Guides Unlimited How Kites Fly

How Kites fly…

I have been a power kiter since the age of 14, and I’ve always been interested in how it is that a kite can fly. So for my research report, I decided to find out.

The Kites, and a brief glossary:

When I talk about kites, I refer specifically to power kites. These are extremely large and powerful kites, resembling scaled down paragliders and to a lesser extent parachutes. They are designed using the same aerodynamic principles as airplanes and as I will show, different design elements affect the flight ofthe kites in various ways.

A typical Power Kite (HQ Crossfire)

Glossary:

Wind Window: The area of the sky in which a kite will fly.

Airfoil: A wing of some description.

Angle of attack: The angle an airfoil is tilted at with respect to the air flowing over it – an example of high angle of attack would be the wings of an airplane

at the moment of takeoff, and an example of low angle of attack would be the wings of the same airplane in level flight.

Profile: What the cross-section of a given airfoil would look like.

The above diagrams show profile shape and angle of attack. The top diagram is of a kite with a low angle of attack.

The middle diagram shows a kite with a different profile shape and a steeper angle of attack.

The bottom diagram shows the same kite as in the top diagram, but this time with a steeper angle of attack.

Theories of lift:

There are essentially two theories of how lift is generated. Both are true, but combining the two is extremely difficult. The first theory is essentially Newton’s second and third laws of motion – namely that change of momentum produces a force, and every action has an equal and opposite re-action. Air is a fluid. Anything that disturbs the flow of a fluid will be subject to forces. If you drag your hand through water, the water molecules you are displacing will push your hand away. In a kiting context the fluid (air) would be moving as well as the kite itself. (1)

(Image: Me. The circles represent gas (air) molecules)

In the illustration above, the slanted surface is moving through a liquid (shown in molecular form) from left to right. The molecules the surface displaces push back against it, resulting in an upwards force as the molecules are deflected downwards. Newton’s laws say that as the direction of the momentum of the molecules of gas is changed, so the direction of the momentum of the object moving through the gas must change. This means that the wing is deflected upwards as the gas molecules are deflected downwards. However, this model is not an accurate version of how it really works. If it was, the maximum lift could be obtained from an almost vertical surface, where the molecules were deflected as sharply downwards as possible. However experiments show us that this is not the case, which brings us on to the second major theory. (1)

Bernoulli said that when an object moves through a liquid or a gas, the velocity of the liquid or gas changes depending on the shape, speed and position of the object. It follows that from this that as speed changes, pressure changes across the surface. (1)

It is by over-simplifying Bernoulli’s theory that many incorrect theories of lift are generated. The “equal transit time” theory states that a molecule passing over the top of an airfoil will reach the back of the airfoil at the same time as one passing over the bottom surface. The molecule the passed over the top must therefore move faster, and so there must be an area of lower pressure on the top of the airfoil – this is said to generate a lift force by “sucking” the airfoil upwards. (1)

The diagram above clearly shows that the air flowing over the top of the airfoil flows further – the assumption is that a molecule flowing over the top will reach the back of the airfoil at the same time as one that flows under the bottom. This is, however, incorrect. In fact, the velocity of a molecule over the  top of the airfoil is considerably higher than that of a molecule passing over the bottom of the airfoil – it will reach the back of the airfoil considerably before a molecule passing over the bottom. This serves to demonstrate that the process is more complex than might be supposed. (1)

So what factors affect the lift of an airfoil?

One major force is drag. If you try to slide your hand quickly sideways through a bucket of water, you’ll feel considerable resistance – you won’t be able to move it freely. This is the force of drag that you can feel. Put simply, drag is the energy contained in the air molecules that isn’t used to lift the airfoil – it resists the airfoil moving through the air, and increases as the speed of the airfoil increases; which leads me to my next point – airspeed. The faster an

airfoil moves through the air, the greater the energy transferred to it by the air molecules and the more lift it will have. Unfortunately when you increase

the lift, you increase the drag too. These things (airspeed, drag and lift) are all linked together, and I will come back to exactly how in a moment. (2,3,5)

Another important factor is something called “aspect ratio”. Mathematically speaking, this is defined as the square of the wingspan of the airfoil, divided by the area. This is effectively a measure of the efficiency of an airfoil – the higher the aspect ratio the longer and thinner the airfoil is, and the more efficient it will be (see “Induced drag” for an explanation of why). Kites are fairly low aspect ratio when compared to airplane wings – this is due in part to problems with the strength of materials and due in part to the problems inherent in making a kite fly very fast – covered in more detail under the section headed “Racekites”. (5,8)

The equations for lift and drag are remarkably similar. I have shown both equations below, along with an explanation of how they both can be used. (5)

Drag:

Cds (Drag) = D*A*0.5*r*V2

Where:

D = Drag coefficient –This is exceptionally hard to calculate, and is usually determined experimentally.

A = Area of airfoil.

r = Air density – a measure of how many molecules there are in a certain volume of air. Proportional to the mass of the air, and also to its temperature.

V = the speed with which the airfoil is moving through the air.

Drag reduces the airspeed of an airfoil and as we shall see, this has a considerable adverse affect on the airfoil’s performance. (3,5)

Lift:

L (Overall lift) = Cl*A*0.5*r* V2

Where:

Cl = coefficient of lift - as this is dependant on the same parameters as the coefficient of drag, the two coefficients are very similar. It has a value between

0 and 1.

A = Area of airfoil

r = air density

V = velocity (2,5)

What?

Well, the lift equation is arrived at by combining both Bernoulli and Newton’s theories of lift. Cl (the lift coefficient) is a value dependant of Newton’s

equations – it is a “gathering together” of a great many complex variables to do with the shape, size, proportions, angle of attack etc. of the wing. The other part of the equation is a simplification of the complex Bernoulli equation – it relates to the air density and pressure at a given moment. (1,2)

Induced drag:

Cdi = (Cl2) / (pi * AR * e)

Where Cl = the lift coefficient

Pi = 3.141 etc.

AR = Aspect Ratio

e = A measure of efficiency. Varies from 0 to 1. This value is a constant for a given airfoil (with a value of 1 signifying maximum efficiency). Theoretically,

the shape with the least induced drag would be a perfect ellipse – perhaps explaining why so many kites look ellipse-shaped in flight. (5)

Overall drag = Cds + Cdi (Drag + Induced drag)

So what do these equations actually mean?

Basically, they determine the properties of a given airfoil. The drag can be reduced by reducing the thickness of the profile (what the cross section of the

airfoil looks like). The other variables could be changed, but it’s not really viable to do so, certainly in the context of power kites. You can’t slow the

speed down because the lift equation says you need it to generate lift. You can’t reduce the area for the same reason, and it isn’t possible to change the air

density. (5,8)

The lift can be increased by increasing the lift constant – but doing so involves increasing the thickness of the profile and so increasing the drag coefficient, slowing the kite down and reducing the lift again. The same is true of the area and speed. Increasing a value to get more speed will inevitably increase the drag too. (2,3,5)

This is where the induced drag comes in. Induced drag is the drag created by air vortices at the wingtips of the airfoil. The size of the induced drag effect

is determined by the equation above. The aim of designers is to reduce the value of the induced drag so as to increase the performance of the airfoil. You can’t decrease the lift coefficient without decreasing the performance of the airfoil, so that’s out. e is a constant, the value of which is dependant on the shape of the airfoil, so that can’t be changed. Pi is another constant. It follows that the way to increase the performance of the wing and reduce induced drag is to increase the aspect ratio. (5)

The higher the multiplier Pi*AR*e, the less induced drag. This explains why airplanes have such long thin wings as oppose to short, fat wings with the same area. However here is a practical limit imposed on how high aspect ratio can be – in the case of airplanes, strength of materials. In the case of kites, the higher the aspect ratio the more difficult the kite is to fly. The airfoil also needs to have sufficient depth to disturb the air enough to create enough lift to fly. (5,8)

An interesting result of the above equations arises from the value of r – air density. Because the gas molecules in air have less energy and move slower in

the cold, the colder it is, the denser the air. The denser the air, the slower the speed of the wing has to be in order to generate the same amount of lift

and drag. It follows that airplanes fly slower in cold weather than in hot weather, and that you can fly a kite in much higher winds in summer than you would in winter. (8)

Bearing all this in mind, let’s look at the equations for my 7.2m2 power kite.

I know that:

• At a given windspeed (10.2m/s) the lift of the kite is equal to my body mass.

• I know my body mass is roughly 75Kg

• I know the effective area of the kite is 6.5m2

• I know the standard air density at ground level is 1.2Kg per m3

This makes the equation:

75Kg = Cl * 6.5 * 0.5 * 1.2 * (10.2) 2

From here it is possible to calculate the missing value – the coefficient of lift. The rearrangement to find it would be:

Cl = 75 / (6.5 * 0.5 * 1.2 * 10.2 * 10.2)

Cl = 75 / 405.8

Cl = 0.18

This shows that a kite is considerably less efficient than an airplane – a Boeing 747, for example, has a lift coefficient of 0.52. (8, 10, 11)

How this has bearing on kites:

There are various different kiting disciplines, which require different things from a kite. For racing in special three-wheeled buggies, speed is the essential

factor, while lift should ideally be reduced to stop the kite overpowering the flier. Other kites are designed for lift, but speed becomes less important in

this case. By changing the variables in the equations above, it is possible to alter the characteristics of a kite to make it perform how you want it to. (8)

Racekites:

These kites are used to go fast in a kite-powered vehicle of some description. The sole purpose of these kites is to move as fast as possible in a straight

line, so matters like ease of use and high lift are not important. This “High speed low lift” effect is achieved by reducing the thickness of the profile – this

lowers the drag by lowering the area of the sail that isn’t actively producing lift. The profile shape is also altered to reduce overhead lift. The aspect ratio

is made as high as possible to lower the induced drag and to increase the speed.  The angle of attack of these kites tends to be fairly small – they rely on Bernoulli rather than Newton’s principle. (1,8)

So why aren’t all kites like that? Why are some kites made to be slower? It comes down to ease of use. If you want a visual representation of why, image this. Pick a spot out in a field somewhere, and stand there. Now extend your arms as far as you can out to the sides, and bring them up so they meet above your head. The area of sky in front of you that you have just drawn out is the area in which the kite will fly – in kiting circles this is called the “Wind Window”. A very fast kite will take off and fly very fast in this area, but it will have so much speed that if you let it fly then when it reaches the edge of the wind window it will simply fly past it because of its own momentum. When this happens the air is no longer pushing against the bottom of the airfoil, but the top. This results in the kite instantly turning inside-out and falling out of the sky. (8)

A typical racekite (U-turn Nitro). Note the thin profile and very high aspect

ratio.

If you’re racing along the ground this doesn’t matter – once you’ve got momentum up then the kite will sit at the edge of the window and fly – once you get up to speed the kite will forever be trying to get to the edge of the window but because you’re matching its speed, it’ll never get there. Therefore when you’re racing, you’re kite will not fly out of the window unless the wind drops drastically. (8)

Beginners kites:

That’s all very well and good, but you can’t just buy a very fast, powerful kite, a buggy (kite powered vehicle) and expect to be able to get up to 50mph across a field. You have to learn how to fly the kites, and this is where it can be  an advantage to have a slow kite. You have a much greater reaction time, less power (due to a reduced aspect ratio and a thicker profile) so you won’t hurt yourself when learning. The profiles of beginner’s kites are also altered so that Newton’s theory of lift is less prominent than Bernoulli’s - in other words, the angle of attack is greatly reduced. This would normally increase

the speed of the kite greatly (by decreasing the drag coefficient), but with a thicker profile this effect is negated, producing a stable, easy kite to fly. (8)

A typical beginner’s kite (Ozone Samurai). This kite has a low aspect ratio and a fairly thick profile.

Lifty kites:

This is the third and (I think) most fun class of kites. These kites are designed to have some speed, but their primary purpose is to throw you

into the air and put you down safely. They can achieve this through manipulation of the factors in the above equations. If we go back to 1999 when the first lifty kite (and, incidentally, the first mass produced power kite) was manufactured (the Flexifoil “Blade mk.1”) we can see what the designers were thinking. I own one of these kites and, speaking from considerably experience, I can say that it is the slowest kite (for its size) that I have ever flown. The reason for this is that it relies almost solely on Newton’s theory of lift. This kite has huge amounts of lift when it’s sitting above your head, due to a very steep angle of attack. This means that when it moves through the air a great deal of energy is transferred to it from air molecules without it having to move very fast. It also means, however, that the drag coefficient is increased considerably. (1,8)

It moves so slowly because it was designed in the days before it was thought that people would want a kite to move fast – racing and so on was unheard of. The aspect ratio of this kite is relatively high for a kite: in fact the high aspect ratio underlines just how heavily Newton’s theory is relied on; there

are kites on the market with much lower aspect ratios that move much faster. (1,8)

Moving on – the Blade is now in its fourth series. So how has it progressed? The Blade II moved faster but had a shallower angle of attack – to my mind, this kite was designed to be smack bang in the middle of all the variables – it was to have speed, but not too much, a considerable angle of attack (but not one that slowed the kite down too much) and, of course, it should be easier to fly. (The Blade I has the turning circle of an oil tanker, and flying it demands a considerable amount of strength even in light winds). The Blade II was designed to be able to do anything – it should be very quick and very lifty. It is quick and lifty, but it doesn’t really excel in either category. (1,8)

The Blade III and IV took a step in the opposite direction from the Blade I – they rely heavily on Bernoulli’s principle, and derive a great part of their lift

from their speed through the air. This is a better approach to take because:

• Increasing the angle of attack will increase the lift coefficient

• But, as I have said before, the lift and drag equations are inextricably linked.

• So the only way to reduce drag is to reduce induced drag.

• Induced drag can be reduced by increasing aspect ratio, or lowering the lift

coefficient.

• Aspect ratio can’t be increased without making the kite too hard to fly.

• But reducing the lift coefficient will reduce the lift. So what can we do?

• We can increase the speed of the airfoil.

By increasing the speed of the airfoil a little and decreasing the angle of attack, we can see a considerable change in the equations. Because the induced

drag equation relies on Cl2, reducing Cl (the coefficient of lift) a small amount greatly reduces the induced drag. We can make the lift equation have the same value as before by slightly increasing the speed of the airfoil – by reducing the thickness of the profile and as a by-product of lessening the angle of attack. The lift equation relies on V2, so we only need a small increase in velocity to have a major effect. (Extrapolated from 5, using 😎

The practical effect of changing the variables in the way suggested above is that we have reduced the induced drag of the kite while leaving the inherent

drag and lift unchanged – voila, we have a kite that performs better than it did before. However you can’t take it too far because if you do, you create

a hard-to-fly racekite, which is no good for jumping. (5,8)

One reason it is a bad idea to have a really fast lifty kite is to do with the actual technique of deliberately jumping with a kite. Without wishing to

go into too much detail, it requires you to place the kite in a certain position and run in a certain direction before sweeping the kite across the top of the window to create lift. A very fast kite would sweep out of the window and lose its lift – while I was learning to fly I personally had this happen – I went over 4m up and (in a panic) did completely the wrong thing – I let the kite fly itself out of the wind window. I dropped like a stone, and still have trouble with my ankle from time to time. So there is also a practical consideration to making lifty kites very slow – you have a longer reaction time. (8)

A lifty kite. (Flexifoil Blade IV). Medium profile, fairly high aspect ratio.

Effect of mass of kite flier:

The mass of the kite flier should not have any effect on the performance of the kite – though the mass of the flier will severely affect the wind strength they are able to fly the kite in. Because the lift and drag equations rely on the velocity2 of the kite, a small increase in wind strength will cause a proportional increase in velocity, but a considerably greater increase in power (lift). This means that flying a kite in 10m/s doesn’t double the power from 5m/s – it increases it much more. This remains true as you work your way up through the wind strengths. This can be a dangerous thing for an inexperienced flier – their kite is flying fine at 5m/s, fine at 10m/s, a bit powerful at 15m/s, then at 20m/s it’s suddenly pulled them very high into the air and dropped them like a stone. (2,3,5,8)

How angle of attack is controlled in kites:

A quick illustration will be useful here:

This is the right-hand side of a typical power kite. The three sets of lines at the top are the “flying lines” – these transfer the power of the kite to

a pair of handles that the flier holds. Adjusting how long these lines are in relation

to each other is what controls the angle of attack of the kite. (6/8)

See bottom for a note on this image

Depowerable kites:

So far in this explanation I have talked solely about “fixed bridle” kites – these kites have a constant angle of attack, and will perform in the same manner in all wind conditions. There is, however, a second class of kites – depowerables. These kites are designed so that through manipulation of a control bar, the angle of attack of the kite can be changed as the kite flies. I don’t have the space here to go into exactly how they do this – though there is a good explanation (written by me some time ago) attached to this document, entitled “Appendix 1” (6/8)

These kites are very useful in gusty wind conditions, as the power they have can be increased or decreased to compensate for changes in the wind strength. They tend to have a fairly thick profile to provide stability, and on the whole will have a lower aspect ratio than fixed bridle kites. They can, however, be used to jump far higher than fixed bridle kites. The reason for this is that they can be launched on minimum power in a wind where the equivalent fixed bridle kite would be far too powerful – then the power can be briefly increased to maximum in order to get the necessary power to jump, and then decreased again to a manageable level once the flier has landed. For this reason it doesn’t matter that the profile is fairly thick and the aspect ratio relatively low – because you can choose when to turn the power on and off, as it were, you can still safely get far more lift and power than you could from even the most powerful and lifty fixed bridle kites. (6/8)

However, these kites are not built for speed. When you’re racing, you don’t need as much power as for jumping – in fact if you try to go very fast with too

big a kite, you will just be pulled downwind rather than accelerated along the ground. Because depowerable kites are heavier than fixed bridle kites (because of the weight of the depower system), slower and less powerful (because of the lower

aspect ratio and the thicker profile) they are very rarely used for serious racing. (6/8)

Stopping the kites:

What I haven’t covered so far is how to stop the kites. If you refer to the picture above you will see that along the bottom of the kite is another row of lines – the function of these lines are to stop the kite. The lines come from the kite to the flier. When they are tensioned, the trailing edge of the kite is pulled forwards so that the airfoil shape is lost – the lift is decreased and the drag is massively increased – much the same effect as an airplane putting full flaps on to lose speed as it comes in to land. Pulling the brake lines hard enough will mean that the kite loses all shape and flying ability and will simply drop out of the sky. The fact that it can sometimes only take a very small amount of tension to stop the kite from full speed goes to show how delicate a line there is between the kite flying and the kite falling out of the sky. (8)

Conclusion:

The exact mechanics of how lift is generated are exceptionally complex – there is a third part as well. Generation of lift relies on the simultaneous conservation of mass, energy and momentum. Newton’s laws concern the conservation of momentum, while Bernoulli’s equations are derived from the conservation of energy. The conservation of mass is extremely complicated, and relies on a set of equations known as the “Navier-Stokes” equations. I have shown them below for the sake of completeness, but I don’t intend to attempt to use them. (1)

(Image: http://www.grc.nasa.gov/WWW/K-12/airplane/nseqs.html) (12)

In the last few pages, I have described in detail the mechanics of how kites fly. I have also detailed how and why kite design has progressed in the last

few years as well as the different types of kite, their uses, advantages and their disadvantages. I haven’t, however, been able to explain every aspect of

kiting. The truth of the matter is that while Newton and Bernoulli’s theories both make sense, even both of them together don’t present an accurate picture of what happens. For example, if both are true; kites shouldn’t take off. They’re not moving so Bernoulli’s theory doesn’t apply - Newton’s is what counts. But if the angle of attack is such that when the kite is overhead, if lifts, then when its on the ground, air molecules should be deflected upwards. Yet kites still take off… I hope to find the answers to why in the future; but for now, at least, it seems that I’ll have to be patient. One problem is that Newton and Bernoulli’s theories are fundamentally incompatible – Bernoulli’s theory says that an airfoil should fly best when the path difference over the bottom and top of the airfoil is as great as possible and the angle of attack is non-existent, and Newton’s theory says that an airfoil that is a fraction of a degree off the vertical will create the greatest lift. In reality neither works all the time – this confusion underlies the whole science of Aeronautics, and makes it very hard to say for certain why wings work as they do. All we can do is keep studying and working, and someday we’ll find the answer. (1,9)

References:

1. http://www.grc.nasa.gov/WWW/K-12/airplane/bernnew.html

An account of the two common theories of lift – the theory that uses Newton’s laws of motion, and the theory that uses Bernoulli’s principles. A very clear source that provided much of the material for my comparisons between the theories.It is important to remember that the two theories are contradictory.

2. http://www.grc.nasa.gov/WWW/K-12/airplane/lifteq.html

This page provided me with the equation for lift, as well as informing me that the value of the lift coefficient is usually arrived experimentally, rather

than calculated. I didn’t use much from the text of this reference in my report.

3. http://www.grc.nasa.gov/WWW/K-12/airplane/dragco.html

Information on the drag coefficient and drag equation. As above, a useful reference as far as the drag equation is concerned, but I didn’t base anything (in the report) on the text in the reference, as it refers to aircraft rather than generically to airfoils.

4. http://www.grc.nasa.gov/WWW/K-12/airplane/short.html

This is the index page from which the previous three references are derived. It forms an excellent source, providing everything I wanted to know about the mechanics of lift and drag. The only real drawback is that the explanations pertain more to airplanes, and had to be adapted to work in the context of power kites. The layout can sometimes be technical and confusing, which is where we come to my next source.

5. http://community.flexifoil.com/showthread.php?t=7953

This is a thread in a power kiting discussion forum. As well as providing me with the link to the other references above, it explains drag, induced drag

and aspect ratio very clearly, and was a great help while I was starting to write this report. Parts of my explanations of why certain kites are suited to certain tasks have been adapted from this page, though I have gone into it in considerably more detail. It also provided me with a definition of the constant “e”, involved in the induced drag equation.

6. http://www.racekites.com/reviews/getReview.asp?reviewID=1607

This is the internet version of the explanation of how a depower kite works. It was written by me (some time ago), and I’m using it as a reference rather

than attempt to condense 7 pages of explanation into a few lines… I think it explains the mechanics of it quite well though.

7. http://www.racekites.com

A power kiting discussion forum of which I am a member. Much of the information headed “Prior knowledge” was acquired in my time as a member, though the individual threads would number well into the thousands if I tried to list them individually. An extremely useful source, because you can ask questions rather than have to decide what someone meant when they wrote a webpage.

8. Prior knowledge – acquired during 3 ½ years as a power kiter.

9. Direct quote “It is a confused area” P. Durnford, head of physics at SudburyUpper School, talking about the fact that neither Bernoulli nor Newton’s equations fully explain flight. He’s a physics teacher, so he should be fairly accurate.

10. http://www.aerospaceweb.org/question/aerodynamics/q0252.shtml

This web page provided me with the value for the lift coefficient of a Boeing 747 – it relies on a NASA study for data, so should be accurate.

11. http://en.wikipedia.org/wiki/Density_of_air

This wikipedia article provided me with a value for the standard density of air – while wikipedia cannot guarantee accuracy, this value agrees with other sources that I checked.

12. http://www.grc.nasa.gov/WWW/K-12/airplane/nseqs.html

This page provided me with the Navier-Stokes equations.

Notes:

Image: The image showing how the lines are attached to a power kite (page 10) comes originally from the Flexifoil blade II VPS instruction manual – the full image can also be seen partway through the attached document “How a depower kite works”. I mention this because I’m having some trouble with the direct link.References: The numbers at the end of the paragraphs represent which sources were used for the text in those paragraphs. Where referencing source 6, I put (6/8) to show that the two sources are basically the same.