I posted about platform angle in another thread the other day. Here's that post reformulated for this thread.
Platform angle measures the spatial relationship of the skier to the outside ski. It consists of two imaginary lines that meet at an angle. The first line extends across the surface of the ski from side to side. That line starts where the tipped ski's inside edge contacts hard snow - and extends to the other edge, the outside edge, of the ski. The second line starts at that same point where the tipped ski contacts hard snow - and travels up to the body's center of mass. The angle created by these two lines needs to be less-than-or-equal-to-90º for the ski to grip on hard snow. See the image by Bob Barnes that
@geepers just posted above for a visual.
Platform angle is independent of edge angle. Low edge angle skis can cleanly grip the snow and produce pencil-thin tracks if appropriate platform angle is maintained (railroad tracks). The relationship of the body to the ski defines whether the ski will grip, not slip, and whether it will produce narrow tracks or wide skidded tracks. This assumes the skier does not rotate the skis and is balanced fore-aft over the skis.
What skiers actually need to know about platform angle is simple. If the ski is slipping/skidding even though it was tipped without being rotated and even though the skier is balanced fore-aft on the ski, the problem may be that the platform angle is too large. To reduce that angle, the skier can
move the upper body farther out over the outside ski, or bring the outside ski closer up under the body. Either of these, or both together, will reduce the platform angle to enable grip.
Common skiing problems make it difficult to maintain a small enough platform angle.
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Leaning in/banking/bracing puts the body too far inside the turn. Angulate instead of leaning the shoulders into the turn.
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Hip-dumping puts the body too far inside the turn. Shorten the inside leg and roll its knee into the turn instead of dropping the hip.
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Pushing the outside ski to an edge puts the body too far inside the turn. Tip the skis without pushing on the outside ski by flexing the inside leg instead.
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Skiing square makes angulation more difficult, and lack of angulation puts the body too far inside the turn. Ski with separation and angulation instead.
Platform angle gets mixed up with edge angle. There are functional reasons for that. If the skier knows to increase edge angle by flexing the inside leg, that flexion can indirectly result in an effective platform angle. That's because flexing that inside leg keeps the inside foot/ski up under the body, which in turn discourages pushing the outside ski outward. Flexing that inside leg also discourages hip dumping since dropping the hip isn't being used to develop edge angle. And inside leg flexion is usually paired with angulation, not with banking, since leaning the whole body is not being used to create the edge angle. The resulting angulation moves the body farther out toward the outside ski. All of these reduce the platform angle. So three of the impediments to maintaining a small enough platform angle listed above can be indirectly eliminated by flexing that inside leg to get the edge angle. Skiers who know to use inside leg flexion for edge angles may not be thinking about adjusting platform angle to get and hold grip, but they are.