There are various carving styles and when freecarving, you can enjoy them all or invent your own . . .
Shoulders square to the board (chest facing the nose of the board) or shoulders parallel to the board.
Riding and leaning into turns with a straight body or carving in a crouched position with more bend in the knees, ankles and waist.
Short turns in the fall line or wide turns from one edge of the slope to the other and both tight and wide turns with all degrees of leaning in.
Leaning in and touching the slope with one hand or both hands or pretty much your whole body or avoiding that contact.
Keeping your upper body calm and moving your lower body/legs or initiating turns with your upper body and letting everything else follow.
At high or low speed, on flat or steep slopes, carving aggressive or effortless laid back turns.
Linking those to S trenches or going full circle on a single turn.
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Circles Carving a circle is actually possible and rumors are you can even keep going after that!
Single Turns Wide single turns and cirlce attempts are fun anyway even though you will likely lose all your speed and end up lying on the slope.
S Trenches or the perfect linking of carved turns is achieved by changing to the other edge very early and clearly before the actual turn (curve). When doing that, other people further up the slope can see the base of your board for a short time before every turn you make.
Jump Turns Have fun with otherwise hardly appreciated bumps by approaching (a rather small) one carving on the edge and changing to the other edge after takeoff while airborne (landing on the other edge and making the turn).
Cutback Leaning uprightly into a half circle turn or a bit more and just before you lose all of the remaining speed at the end of the turn, spin to the inside (180 degrees) until your nose is facing down the fall line and you can pick up speed again. That way you can do wide turns past the point where you would be able to link turns and nevertheless can keep going without having to stop, sit and turn around. Cutbacks can be stylish moves and feel awesome when done in a fluid way but this lousy attempt captured on film should at least illustrate the idea . . .
Speed You probably won’t want to use all speed options steep slopes have to offer. To control your speed you don’t need to skid. Carve tighter turns or hold them longer so that you carve uphill a bit at the end of each turn. Because most steep slopes are rather narrow the real challenge is that you don’t have much time and space to get into the next turn. Practicing these late but quick edge transitions on easier slopes is a great practice for the steep ones!
Bodyslides Especially on steep slopes it’s easy to turn a problem (skidding out) into a blessing. Go over the limit on a heelside turn and slide some distance with your body – until you set the snowboard into the snow again and continue carving as if you planned it that way.
‘Extreme Carving’ or touching the slope with your whole body can also be done without ever getting off the edge though! Great pictures showing that can be found in the ExtremeCarving Clips (for example Stoked). Narrow (race)boards are not so good for that riding style.
Slope Terrain Carving up the side of a bank on the slope can be like carving up the face of a wave so it can be fun to scan a slope for special features and trying to include them somehow.
Limbo A natural adaptation of this popular dance for the slope is Limbo Riding or the Limbo Challenge.
Switch Carving backwards is fun on well groomed slopes. Probably the most stylish transition from forward to backward carving can be seen in the Pure Boarding clip Carve it up.
Freestyle tricks can be done also when you’re not riding backwards. (Some that is) Especially for turning edge transitions into a show . . .
Safety Only do what’s fun to you and wait until the slope is less crowded to experiment with carving styles and tricks. Be aware of traffic above you and yield to idiots – it’s better than getting into a collision.
Of course you can also ride powder with freecarveboards!
Advanced riders also jump when absolutely necessary :) ride over water and have the option of sand- and rockboarding in summer.