Here is the full original post from Bob Barnes on Critical Edge angle / Platform Angle. Thanks to the Wayback Machine...
Edit: Just in case it ever disappears from the Internet Archive...
Krazzy Legs--I suspect that it's a bit more complicated than you've been imagining--or perhaps less. The surprising fact is that edge angle on the snow surface has nothing to do with how well a ski grips or slips. Nothing! Indeed, there are many situations where a ski with a higher edge angle will not hold and carve as well as a ski with a lower angle. "Booting out" is one of them, of course, but there are other situations too. I'll get to that later, but let's look first at how edging influences a ski's grip, if the edge angle on the snow has nothing to do with it.
There are two ways (at least) to measure and describe edge angle, and they are both important in skiing but for different reasons. The first and most common is to describe the edge angle relative to the snow surface. The second--and the one that matters here--is to describe the edge angle relative to the force the skier applies to the ski. This is the intriguing concept often called "critical edge angle," or more recently "platform angle" (both terms originated, I believe, by Ron LeMaster). We've discussed these things before at EpicSki, but it's time to raise them again because they're very relevant to your original post. It's not easy to explain, from my experience, but once you get it, it may create an "ahah!" experience that brings many things into focus. Here goes....
"Critical Edge Angle" or "Platform Angle"
Imagine standing still on a very slippery, icy staircase. If the steps are level or tilted slightly toward the staircase, you won't slip off. But if the steps tilt out away from the staircase, you're probably doomed. Here's a crude illustration of what I'm describing:
Fig. 1. When the platform is level (A), you won't slip off no matter how slippery the surface because the force you apply to the step (straight down, due to gravity) is perpendicular to the step surface. When the step tilts toward the "hill," as in B, gravity tends to pull you toward the staircase. But when the platform tips away from the hill as in C, gravity will cause you to slip off the step.
Assuming the edge is sharp enough, a ski with pressure on it will carve a little "step" in the snow surface very similar to the steps of the staircase in the example in Fig. 1. When standing still or traversing across the hill in a straight line, gravity's straight-down pull is the only significant force, so the angle of the step cut by the edge works the same way as the steps on the icy staircase. When the ski edge is level (perpendicular to the downward pull of gravity) as in skier A1 or tilted a little toward the hill (B1), the ski will hold. When the edge tips downhill slightly (skier C1), it releases as the force of gravity literally pushes the ski out of its little notch, off its step. Here's an illustration:
Fig. 2. When standing still or traversing, the force applied to the ski (red arrows) is vertical, due solely to gravity acting on the center of mass. Skiers A1 and B1 will hold because the "platform angle" is 90 degrees (A1) or less (B1) from the angle of the force applied to the ski edge. Skier C1 will slip, just like the person standing on the slippery, tilted step above (C). Note the small notches or "steps" carved into the snow by the skis, very similar to the steps on the staircase in the first illustration.
In the second illustration, it's important to note that it does not matter how steep the hill itself is. The steeper the hill, the greater the edge angle relative to the snow surface, but the angles of the "steps"--the "platform angles"--do not change. In other words, you really do not need to tip your skis any more to hold on a steep slope than you do on a shallow slope. As we've all experienced, all it really takes to hold an edge when standing across a hill or traversing is a little ankle tension to cause just slight angulation to tip the skis to "critical edge angle" of level or slightly tipped into the hill. Likewise, releasing the edge to start a new turn involves little more than relaxing the ankle (or ankles) to let go of the mountain and let the skis slip.
Finally, in a turn, other forces arise. Centrifugal force, resulting from the turn itself, pulls out away from the center of the turn, and we lean (incline) into the turn for balance. (Please do not argue about centrifugal force here--no matter how you may prefer to explain the phenomenon, your body knows perfectly well that it needs to lean into a turn for balance!) These combined forces and the resulting lean of the body (center of mass) cause the direction of the force applied to the ski to tip away from vertical. As we incline into the turn, our skis naturally tip to a higher angle against the snow surface (unless we work hard to prevent it), but the critical edge angle that creates the platform angle stays the same, relative to the now-tilted force. And the ski's tendency to grip or slip depends as before on that angle--not on the edge angle on the snow. In other words, it is the shape of the skier's body--"angulation" or the lack thereof in ankles, knees, hips, and spine--that determines grip, NOT the degree of inclination, which largely influences the ski's edge angle on the snow.
Fig. 3. Here, skier A2 is standing still or traversing and therefore "vertical." His ski grips because of slight angulation (lateral angles, essentially) in the ankles, knees, and hips, which creates the platform angle of less then 90 degrees to the (vertical) force applied to the ski. Skier B2 is in almost exactly the same posture as skier A2, but because he is turning, his whole body--and skis--tip into the turn. The platform angle remains the same as skier A2, even though the edge angle on the snow has increased. Skier C2, even though his edge angle on the snow is about the same as skier A2, does not hold because he is "banking"--leaning his upper body into the turn and causing the platform angle to increase greater than 90 degrees to the angle of the force he applies to his ski.
So that's "critical edge angle" or "platform angle" in a nutshell. Basically, if the ski is tipped perpendicular or to an acute angle with the line of force, the ski will tend to hold. When tipped to an obtuse angle (greater than 90 degrees) to the line of force, the force will tend to push the ski right off its platform and cause it to skid, no matter how high the edge angle on the snow surface. (Of course, if you want to get picky and technical, factors such as the ski's torsional stiffness--how much it twists along its length when tipped on edge--come into play, skewing the numbers somewhat. Overall sharpness, base and side edge bevels, and snow conditions factor in as well.)
---
So, if it does not influence the ski's ability to hold, what DOES edge angle on the snow do? It plays an entirely different, but no less important, role, and as skiers, we must control both edge angle on the snow AND platform angle independently, but simultaneously, continuously, and accurately. Essentially, a ski's edge angle on the snow, combined with its sidecut radius (and sufficient pressure to bend the ski, properly located), influences the size of the turn the ski "tries" to carve, as the following illustration shows:
Fig. 4. On hard snow, the higher the edge angle (on the snow), the tighter radius turn the ski wants to carve. The basic formula is sidecut radius X cosine of edge angle = carving radius. (In soft and deeper conditions, sidecut and edge angle are less significant, as it is primarily the ski's flotation and flexibility, combined with the amount and location of pressure on it, that causes it to bend.)
Here too, the simple formula represents only an approximation, as torsional stiffness, flex pattern, sidecut shape, fore-aft pressure distribution, snow conditions, and other skier movements and factors all influence ultimate turn shape and carving radius. And, of course, in powder, crud, and other soft-snow conditions, sidecut plays a much less significant role.
How can a ski hold LESS well when tipped to a higher edge angle?
Because edge angle on the snow plays such a significant role in the carving radius of a turn, too much edge angle can actually cause a ski to hold less well than "just enough" edge angle. Especially at high edge angles of 45 degrees and up, a slight change in edge angle can have a tremendous influence on the ski's carving radius. For example, an edge angle (on the snow) of 60 degrees (cosine = .5) creates a theoretical carving radius of one half the ski's sidecut radius. Increasing the edge angle just 15 degrees further from 60 degrees to 75 degrees (cosine = .26) nearly cuts the theoretical carving radius in half again--about one quarter of the ski's sidecut radius! When the ski bends into a tighter radius arc than the turn the skier is trying to make, it will not carve--or hold--nearly as well as when tipped to the optimal angle. Conversely, if you let the ski tighten the turn to whatever radius it bends into, it will cause a dramatic increase in the g-forces (centrifugal force) caused by the turn. That can cause the snow itself to break away under the load, and can also increase the stress on the body, making it more difficult to sustain the intense force--either way resulting in the ski skidding because of too-high edge angles.
---
Whew! Well, that was a good exercise for me, as I've wanted to create some illustrations to try to help explain some of these technical concepts. I hope they help clarify some interesting technical details and potential paradoxes of skiing! As others have suggested, Krazzy Legs, it is at least possible that what you've described as "booting out" could be due to some of the other reasons that skis will break away and slip or skid due to extremely high edge angles, as I just described. Of course, it could be that you've booted out, too. It does happen, especially on very narrow skis without much "lift" under the boots. And some boots are wider and more prone to booting out than others.
If you have some video....
Best regards,
Bob Barnes
Edit: Just in case it ever disappears from the Internet Archive...
Krazzy Legs--I suspect that it's a bit more complicated than you've been imagining--or perhaps less. The surprising fact is that edge angle on the snow surface has nothing to do with how well a ski grips or slips. Nothing! Indeed, there are many situations where a ski with a higher edge angle will not hold and carve as well as a ski with a lower angle. "Booting out" is one of them, of course, but there are other situations too. I'll get to that later, but let's look first at how edging influences a ski's grip, if the edge angle on the snow has nothing to do with it.
There are two ways (at least) to measure and describe edge angle, and they are both important in skiing but for different reasons. The first and most common is to describe the edge angle relative to the snow surface. The second--and the one that matters here--is to describe the edge angle relative to the force the skier applies to the ski. This is the intriguing concept often called "critical edge angle," or more recently "platform angle" (both terms originated, I believe, by Ron LeMaster). We've discussed these things before at EpicSki, but it's time to raise them again because they're very relevant to your original post. It's not easy to explain, from my experience, but once you get it, it may create an "ahah!" experience that brings many things into focus. Here goes....
"Critical Edge Angle" or "Platform Angle"
Imagine standing still on a very slippery, icy staircase. If the steps are level or tilted slightly toward the staircase, you won't slip off. But if the steps tilt out away from the staircase, you're probably doomed. Here's a crude illustration of what I'm describing:
Fig. 1. When the platform is level (A), you won't slip off no matter how slippery the surface because the force you apply to the step (straight down, due to gravity) is perpendicular to the step surface. When the step tilts toward the "hill," as in B, gravity tends to pull you toward the staircase. But when the platform tips away from the hill as in C, gravity will cause you to slip off the step.
Assuming the edge is sharp enough, a ski with pressure on it will carve a little "step" in the snow surface very similar to the steps of the staircase in the example in Fig. 1. When standing still or traversing across the hill in a straight line, gravity's straight-down pull is the only significant force, so the angle of the step cut by the edge works the same way as the steps on the icy staircase. When the ski edge is level (perpendicular to the downward pull of gravity) as in skier A1 or tilted a little toward the hill (B1), the ski will hold. When the edge tips downhill slightly (skier C1), it releases as the force of gravity literally pushes the ski out of its little notch, off its step. Here's an illustration:
Fig. 2. When standing still or traversing, the force applied to the ski (red arrows) is vertical, due solely to gravity acting on the center of mass. Skiers A1 and B1 will hold because the "platform angle" is 90 degrees (A1) or less (B1) from the angle of the force applied to the ski edge. Skier C1 will slip, just like the person standing on the slippery, tilted step above (C). Note the small notches or "steps" carved into the snow by the skis, very similar to the steps on the staircase in the first illustration.
In the second illustration, it's important to note that it does not matter how steep the hill itself is. The steeper the hill, the greater the edge angle relative to the snow surface, but the angles of the "steps"--the "platform angles"--do not change. In other words, you really do not need to tip your skis any more to hold on a steep slope than you do on a shallow slope. As we've all experienced, all it really takes to hold an edge when standing across a hill or traversing is a little ankle tension to cause just slight angulation to tip the skis to "critical edge angle" of level or slightly tipped into the hill. Likewise, releasing the edge to start a new turn involves little more than relaxing the ankle (or ankles) to let go of the mountain and let the skis slip.
Finally, in a turn, other forces arise. Centrifugal force, resulting from the turn itself, pulls out away from the center of the turn, and we lean (incline) into the turn for balance. (Please do not argue about centrifugal force here--no matter how you may prefer to explain the phenomenon, your body knows perfectly well that it needs to lean into a turn for balance!) These combined forces and the resulting lean of the body (center of mass) cause the direction of the force applied to the ski to tip away from vertical. As we incline into the turn, our skis naturally tip to a higher angle against the snow surface (unless we work hard to prevent it), but the critical edge angle that creates the platform angle stays the same, relative to the now-tilted force. And the ski's tendency to grip or slip depends as before on that angle--not on the edge angle on the snow. In other words, it is the shape of the skier's body--"angulation" or the lack thereof in ankles, knees, hips, and spine--that determines grip, NOT the degree of inclination, which largely influences the ski's edge angle on the snow.
Fig. 3. Here, skier A2 is standing still or traversing and therefore "vertical." His ski grips because of slight angulation (lateral angles, essentially) in the ankles, knees, and hips, which creates the platform angle of less then 90 degrees to the (vertical) force applied to the ski. Skier B2 is in almost exactly the same posture as skier A2, but because he is turning, his whole body--and skis--tip into the turn. The platform angle remains the same as skier A2, even though the edge angle on the snow has increased. Skier C2, even though his edge angle on the snow is about the same as skier A2, does not hold because he is "banking"--leaning his upper body into the turn and causing the platform angle to increase greater than 90 degrees to the angle of the force he applies to his ski.
So that's "critical edge angle" or "platform angle" in a nutshell. Basically, if the ski is tipped perpendicular or to an acute angle with the line of force, the ski will tend to hold. When tipped to an obtuse angle (greater than 90 degrees) to the line of force, the force will tend to push the ski right off its platform and cause it to skid, no matter how high the edge angle on the snow surface. (Of course, if you want to get picky and technical, factors such as the ski's torsional stiffness--how much it twists along its length when tipped on edge--come into play, skewing the numbers somewhat. Overall sharpness, base and side edge bevels, and snow conditions factor in as well.)
---
So, if it does not influence the ski's ability to hold, what DOES edge angle on the snow do? It plays an entirely different, but no less important, role, and as skiers, we must control both edge angle on the snow AND platform angle independently, but simultaneously, continuously, and accurately. Essentially, a ski's edge angle on the snow, combined with its sidecut radius (and sufficient pressure to bend the ski, properly located), influences the size of the turn the ski "tries" to carve, as the following illustration shows:
Fig. 4. On hard snow, the higher the edge angle (on the snow), the tighter radius turn the ski wants to carve. The basic formula is sidecut radius X cosine of edge angle = carving radius. (In soft and deeper conditions, sidecut and edge angle are less significant, as it is primarily the ski's flotation and flexibility, combined with the amount and location of pressure on it, that causes it to bend.)
Here too, the simple formula represents only an approximation, as torsional stiffness, flex pattern, sidecut shape, fore-aft pressure distribution, snow conditions, and other skier movements and factors all influence ultimate turn shape and carving radius. And, of course, in powder, crud, and other soft-snow conditions, sidecut plays a much less significant role.
How can a ski hold LESS well when tipped to a higher edge angle?
Because edge angle on the snow plays such a significant role in the carving radius of a turn, too much edge angle can actually cause a ski to hold less well than "just enough" edge angle. Especially at high edge angles of 45 degrees and up, a slight change in edge angle can have a tremendous influence on the ski's carving radius. For example, an edge angle (on the snow) of 60 degrees (cosine = .5) creates a theoretical carving radius of one half the ski's sidecut radius. Increasing the edge angle just 15 degrees further from 60 degrees to 75 degrees (cosine = .26) nearly cuts the theoretical carving radius in half again--about one quarter of the ski's sidecut radius! When the ski bends into a tighter radius arc than the turn the skier is trying to make, it will not carve--or hold--nearly as well as when tipped to the optimal angle. Conversely, if you let the ski tighten the turn to whatever radius it bends into, it will cause a dramatic increase in the g-forces (centrifugal force) caused by the turn. That can cause the snow itself to break away under the load, and can also increase the stress on the body, making it more difficult to sustain the intense force--either way resulting in the ski skidding because of too-high edge angles.
---
Whew! Well, that was a good exercise for me, as I've wanted to create some illustrations to try to help explain some of these technical concepts. I hope they help clarify some interesting technical details and potential paradoxes of skiing! As others have suggested, Krazzy Legs, it is at least possible that what you've described as "booting out" could be due to some of the other reasons that skis will break away and slip or skid due to extremely high edge angles, as I just described. Of course, it could be that you've booted out, too. It does happen, especially on very narrow skis without much "lift" under the boots. And some boots are wider and more prone to booting out than others.
If you have some video....
Best regards,
Bob Barnes
