Stability Considerations for Single Line Kites

I started writing this in 1973 but found that understanding why single line kites fly (or rather, why they don't fly) was more difficult than I thought it would be.  Kirri (eldest daughter) enjoys reminding me that my life's goal then was to have the field pinned down by the time I was 35. Now 57, I still don't have a very good understanding; not quantitative, not able to predict by how much something has to changed by to get a defined effect- yet!.  However, I'm now quite often able to predict in which direction a kite's behaviour is likely to be shifted by a particular change, and can offer some plausible theories as to why.

The aim I have in writing this now is to test these theories against other kiteflier's experiences and use this process for further refinement. I don't have explanations for everything, but the explanations that are offered must either hold up against every proposed example, be modified so that they do or be abandoned.

So here it is, shoot it down!

 Stability Considerations for Single Line Kites, a work in progress.   May '04

What is 'stability'?

Stability for a single line kite is when it maintains it's angle in the sky in a vertical plane directly downwind from where the line is attached or held, without excessive lateral movement or any of the other myriad misbehaviors that kites can be subject to. 

The most common form of instability starts as rotational and/or lateral oscillations gradually building into a figure eight pattern of flight that can then progress to a series of loops to one side or the other eventually resulting in a crash.  In the following, this type of instability is called "volatile instability". 

The other main type of kite instability, when a kite, often gradually, leans off to one side until, in the limit, it is lying on it's side on the ground at one edge of the wind, is called Edging, and is not really just one sort of instability, but many, with different characteristics and causes.

But before discussing why kites sometimes don't fly the first question is why sometimes they do.

How does a kite "know" where up is?  Usually gravity has it's way, most things try to get as close to the earth as they can.  How then are kites able to be so contrary, able to do exactly the opposite- that is to get as far away from the earth as their lines and aerodynamic efficiency will let them.?

The answer is very simple, and is about the only certainty in single line kite flying: The lift forces operating on a kite when it is flying must be above where it's weight is acting to hold it down.  These two points and the distance between them are an arrow that points a kite towards the sky. 

Some other relationships appear to be generally true but aren't yet proven, others apply only in narrow circumstances and there are many unknowns but this is known for sure:

"The point where the net lift forces act (called the centre of pressure, cp) must be above where the net weight force acts (called the centre of gravity, cg) or else a kite cannot fly."

This is the First Law of Single Line Kites.

Volatile Instability.

For a perfect kite in steady flight in entirely smooth wind, the kite's cg and cp will always lie in the same vertical plane.  That is, the kite's centre line will seem to point straight up when viewed from upwind. 

In the real world of turbulent flow, even a perfect kite will be continually tilted and shifted one way and the other.

Instability results when a kite under or over reacts while correcting from such displacements.

For stability considerations, the disturbances that are of greatest concern are angular displacements in a plane at right angles to the flying line.  Diagram   That angular displacements matter most is clear from considering that displacements and corrections that don't disturb a kite's vertical orientation are very unlikely to result in any problem. At worst they might cause a kite to momentarily fly at a higher or lower angle or a few degrees out of alignment with the true wind direction, but lift, drag, line tension and line angle (laterally) will soon act in concert to bring the kite back to it's equilibrium position- and providing the kite's centre line remains in a vertical plane while this occurs, all will be well.

Where then is a kite's pivot centre, pc, as it corrects back into the vertical plane from any angular displacement that occurs?

This is an important question because the answer determines the amount of leverage that a kite's weight will have as it drives this correction and the lateral line, displacement that will occur before this correction completes. diagram

This concept of a pivot centre, pc, doesn't only apply when a kite stays in one place and pivots around this centre by a few degrees either way.  A kite can be moving and rotating at the same time and this combined motion can be resolved at any instant into movement in some straight line direction and rotation about a point on the kite's centre line. When a kite is moving and rotating, the pc will be at the point at which a line through the centre of the curve that the kite is describing at any instant intersects the kite's centre line at 90degrees. diagram

To simplify discussion of the pc, it's sensible to consider only those forces that operate in the plane of the kite's lifting surface(s) as having influence.  Although not strictly true, this is substantially correct- and the extent of any errors that do derive from this assumption can be determined by checking predictions against real kites.

A further simplification that might not provide satisfactory predictions for some kite styles (particularly those that fly at low angles of attack and low line angle- diagram-) but is likely to be satisfactory for most, is to assume that the component of line tension in the plane of the kite's lifting surfaces is trivial- that is, the flying line is near enough at right angles to this plane. 

After making these simplifying assumptions, it can be seen that the forces and their points of application that determine the pc are:  weight x sine A of A acting at the C of G, lift x sine A of A acting at the C of P, drag  x cos A of A acting at the C of D, plus any aerodynamic forces generated by lateral area(s) acting at its centre of pressure.

Except for when the centre of pressure for lateral area is forward of the pc all of these forces times the respective distances of their points of application to the pc will act to restore any displacement from vertical that occurs diagram. If the kite is not actually rotating- that is in the instance just after some external angular displacement has occurred and before the restoring forces have had any effect, the only force resisting these restoring moments will be the kite's rotational moment of inertia, including that of enclosed and entrained air mass. For this special static case the pc can be determined by resolving these forces. diagram

As soon as some angular movement towards restoring the kite to vertical orientation occurs, there will be an additional force resisting correction- and that is the extra drag created by this angular velocity, which for each of it's components, will be proportional to the square of that parts distance from the pc.  For kites of all shapes, even circular discs, these drag forces will themselves move the position of the pc at least a little.

Being sensitive to angular velocity, these forces are also the main damping effect acting to prevent over correction- and the fundamental reason why higher aspect ratio kites tends to be less inclined to volatile instability but more likely to suffer from some form of edging. 

Except for when significant structural deflections occur, the rotational inertia of the kites' skins and structure will not act to reposition the pc as during rotations but inertial resistance from enclosed and entrained air mass may do so, depending on their disposition.

In practice, where will the pc generally be?

Clearly it cannot be below the kite's cg for any sustained period -or else the kite will be in violation of the first law- and try to turn right over.

Because the lateral area's centre of pressure cannot be substantially forward of the cp without causing terminal edging,- diagram,  generally the pc will lie between the kites cp and it's cg, and for any particular kite will lie at some particular point  between them, shifting up or down with the kite's angular rotational speed and in response to frame deflection and/or any other load dependent shape change.

Where this pivot centre lies is fundamental to the almost impossibly complex interrelationships that determine a kite's stability or lack of. 

The First Law does not to say that the greater the distance between the cp and the cg for a given kite, the more stable it will be.  In fact, because of the way that angle corrections interrelate with aerodynamic forces, substantially increasing the distance between a kite's cp and cg to will be likely to increase the tendency to volatile instability unless very considerable aerodynamic damping of lateral oscillations is incorporated in the design (for example by tails, wingtip drag or sufficient and suitably placed lateral surfaces). 

The simplest way to move a kite's cg tail-ward is to just add weight to the tail (or to the kite's trailing edge if tail-less).  As weight is added, initially the kite's tendency to exhibit volatile instability will increase, but if an extreme amount is added (perhaps even requiring multiples of the kite's initial weight) volatile instability will again reduce-but by this stage the kite will likely be staggering under the weight and barely flying.

The forces that act on a kite in steady state flight are the aerodynamic forces of lift and drag, weight, and line tension.  Weight remains constant with increasing wind velocity.  Lift and drag increase with the square of the wind velocity however, and these are respectively the source of destabilising forces and the forces available to damp out any disruptive oscillations caused by interactions between the lift force and the kite's weight. 

Line tension, the vector sum of all the other forces when a kite is in steady state flight can also have a role in both stabilising and destabilising a kite, but only when the kite is flying off centre- that is when the line does not lie in the plane of the other forces.

When a kite moves to get it's cg back into the same vertical plane as it's cp after something has caused it to get out of position (turbulence, a wind shift or whatever), there will be an increase in the apparent wind velocity over parts of the kite's surfaces relative to others.  Even small differences in air velocity over different parts of the kite as a correction occurs will cause much larger differences in aerodynamic forces- which are proportional to velocity squared.  The interactions between these aerodynamic forces and a kite's weight (and it's inertia) can cause lateral oscillations to develop.  Flags flap for the same reason- because their weight interacts with aerodynamic forces- evidence for this being that lighter flags flap less and presumably a weightless flag would not flap at all except for moving to stay in line with any changes in wind direction.  In the case of kites, these lateral oscillations can build to become violent figure eight's, and eventually loops, causing the kite to crash in this familiar way.

What happens is that as a kite's weight pulls it back into the vertical plane after some disturbance, the correction 'overshoots', setting the initial conditions for a further correction and so on at ever increasing amplitude unless adequately damped by drag forces  Drag from tails and wingtips will always act to damp such oscillations, and lateral area (that is area in the vertical plane) will generally also do so. Explanation of disposition of lat area- has to be disposed around pivot centre not cg, not cp that is disposed towards the rear rather than balanced relatively equally on either side of the cp could in some cases contribute to the destructive ebuild up of lateral oscillations rather than assist in damping them- by acting as .  - need to come up with an actual example of this to prove it for myself.

An example of an effect that can drive the build-up these oscillations is when a kite's lifting surfaces deviate from a plane at 90degrees to a vertical plane through the kite's line during correction from an angular displacement, -which, borrowing another term from aeroplanes, can be called "banking".

A clear way to describe this effect is to consider one such mechanism: Bridle Line Stretch.

When a flat rigid kite with bridling in the lateral plane diagram is square to the wind (that is, stalled) it's clear that if the bridle(s) on the left side are longer than the bridle(s) on the right side, the kite will tend to move to the right.  When a kite flying at a normal angle of attack, suffers some angular displacement (from turbulence or whatever) and starts to turn or rotate to correct this, the side (wing) of the kite that's flying faster will generate more lift than the side that's flying slower.  Therefore the faster side bridle will be taking more of the total line load and must , all materials being elastic, stretch to some extent.  If significant, this stretch will cause the angle of the kite to the wind in the lateral plane to displace from 90degrees enough, (that is the kite will bank enough) to make it turn even faster as it corrects.  Unless suitably damped, the kite's weight acting with the leverage of the distance between it's cp and cg to correct the original angular displacement will then cause the correction to overshoot, often starting the escalating oscillations of volatile instability 

This mechanism is a type of positive feedback akin to when a microphone picks up noise from an adjacent speaker and sends it back through the amplifier in an ever-escalating loop.

Many kites, particularly small-framed kites have line attachments (bridles, keels etc) only along their centre line, so there are only aerodynamic restraints to limit their banking angle during turns.  Generally such kites will therefore be built with some dihedral diagram to include tip fins, projecting line attachment point as dihedral equivalents.   To generate such aerodynamic limits to banking angle- but any means of moving the hinge point of the line attachment out from the kite will have similar effect.  A corollary to this is that kites that do have bridling or other line attachment in the lateral plane to prevent banking (such as sleds) can employ anhedral to provide lateral area but kites which are free to hinge in the lateral plane must use dihedral, some equivalent or at least be flat (because the surface that a kite flies on is that of a sphere defined by the line length, flat kites do in fact have a minimal amount of dihedral when viewed from this curved reference surface) or they will bank uncontrollably

While damping forces (tails, drogues, drag generally) are the primary means used to prevent these movements building destructively, inertial forces, by slowing the rate at which such movements can accelerate, also play a generally positive role in preventing runaway volatile instability- providing they're not so high as to slow the rate of recovery so much that the kite runs out of sky before getting itself pointed upwards again.  Inertia is a double edged sword with respect to kite stability though- not only does it resist sudden movement and by doing so assists in preventing aerodynamic forces that are proportional to velocity squared from getting out of control but once any movement is established, (rotational, linear or some combination) it acts to maintain this movement.

So, there is a sort of fight going on between aerodynamic forces (generally lift) trying to cause destructive lateral oscillations to build, and other aerodynamic forces that are acting to damp these oscillations.  Because all these forces increase with the square of wind velocity, they usually stay fairly much in constant ratio (subject of course to angle of attack changes and shape distortions that can affect this proportionality). The ratio of damping to lift forces can be increased either by increasing drag (and the greatest effect will derive from applying additional drag as far from the cp as is practicable) or by decreasing lift forces.  This latter often overlooked.

The problem for stability is that the weight force- which is the only force available to keep the kite pointing upwards- does not increase with the square of wind velocity but is constant.  The underlying relationship defining volatile instability is therefore not independent of wind speed.  Aerodynamic forces become increasingly unruly as wind speed increases but the weight force that must keep the kite pointing upwards stays constant so sooner or later loses the fight and is overwhelmed.

Second 'Law' of Single Line Kites:

"As wind speed increases, unless structural failure or some other type of instability intervenes first, all kites eventually become Volatile Unstable."

For a Kite to fly well, holding station reliably without using more than it's allotted piece of sky, it must react quickly to correct any minor wind induced angular displacement, and do so with the minimum of sideways movement.  To be able to do this, the kite's weight should have as much leverage as possible to apply to correcting the offending angular displacement and must not be overdamped when doing so.  Nor may the kite's rotational moment of inertia be so great as to unnecessarily slow the rate of correction.  These being exactly the factors that also promote volatile instability, kites that fly well will therefore be just on the verge of volatile instability.

Designing a kite to fly well across the range of wind speeds from light to strong is therefore about holding volatile instability just at bay while simultaneously not allowing the kite to become prey to any other form of instability. 

If kites didn't yet exist, this would seem to be a hopeless task.  Fortunately, they do exist, there are plenty of examples of successful solutions to this apparently impossible balancing act there in the sky for us to see- all designed, it must be said, without the benefit of any comprehensive theory.  As for many complex things, first we make them work, then we try to figure out why!

Other types of Single Line Kite instability:

Volatile instability is the "traditional" and most common form of kite instability, in fact so pervasive that often the term 'unstable' is taken automatically to mean 'volatile unstable'

However, there are many other ways that kites can behave badly, some that are relatively simple to understand (and usually to cure) and others, grouped under the heading "Edging" that can be very difficult- far more so than volatile instability for which there is just one known cause (the kite as a pendulum interacting with aerodynamic forces to build up destructive oscillations) and known cures as tabled later- albeit that the required cures may not fall within acceptable aesthetic or even physically practicable limits for some designs or sizes of kites.

Firstly in the "easy" group are Luffing and Stalling, two fundamental flight killers that can occur even when a kite is not laterally displaced with respect to the wind:

Stalling.  A term borrowed from the world of aeroplanes, stalling occurs whenever the angle at which the resultant of lift and drag forces acting on a kite, when measured relative to the wind direction, is less than the kite's line angle similarly measured.  Basically, all this pedantic wording is saying that if there's no net upward force on a kite it will sink.  Conventionally, stalling is usually associated with high angle of attack, but kites can also be regarded as stalled even if they are lying at a low angle of attack but still can't generate enough lift to offset their weight, the lines weight and any vertical component of line tension- because there is insufficient wind.  The more wind there is, the less likely that a kite rigged in any particular way will stall.  Also, down to some minimum, the lower the angle of attack that a kite is rigged to fly at- by length of bridles, placement of keels, weight balance or some combination of these, the less likely it will be to stall in any given wind speed.  This minimum angle, which varies depending on many weight and aerodynamic factors, will define the least wind speed in which a kite is able to sustain flight- often called the threshold flying speed, or just the threshold.

Luffing.  A term borrowed from sailing; luffing refers to sails flapping when they are past head-to wind.  For kites also, luffing occurs when the angle of attack becomes zero or negative.  Because kite lines have no ability to resist compressive loads, when a kite luffs, it will often then dive right to the ground, fluttering.  This can be a serious and dangerous event, especially if the kite then bounces. recovers, and accelerates back into the air under full power- often just to repeat the same cycle again and again. 

A kite can luff if there is a sudden wind downdraft striking the kite on its upper surface, but most kites will automatically recover from this type of luff when the downdraft passes- as pass they must because the earth's surface is a fence that ensures the wind will on average flow parallel to it.

Kites can also luff, or have a greater tendency to luff because of various design, construction, or rigging features.

The most common reason for this type of luff is when a kite is rigged (by bridling, positioning of it's keels, weight balance or some combination of these things) such that it's angle of attack when flying is so low that a minor wind disturbance or overflying situation can trigger a luff. 

Apart from these rigging factors, a kite's shape when regarded as an airfoil also has a strong effect on how likely a kite will be to luff at any given rigging angle- and how quickly it will recover from a luff.  Reflexive airfoil sections- that is, forms that are significantly convex from below, are luff resistant.  Soft kites are often built with reflexive rib profiles and framed kites often have bent up noses for this reason.

Other "easy' group forms of kite misbehaviour are; Surging, Asymmetry and Line length effects.

Surging.  When a kite is stall prone, it may hang stalled at a low flying angle until a gust or a tug starts it flying- and once started it will then surge up to a high angle of flight.  The wind speed as the kite experiences it during this surge will be the vector sum of the actual wind speed plus the kite's own flying speed, (called the apparent wind speed) but when it gets to the apex, the apparent wind speed will drop back to the actual wind speed, and if this is less than the kite's threshold wind speed it will stall and drift back down again.  Depending on the kite's design and rigging angle, it is not unusual then for it to re-engage the wind and surge again- and again.  The cure is obvious, fly in stronger wind or decrease the kite's angle of attack so that it has a lower threshold speed.  But unfortunately, maybe it wont be this simple:  The reason that the kite will have been rigged to such a high (and stall prone) angle of attack in the first place is likely to be that the kite is volatile unstable at lower rigged angles of attack.  The reason for this is that rigging a kite to fly at higher angles of attack moves its cp closer to it's cg.  The cp, centre of pressure of a kite is easily determined; it is the point at which a continuation of the flying line attached to the kite's bridles or keel(s) would intersect with the kite's lifting surface(s). Clearly, by for example shortening a kite's rear bridles, increasing the kite's angle of attack will move this point, the cp, towards the kite's trailing edge. Diagram.  As the kite's cg (centre of gravity) position doesn't change significantly (for flat kites anyway) with angle of attack, the effect will be to shorten the kite's pendulum length, thereby decreasing its' tendency to volatile instability.  Therefore, reducing the kite's angle of attack will reduce surging tendencies but will exacerbate volatile instability, maybe to a destructive extent.  See under Problems and Solutions for alternative cures.

Asymmetry.

Small differences in dimensions or construction between one side of a kite and the other can cause a kite to progressively lean more and more to one side as wind speed increases.  Use of fabric that doesn't have it's warp and weft exactly square to each other, and anything else that causes one side to stretch differently can have the same effect as will frames that are stiffer on one side than the other.  Generally, a minor asymmetry will amplify any existing tendency to instability rather than in itself cause particular behaviour.

For a kite that's basically volatile unstable, it will cause the volatility to manifest earlier and more aggressively.  For kites that tend to edge, asymmetries will not only determine which side the edging will be towards, but will also cause it to initiate at a lower wind speed and progress more rapidly.

Obviously, the effect of any asymmetry will relate to kite size- great accuracy of construction is absolutely crucial to good flying for small kites, but even a discrepancy of 100mm or more may well not have any noticeable effect on a kite of 50sq.m.

For most kite styles there are known adjustments that can be made after manufacture- usually even in the field- to correct any asymmetrical flying.  For bowed fighter kites of the Indian or Nagasaki Hata etc type, adding tassles (drag) to one wing tip is the usual, though an adjusting string that can apply a small pucker to either wing tip works at least as well.  For delta's, a similar adjusting cord but applying the pucker to the main sail's trailing edge adjacent to the spine on one side or the other is effective.  For parafoils, it's usual to shorten the second bridle from the front on the side opposite that to which the kite tends toward.  Except for cellular kites, using bridle adjustments to twist a kite one way or the other is rarely effective- because it's often a 50/50 call whether decreasing the angle of attack of one wing will increase it's lift or decrease it relative to the other side, and in fact the effect might be opposite at different wind speeds.  Adjustments usually work by decreasing the lift (usually by reducing the area) of whichever side is too powerful, but adding drag to that side can also be effective.

Weight imbalances are different to other asymmetries in that they have greatest effect in light wind, decreasing effect as wind gets stronger.  As a cure for any asymmetry that has effect through aerodynamic forces, applying weight to hold down the dominating side can only be effective at one particular wind speed.  Aerodynamic forces increase as the square of the velocity, so at higher wind speeds the effect of such lateral weight imbalance will gradually fade as the aerodynamic forces assert their dominance.

Kites are sometimes made deliberately and grossly asymmetric for visual effect.  Designing such kites to fly well over a range of wind speeds should be a practical impossibility because, although they can be laterally balanced weight wise, as wind speed increases, lift and drag forces will not increase at the same rate for wings of significantly different shape.  Such kites can therefore be aerodynamically balanced only at specific wind speeds.  Fortunately, kitemakers generally don't know this so they make wildly asymmetric kites that fly very well in spite of this irrefutable theory.

Line length effects. 

A Kite's stability is affected by how long a line it's flying on for the simple reason that for the same lateral displacement of the kite, the sideways component of line pull trying to pull the kite back to the centre of the wind will be greater if the line length is shorter.

Clearly because the distance that a kite will move sideways before it recovers is proportional to its size (as well as to design, rigging and wind factors), it's the ratio of line length to kite size rather than line length in an absolute sense that's significant.

When a kite moves out of alignment with the wind direction (or when the wind direction changes for the same effect), some part of the pull on the kite's flying line will then act to bring the kite back into alignment.

If the sideways movement was as a result of a wind shift, this lateral component of line tension will then pull the kite will be pulled into alignment with the new wind direction- and all will be well.

If the sideways movement was as a result of incipient volatile instability, this pull component is very likely to provide positive reinforcement of the volatile instability, and can, if the line is very short- say a few multiples of the kite's principle dimension excluding any tail- be sufficient extra provocation to cause the kite to become unmanageable.  This effect is well known to kitefliers, and is especially noticeable when pulling kites in.

If the sideways movement was a result of some form of edging behaviour, this pull component will not make much or any difference, except that the kite will get to it's edge limit much sooner- not having so far to travel.  For a kite that's inclined to edge, anchoring a loose main line between two points at right angles to the wind, then attaching the kite on a short line to the centre of this line will not stop the edging, but provided it doesn't have a really extreme case, will at least restrict the kite to a smaller patch of sky while still allowing it fly at reasonable height.

How a kite behaves when flown on a short line can therefore be a useful indicator of whether some particular instability is of the volatile or edging type. 

There is another unrelated stability effect of line length:  Wind is generally (over time, always) lighter and more turbulent close to the ground. Therefore, in places where there are a lot of upwind obstructions (most inland places), extra turbulence close to the ground can be avoided by flying higher- provided that the kite is able to cope with the greater wind speed at altitude.  A special effect of flying very close to the ground is that tails and other drag devices trailing a kite being lower, may experience substantially less wind than the kite itself is subject to.  The drag that drogues and tails provide is usually closely matched to a kite's minimum requirement- otherwise the kite will not fly at as high an angle as it is able to, so it is not uncommon for kites flown close to the ground to be unstable because of this effect as the same time as being subject to short line instability from above.

And now for the hard basket:

Edging.

As already described above, sometimes kites will slowly lean over and fly off to one side or the other as wind speed increases, even to the extent that they eventually lie on their side on the ground at one edge of the wind envelope.

Some specific asymmetries might be a cause of Edging, but generally, asymmetry in construction, flexibility or bridling is not a fundamental cause.  When present, asymmetry tends to exacerbate existing tendencies.  If a kite tends to volatile instability, any asymmetry will bring it on earlier, if it tends towards edging then asymmetry will cause this to occur at lower wind speed and more severely.  Asymmetry may cause a kite to lean towards one side or the other, but this is not in itself edging

It's true that perfect symmetry can delay the onset of edging, but a useful analogy for this is balancing a triangle on it's point:  Even when perfectly made and balanced, sooner or later something will cause such an unstable structure to tip one way or the other, and it will then fall until one edge is lying on the supporting surface. 

Edging is like this.  Even if generally flying perfectly straight, sooner or later something will tip any kite- whether it be turbulence, a wind shift, or some asymmetry in construction or materials revealed by increasing wind speed.  If and how it recovers from such an angular displacement is the key to kite stability.  The goal when designing kites therefore is that when some angular displacement occurs, they should settle back quickly to their original orientation, rather than either develop an escalating lateral oscillation (Volatile instability) or fall right off to one side in some type of Edging.

A characteristic of edging is that it can occur to either side: as wind speed increases.  A kite that's perfectly symmetrical in every respect will edge with equal enthusiasm either way.

As wind speed increases, either volatile instability or some type of edging will manifest and there is a point of view that that, especially for larger kites, edging is far less dangerous than volatile instability -or luffing or having something break for that matter.

However, edging often intrudes well before it's welcome and can be difficult to identify (as to type) and desperately difficult to cure.

There are many different causes for this type of kite misbehaviour:

Edging caused by Scoop effects

This type is first out of the blocks, because it's by far the easiest edging cause-and-effect to describe and understand.

An example: an open leading edge trapezoid soft kite with leading edge wider than trailing edge will be a prime candidate for edging behaviour.  Diagram   When such a kite gets even fractionally out of alignment with the wind direction, drag forces on the wingtip that lags will be greater than drag forces acting on the leading tip.  This will cause the kite to lean more to that side until countervailing forces, such as the kite's weight acting with the leverage of the distance between it's cp and cg, and aerodynamic forces on keels limit this lean.  Leaning, and with the moments around the kites cp in balance rather than working to make the kite either straighten up or lean further, the kite will then fly sideways across the wind until it is either lying on the ground (if the equilibrium between the various moments sets a lean angle approaching 90degrees or more) or still flying but well off centre if the equilibrium angle is substantially less than 90 degrees. Classic edging!

Nor is it necessary for such a kite to be trapezoid in shape.   A conventional rectangular parafoil will behave the same way if it's keels have loose leading edges.  For such kites, it's not even necessary to get out of alignment with the wind, because the keels are incapable of alignment anyway- they will either flop to the right or to the left, pulling the kite off into an edging situation in the same way as described in the first example.

Nor is it only soft kites that are subject to this type of edging; any kite (such as a Delta) with a keel in its forward half that has a loose leading edge will be susceptible. 

And, an open keel type Delta would also be susceptible if the open keel's leading edge is substantially forward  of the kite's cp

Edging Caused by Drag Forward of a Kite's CP.

In fact a more general case of edging is kites that have substantial drag forward of their cp.  The open keel delta that was the final example from the previous category is in fact also an example of this.  The shape generating drag doesn't need to be open at it's front. 

A common technique to reduce volatile instability is to build or rig a kite with some amount of 'nose up'.  Prime examples of this for framed kites are Indian Fighters and Nagasaki Hata's diagrams . Bowed fighter kites of this general type are designed to be volatile unstable at low apparent wind speeds but to edge in stronger winds.  This allows the flier to spin the kite (by releasing line tension until it is volatile unstable) until it's pointing in the desired direction, then to pull in line to increase the apparent wind speed, causing edging. 

Bowed fighters are caused to edge by frame flexibility that allows the kite's skin forward of the bow to form a 'V' and increase it's angle of attack when the apparent wind speed increases.  Because this triangle is forward of the kite's cp it can, if suitably bent up (that is when the apparent wind speed is strong enough), catch wind from one side or the other to such an extent that the kite's weight and other more rearward lateral aerodynamic forces are insufficient to affect a recovery.  In this circumstance, such a kite will edge.  The special challenge when designing bowed fighters is to make them behave linearly rather than to fly a curve (trending either up or down) when flying in their edging mode.

It is also a common technique for reducing volatile instability, to rig soft kites with 'nose up'.  Because it's not a total answer when the tendency to volatility is severe, sometimes this is taken to extreme- to an extent that increases line pull a lot, causes the kite to fly at a villainously low angle and promotes edging as well. Unlike for fighter kites, edging for this type of kite is highly undesirable, not least because it will then stray into neighbour's sky space.  Drag at the front of a kite causes edging because, as for the examples above, such a kite will be like a triangle balanced on it's point when exactly straight on, but stable when it is somewhat side on- at the angle for which it's weight moment and the drag moments of its afterbody exactly balance the moment of the kite's frontal area drag that is trying to cause it to lean more.  Diagrams.

Edging Caused by Non-Chordwise Flow.

A plausible theory as to why some styles of keel-less kites edge, is that when they are angularly displaced, wind flow, instead of bending to flow parallel to the kite's centre line, just flows diagonally across the kite.  This can only occur in the absence of substantial dihedral, anhedral and other substantial lateral area acting in a keel like way to direct the wind flow and straighten up the kite.  diagram

Such kites effectively becoming asymmetrical.  Reconcile earlier passage saying that asymmetry is not generally a cause of edging.  For certain (many) shapes there will then be a tendency for the resulting re-balancing of aerodynamic and weight forces to exacerbate the initial lean rather than correct it.  A cure for this type of edging is, of course, to add keels, dihedral, anhedral or other flow directing lateral surfaces- but aesthetic considerations, especially for theme kites such as animals and sea creatures often restrict this choice.  If Dihedral is to be used to act as a 'keel', there has to be a lot of it to make a difference.  A rough rule of thumb for kites of aspect ratio 1.0 would be that the amount of 'bow' has to be about 1/5th of the kites span (diagram).  This is an amount of curvature that is almost not attainable for soft kites because unless exceptionally chubby, lateral components of bridle loads will cause compressive collapse in their mid-sections.  Anhedral is another possibility, as for sleds for example, but again, have to provide substantial lateral area to work.  Tails are another possibility but have to have substantial weight relative to the weight of the rest of the kite if they are to prevent edging for this type of kite.  Light weight tails, such as drogues on 'Y' bridles are not successful.  The reason for this is that once a kite starts moving sideways, unless the kite's tail moves sideways faster than the body of the kite is moving, the kite will not straighten up. A tail can only 'get in behind' a kite that's angling sideways across the wind and make the kite's nose point upwards again if it has enough weight relative to its drag. 

Edging caused by wingtip drag,

A technique often used to reduce volatile instability for kites that are wide relative to their length is to contrive to have extra drag as far out(laterally) from the kite's cp as possible- typically at the wingtips.  For framed kites (though this would also work just as well for soft kites) fabric scoops or pockets are sometimes used. Diagram, but more commonly (Genki's high aspect ratio Deltas etc), the wing tips are relatively unsupported by structure so that they contribute drag but little lift.

For soft kites, more usually the wingtips are just made exceptionally fat or, for open leading edge soft kites, the depth of the opening is progressively increased until volatile instability is under control.  For lower aspect ratio kites, (like many parafoils) the depth is usually increased across the entire leading edge, but for higher aspect ratio kites it is preferable to increase the depth only at the tips so that the overall drag increase does not cause unnecessary reduction in the kite's flying angle.

Wing tip drag provides a damping effect at small cost in total drag increase because of the maximum leverage the tips have over rotational effects.   If a kite starts to rotate around it's cp, so that one tip is experiencing 10% more wind and the other 10% less wind than the average flow over the kite, the drag on the faster tip will increase by 21% while that on the slower tip will reduce by 19%.  Especially if the kite is wide relative to it's length, any inclination for such rotations to build into volatile instability is likely to be promptly damped.  

This is such a powerful effect that it seems surprising it isn't a corner stone defence against volatile instability at least equal to the use of tails. 

Unfortunately, however, it 's only effective for kites that are wider than they are long and tends to cause edging as wind speed increases, while tails do not.

Wingtip drag can cause edging when increasing wind speed causes drag at the tips to increase without commensurate increases in lift, resulting in overdamping of rotational displacements and corrections.  Drag can and usually will (about the only exception being wings increasing their lift by 'cambering up', as fabric stretches) increase faster than lift in stronger winds as wind speed increases because of shape distortions caused by bending of frames, skin stretch and proportional loss of inflation pressure (soft kites). All materials are elastic to some extent, so these deformations are inevitable, especially in the upper windspeed ranges for which edging becomes a problem.

However, for true edging rather than just a slower correction from any angular displacement, the total moment around the kite's cp of all the aerodynamic forces when the kite is in the 'leaned over' mode, has to be such as to increase rather than decrease the lean or else correction will eventually still occur. diagram

Unfortunately, fulfilling this more general condition seems in practice to be almost unavoidable when wingtip drag increases faster than general lift forces.

For soft kites, the deformation that causes this form of edging is relative loss of internal inflation pressure as wind speed increases.  Although it generally seems that soft kites inflate better and better as wind speed increases, this is not so, or at least not always so.  For ram air inflated kites, internal pressure can never be greater than stagnation pressure, except momentarily for valved kites that can retain higher pressure for a time when the apparent wind speed drops.  In practice, because of leakage, internal pressure will always be less than stagnation pressure.  For kites where most losses are through porous fabric and very small holes along seams, leakage will increase disproportional as pressure increases, and especially so if the inflation area is small relative to the total area,  true?  For such kites the size of the un-inflated 'bubble' along any parts of the leading edge that are not open will increase with increasing windspeed is proof that this is in fact happening.

Edging caused by rotational inertia effects.

When a kite is tipped a bit by turbulence or a wind shift, the time it takes to restore it's orientation determines how far to the edge of the wind window it will fly before this correction is completed.

The further away from it's cp that a kite's mass is disposed the greater it's rotational inertia will be relative to it's actual weight.  This is the flywheel effect; two wheels can be the same mass but if one has more of it's mass disposed in a rim at a greater diameter, it's rotational inertia will be higher, and it will require the application of a greater force to get it to the same speed of rotation in the same time.

Most affected by this type of edging are high aspect ratio kites- kites that are wide relative to their length. 

Although kites that are long relative to their width also have substantial mass positioned far from their cp, by the same fact, their weight also has greater leverage to restore the kite to vertical from any angular displacement- they're a longer pendulum.

For wide short kites (high aspect ratio) the distance between their cp and cg will be small- they are short pendulums.

For soft kites, there is an added effect; although the air trapped in the kite's internal spaces has no weight- it's neutrally buoyant- it does have mass.  This air mass, or such of it that is disposed away from the kite's cp (and in this case, it can be to the rear equally as effectively as to either side) will add to the kite's rotational inertia and slow the time it will take the kite to recover from any angular displacement.  For a small soft kite, the enclosed air mass will be insignificant relative to the kite's weight, but because air volume ( and hence, mass, at 1.23kgms /cu.m) scales with the cube of dimension, while soft kite weight generally scales with the square of dimension, for very large soft kites the mass of enclosed air, can be many times more than the kite's weight. -re-word this to correct units

The hypothesis here is that if a kite's rotational inertia is large enough relative to it's weight acting as a pendulum of length equal to the distance between it's cp and cg, it may take so long to correct from an angular displacement that as to fly right to the edge of the window before adequate correction occurs- a type of edging.

Edging caused by having long bridles in the lateral plane,

Edging caused by inflexible tails

Edging caused by stretch of bridles on the faster flying side; so called "two line edging"

For all types of Edging, a kite's weight and where it is centred is crucial.  Making a kite proportionally heavier and especially adding weight to the rear of the kite, will counteract edging, as will rigging the kite to fly at a lower angle of attack (effectively moving the cp further from the cg to increase the leverage that the kite's weight can exert to correct any angular displacement).

But, the greatest influence is from aspect ratio- how wide a kite is relative to it's length.  High aspect ratio kites tend to be more susceptible to Edging because more of their mass (including the mass of enclosed air for soft kites) is further out from the centre of rotation as is more of the drag force that acts to damp angular movement, while the leverage available to the kite's weight for overcoming inertia and damping is less and the aerodynamic correcting forces from the rudder effect of a longer body are also less.

Do kites scale?

That is, if a kite design flies when made at a given size, will it also fly when made larger or smaller?

From above, at any given wind velocity, the aerodynamic forces on a kite are proportional only to area and therefore have the units of length squared.

The force that must prevail over these aerodynamic forces and keep a kite pointed upwards if it is to stay flying is it's weight and only it's weight, notwithstanding that contriving a good balance between lift forces and damping forces will make the job that weight force has to do easier.

Therefore, at a given wind velocity, it's a kite's weight/area ratio that is the underlying determinant of stability.

Of course, specific details of shape, structure, angle of attack and flexibility determine whether any given design of kite will fly, but the basis for stability is the weight/area ratio, for the reasons just outlined.

Third 'Law' of Single Line Kite Stability:

"Kites will generally fly similarly in larger and smaller sizes provided that their weight/area ratio remains constant." 

This is not just an observation of what actually happens, it's supported by a theory also, as above. 

There are two obvious exceptions to the scalability of kites with equal weight/area ratios:

One is for kites so small that the thickness of the layer of air molecules adhering to their surfaces significantly change the kite's shape with respect to airflow- but it's hard to imagine that this will be a noticeable effect for any kite with lifting area of more than say 25 sq mm- that is a kite of 5mm x 5mm.

The other is that aerodynamic forces are not always proportional to the velocity of the wind squared.  When flow changes from laminar to turbulent there can be sudden and significant changes.  The boundary between laminar and turbulent, called transitional flow is defined by Reynolds Number, which is proportional, for our purposes, to the wind velocity times the length of the flow path over the kite.  Reynolds number is basically a measure of how likely it is that flow will become turbulent.  Even at the same velocity, the greater distance that air has to flow over a surface, the more likely it is that the flow will 'trip' from laminar to turbulent flow. In practice the critical Reynolds number value can vary enormously but at the often-used value of 100,0000, for a kite, irrespective of it's size, flying at 0 5m/sec, the point at which flow will transition from laminar to turbulent will be roughly 0.3m back from the leading edge. At 10m/sec this distance will be just 0.15m.  This indicates that only for very small kites flying in light winds is any significant part of the flow over a kite going to be other than turbulent.  Further, in practice, kites become more unstable with increasing wind speed rather than the other way around.  Although kites obviously fly in wind speeds below 5m/sec, lower wind speeds than this have been excluded from scaling and stability considerations because any kite that is stable at 5m/sec will generally fly at all lower wind speeds down to it's threshold (stall) speed also.

Two exceptions to this are kites (fighters for example) with frames that need to flex a little before they become stable and ram air inflated kites that may need a minimum wind speed before they will take their correct shape, but neither of these exceptions are to do with transitional flow.  The reason why kites tend to be stable at lower wind speeds is very likely to be because at such lower velocities, aerodynamic forces aren't sufficiently energetic to get any oscillations started in the pendulum defined by the kites weight and the cp to cg distance.  Generally therefore, Reynolds number considerations don't seem likely to disturb the general scalability of kites except for small kites flying in light winds.

Scaling of Framed Kites

As framed kites are made bigger, they tend to get heavier in proportion to their area because their structures are generally subject to bending loads.  This is the same underlying relationship that places a limit on the size of birds (the ones that fly, not ostriches and the like) and even on aeroplanes.  Use of higher strength materials such as carbon fibre tube can enable larger framed kites to be made with the same weight/area as smaller versions in lower tech materials but by 10sq.m or so most framed kites will be proportionally heavier.  Therefore most framed kites will fly significantly differently when made in larger sizes.  The most noticeable effect will be that they'll require more wind to fly in.  With respect to stability, generally larger framed kites, being proportionally heavier, will have more weight force available to correct any angular displacement that might occur proportional to wind generated aerodynamic forces at a given wind speed.  This will increase any tendency to volatile instability, requiring more damping from tail, lateral area or wing tip drag for the maintenance of stable flight but this effect is often obscured because larger kites are usually more flexible than smaller versions of the same design.  Flexibility generally decreases lift forces and increases drag forces, thereby reducing volatile instability and causing the kite to fly at a lower angle for a given wind speed- but this is not so much a stability effect.  The reason that larger kites tend to be more flexible is because makers rarely manage to maintain the same proportional frame stiffness as they scale up, generally because they are trying to minimise frame weight so that the kite's wind threshold will not be too much higher than that of smaller versions of the same design.

Scaling of Soft Kites.

For soft kites the weight/area ratio does remain almost exactly constant provided that the fabric weight per sq.m isn't changed.  In practice, fabric in the range of 40gms/sq.m to 50gms/sq.m is commonly used for all soft kites.  For the smallest sizes it's far stronger than necessary, but lighter fabric is just not available - or not at bearable prices.  By 50sq.m, kite projected area, 45gm/sq.m fabric is appropriately loaded, but judicious use of reinforcements allows flying up to 60km/hr winds at least- about the safe limit for large kites anyway.  For very large sizes, even up to 1000sq.m, it is still possible to use fabric in the range 45gm/sq.m to 50gm/sq.m by extensive use of the "super ripstop" system of sewing on Spectra cord reinforcements to a 1.5m to 2.0m grid pattern- and using thru cords instead of ribs. There is only one small exception to this.  Seams are proportionally heavier for smaller kites- but even this is maybe offset by heavier bridles and reinforcing on the larger kites.

Therefore by the constant weight/area principle from above, unlike framed kites, soft kites should generally scale.

But, by observation, single line soft kites do not seem to scale.

In very small sizes they seem to be disproportionately volatile unstable and at the other end of the size range, exhibit less and less volatile instability but an increasing tendency to edge

For small ram air inflated (that is, soft) kites, there seem to be three possible other scaling influences:

Firstly it is possible that Reynolds number considerations (from above) are having some effect for kites with chord dimensions of less than 1m say.

Secondly, manufacturing inaccuracies have a much greater effect on small kites than large kites.  It's noticeable that such inaccuracies do have an increasing tendency to cause left or right wing bias as smaller and smaller soft kites of a given design are built, but when these bias's are tuned out by any of the various adjusting techniques available (making the bridles asymmetric for example), the volatile instability remains even after the bias has been neutralised.

Thirdly, fabric stiffness: This is undoubtedly a factor for small soft kites in light winds.  Made of typical 45gm/sq.m coated ripstop nylon fabric, a kite of 8sq.m's will take a clean smooth form in almost any wind strong enough for it to fly at all, but the same design scaled down to 2sq.m will remain distorted and wrinkly even in winds of 5m/sec or more. 

It could be expected that the greater surface roughness would if anything promote turbulent flow at a lower wind speed, perhaps compensating for Reynolds number effects relative to larger kites, so it's hard to see this having any significant scaling effect.

What might have an effect is the noticeably greater overall stiffness of the smaller kite.  Whereas the 8sq.m kite from the example above will bend and flex noticeably as it fly's, even in quite light wind, a 2sq.m version does not, even in stronger wind.  Perhaps the flexing of the larger kite's form in response to applied aerodynamic forces somehow smooths out or even reduces the effects of these forces which are, as explained above, the driver of volatile instability.  This hypothesis is pure conjecture at this stage, but testable in various ways.

For very large soft kites, fabric stiffness, or rather the relative lack of it, has another non scaling effect: For kites of 50sq.m and more, fabric stiffness does in fact seem to still play a critical role in promoting initial inflation and preventing collapses of form while such kites are flying in light to medium winds.  An open leading edge kite of 50sq.m made with soft finish fabric will be more difficult to launch and will  collapse more often than the same design of kite made of stiffer but identical weight fabric.  An open leading edge soft kite of 20sq.m's is noticeably easier to start and clearly less subject to partial or total collapses while flying than a 50 sq.m version of the same design- and even larger open leading edge soft kites (like 200sq.m's and bigger) can become virtually unflyable unless designed (by use of valves or restricted inflation area) so as to retain internal pressure through lulls to a greater extent than is required for smaller ram air inflated kites.  This does not explain their tendency to edge, however.

As discussed in "edging caused by rotational inertia" above, for very large soft kites, the huge mass of air they have to swing may cause them to take so long to correct from an angular displacement that they fly right to the edge of their window before adequate correction occurs.  The reason that the tendency to edging increases and volatile instability decreases as soft kites of a given design are made larger and larger, could therefore be that the mass of air contained within the kite increases disproportionately as it's area increases.  A typical large soft kite with 50 sq.m of lifting surface will weigh about 10kgms and enclose roughly 2kgm mass of air (the density of air is 1.23kg/cu.m).  There is no weight effect of this enclosed air mass, it's neutrally buoyant in the atmosphere, but there are inertial effects in that it requires the application of force to get it moving and to stop it moving.  The same kite design scaled down to 5 sq.m (1/10th the area) will weigh 1kgm and only enclose 20gms of air (1/100th the mass contained by the kite that's 10 times as big by area and weight).  A version of the same kite with 500sq.m of area will weigh 100kgms but enclose 2tonnes of air inside it's internal spaces.

If the cause of edging tendencies as soft kites are made larger is not the disproportionate increase in the rotational inertia of enclosed air then what other explanation can there be?:

One possibility is that very large kites are usually flown relatively low, rather like flying a kite with 1m wingspan on just 2 m's of line.  Analogously, would such a small kite be able to recover from a typical angular displacement before it also was on the ground to one side or the other?  In other words, is the observed behaviour edging or is it just the first lateral movement of what would become volatile instability if there was room.

Another possibility is that the large soft kites that are observed to edge are doing so by one or more of the causes described in the Edging section above and that any connection to size and scaling sis unrelated.

Unanswered questions: -

Why do 4m pilots with 2 extra cell not fly?- aspect ratio.

Why did the 4m pilot, standard pattern but with 180mm cut off TE, edge badly until bridled BACK- July '04

Why did the April '04 model 4m pilot with slightly reflexive profile not fly?

Why did Jurgen Ebinghaus' fish respond so well to such a minor increase in tail thickness?

1984; Double Snake and Kodak kite edging- snake fixed by 2 point bridle.  Could Kodak edging also have been cured by single plane bridle- both problems were something also to do with having laterally inflexible tails?

Tails, drogues and other trailing drag devices.

Tails are self-supporting drag devices.- talk about weight versus drag Tails and drogues- weight versus drag, tails are self-supporting. 

To be defined as a tail, a trailing device must be hinged in at least one plane.  Completely flexible tails, for example those attached by just one cord, apply all their weight at the attachment point laterally rigid tails that are hinged w.r.t angle of attack are part of the kite for cg determination purposes but not for the purposes of determining cp position.

Distance between kite and tail.  From the discussions of rotational inertia and edging, it's clear that the time it takes for a kite to restore itself to vertical orientation from an angular displacement determines how far to the side it will fly before the correction is completed.  The distance between a kite and the main drag elements in any tail it may have also affect this time/lateral displacement.  Say that a kite with a drogue tail gets angularly disturbed by 10 degrees or so and moves sideways by 3metres in the process of recovering.  If the distance between the kite's cp and the drogue is also 3m, the drogue may well lag in matching the kite's sideways displacement by 2 metres resulting in the drogue's angle to the kite being 30degrees or so and it's pull on the kites trailing edge will then act to make the kite's initial angular displacement more severe.  This will cause the kite to travel even further sideways before correcting forces- like it's weight and the lateral component of line tension (which, for a given sideways displacement is greater for shorter lines of course)- can effect a correction, if they are indeed capable of doing so at all before the kite has crashed.

If the distance between the kite and it's drogue is then increased to say 6m, halving the angle, the amplifying effect of the drogue's drag on the kite will also be halved- perhaps allowing the restoring forces of weight and the lateral component of line tension to correct the kite's initial angular displacement before the kite has moved too far out of alignment with the wind direction.

For tails that are flexible, there is no consistent point at which the drag forces act, but the general principle still applies- that when this type of instability occurs, that is for kites that tend to recover from angular displacement too slowly, long tails will work better than short ones, even when they contribute the same drag.

However, there is a limit as to the extent to which the distance between a kite and the drag generated by it's tail will solve some stability problems, and this is best understood by looking at an extreme case:

Snagged tail; A special case of the tail length relationship to stability can be examined by considering what happens when a kite's tail snags on something immoveable.   Provided a kite with a snagged tail does not move more than a (very) few degrees out of alignment with the wind direction, it can remain perfectly stable- because the snagged tail, will restrain any tendency towards angular oscillation.  If however, the kite moves significantly sideways, or if the wind direction shifts ten degrees or so, the snagged tail will start to pull sideways on the trailing edge of the kite, starting a then unstoppable dive.  A kite with a drogue on a VERY long line will behave in exactly this way also - stable with respect to angular disturbances that don't also cause significant lateral displacement but unable to recover if lateral displacement of more than a certain magnitude occurs.

Examples to consider.

Avant Garde box- edging?

Reduction of the vertical distance between cg and cp as angle of attack reduces.

Arcs flying as single line kites- long lateral bridles, high aspect ratio, anhedral

Does the kite rotate about its cp or it's cg?

.

General principles.

"Every individual kite has its own set of physical laws"- Volker Hoberg

"And these laws are not necessarily the same on successive days"-Jurgen Ebinghaus' corollary

Anhedral versus dihedral- a flat plate has dihedral for a finite line length.

Small things make can make big differences- eg the JE Fish.

Accuracy is more critical on smaller kites- obvious but true.

Lateral symmetry is generally the highest priority in practical kitemaking.

It's almost always true that instability (of all types) increases with wind speed. (fighters the exception)

Stability changes as 'rigged' angle of attack changes.

Stability changes as line angle changes.

Techniques.

Lateral area- keels, flares and other vertical surfaces

Wingtip drag devices.

Nose-up attitude- fighters, trilobites etc.

Duct tape- useful for trying fabric dimensional changes.

Pulleys to allow banking for laterally bridled kites.

Definitions:

Cp, C of P:  Centre of Pressure.  The point at which the kite's lift forces are deemed to act.  cp will change with angle of attack, some flow conditions (see Reynolds number above) and with changes of shape (caused by frame or skin flex for eg.)

Cg, C of G.  Centre of gravity. The point at which the kite's weight forces act.

pc.  Pivot centre, the point about which a kite rotates as deviates angularly from the vertical planes or corrects

aa, A of A.  Angle of attack.  Strictly, the angle between the plane of the kite's lifting surfaces and the wind , but for general purposes, the angle of the plane of the kite's lifting surfaces to the horizontal

pp.  pull point.  The point on a kite at which the line pull acts.