Kiteboard Theory - Thread 2: Lift/Drag Ratio and Performance

Postby James on Sun Jul 29, 2007 3:03 am

The lift/drag (L/D) ratio of a kite is the most fundamental characteristic that defines its performance. It is the result of many design parameters that can be summed up as one simple value, much the same way that an engine's horsepower is the quantifiable result of a myriad of design features.

A kite's secondary, but also important performance characteristic is it's maneouverability, or turning characteristic. Other charactersitics include range of trim (depower) and various convenience and safety characteristics which are not generally related to maximum performance. I won't be focusing on these other factors in this post.

Now, back to the L/D ratio: Anecdotal descriptions are often made of kite performance, such as "quick across the window" and "flying far forward", but these descriptions are all simply functions of the L/D ratio. The L/D ratio has two components: 1) lift, which is the useful aerodynamic force created perpendicular to the free airflow past the kite, and 2) drag, which is the parasitic aerodynamic force parallel to the airflow. (It is worth noting that the free airflow over the kite is exactly the same thing as the apparent wind at the location of the kite.) Lift is created, as with all aerofoils, by the interaction of the kite with the airflow, and resulting differential pressures above and below the kite's surface. Drag is also caused by the airflow over the kite, generally by surface friction and turbulence. Many design factors affect lift and drag, and I'll cover some of these in a future thread. For now, here is a link that I googled, which appears to depict these principles, although I only glanced at it superficially: http://www.auf.asn.au/groundschool/umodule4.html

Here's an example: Suppose that you are standing still on a beach, flying your kite steadily overhead in a steady wind. The kite is exerting about 40 pounds of tension, via the lines, on your bar and harness. If the kite is really flying exactly overhead, with the lines completely perpendicular to the airflow, then that means that your kite and lines have no drag whatsoever, and therefore an infinite L/D ratio (40 lbs lift, 0 lbs drag). But that's impossible, because even the most efficient aerofoils generate some drag, and in the case of the kites we use, the drag is typically between 1/5 and 1/7 of the lift, which results in L/D ratios between 5:1 and 7:1. Because your kite and lines have some drag, they will be flying a little downwind of directly overhead. If there are 8 pounds of drag, which is 1/5 of the 40 pounds of lift, then the kite will be flying 1/5 as far back as it is high. So, if it is 100 feet high, it will be flying 20 feet back from directly overhead. This would represent a L/D ratio of 5:1. Get it?

Ok, now I'm going to complicate things just a little. Supposing that the kite and lines weigh 8 pounds, the kite is actually generating about 48 pounds of lift in order to support itself and also exert 40 pounds of tension on the bar and harness. So, taking the weight of the kite into consideration, the L/D ratio in this situation is actually about 6:1 (48 lbs lift, 8 lbs drag), even though the angle of the kite and lines suggests about 5:1. The windier it is, and the greater the lift that the kite is generating, the less the effect the kite's weight will have on its apparent L/D ratio.

If you want to compare the L/D ratios of different kites, try flying them overhead, exactly side by side. The one that flies farther forward will be the one with a higher L/D ratio. Also, the trim (depower) of the kite will affect its L/D ratio, and you can experiment by flying your kite overhead and sheeting the bar in and out until you find the exact trim that causes the kite to fly the farthest forward. This brings up a couple of other points:
1) The apparent windspeed, or airflow past the kite, will also affect its L/D ratio. Any aerofoil can generate slightly different L/D ratios at different speeds.
2) The trim that causes the kite to fly farthest forward is not necessarily the same trim that will result in the most lift or line tension. For a given kite, it is quite likely that the maximum force, tension, or whatever you want to call it, is caused by sheeting in the bar as far a possible without inducing aerodynamic stall (to be discussed in a later thread). But the best L/D ratio might result from sheeting the bar out a little, reducing lift a bit, but reducing drag proportionately more.

So, why is L/D ratio so important? Because a higher L/D ratio results in a kite that pulls in a more beneficial, or efficient direction. All other things being equal, it'll let you kiteboard faster, point more upwind, jump higher and longer, and stuff like that. Suppose that you are kiteboarding at 20 mph, in a 15 mph wind, and you are going 10 degrees upwind with a big, efficient kite (high L/D ratio) and a Spleene Session or flat plywood board. This is the example that I presented in my previous thread about apparent wind, and as I explained in that thread, the apparent wind would be blowing at an angle of about 33 degrees from straight ahead.

Now consider this:

1) If you are kiting in a dream world, and your kite has an infinite L/D ratio (no drag), then the kite would be pulling exactly at a right angle (90 degrees) to the apparent wind. That would mean that the lines would be pulling 33 degrees forward from straight sideways, which is more than enough to make good progress with good edging technique.
2) But if you are kiting in the real world, and your kite has a L/D ratio of 6:1, it will be flying about 9 degrees back (derived from simple trigonometry: Arctan[1/6]) from a right angle to the apparent wind. That means it will be pulling about 33-9=24 degrees forward from straight sideways, which is probably about the threshold for maintaining speed without having to bear off, even with the right board and technique.
3) If you are flying a lame or poorly trimmed kite with a L/D ratio of only 4:1, it will be flying at 14 degrees back from a right angle to the apparent wind, which means 33-14=19 degrees forward from straight sideways, which won't possibly keep you going unless you bear off to improve your apparent wind angle, which will result in going a bit downwind instead of a bit upwind.
4) Bonus point: Your kiteboard also has a theoretical maximum L/D ratio of its own, specific to a given speed and perfect riding (edging) technique. I don't know what the maximum L/D ratio of any board is, but my wild guess is that they typically fall somewhere between 2:1 and 4:1. I do believe that my Spleene Session 141 has close to double the L/D ratio of my first generation (red with yellow sun) Naish TT Sol 125. (Simply put, the TT Sol is smaller and generates less lift, but because it has a lot more rocker, it also generates more drag. It's fun and agile, but like most freestyle twin tips, not very efficient.) If you're into math, you can deduce that you'd theoretically need a board with a L/D ratio of at least 2.2:1 in order to make example 2) work, but considering waves, less-than-perfect technique, and stuff like that, you'd probably actually need a board with a considerably better L/D ratio than that.

Another tidbit: The tension or pull from a kite is actually a combination of both lift and drag, but mostly lift in the case of high L/D ratios. The higher the L/D ratio of the kite, typically the bigger kite you can fly to exploit its potential.

And another: A parachute would have an abominable L/D ratio because it generates almost all drag and no lift. You could kiteboard with a parachute, but you'd probably be stuck riding at an angle of about 45 degrees downwind, relative to the true wind direction. That would result in a lot of walking.

One more thing, regarding the notion of how fast a kite crosses the "window" or "power zone": Consider standing on the beach while you fly your kite right across the deepest part of the power zone, just above the ground, immediately downwind of you. That's when your kite will generate the most force (and power, if you want to get technical) because it creates the fastest apparent wind. If your kite has a L/D ratio of 6:1, it will cross the deepest part of the power zone at roughly six times the true windspeed (and its apparent wind will be about the square root of (1^2 + 6^2) = 6.08 times the true windspeed. The reality is that your kite probably won't go that fast because it will generate so much force that you'll get dragged downwind, which has the effect of moderating the apparent wind. (That is, both your apparent wind and the kite's apparent wind: If the true wind is 15 mph, and you get temporarily dragged downwind at 8 mph as the kite crosses the power zone, then the apparent wind passing you will be only 7 mph, and the kite's speed and apparent wind will also be greatly reduced.) Kites that seem to cross the window fastest are generally just the smaller, less powerful ones because they don't drag the kiter as much. This is frankly more significant than their L/D ratios in this particular circumstance. If you can stand still while you fly a small trainer kite across the power zone, you probably know that that kite will move insanely fast, and generate some serious force.

That's all for now,
James

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