* annoying physics pedantry:  You're always at 1 gee when you're in the earth's gravity well, but when you move in parabolic arcs on waves, you trade some inertia for lift, which gives you a 'weightless' feel.  ...so you're not really experiencing a 'low gee' environment at the peak of a wave, but the gravitational moment you express (your weight times one gravity, minus upward inertia) is less.

Wave Wheels are an extension of Flatwater Cartwheels, done (as the name suggests) on a wave or in a wave train.  Because they're done in a dynamic environment, they're both more demanding technically and easier physically than their flatwater counterparts- you can use the power of the waves to help you, but in order to do so you must be able to work with the timing that the waves will impose upon you.

In order to understand how to take advantage of the wave, it's important to understand how a wave works.  A wave is formed when fast-moving water slows down- because water is incompressible, it will pile up- meaning that the upstream face of a wave is made by water that is slowing in it's downstream flow, trading it's downstream speed for vertical lift.  Conversely, on the back side of the wave, water is accelerating, moving both downstream and downwards relatively quickly.  In a wavetrain, the water in the troughs of the waves is moving the fastest, while water at the peaks of waves is moving the slowest.

If a wave is breaking, it's collapsing not just upstream, but downstream as well in most cases- meaning that not only are you unlikely to get a good launch from this wave (instead, you'll get a chest full of water and lose all your launch speed) you're also unlikely to get a good launch stroke- the collapsing wave will have a turbulent internal structure and as often as not will provide poor paddle support for a wavewheel.

How it works

A Wavewheel is done by taking advantage of the moment of weightlessness you get near the peak of an unbroken wave.  Your objective is to accelerate through the trough of the wave and up it's face in such a way that your trajectory goes beyond the peak of the wave- and before you land, the trick is to get the boat rotated vertically enough that the accelerating water into which you're initiating the bow doesn't flatten you out.

The approach: Your stroke should begin in the trough, where the fast water will help you accelerate up the wave.  As you approach the top of the wave with speed, you should begin to edge the boat over in anticipation of slicing the boat in the vertical plane.  The stroke should be started early enough that it's complete before you crest the wave.

The launch: The launch is essentially a boof- you want to wheelie the boat slightly up the wave, and launch off the crest.  Timing and pitch control (in the course of this boof you want to introduce some roll to one side or another and actually pitch past vertical downstream) are important in this maneuver, and it's vital that as you crest the wave, your bow should be airborne, your weight be moving downstream and forwards in the boat, and your boat be over on edge.  As with any boof, you'll shoot your hips forward on the forward stroke, in order to keep the bow from falling prematurely into the following trough, and you'll finish the boof stroke by using it's force to help you sit forward in the boat.  The feeling will be that as you launch and sit forward while edging over to the side of the stroke you're taking, that you get a moment where the bow is weightless while the stern is still being lifted by the wave.  Use that final moment of lift to launch your weight forward, complete winding up your torso, and then begin your reverse stroke.

The reverse: The reverse stroke should begin at or before the moment where your hips cross the crest of the wave- you want your paddle to engage the water that is slowing in it's downstream progress and rising, rather than accelerating downstream and falling. If you attempt to do your reverse stroke against the downstream side of the wave, you'll find that the water there is accelerating in the same direction as your stroke, meaning that your purchase will be minimal.

A successful reverse will begin with your torso already wound up and your weight committed forward, towards where you'll be when you end up vertical on your bow station.  The reverse is a paddle placement stroke, it cannot be stressed enough that most of the work should be done by your torso- that is, you should be unwinding your torso to bring the stern up/bow down- if you try to move everything with your arms, you'll discover that it's terribly inefficient and unlikely to work.

Also note that when you initiate your end into the first trough, you want to get your rotation done before you get down into the trough- in the trough, water is at it's fastest, accelerating against the direction you're initiating- so get that bow initiated into the back of the wave you're launching from, and if you're used to flatwater cartwheeling, you'll need to get the boat past where you're used to throwing it... in order to balance against the accelerating water in the trough.

Keeping it going: Once you've managed to end up in the trough of the next wave, vertical, you'll appreciate having some balance and control in order to time things to get the next end down.  For tips on working on your balance, read up on bow stalls.

Once you're vertical in the trough, approaching the next crest, you don't need as much lift or launch as you did to get things started, but you'll need some.  Because you just came from someplace high, you'll likely be bobbing low in the water, and you'll get some lift as you bob vertically going from the 'high gravity' trough to the 'low gravity' peak.*  Usually, your bob rate will put you at a 'launch' moment by the time you reach the next peak, which is where you'll do your next move.

If you're approaching the next crest on your bow, looking to go towards the stern, wind up your torso and reach across your body to drive your stern down/lift your bow up.  Wait until you reach that moment of weightlessness near the top of the wave, and unwind your torso to slice the next end through.  Note that as the water in the wave slows as you near the peak, the natural effect is that your stern will pitch forwards, downstream, where you want it to go.  If you're approaching the next crest on your stern, looking to go towards the bow, again wind up your torso, ahead of the rotation of the boat, and time your smash stroke to occur against the face of the oncoming wave, near the crest, at your peak bob moment.  For a more thorough discussion of these strokes and techniques, read up on flatwater cartwheeling.

Variations:  Paddling wouldn't be fun if there weren't more challenges to be had out there- so there are some other variants of the wavewheel to mess with...

Splitting it up:  You can pump up the degree of difficulty for a series of wavewheels by putting a half-pirouette into the moment you have between wave crests.  This requires good balance and better timing, but looks pretty flash and is lots of fun.  If you're super cool, you'll be able to do this on the stern as well as on the bow without missing an end.

Barrel Rolling:  Instead of reversing the stroke in order to rotate end-over-end, it's possible to use your launch to roll the boat in air and land either upright or on a brace on the other side you started from.  The approach and launch are identical to that of the wavewheel, but the reverse stroke and body mechanics are entirely different- instead of unwinding your torso, you're performing a hipsnap as though you were rolling on your back deck... against a low-brace that travels overhead as you invert... :-)  Once you've gotten purchase and begun your hip-snap, be sure to get your off-side paddle blade under the boat ahead of you, so that when the boat comes down you're not all crossed up underneath it. Finish by switching active blades, and you'll be on a brace on your other side.

Reverse-wheeling:  There's another way to cartwheel using waves- instead of using those magical moments of lift you get at the peak, you can use the accelerating water in the troughs to help drive your ends through- the timing for reverse wheeling is also different, as your stroke placement is also different for this.  If you're in a low-volume boat (like a squirt boat) that makes it difficult to get enough speed or bob to get good launch separation, reverse-wheeling is often easier and the feeling is 'doing more with less', very cool.

Other considerations:  I suppose it should go without saying that wavewheeling in shallow water, or in water with shallow troughs, can be hard on boat, boater, paddle, helmet, ego... it's probably best to avoid this move and it's cousins unless you've got a healthy amount of water under you.  Also, try to make sure there's nobody surfing in the trough you're wheeling into- you don't want to deliver a tomohawk chop with your stern into anybody... not unless they really had it coming. :-)  Be safe, have fun!

Do you have questions about this article or comments on how I might improve it? Please let me know.