An understanding of the physics of snowboarding is useful to snowboarders of all skill levels because it allows them to identify those key physics principles enabling them to properly execute certain moves, which is useful from a performance point of view.

A snowboarder typically gains speed by converting gravitational potential energy into kinetic energy of motion. So the more a snowboarder descends down a hill, the faster he goes. The two pictures above show a snowboarder going down a mountain. However, since the side of the mountain is very steep, the snowboarder must prevent himself from going too fast and losing control. He does this by skidding his board on the snow, in a controlled zig-zag pattern (shown in the first picture). This creates frictional resistance with the snow and prevents his speed from reaching dangerously high levels.

A common snowboarder stunt is to jump off a helicopter and land on the side of a mountain, before racing down. The landing force experienced by the snowboarder is reduced because his normal velocity component relative to the mountain surface, just before landing, is small. This is a result of the side of the mountain being at an inclination (i.e. not flat).

In the following section skidding will be discussed.

Amateur (less experienced) snowboarders typically skid around their turns. This occurs when the snowboard is tilted on its edge and the exposed base of the board "plows" into the snow head on. Although the skidding can be controlled and the turn successfully executed, it ultimately results in a significant loss in speed, which can be undesirable. This occurs because the "plowing" action generates frictional resistance with the snow, by physically pushing it. This frictional resistance is significantly more than the resistance seen if the snowboard were to glide on the snow, either with the base of the snowboard flat on the snow (while moving in a straight line in the direction of the snowboard), or with the edge of the snowboard planted into the snow (while carving around a turn, to be discussed). In both these cases, the snowboard is pointed in the same direction as its velocity (which is the same as the velocity of the snowboarder). This is a necessary requirement for minimizing snow resistance, and maximizing speed.

The figure below illustrates a turn that is executed while skidding.

The path "swept" by the snowboard is the result of plowing the base of the snowboard through the snow. This happens when the snowboarder turns his snowboard too sharply into the turn. This results in the momentum of the snowboarder not changing direction quickly enough to match the direction the snowboard is pointed.

However, in some cases, a degree of skidding is unavoidable, but the key is to minimize it in order to minimize the speed reduction during the turn.

The most efficient turn occurs when the snowboarder does a purely carved turn, in which the snowboard is pointing in the same direction as its velocity. The figure below illustrates this.

As shown in the figure above, in a purely carved turn there is no skidding, and the only snow resistance present is the very small sliding friction between snowboard and snow. As a result of this minimal level of friction between snowboard and snow, the speed reduction of the snowboarder is minimized, and he is able to navigate the course faster. Carving turns is one of the more interesting areas of study in the physics of snowboarding.

It takes quite a bit of skill to execute a carved turn. Top level snowboarders are typically the only ones who are able to do it consistently. The picture below shows a snowboarder executing a purely carved turn.

Source: http://www.flickr.com/photos/tonythemisfit/3270147185

The physics of carved turns will be described next.

The physics behind carving is different from the physics behind skidding. Unlike skidding where a snowboarder pivots into a turn, a carved turn is initiated by the snowboarder easing into the turn.

Snowboards are manufactured with a sidecut on both sides. The amount of sidecut determines the curvature of the snowboard, which is of a certain constant radius along the sidecut edge. The figure below illustrates a sidecut snowboard, where

Source: http://www.flickr.com/photos/robbie1/2067112

The sidecut helps snowboarders make purely carved turns. It affects the physics by influencing the radius of purely carved turns, as will be discussed.

A purely carved turn can be done with a snowboard that is flat on the snow or tilted at an angle to the snow. The figure below illustrates a snowboard that is tilted at an angle

(Note: In reality the snowboard edge is pressed into the snow, for a given angle

When the snowboard is flat on the snow, a purely carved turn is executed when the radius of the turn

When the snowboard is not flat on the snow, and

Snowboards can be manufactured with a camber which is opposite to that shown in the figure above. In other words, the ends of the snowboard touch the ground while the middle of the snowboard is elevated. This is done to control how much the snowboard flattens out when the weight of the snowboarder is applied to the board. A flat snowboard distributes the weight of the snowboarder more evenly over the snow surface, which means the snowboard doesn't dig into the snow as much, and snow resistance is reduced. This is useful when snowboarding with no tilt on the board. Alternatively, if the snowboard is manufactured flat, then the middle of the snowboard would sink more than the ends when the snowboarder's weight is applied, and movement through the snow would be more difficult. However, the amount that the middle of the snowboard bends when a given weight is applied depends on the stiffness of the snowboard, which can vary in different snowboards.

There are times when reverse camber is desirable, such as when carving a turn, where the snowboard is tilted at a certain angle

To understand why a reverse camber is necessary when making a purely carved turn at some tilt angle

The projection of the sidecut radius

Therefore, the snowboard needs to have a reverse camber such that the sidecut radius, when projected onto the snow surface, is a circle. The reverse camber must be great enough to shorten the length of the semi-major axis so that it equals the length of the semi-minor axis, which gives us a circle (or very close to it). This allows the inside edge of the snowboard to make a purely carved turn. The figure below illustrates this.

The right amount of reverse camber reduces the length of the semi-major axis (in the previous figure) so that its length equals the length of the semi-minor axis (length

In the next section we will take a closer look at carving and how it relates to sidecut edge penetration into the snow.

For a given tilt angle

A snowboard with a smaller sidecut radius (and larger gap between sidecut edge and snow surface), can accommodate a greater amount of reverse camber, which means it can carve smaller radius turns. A snowboard with a larger sidecut radius (and smaller gap between sidecut edge and snow surface), can accommodate a lesser amount of reverse camber, which means it is best suited for carving larger radius turns.

Therefore in summary, snowboards with a larger sidecut radius

Given the complexity of all these inter-related factors, the ability of a snowboarder to make a purely carved turn comes down to his ability to recognize the terrain and make adjustments, based on the factors just mentioned. Clearly, carving adds substantial complexity to the physics of snowboarding.

In the next section we will look at the forces acting on a snowboarder that is going around a purely carved turn.

As explained in the previous section, making a purely carved turn is desirable for a snowboarder since it minimizes how much he slows down. Thus, it is useful to analyze the forces acting on a snowboarder during such a turn.

To begin the analysis, we must first define the orientation of the snowboarder on a slope of arbitrary inclination (which is the most general case). This is necessary because the force of gravity affecting the motion of the snowboarder changes depending on which direction he is going along the slope. The figure below shows a schematic defining the orientation of the snowboarder on the slope.

Where:

The coordinate system

(Note, we are assuming that the surface of the slope is planar and that three-dimensional effects are negligible).

Next, set up the free body diagram of the snowboarder, as shown in the schematic below.

Where:

Note that

The center of mass

where

Apply Newton's second law in the

The centripetal acceleration is given by

This equation is substituted into equation (2).

We can approximate the system as being in rotational equilibrium, which means there is zero moment acting on the system about the center of mass

Combine equations (1)-(3) and solve for the angle of lean

Note that the mass

To illustrate the use of the above equation, let's do a sample calculation. For example, let's say at a given instant

From before, the radius

When snowboarding on a slope, the radius of the turn

As a final check in the above solution, we must look at the angle of the force applied to the snowboard to ensure that it does not slip on the snow. But before doing that we must first acquire some background understanding, which will be given in the next section.

There are two cases to consider with regards to snowboard slippage and how to prevent it. The first case is when the snowboard is on a horizontal and flat snow surface. To avoid slipping, the force applied to the snowboard by the snowboarder's foot must be perpendicular (at 90°) to the plane of the snowboard in contact with the snow. This is because the friction between the snowboard and the snow is very small so any sideways force can cause the snowboard to move (slip).

The second case is when a snowboard is on a sloped snow surface. To avoid slipping, the snowboard must be pressed into the snow at a certain tilt angle, such that the component of the applied force, parallel to the plane of the snowboard, points into the snow. The schematic below illustrates this.

Where:

To prevent slipping, the angle

However, if the angle

By geometry, this means that for no slipping,

We can now check the sample calculation in the previous section, to see if the snowboard slips on the snow.

We must check the angle of the applied force

In the next section we will look at aerial tricks.

For some tricks, a snowboarder performs aerial acrobatics, spinning and twisting in the air. The basic physics principle at work here is the conservation of angular momentum. The angular momentum of the snowboarder is determined at takeoff (from the ramp), and cannot be changed once the snowboarder is airborne. So to make turns in the air the snowboarder must give himself initial rotation upon takeoff. Once airborne, the snowboarder can alter his body shape in order to produce an impressive aerial display of tricks and twists for the crowd, during which his angular momentum remains constant.

When it comes to aerial tricks, the physics of snowboarding is similar to the physics of skateboarding.

The picture below shows a snowboarder performing a frontside 180.

Source: http://www.flickr.com/photos/f-l-e-x/2319853663

In the next section we will look at pumping on a half-pipe.

Pumping on a half-pipe is used by snowboarders to increase their vertical take-off speed when they exit the pipe. This enables them to reach greater height and perform more aerial tricks, while airborne. The principle is exactly the same as for skateboarders pumping on a half-pipe.

The figure below shows a snowboarder in the curved portion of the half-pipe.

Source: http://www.flickr.com/photos/skaty222/3377825536

The figure below shows a snowboarder after he has exited the half-pipe and is airborne.

Source: http://www.flickr.com/photos/[email protected]/4338676131

The snowboarder is able to increase his speed on the half-pipe with his feet remaining firmly on the board. This begs the question, what is the physics taking place that enables the snowboarder to increase his speed on the half-pipe?

To increase his speed, the snowboarder crouches down in the straight part of the half-pipe. Then when he enters the curved portion of the half-pipe he lifts his body and arms up, which results in him exiting the pipe at greater speed than he would otherwise.

The basic snowboarding physics behind this phenomenon can be understood by applying the principle of angular impulse and momentum.

The schematic in this analysis is given below.

Where:

It is assumed that the half-pipe is a perfect circle with center at

The physics can be analyzed as a two-dimensional problem.

Now, apply the equation for angular impulse and momentum to the system (consisting of snowboarder plus board):

Where:

Σ

Here we are assuming that the body can be treated as rigid at positions (1) and (2), even though the snowboarder does in fact change his moment of inertia between these two positions. But as it turns out, when using this equation we only need to know the initial and final values of the moment of inertia of the body.

The line of action of the normal force

In the above equation isolate

Now,

Where:

In the above equation for

At positions (1) and (2), the velocity of the center of mass

These two velocities are parallel to the half-pipe since the body is rigid at positions (1) and (2).

Looking at the above equations for velocity, if the snowboarder makes

By continually pumping his body (by crouching down and lifting his body and arms up in the curved portion of the half-pipe), the snowboarder is able to continually increase his velocity, eventually allowing sufficient height to be reached (upon exiting the half-pipe) to perform a variety of mid-air tricks.

A more intuitive (non-mathematical) explanation of the physics taking place here is that pumping adds energy to the system in the same way that a child pumping on a swing adds energy, and results in him swinging higher. Therefore, the physics of pumping on a half-pipe is similar to the physics of pumping on a swing.

As a snowboarder lifts his arms and body up he feels resistance due to the force of centripetal acceleration which tends to push his body away from the center of rotation

If you want to see a really interesting problem related to the physics of snowboarding, check out this analysis for determining the optimal trajectory for a maximum jump on a half-pipe.

In the last section we will look at basic snowboard maintenance required for optimal performance.

Good snowboard maintenance also ties into the physics of snowboarding by optimizing the performance of the snowboard on the snow, as explained in the points below

• Waxing the bottom of a snowboard protects it from wear and water penetration, the latter of which can damage the snowboard. Wax also makes the bottom of the snowboard waterproof, reducing wet-drag (suction) friction, which is caused when excess water collects at the bottom of the snowboard.

• The edges of the snowboard must be kept sharp using a stone grinder, much like skate blades, to allow for easier turning and edge control.

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