’s position to the jumper. The grey horizontal line can represent either the X or Y-AXIS depending on whether a front or side view is being implemented.

There are four of these lines in all, passing through the jumper at 45degree angles relative to the Wind-AXIS system. In order to identify which orientation a jumper is in, we compare the person’s MSP (mean spine position) with the OB (orientation borders).

Below are various examples of comparing the MSP to the OB in order to determine the resultant orientation. In the images below, we examine each body orientation by looking at the person first from the front, and then the side. There is only one example of Edge-flying (right), as the other side would be a mirror image of the first. The frontal view looks straight down the X-AXIS (roll), the edge-on view is looking at the flyer straight down the Y-AXIS (pitch) – to be elaborated on shortly.

Belly

Fig 9b, edge on view For "body flight theory" article
Fig 9b, edge on view — Image by Niklas Daniel
Fig 9a, frontal view For "body flight theory" article
Fig 9a, frontal view — Image by Niklas Daniel

Back

Fig 10a, Frontal view For "body flight theory" article
Fig 10a, Frontal view — Image by Niklas Daniel
Fig 10b, Edge on View For "body flight theory" article
Fig 10b, Edge-on view — Image by Niklas Daniel

Head-up

Fig 11a, Frontal view For "body flight theory" article
Fig 11a, Frontal view — Image by Brianne Thompson
Fig. 11b: Edge-on view
Fig 11b, Edge-on view — Image by Brianne Thompson

Head-down

Fig 12a, Frontal view For "body flight theory" article
Fig 12a, Frontal view — Image by Brianne Thompson
Fig 12b, Edge-on view
Fig 12b, Edge-on view — Image by Brianne Thompson

Edge Flying

Fig. 13a: Frontal view
Fig 13a, Frontal view
Fig. 13b: Edge-on view
Fig 13b, Edge-on view

Range of Motion

There are a few body postures and flight modes that appear to break the MSP/OB rules at first glance. Body-flight is not a ridged undertaking and requires for some range-of-motion in order for a person to stay balanced and mobile. This means a jumper can alter their body posture considerably while remaining in his or her original orientation.

Range of Motion

Fig. 14a Range of Motion
Fig 14a, Range of Motion — Image by Brianne Thompson
Fig 14b, Range of Motion
Fig 14b, Range of Motion — Image by Brianne Thompson

Fig. 14a (left): Niklas Daniel maintains his balance while back-flying, although the body posture resembles that of a belly arch. Fig. 14b (right): Niklas Daniel transitions from Head-up to Head-down via a front flip. During the transition, Nik pauses and flies the position in the image in a neutral fashion before continuing (see video below).

AXIS Flight School Instructor Niklas Daniel demonstrates the Sit fly to Head down front flip transition.

Fig. 14b presents some issues that need to be addressed. I am in a head-up orientation, and even though I am looking behind me through my legs, in my opinion, this posture should be considered head-up. The MSP however closely resembles that of a belly flyer, with the front of the torso leaning onto the relative wind, and the top of the head is presented to the relative wind with the visual field being upside down.

As determined earlier, line of sight does not affect heading or orientation. So we must pay close attention to the MSP and OBs with respect to the relative wind. In addition, it is worth noting that vertical flying orientations can implement belly and back flying surfaces simultaneously. Looking at the image above, one can see that there is a balanced amount of belly and back flying surfaces being implemented to maintain this posture. To a certain extent and depending on your flying skills, you can “stretch” a maneuver a little across the OB line before losing stability.

(Side note: Curling the body in the manner demonstrated in Fig. 14b does not bring orientation into question while flying in an Edge orientation.)

Flight modes that incorporate a horizontal component such as angle/dynamic flying, which can also blur the defined lines of the OBs are covered in more depth further down in this article.

Skydiving Coordinate System

That concludes Episode 2 – below the series content is summarised.

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

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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