i wonder what the formula is for maximum height?
board speed x kite speed x wind speed squared x lift ratio x projected area/ density and humidity?
Convert all of your kinetic energy into potential energy.
That's exactly correct.
As with any aspect of kiteboarding, the most aerodynamically efficient (L/D ratio) kites are best. That said, a fast turning kite will help you redirect forces quickly to achieve the best height. Then, the biggest kite will result in the slowest sink rate, and therefore the best hangtime.
Following is copy from an article I wrote years ago on the dynamics of jumping
(original post: http://kiteboardbc.com/phpBB3/viewtopic.php?f=1&t=175
It takes energy to jump. Where does that energy come from?
The answer is kinetic energy: specifically that resulting from your forward motion through the air. Not your motion over the water, and not relative to the earth. Just relative to the air.
Through the manipulation of aerodynamic forces, your kite can be used to convert kinetic energy (an exponential function of airspeed) into potential energy (a linear function of height). In a particular set of conditions, there is a maximum possible theoretical height of jump that can be achieved, due to the physical law that energy must be conserved. You can't create energy from nothing. With an ideal kite, and ideal technique, this theoretical height may be approached, but it can never be exceeded.
I should mention that there are a few other sources of energy that can augment the height of a jump. They are:
1. Kinetic energy related to the vertical component of your speed over the water as you ride up a wave face.
2. Electrochemical energy stored in your muscles that can be converted by contracting your muscles to accelerate your mass upwards against the vertical force of the water against the board.
3. Kinetic energy related to vertical air currents as described in "Kiteboard Theory - Thread 3: Lift, Looping and Hangtime".
These sources of energy are usually minor and I won't dwell on them any more in this thread.
Now, back to the conversion of kinetic energy to potential energy:
To achieve the highest jumps, you must start with lots of kinetic energy, as a function of airspeed. There are two obvious factors that are relevant to doing this:
1. Ride in strong wind.
2. Maximize your apparent windspeed at the instant you take off. This means riding fast in a relatively upwind direction. That's why carving hard upwind without losing too much speed is vital to good jumps.
Assuming that all of your basic technique is good, your highest jumps will result from efficiently converting as much of your kinetic energy as possible into potential energy. Ideally, at the apex of your jump, you will have no kinetic energy at all, which means that your horizontal airspeed will be zero, which means that you will be swinging below your kite downwind at exactly the same speed as the wind. This scenario can generally be achieved with the right timing.
Here are the fundamental factors to putting it all together:
1. The windier the better.
2. Just before jumping, ride fast and carve hard upwind to maximize your apparent windspeed.
3. Send your kite back aggressively to take off. The best technique is a matter of trial and error.
4. While jumping, your kite should be trimmed for "minimum sink rate", which might be different than the trim for maximum L/D ratio. That probably means your bar should be trimmed as tight as possible without inducing any aerodyanamic stall. You can probably only know for sure that you have ideal trim if you use telltales (which I'll go over in another thread).
5. Keep your kite back just enough that your pendulum motion matches as closely as possible to the windspeed and direction when you are at the apex of your jump. Again, trial and error. If you actually get it right, and you happen to be smoking at the apex, you could blow gentle concentric smoke rings. (After the apex, don't forget to dive your kite aggressively forward, or you'll do a nasty backflop.)
Here are a couple more thoughts about energy conversion and conservation:
1. No matter what, you'll never convert all of your kinetic energy into potential energy because there will always be some losses relating to aerodynamic drag, which effectively energizes the air by way of turbulence.
2. As I mentioned before, kinetic energy is an exponential function of airspeed, but potential energy is a linear function of jump height. That means that if you double the airspeed at lift off, your theoretical best jump height will be four times as high. Or another example: If you have the right equipment, nerve and skill, you should be able to jump nine times as high in 45 knots apparent wind as you could in 15 knots apparent wind (17-18 mph on iKitesurf), which could be pretty !@#$% high.