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Measuring snow properties relevant to Mittuniversitetet snowsports & outdoor 10.06.2019 Development of measuring method to analyze snow properties

Measuring snow properties relevant to snowsports & outdoor

Development of measuring method to analyze snow properties

Sebastian Klein

Självständigt arbete Huvudområde: Mechanical Engineering MA,Thesis Högskolepoäng: 30 hp Termin/år: ST 2019 Handledare: Mikael Bäckström Examinator: Andrey Koptyug Kurskod/registreringsnummer: H4X94 Utbildningsprogram: Sportteknologi

Based on the Mid Sweden University template for technical reports, written by Magnus Eriksson, Kenneth Berg and Mårten Sjöstr öm. i Measuring snow properties relevant to Mittuniversitetet snowsports & outdoor 10.06.2019 Development of measuring method to analyze snow properties

Abstract Snow is a common surface on which a lot of sports competitions take place. We know a lot about our equipment, but there has been done very little research on the snow itself regarding the use in sports. The aim of this project is to create a measurement device to investigate the properties of different snow types. The snow compound on the ski slopes nowadays does not only exist of natural snow, a big part of it is machine-made snow and the most common one is produced with snow guns. There are different theories why skis glide on snow and that is why a lot of research has been done on the snow behavior. But the main goal in the ski industry is to improve the equipment. The measurement tool should be compact, so it is possible to carry it around on the ski slope, waterproof and should give electronic data, not like previous devices where you have to measure by hand. Additionally, it was decided to measure the surrounding data because it also has an influence on the snow state. First, a 3D-model has been created on the PC to have an idea of how the device should work and look like. The model consists of a tube, rails, a top part, and a falling weight. This device was very detailed, so it was decided to build a simpler prototype first to set up the sensors and check if everything is working. An Arduino has been set up to measure the sinkage depth with an ultrasonic sensor and an IMU to measure the inclination of the slope. Another Arduino has been programmed to measure the surrounding data like the air and snow temperature, humidity as well as the altitude. Inside the falling weight an accelerometer is placed to measure the acceleration during the impact and the deceleration due to the snow. A load cell is mounted on the bottom of the falling weight to measure the force during the impact and deceleration. All the data gets later evaluated in a MATLAB-application. A GUI was created for easier handling of the data. A database got created, so it is possible to save evaluated data and compare it later on.

Keywords: snow, hardness, ski, compaction, ski-snow interaction

Based on the Mid Sweden University template for technical reports, written by Magnus Eriksson, Kenneth Berg and Mårten Sjöstr öm. ii Measuring snow properties relevant to Mittuniversitetet snowsports & outdoor 10.06.2019 Development of measuring method to analyze snow properties

Zusammenfassung

Auf Schnee werden sehr viele unterschiedliche Sportarten mit unter- schiedlichem Equipment ausgeführt. Es wird sehr viel getan diese Aus- rüstung zu verbessern, jedoch wurde bisher sehr wenig Forschung betrie- ben im Bereich des Schnees, welcher für diese Sportarten essenziell als Untergrund ist. Dieses Projekt beschäftigt sich mit der Entwicklung eines neuen Messgerätes, mit dem es möglich ist, die Schnee Eigenschaften zu messen. Heutzutage besteht der Schnee, auf dem wir uns fortbewegen, nicht nur aus Naturschnee. Ein großer Anteil des Schnees wird mit Schneekanonen erzeugt. Dieser Schnee unterscheidet sich von seinen Ei- genschaften, wenn ein Schi darüber gleitet. Es gibt unterschiedliche The- orien warum ein Schi auf Schnee gleitet und die Wissenschaft beschäftigt sich mit diesem Thema schon seit langer Zeit. Die Industrie betrachtet hierbei jedoch nur ihre Produkte und nicht den Schnee. Das entwickelte Mesosystem sollte kompakt sein, da es möglich sein sollte es auf der Ski- piste zu transportieren. Ebenfalls sollte es wasserdicht sein und elektro- nische Daten liefern, im Gegensatz zu älteren Systemen, bei denen mit der Hand gemessen wurde. Zusätzlich sollten Umwelteinflüsse gemessen werden da sie das Ergebnis verändern können. Am Anfang wurde ein CAD 3D-Model erstellt, um eine Vorstellung zu erhalten, wie das Ge- rät aussehen sollte. Es besteht aus einer Röhre, Schienen, einem Fallge- wicht und einem Deckel. Dieses System war sehr detailliert und es wurde entschieden ein simplerer Prototyp zu entwickeln, um die Sensorik zu testen. Es wurde ein Arduino programmiert, um die Eintauchtiefe mittels Ultraschallsensor und mittels IMU die Neigung zu messen. Ein zweiter Arduino wurde verwendet, um die Umwelteinflüsse, wie Schnee- und Lufttemperaturen, Luftfeuchtigkeit so wie die Höhenlage zu messen. Im Inneren des Fallgewichts wurde ein Beschleunigungssensor angebracht, der die Beschleunigung und anschließende Abbremsung durch den Schnee misst. Am Boden des Fall Gewichts wurde eine Kraftmesszelle in- stalliert um die Kraft während dem Auftreffen und Abbremsen zu messen. Die so erhaltenen Daten werden mittels einer MATLAB-Applikation ausgewertet. Für eine leichtere Bedienung wurde eine GUI erstellt. Eben- falls wurde eine Datenbank kreiert, um die ausgewerteten Daten zu sam- meln und gegebenenfalls zu vergleichen.

Schlüsselwörter: Schnee, Härte, Schi, Schi-Schnee Interaktion

Based on the Mid Sweden University template for technical reports, written by Magnus Eriksson, Kenneth Berg and Mårten Sjöstr öm. iii Measuring snow properties relevant to Mittuniversitetet snowsports & outdoor 10.06.2019 Development of measuring method to analyze snow properties

Acknowledgments I want to thank all the people from the Mid Sweden University that supported me in this project, especially Mikael Bäckström and Andrey Kop- tyug. I want to thank the staff from the UAS Technikum Wien to make this Double-Degree possible. But I am most thankful to my parents and the rest of my family as well as my friends, who supported me all these years and helped me to finish my studies.

Based on the Mid Sweden University template for technical reports, written by Magnus Eriksson, Kenneth Berg and Mårten Sjöstr öm. iv Measuring snow properties relevant to Mittuniversitetet snowsports & outdoor 10.06.2019 Development of measuring method to analyze snow properties

Index Abstract ...... ii Acknowledgments ...... iv Index ...... v Abbreviation ...... 1 1 Introduction...... 2 1.1 Background ...... 2 1.2 Purpose ...... 3 1.3 Aim ...... 4 1.4 Problems ...... 4 2 Basics and state of the art...... 5 2.1 Impact on the environment ...... 5 2.2 Snow types ...... 5 2.2.1 Natural snow 5 2.2.2 Artificial snow 11 2.2.3 Dry and wet snow 14 2.2.4 Snow storage 14 2.3 Ski equipment ...... 15 2.3.1 Ski base 15 2.3.2 Wax 17 2.3.3 Velocity 18 2.4 Ski-snow interaction ...... 19 2.4.1 Gliding on snow 19 2.4.2 Compaction and plowing 22 2.5 Snow mechanics ...... 23 2.5.1 Water content 24 2.5.2 Compaction of snow 25 2.5.3 Temperature 31 2.5.4 Acoustics 31 2.6 Ski slope preparation ...... 33 2.6.1 Common preparation 34 2.6.2 Additional preparation for races 37 2.6.3 Other usage of snow preparation 39 2.7 State of the art – measurement devices...... 40 2.7.1 Kinosita-type hardness gauge 40 2.7.2 Gauges for testing sand in or for golf course sand bunkers 41 2.7.3 Soccer turf measurement 43

Based on the Mid Sweden University template for technical reports, written by Magnus Eriksson, Kenneth Berg and Mårten Sjöstr öm. v Measuring snow properties relevant to Mittuniversitetet snowsports & outdoor 10.06.2019 Development of measuring method to analyze snow properties

2.7.4 SnowMicroPen® 44 3 Methods ...... 46 3.1 Profile of requirements...... 46 3.2 Setup and evaluation ...... 46 4 Results 1 – Considered solution ...... 49 4.1 Construction...... 49 4.2 Measurement devices inside the tube ...... 51 5 Results 2 – Actual solution ...... 53 5.1 Construction...... 53 5.2 Measuring the ground distance ...... 54 5.3 Measurement of the surrounding factors ...... 56 5.4 Measurement device inside the tube...... 58 5.5 Manual measurement of the snow ...... 60 5.6 Evaluation ...... 60 5.6.1 Start page 60 5.6.2 Depth evaluation 61 5.6.3 Evaluation of surrounding data 64 5.6.4 Evaluation of missile data 67 5.6.5 Database 70 6 Results 3 – Anticipated results ...... 72 6.1 Acceleration data...... 72 6.2 Force data ...... 73 7 Conclusion...... 74 8 Discussion ...... 75 8.1 Improvement of the construction ...... 75 8.2 Improvement of measurement equipment ...... 75 8.3 Acoustic implement ...... 76 8.4 Improvement of evaluation ...... 76 9 Bibliography ...... 78 Appendix ...... 84

Based on the Mid Sweden University template for technical reports, written by Magnus Eriksson, Kenneth Berg and Mårten Sjöstr öm. vi Measuring snow properties relevant to Mittuniversitetet snowsports & outdoor 10.06.2019 Development of measuring method to analyze snow properties

Abbreviation

Acronyms CAD – Computer Aided Design GUI – Graphical User Interface IMU – Internal Measurement Unit MIUN – Mid Sweden University OLED – Organic Light Emitting Diode PE – Polyethylene RTC – Real Time Clock SLF – Schnee und Lawinen Forschung (Snow and Avalanche Research) SMP – SnowMicroPen

Mathematical

퐴퐶 – contact area 푃 – normal load 퐵 – ski width 푆 – surface area c0 – speed of sound in air 푉 – velocity ci – speed of sound in ice ∆푦 – vertical compaction dis- 푑 – depth tance ̅ 퐹 – resistance force 𝜌푠 – density of snow

퐹푐표푚푝 – compaction force 𝜎 – compressive strength of ice

푓푑 – dry friction force 휏 – shear strength of ice

퐹푖 – frontal impact force 휇 – friction coefficient 퐹푁 – normal force 휇푑 – plastic deformation of the 푔 – gravitation snow surface

ℎ – height 휇푑푟푦 – dry friction coefficient

퐻 – hardness of snow 휇푖 – heat conduction to the snow 퐿 – length of a ski 휇푚 – snow melting

푚푐 – mass of weight C 휇푝 – ploughing into the snow

푀푔 – force of air 휇푟 – heat conduction to the ski

Based on the Mid Sweden University template for technical reports, written by Magnus Eriksson, Kenneth Berg and Mårten Sjöström. 1 Measuring snow properties relevant to Mittuniversitetet snowsports & outdoor 10.06.2019 Development of measuring method to analyze snow properties

1 Introduction 1.1 Background Everybody knows what snow is. It is white and cold and if somebody talks about snow, everybody is thinking about star-shaped crystals. But snow does not always have this distinctive shape, there are a lot of different shapes and sizes. Nowadays it is not only the natural snow from the clouds that is lying on the ski slopes, but also artificial snow is a big part of the snow compound. Today most of the ski resorts nowadays have their own machines to produce snow and the lift operators want to guarantee the tourists a good experience on the slope and for that they need enough snow to attract more tourists. This snow guarantee is stated by many authors in the literature as the 100-day-rule (König and Abegg 1997) (Scott, McBoyle and Minogue 2007) (Dawson, Scott and McBoyle 2009). It says, that the slopes are skiable at least 100 days per season. They investigated different ski resorts and stated that, if the global warming keeps on, more and more resorts need more artificial snow or even have to close because it is not possible to produce enough snow to guarantee 100 days of snow on the slopes. But producing snow costs a lot of energy and further a lot of money. For the economic influence of snow, the region of the Alps will be considered. According to the Professional Association of the Austrian Cable Cars (2011) and Austrian Panel on Climate Change (2018) about two third of the ski slopes are provided with snowmaking facilities. In the season 2017/2018 about 528 million euros have been in- vested in the skiing slopes and about 108 million euros have been in- vested in snowmaking in Austria (WKO 2017). The question is if the artificial snow influences the experience for skiers on the slope. There have already been done some research on the properties of snow, but most of them have been conducted a long time ago, where artificial snowmaking was not as common as nowadays and the used measurement equipment is outdated. There are some newer researches about the snow properties, but these have been more concentrated on avalanche research and on snowy roads and not so much on the snow on a ski track.

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1.2 Purpose It is important to build a measurement device to investigate the different snow conditions in order to classify it in different aspects. There have been done some investigations on the snow properties, but most of them have been conducted a long time ago and with very old measurement equipment. So it is important to verify these investigations and develop the understanding about snow with the equipment that is available nowadays. First, you have to measure the hardness in order to correlate the results with the friction between the ski and the snow. It is possible to see under which conditions it is possible to go the fastest and in the next step to research on how it is possible to have these properties for example in an alpine ski race. Which is another point in investigating the surface hardness of snow, because not every snow sport needs the same surface. For alpine skis the desired surface is as hard as possible to go very fast. But for a common user or even beginner this is not the proper surface to ski or snowboard on, in terms of safety reasons. First, most of the riders would not handle the speed and it is quite hard to break on a hard and icy surface. Secondly if they fall the injury risk is higher because the impact is higher on a harder surface. Following this, it is also important for the industry of safety products to investigate the hardness of the snow. For example, for the producers of helmets, back protectors and wrist protectors it is necessary to find out, if their way of testing is the right one. It is important to investigate if they use the right force and if the application of the force is accurate. In other snow disciplines the snow has to have a completely different condition, like the landing area at freestyle competitions. Here, the snow is very soft, so the athletes do not hurt themselves when they crash at the landing. It is commonly known that there are different conditions of the snow hardness at different disciplines and also the preparation and grooming are done differently, but until now there is no regulation and standard of the snow hardness at competitions. With this device it should be possible to research on the snow hardness and produce a table of requirements for different disciplines of snow sports. Furthermore, it would be possible to use this measurement device to measure the hardness of the snow on the street and after the treatment with sand or salt.

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1.3 Aim The aim is to develop a new measurement device, that measures the snow properties on the surface of a ski track. For this a load cell and an accelerometer will be used, but also other sensors to measure the surrounding conditions like the temperature and humidity. This device should be lightweight and easy to carry, so it is possible to measure on the ski slope.

1.4 Problems The challenge in this project is the nature and consistency of the snow itself. It cannot be treated as a solid medium, because the snowpack consists of big crystals and these are only connected through small bonds. Since the aim is to develop a new measurement setup for snow properties, a big question is what to measure, because a lot of the parameters of snow influence each other. One parameter, the hardness, does not influence other parameters of the snow but is influenced by a lot of other parameters, for example the temperature or the preparation of the snow. But this property is strongly influencing the behavior of other materials touching the surface, like a ski. The hardness of snow is the resistance force for deformation of the snow. To detect the snow hardness the force that is used to penetrate and compress the snow gets measured. When the aim of the device is the measurement of the hardness, the problem is, that the hardness measurement is completely different of a porous medium compared to the measurement of normal solid building material. There is a high variability in the density of snow and the temperature has a big influence on the snow, so the field measurements get strongly influenced by the weather.

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2 Basics and state of the art 2.1 Impact on the environment The snow depth on a ski slope is considerably larger than off-piste because of the artificial snowmaking. Keller, et al. (2004) observed that the snow density increased during the winter season when they measured a density of 500 Kgm-³ in mid-December and a maximum of the compacted snowpack at a density of 700 Kgm-³. On the other hand, the snow density off-piste was measured with 400 Kgm-³ at the end of the winter. The density on the slope got increased by grooming the track, and on the off-piste the snow got denser by settling the new snow after a snow fall. They could confirm that the groomed slope’s density is not homogeneous. Ac- cording to them the thermal conductivity, snow density and snow hardness of the snow on the slope were scientifically higher than off-piste. In the case of hardness, it was 36 N on the groomed slope and in the case of off-piste it was 0.6 N. They could confirm by measurements, that there is no linear relationship between snow density, thermal conductivity and snow hardness. Normally the snow on the slope disappears about four weeks later than off-piste (Rixen, Häberli and Stöckli 2004) (Keller, et al. 2004). This means the vegetation under the ski slopes has less time to grow at the beginning of spring. 2.2 Snow types 2.2.1 Natural snow When natural snowflakes get “produced”, first the water on the ground from any source like the sea, big lakes and also on the land evaporates and forms clouds. When the water is in the atmosphere it cools down and gets back to its liquid state, this is known as nucleation. To form snow these water droplets need foreign nucleation, this is normally salt or dust. Also, the temperature has to fall below 0 °C for the possibility of snow. The number of nuclei, that are needed, depends on the temperature. At - 40 °C no nuclei are needed for snow. Then the ice crystals grow due to the diffusion between the water droplet and the ice crystal and because of the movement of the ice crystals inside the cloud. The crystals collide and gain mass due to riming. If these ice crystals get heavy enough, they fall down from the cloud. There are a lot of different shapes for these snowflakes. The star shapes, or dendrite, is the most known one, but there are many other differently shaped snow crystals. The shape depends on the temperature and the supersaturation during the fall of the crystal. By

Based on the Mid Sweden University template for technical reports, written by Magnus Eriksson, Kenneth Berg and 5 Measuring snow properties relevant to Mittuniversitetet snowsports & outdoor 10.06.2019 Development of measuring method to analyze snow properties looking at the different forms you can see, how big the difference between the air layers was. Wind-driven snow consists of fragmented snowflakes because they bump into each other during the fall. The shape determines where the metamorphism starts once the snow crystal is on the ground (Lind and Sanders 2004) (Karlöf, Axell and Slotfeld-Ellingsen 2005). In Figure 1 you can see different types of snowflakes. They all have a hexagonal shape. The reason for this will be explained more detailed in the following chapters.

Figure 1: Types of atmospheric snow crystals (source: (Lind and Sanders 2004))

Faceting and branching The understanding of why snowflakes look like how they look comes from the work of crystallography and metallurgy. A lot of scientists have been researching in these fields for decades. Nowadays it is possible to control the growth and the size of a crystal. Faceting (flat crystalline surface) is the main part of the crystal growth. The droplet freezes and then it forms facets because some parts collect material faster than others. The condensed molecules are attracted to round surfaces with a roughness on the atomic scales because there are better molecular bindings. The flat surface in the middle is less attractive because there are less possible chemical bonds. The geometry of the crystal is dependent on the geometry of the water molecule. When there is only faceting during the growth, the result is most likely just a hexagonal shaped crystal. These are also called prism facets. Sometimes you can still see the initial crystal in the center of complex shaped snow crystals. But faceting is not the only process in the creation of snow. When a crystal is relatively large, like more than half a millimeter, or the growth happens rapidly it starts to build

Based on the Mid Sweden University template for technical reports, written by Magnus Eriksson, Kenneth Berg and 6 Measuring snow properties relevant to Mittuniversitetet snowsports & outdoor 10.06.2019 Development of measuring method to analyze snow properties branches. This effect is called Mullins-Sekerka instability (Mullins and Sekerka 1963) (Mullins and Sekerka 1964). It explains the process of how the complex shaped crystals grow. When snow crystals grow, they use the water vapor around them. The diffusion plays a major role in this process because it takes a certain time for the molecules to reach the crystal. The growth is “diffusion limited”, because various regions try to get the molecules to grow. If there is a part that sticks out, the molecules will prefer this one, because it is easier to reach, and the diffusion distance is shorter. These parts accumulate more molecules and grow faster. By growing out these branches they get even bigger and build more side branches, initialized through random bumps or faceted tips. But the starting points are the six corners of the hexagonal crystal and therefore a snowflake has six arms. In crystal growth, the faceting and branching are the processes you have to consider. The faceting is there to stabilize, get flat surfaces and simple shapes. If there would only be faceting, all the crystals would have a simple prism shape. On the other hand, the branching is an inconsistent process that drives the crystal to complex shapes with a lot of structures, but no symmetry. The coaction of these two processes is important and is the reason why the appearance of snowflakes is as it is (K. Libbrecht 2007) (Yokoyama 1993).

Snow crystal shapes In Figure 2 you can see the schematic drawings of different snow crystal shapes and in Figure 3 you can see the same crystal shapes under the microscope. The stellar dendrite (Figure 2 a) and Figure 3 a)) are the most recognized snow crystals. They got their name from their star-shape look and the many branches. These crystals are relatively large, and you can see them easily on black fabric. They appear at a temperature of about - 15°C. In Figure 2 b) and Figure 3 b) you can see columnar snow crystals. They are very common, but because of their size, they are not so easy to spot especially the small and thin ones, these are called needles. They appear at a temperature of around -6 °C. Capped columns (Figure 2 c) and Figure 3 c)) are not so common. They form when they fall through different air temperatures. First, a column gets formed and then plates grow on the ends and sometimes they form even more layers of caps and columns. The caps get formed in air layers of -15 °C and the columns at -6 °C. In d) of Figure 2 and Figure 3 you can see triangular crystals. These get formed by the aerodynamic effects and are very small. The fernlike stellar dendrite (Figure 2 e) and Figure 3 e)) is similar to the stellar dendrite but even

Based on the Mid Sweden University template for technical reports, written by Magnus Eriksson, Kenneth Berg and 7 Measuring snow properties relevant to Mittuniversitetet snowsports & outdoor 10.06.2019 Development of measuring method to analyze snow properties larger and leafier. The sidearms run parallel to each other, but the crystals are not symmetrical. This kind of crystals get a size up to 5 mm. In Figure 2 f) and Figure 3 f) you can see diamond dust crystals. These are the small- est crystals and they have the simplest shape, the hexagonal prism. They appear at bitter cold weather. If two six-branched snow crystals collide, they can get stuck together and form a twelve-branched snow crystal (Figure 2 g) and Figure 3 g)). Sometimes the water droplets inside the cloud freeze to the crystal and then form a rimed snowflake or also called graupel. If it is completely covered in these water droplets it is called rime (Figure 2 h) and Figure 3 h)) (K. G. Libbrecht 2018) (K. Libbrecht 2007). In Figure 4 you can see a morphology diagram of snow crystals. It is the supersaturation, the water vapor in the air when the humidity is over 100%, compared to the temperature. It was first developed by the Japa- nese physicist Ukichiro Nakaya. It is possible to see that at lower supersaturation the crystals build out prism plates, normal prisms and hollow columns at -3 °C to -10 °C. At higher supersaturation, the shapes get more complex, because there are more water molecules in the air that can be accumulated by the crystal. At very cold temperatures plates or columns will grow depending on the supersaturation of the air.

a) b) c) d)

e) f) g) h)

Figure 2: Schematic shapes of snow crystals; a) stellar dendrites, b) columns and needles, c) capped columns, d) triangular crystals, e) fernlike stellar dendrites, f) diamond dust crystals, g) twelve-branched snowflakes, h) rimed snowflakes (source: snowcrystals.com)

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a) b) c) d)

e) f) g) h)

Figure 3: Pictures of different snow crystals under the microscope; a) stellar dendrites, b) columns and needles, c) capped columns, d) triangular crystals, e) fernlike stellar dendrites, f) diamond dust crystals, g) twelve-branched snowflakes, h) rimed snowflakes (source: snowcrystals.com)

Figure 4: Morphology diagram of snow crystals (source: (K. Libbrecht 2007))

Snow metamorphism After the snow is on the ground the structure of the crystals and the grains and in further consequence the snow properties change. This process is called metamorphism. There are two types of metamorphism the equi- temperature metamorphism and the temperature gradient metamorphism.

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2.2.1.1.1 Equi-temperature metamorphism Because of the thermodynamic instability of the highly faceted snow crystals, a high surface to volume ratio, the equi-temperature metamorphism happens. The snow crystal with high surface to volume ratio (for example dendrites) are very unstable and want to change their form rapidly. At first, the branches disappear and when this happens, the snowpack shrinks because of the lower particle size. On the other hand, the grain size in general increases. This happens because of the more efficient condensation of large particles compared to the small ones, which means that big ones grow faster. The small particles have a higher radius of curvature and therefore a higher vapor pressure compared to large particles. The sublimation process is more efficient of small particles. This type of metamorphism is destructive, the original shapes get destroyed and the density increases (S. C. Colbeck 1982). In Figure 5 the cycle of the equi-temperature metamorphism is shown. In the beginning, you can still see the branches and after a while just the core is intact. But it grew and got rounder. This break down of the dendrites and rounding of the grains result in a less stable snowpack. During the rounding of the grains, the contact points between the grains get stronger. This bonding occurs by the redistribution of water molecules that fill up the hollows between the grains. The available heat is an important factor for the redistribution and the rate of metamorphism increases with higher temperature. If there is high pressure on the snowpack the metamorphism rate increases. This is of importance for the preparation of the snow. This means when the groomer goes over the snow it increases the sintering rate. Summarized the equi-temperature metamorphism leads to:

• Rounding of grains • Increase of particle size • Increase of density • Structural change due to sintering

To allow the equi-temperature metamorphism to occur, the temperature gradient in the snowpack has to be low (Karlöf, Axell and Slotfeld- Ellingsen 2005).

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Figure 5: Evolution of snow crystal during equi-temperature metamorphism in days (source: (Karlöf, Axell and Slotfeld-Ellingsen 2005))

2.2.1.1.2 Temperature gradient metamorphism Most of the time the snowpack is just a seasonal variation. The surface of the snowpack is influenced by the temperature of the atmosphere. On the other hand, on the ground underneath the snow, there are constantly 0 °C. If there is a strong temperature gradient (>10 °C m-1) the temperature gradient metamorphism happens. This process creates hoar formation and increases the size of the snow particles. The occurring grains are an- gular and are poor for sintering. This means that the density and the structural strength of the snow get reduced. Because of the temperature gradient, the vapor between the pores starts to wander between warm and cold. This means a temperature difference from the bottom to the top in the alpine snowpack. If the vapor hits an ice crystal, it starts to freeze on its bottom and the crystal begins to grow. At the same time, the crystal starts to sublimate at the top and so new vapor gets created. This process leads to a complete renovation of the snowpack (Schneebeli, SLF 2018). 2.2.2 Artificial snow Nowadays it is common for nearly every ski resort to have some artificial snowmaking device. In the following part this artificial snow will also be called machine-made snow. To produce machine-made snow a lot of different devices have been built.

Snow gun The most common device is the snow gun with a fan or snow lances. When the temperature drops below -2 °C snow can be produced with

Based on the Mid Sweden University template for technical reports, written by Magnus Eriksson, Kenneth Berg and 11 Measuring snow properties relevant to Mittuniversitetet snowsports & outdoor 10.06.2019 Development of measuring method to analyze snow properties these machines. To start working a snow gun needs water, that is normally stored in a man-made pond located in the ski resort, and electricity. It produces a fog by shooting out the water with high-pressure through small nozzles which creates a mist. The water gets shot into the air about 6-9 m high and a similar process to the natural snowmaking starts and the nucleation begins. But the process is way shorter, and the snow has less time to freeze and form complex shapes (Lind and Sanders 2004). There are two different types of snow guns that are commonly used, the fan snow guns and so-called stick or lance snow guns. A fan snow gun uses a propeller in the back to blow out the water into the air to get a longer hang time for the mixing and freezing. These guns are known for their wide range, high capacity in all weather condition, low wind sensi- tivity and good overall performance. The fans can be portable or station- ary and can be mounted everywhere and have a swing arm to change the target area. On the other hand, the lances are tower mounted with a high mast of about 6-9 m height. Due to their height, the water has the necessary amount of time to freeze in the air. Lances are limited in their throw and very wind sensitive (Snowmakers 2018). Riding on natural snow is a completely different feeling than on machine-made snow. Not only off- road, but also on the ski track because of the different consistency of the snow crystals. The machine-made snow consists of much smaller grains and is round. It is also very compact and has less air chambers between the grains. By producing snow, the ski area operators want to guarantee snow also during the spring months and a good base layer of snow at the bottom. The artificial snow is much denser and therefore a good base for heavily used ski track. If you have a slope with only machine-made snow, it gets more compacted and harder. So if there is no snowfall, the track has a higher stability (Lind and Sanders 2004) (Delonge 2005). Moismann (1987) investigated the difference of artificial and natural snow and showed that:

• The snow profile of the artificial snow is more homogenous • The ice crystals are spherical and not dendritic • The melting process is slower due to the increased snow mass • The artificial snow contains more ice layers and lenses

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Snow containers If the weather is too warm, it is not possible to produce snow with the snow gun. But a lot of manufacturers of snowmaking devices have invented a product to generate snow even up to a temperature of +35 °C. These machines are normally in a container and transportable, so it is possible to build ski tracks for freestyle events or cross-country events nearly everywhere and even during summer. For ski resorts, there are also fixed versions that have a higher output of snow up to 2000 m³ per day. This system is based on the principle of fragmented ice production. Water flows over cool rollers, freezes and then it gets crushed to fine ice crystals. Then the particles get spread via a flexible hose. Precooling of the water is not necessary. These ice crystals appear white and have firn like consistency. According to the producers, this snow has excellent sliding characteristics. This artificial snow has a better cooling potential than regular snow and so it melts slower (SnowBOX GmbH 2009).

Snow chamber A new way to produce more natural like artificial snow has been invented by Neuschnee GmbH. To produce the best snow for skiing they use a temperature of about -15 °C because at this temperature so-called dendrites get formed. At a lower temperature like -10 °C the snow crystals would look like columns (Delonge 2005). To generate snow a so-called “cloud chamber” was built and water vapor gets sprayed into this chamber. Then small water droplets as a fog get added with pressurized air at a temperature of -15 °C under laboratory conditions. The water droplets freeze and the vapor freezes onto the droplets to form dendrites or at lower temperatures other crystal shapes. The construction consists of an aluminum structure and a polyethylene canvas with a volume of 2.7 m³. To create the fog that is infused into the chamber an ultrasonic atomizer is used. The fog is continuously added and a fan provides circulation inside the chamber. The ice particles inside the chamber are the condensation nuclei to create ice crystals. This snow is more lightweight and has a smaller density than conventional artificial snow. This also means that they have a smaller water consumption and lower energy usage. Out of one m³ of water, it is possible to produce 15 m³ of snow (Enzenhofer, et al. 2016). This product is still a start-up project and the cloud chambers are not commercially available at the market, so this kind of snowmaking will not be considered for testing.

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2.2.3 Dry and wet snow There is also another way to distinguish between two snow types, the wet and the dry snow. Right after the snow has fallen there is very less liquid water present in the snowpack and this type of snow is referred to as dry snow. On the other hand, during the melting season, there is a lot of liquid water in the snowpack and this snow is called wet snow (Fierz, et al. 2009). Because of this there is a divergence in dry and wet lubrication when riding on snow. But this will be discussed later in the chapter “2.4 Ski-snow interaction” and in the chapter “2.5 Snow mechanics”.

2.2.4 Snow storage Due to the warm winters and less snow in the skiing areas the resorts started to store the snow from the previous season and put it on the slopes again at the beginning of the next season. So it is possible to start the skiing season earlier and to have a ground layer for the upcoming season. It is more efficient and saves money and energy compared to the artificial snow production. Currently, there are two systems on how to save the snow during the warm months. The first one is to cover the snow with a layer of sawdust. This layer is about 40 cm thick. The alternative is to cover the snow with a geotextile. Normally two layers of geotextile are used and the biggest provider of geotextile for snow storage is the Nor- wegian company Geosynthia. The properties of the snow change during the storing in the warm months. If the snow is stored for one season, the density increases to about 500-700 kg/m³. When the snow is stored for two years it becomes icier. Because of the melting and recrystallization there are big junks of ice in the different layers of the stored snow. When cov- ering the snow with sawdust there is a loss of volume to about 20% of the initial amount and when covered with geotextile a loss of about 50%. Nowadays also glaciers get covered in geotextiles over the summer to prevent them from melting (Söderström 2018).

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2.3 Ski equipment An important part of the ski-snow interaction is of course the ski equipment itself. In Figure 6 you can see the different layers of a alpine ski built with a sandwich construction. On the top you have the so-called top sheet. It usually consists of a polyethylene sheet that has to be durable and has only an optical aspect. The next layer is a tri-axial fiber cloth out of carbon or glass fiber, depending on the quality of the ski. This cloth is authoritative for the bending and torsional stiffness of the ski. In the middle you have the core out of wood in a high-quality ski or foam on a ski with less quality. Underneath this layer is another layer of fiber cloth and then the ski base consisting of polyethylene. On the side there are the side walls out of ABS or polyurethane and the steel edges. All the parts are connected with epoxy resin.

Figure 6: Layers of a ski For the friction of a ski, the running surface is of big interest. It gets treated by carving a structure in the surface and waxing. By doing this right it is possible to lower the friction of the ski on the snow. 2.3.1 Ski base The requirements for a ski base are: abrasion resistant, as hydrophobic as possible and porous enough to hold wax (Glenne 1987). There are normally two types of different ski bases, the extruded PE-HD-HMW or the sintered PE-HD-UHMW. For less expensive skis the extruded PE-HD- HMW is used because the production costs are lower. A thermoplastic material gets melted in a heated cylinder. In an extrusion screw it gets homogenized and is then pressed through a flat film extrusion die. After that, it gets cooled or milled. When the ski is from higher quality the standard product for the ski base is the sintered PE-HD-UHMW. During the sintering process a powdered plastic with high molecular weight is

Based on the Mid Sweden University template for technical reports, written by Magnus Eriksson, Kenneth Berg and 15 Measuring snow properties relevant to Mittuniversitetet snowsports & outdoor 10.06.2019 Development of measuring method to analyze snow properties used. High-molecular polymers like UHMW-PE have such a high viscos- ity, that it is not possible to extrude them. In Figure 7 you can see the steps of the sintering process. At first, the material gets homogenized in a blender, then it is filled into a form and compressed using heat and pressure. The small grains melt and the boundaries fuse into a compact structure. Then the pressed disc with a diameter of about 1000 mm gets processed further. For the ski base, the desired film gets peeled of the role. Because of the limited height of the forms two of these sintered discs have to be welded together before peelingoff to get the running surface for snowboards, because of their bigger width (ISOSPORT 2017).

Figure 7: Scheme of the sintering process (source: (ISOSPORT 2017))

Structure For optimizing the speed of the ski at wet conditions the people, who prepare skis for the professional athletes, roughen the ski base, put in small diagonal and longitudinal grooves, heat treat the ski base and add the right wax. This way the wetted contact area gets smaller by channeling of excess water and increased hydrophobicity. You can see the functional variation of the sliding resistance compared to the roughness of the running surface in Figure 8 (Glenne 1987).

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Figure 8: Functional variation of sliding resistance versus surface roughness (source: (Glenne 1987))

Temperature effect of the ski base If a black surface gets heated by solar light while lying in the snow, it is about 45 times more absorptive than a white polyethylene base. This means if you switch from a white to a black running surface, it is possible to generate about 91 W more heat per ski, which means, you can double the calculated frictional heat production at a speed of 4.5 m/s or about four times more at a speed of 40 m/s. It could be that the effect of solar heating is overestimated. But it shows that a black running surface runs on a significantly higher temperature compared to a white ski base, which concludes that the color of the running surface is important. Even if the solar effect is overestimated, it is important for Nordic skiers, because there is still a significant difference according to Colbeck and Perovich (2004). 2.3.2 Wax There are two types of waxes, the hard wax and the liquid wax. To apply the hard wax, it gets heated up with an iron and is worked into the base. After re-hardening, the surplus material gets scraped off with a blade. The leftover layer of wax is between 0.005 and 0.02 mm thick. If it would be thicker, it would attract dust, and this increases the friction (Lind and Sanders 2004). To apply the liquid wax, you simply take a sponge and rub it on. There are different waxes for different temperatures and snow conditions. Normally the manufacturers dye them differently, so it is easier to distinguish between them, this is just the result of artificial dying. When looking closer at the material, you will work out, that the polyethylene (PE) has an amorphous and a crystalline part in his structure. The long chains in the UHMW-PE form the crystalline part, and it has also a

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large part of amorphous structure to absorb the wax. In Figure 9 you see the structure of UHMW-PE. The wax particles are just in the amorphous part and fill up the open structures. There is no wax in the crystalline part. To measure the ratio of amorphous to crystalline parts, you measure the density. The lower the density, the more amorphous parts are in the UHMW-PE (Karlöf, Axell and Slotfeld-Ellingsen 2005).

Figure 9: Structure of the UHMW-PE; crystalline and amorphous parts (source: (Karlöf, Axell and Slotfeld-Ellingsen 2005)) In Figure 10 you can see the different contact angles Ɵ from a water droplet on a hydrophobic and a hydrophilic surface. The angles are a good approximation of the adhesion (Jellinek 1957). The adhesion is a good indicator of the friction between two surfaces. Regarding the contact angle, you can say that with a higher contact angle the coefficient of friction is lower.

Figure 10: a. Water droplet on a hydrophobic surface; b. Water droplet on a hydrophilic surface (source: (Karlöf, Axell and Slotfeld-Ellingsen 2005)) 2.3.3 Velocity According to Glenne (1987) the velocity has a big influence on friction. But the runner’s velocity varies also a lot with the change of other parameters like the temperature. Colbeck (1992) summarized the influence of

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the velocity as followed: When the velocity increases at a speed from 5 m/s – 10 m/s also the friction increases. On low speeds of 0.03 m/s, the friction of the slider is still the same as the static value and until 5 m/s the friction decreases rapidly (Bowden and Tabor 1964). Colbeck (1988) defined these characteristics of the decrease and the increase of friction at high and low speeds with the dynamics of the water film. 2.4 Ski-snow interaction When talking about the ski-snow interaction you talk about how fast or slow the ski glides over the snow. To answer this question, you have to look at the friction between the slider material and the snow. According to Hämäläinen and Spring (1986) the friction coefficient consists of a lot of different parameters (Equation 1):

휇 = 휇푟 + 휇푖 + 휇푚 + 휇푑 + 휇푝 Equation 1

• µr → heat conduction to the ski

• µi → heat conduction to the snow

• µm → snow melting

• µd → plastic deformation of the snow surface

• µp →plowing into the snow

Also, the temperature has a big influence on the gliding. When sliding at low speed with metal or plastics a linear increase of the friction at decreasing temperature has been observed by Meller (1974). 2.4.1 Gliding on snow There are different theories about why or how a ski slides over the snow. This chapter will have a look at the most common theories.

Meltwater film If you talk about meltwater lubrication it is assumed, that there is a liquid film between the two gliding surfaces, the bottom of the ski and the snow. This is the most common theory about the gliding on snow. This liquid film has to be thicker than the roughness of the surface, so the two surfaces are really separated and have no contact (Karlöf, Axell and Slotfeld- Ellingsen 2005). This water film has been measured by Ambach and Mayr (1981). They said that it is only possible to measure the water film during gliding because otherwise, it would freeze instantly. They also observed that the thickness of the film is dependent on snow temperature, air temperature, speed, and preparation of the gliding surface. The preparation

Based on the Mid Sweden University template for technical reports, written by Magnus Eriksson, Kenneth Berg and 19 Measuring snow properties relevant to Mittuniversitetet snowsports & outdoor 10.06.2019 Development of measuring method to analyze snow properties of the gliding surface means different structures and different waxes. Also, the gliding properties of the used waxes by TOKO suited the proposed temperatures regarding the thickness of the film. From -6 °C to -11 °C they monitored an improvement of the gliding properties and at the same time an increase of the water film. The origins of the meltwater have been summarized by Slotfeldt-Ellingsen and Torgersen (1983):

• The liquid phase which coexists with ice during a normal melting-freezing process • By precipitation of supercooled water droplets or condensation of water vapor • Water with a lowered freezing point due to dissolved impurities, capillary or surface effects • Water caused by melting from frictional heat • Water caused by pressure-melting (only at temperatures above - 2°C) (Reynolds 1899) (Barnes, Tabor and Walker 1971)

Surface melting There is also a new theory about how gliding on snow is possible. Despite the pressure melting is taught in a lot of textbooks, if you have a look at the calculations you can clearly see, that this procedure cannot explain all of the sliding because you would need a temperature near the melting point to have the conditions to glide on snow. The same theory is used to explain the sliding on ice because it is the same material but if you ice skate at about 0 °C, it would be quite dangerous. It has to be around the melting point because the melting point gets just lowered a little bit by pressure melting. The new theory of surface melting says that there is always a liquid film on the surface. It “builds a thin coating of its liquid phase below the normal melting point even if the temperature is the same inside and outside the solid. The molecules on the surface have the lowest chemical bonds and they vibrate more violently as the temperature warms them. At a significant higher temperature, but below the melting point, the molecules start to build a liquid-like layer.” (Wettlaufer and Dash 2000)

Dry friction When talking about dry friction the dry is referred to the snow. Very dry snow is present when the meltwater ratio is very low, this is normally the case at very cold temperatures. The dry friction then happens, because there is no lubrication between the slider and the snow, and they have

Based on the Mid Sweden University template for technical reports, written by Magnus Eriksson, Kenneth Berg and 20 Measuring snow properties relevant to Mittuniversitetet snowsports & outdoor 10.06.2019 Development of measuring method to analyze snow properties direct contact. Dry friction occurs at very low temperatures and at a low speed. The theory by Bowden and Tabor (1964) says, that the harder surface will cut into the weaker one and the friction will increase. Since PE is softer than ice you have to adapt the hardness of the sliding surface to match the hardness of the snow (Karlöf, Axell and Slotfeld-Ellingsen 2005). This friction, without any meltwater lubrication, is even described as riding on the sand by Bowden (1953). By looking at this problem more precise: “The total area of the ski bottom that makes contact with these ice grains, 퐴퐶is given by (Equation 2):

퐴퐶 = 퐹푁 /𝜎 Equation 2 where 𝜎 is the unconfined, compressive strength of the ice and 퐹푁 is the normal force, the weight of the skier. We assure that dry friction results from the shear fracture of the asperities over the contact area of the ski bottom, 퐴퐶. The total dry friction force 푓푑, becomes (Equation 3, Equation 4): 푓푑 = 휏퐴퐶 = 퐹푁휏 /𝜎 Equation 3

Or 휇푑푟푦 = 휏/𝜎 Equation 4 which 휏 is the shear strength of ice. Using measured values of the tensile and compressive failure stresses for ice, we find that the coefficient of friction for dry snow, 휇푑푟푦 drops from 0.32 at 0 °C to about 0.13 at -32 °C.” (Lind and Sanders 2004)

Mixed lubrication This kind of friction is the most common when riding on snow. There is direct contact like at the dry friction, but also a meltwater film between the snow and the gliding surface at another part of the ski. It is a combination of the two spread over the whole length of the ski. The thickness depends on the used wax, the snow temperature, the running surface temperature and the velocity. It is always important to use the proper wax on the proper snow surface at the right temperature (Karlöf, Axell and Slotfeld-Ellingsen 2005).

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In Figure 11 a) you can see a polished hard slider going over old dry snow, where the ice grains are smooth due to the melting and refreezing cycle. Here the ski surface will deform elastically. When there is a hard slider and dry new snow, the ski surface will polish the hard ice crystals by frac- turing them (Figure 11 b)). In Figure 11 c) a soft slider glides over the old snow with meltwater lubrication, but the film is not continuously over the whole surface. In Figure 11 d) you can see a soft slider on new dry snow. In this scenario, the ski surface gets smoothened by the sharp ice crystals. The least friction occurs at the meltwater lubrication in Figure 11 c)

Figure 11: Interaction of ski and slider surface at different conditions (source: (Lind and Sanders 2004))

2.4.2 Compaction and plowing The plowing effect is an important term when riding on a non-groomed track. The energy for sliding has to be more than the energy loss from the compaction and displacement and also the lifting of snow particles. Glenne (1987) proposed some equations for compacting and plowing. The quasi-plastic compaction, that occurs, can be described as followed (Equation 5):

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∆푦 퐹 = ( ) 푃 푐표푚푝 퐿 Equation 5

Where ∆푦 is the vertical compaction distance, the length of the ski is L and the normal load is 푃. For the displacement or frontal impact resistance he proposed the following (Equation 6):

퐹푖 = 𝜌푠 퐵(∆푦)푉² Equation 6

When 퐵 is the ski width, 𝜌푠 is the density of the snow, 푉 is the velocity and ∆푦 is again the vertical compaction distance. There is currently no equation for the lift, but it has an unremarkable influence when riding in the deep snow (S. C. Colbeck 1992) (Karlöf, Axell and Slotfeld-Ellingsen 2005). On the groomed track the plowing can have an influence on the riding. There are authors that say it is negligible (Lind and Sanders 2004) and some have the opinion that it makes a huge difference (Karlöf, Axell and Slotfeld-Ellingsen 2005) (Hämäläinen and Spring 1986). Since alpine skiing has gotten a high-tech performance sport and every aspect, even if it just has a small influence, can be of advantage if considered. In professional skiing, a ski with better compaction and plowing properties could possibly be an advantage and the athlete can win a race easier. 2.5 Snow mechanics The main variables that have an influence on the sliding snow resistance have been summarized by Glenne (1987):

• Snow crystal size and angularity (metamorphism) • Bearing load on snow (local contact pressure) • Slider area, shape, and elasticity • Base material (hydrophobicity) • Material texture • Sliding velocity • Snow compressive strength • Snow moisture and meltwater • Snow density and compaction • Snow crystal hardness

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The snow crystal size and angularity are described in the chapter “2.2 Snow types”. Everything regarding ski and rider is discussed in the chapters “2.3 Ski equipment” and “2.4 Ski-snow interaction” and the remaining parts like snow compressive strength, moisture and meltwater, density, compaction and temperature are characterized in the following chapter. 2.5.1 Water content The snow gets wet when it starts raining or the snow begins to melt. The liquid water infiltration depends on a lot of factors, like snow structure, temperature, slope angle and the amount that gets into the snow. It is dif- ficult to measure the liquid water content right. The wetness of the snow has as well a big influence on the snow mechanics. If the liquid water content is low in the snow, it can reduce the strength of the snow (Techel and Pielmeier 2011). The strength of temperature gradient snow is way lower at lower liquid water content. Techel, Pielmeier and Schneebeli (2011) and also Colbeck (1982) detected a loss of strength at about 8 vol % in seasonal snow. If you look at the snow from an electromagnetic point of view it is a heterogeneous dielectric material consisting of three com- ponents: ice particles, air and liquid water. The dielectric function of ice and water is depending on frequency and temperature (Evans 1965). Therefore, also the function of snow is dependent on these factors (Denoth 1989). There are a lot of measurements on how to identify the liquid water content in snow, but most of them are time-consuming and have to be done in the laboratory. Less time consuming and also measur- able in the field are the snow fork, denothmeter (Figure 12) and the hand test. In Table 1 you can see the indexes for the hand test. The hand test is a common way to detect the wetness of the snow in avalanche research and it is also used in the international observational guidelines (WSL 2008), but it is not very accurate. The snow fork was invented by Sihvola and Tiuri (1986). It consists of two spikes that get pushed into the snow. The device operates at about 1GHz. It measures the changes in the reso- nance curve between air and snow and at the same time the real and the imaginary part of the permittivity. When it is inserted into the snow it compresses the snow which gives an error of about 2% in the real part of the permittivity (Sihvola and Tiuri 1986). The first denothmeter was introduced by Denoth (1989). It is a simple plate condenser and consists of a steel plate of 10 x 13 cm². With this device the permittivity of snow can

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be measured but to solve the imaginary part a separate density measurement has to be done, so it is possible to calculate the liquid water content (Techel and Pielmeier 2011).

Figure 12: Denothmeter (left), Snowfork (right) (source: (Techel and Pielmeier 2011))

Table 1: Hand test for estimating the liquid water content in the snow (source: (Techel and Pielmeier 2011) )

2.5.2 Compaction of snow An important factor for an impact test is the compaction and the density. It describes the behavior of the snow after an impact. Since snow is a highly porous material it has high and largely irreversible compressibility. This is the biggest difference to ice and other engineering materials (Meller 1974) (Abele and Gow 1975).

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Density The Youngs modulus gets higher if the density increases and it especially gets higher with time during sintering. When the snow gets groomed it is a lot higher compared to the natural process (Meller 1974). Wakahama and Sato (1977) investigated the deformation of snow with a cylindric impactor and observed an increase of the plastic wave velocity at an increase of density with dry snow. They also observed that, when the snow gets impacted, just the first few millimeters get compressed and the underly- ing snow is not affected by the compaction. In Figure 13 the compression strength compared to the density is shown and that with higher density the compression strength increases. But on the other hand, wet spring snow has high density but low strength.

Figure 13: Density compared to compression strength (source: (SLF 2018)) Figure 14 shows the different densities in the snow layer to a depth of 4 cm on the ski slopes. You can see that the highest density is about 460 kg/m³ and this is the highest density you can compact the snow with a caterpillar grooming device. The first layer is mainly compacted by the skiers going over it (SLF 2018). To measure the density a normal scale is used. You take a tube and insert it perpendicular to the top snow layer. Then you measure the tube without and with snow and since you know the dimensions of the tube you can calculate the density (Nachbauer, Schröcksnadl and Lackinger 1996).

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Figure 14: Density of different snow layers on the ski slope (modified source: (SLF 2018))

Compression Theile, et al. (2009) executed an impact loading test where they compressed snow inside a tube with a ski base material at different loads. In Figure 15 you can see their results of two consecutive impacts. The first one has an oscillation at the beginning, because of the failure of the bonds from the surface grains. After some time, the force starts to rise continuously and at the end, you can see the unloading. At the second impact the force starts to rise continuously from the beginning, this means that the deformation and failure of the weak surface bonds are permanent.

Figure 15: Force-displacement curve of two consecutive impacts (modified source: (Theile, et al. 2009))

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Another interesting result is shown in Figure 16. It displays the loading and unloading process on an impact on snow. You can see that the total displacement of the snow is just 22 µm at 140 N and according to Theile, et al. a standard deviation of 20% is quite reasonable when measuring snow. The loading follows another path than the unloading, so this means that the loading curve is a hysteresis loop. At first, the ski surface has contact to only a few grains and these have to bear all the load. At this point, the bonds fail and afterwards more and more grains get into contact with the ski base and reach a constant value of 0.3 N per grain. To cluster the deformation Theile, et al. suggested four types of deformation:

• Brittle failure of the bonds of the grains at the surface o Completely displaced • Highly localized failure of the ice on top of the grains at the contact with the ski o Mixture of plastic flow and micro-cracking • Elastic deformation of the ski base and the snow matrix o At first 2-3 µm and then 0.5 µm • Delayed elastic deformation of the snow matrix o Fully recovered after unloading (20 µm)

When looking at the ski, the energy dissipated is calculated as followed

“The total energy dissipation of a ski, P is simply P = µvFn where µ is the frictional coefficient of the ski on snow, v is velocity and Fn is the normal load. For a racing ski, µ = 0.1, v = 20 m/s and Fn = 400 N which yields 800 J/s. The area of the hysteresis loop (860 x 10-6 J) corresponds to the energy lost to compaction of around 103 mm2 of snow. A 7-cm wide ski, moving with 20 m/s, compacts 1.4 x 106 mm2/s of snow. Hence the energy lost to snow compaction of this ski amounts to approximately 1 J/s, 0.1% of the total energy dissipation. Therefore, snow deformation can be neglected on a hard ski track leaving thermal energy dissipation the dominant process.” (Theile, et al. 2009)

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Figure 16:Loading and unloading cycle of the impact (source: (Theile, et al. 2009))

Yosida, et al. (1957) tested the snow on its compressibility with impact tests of a cylinder on a block of snow and defined 4 different types of snow and in Figure 17 you can see the resistance force of these different snow types:

Figure 17: Four types of resisting force of composite snow; A) soft compact snow. B) wet granular snow, C) compact snow, D) soft fresh snow (source: (Yosida, et al. 1957)) • A-type = soft compact snow o Peak of resistance force at the beginning then steady o Considerably uniform in its structure o No distinct stratification o Rods about 1mm • B-type = wet granular snow o Oscillogram of the resisting force o No region between compressed/undeformed snow ▪ No distinct limited region of compressed snow o Like gelatin gel when deformed o Linked by weak viscous forces o No determination for the time of relaxation of wet snow → guess 0.5 s

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• C-type = compact snow o Resisting force rises stepwise o At each step wavy o Conclusion of the different snow layers o Mix of a- and b-type snow • D-type = soft fresh snow o Connection between snow crystals weak, nearly no resistance force o But after compression

Colbeck, Shaw and Lemieux (1978) detected during their compression test that with increasing liquid water content, snow can get compressed easier. Floyer and Jamieson (2006) investigated on how an impactor pen- etrates the snow surface. In Figure 18 you can see a schematic about a spike penetrating the snow. The arrows show the hypothetical velocity vector of snow particles. The deformation zone is the area under the round tip that gives feedback about the movement of the rod and the “compaction zone” is a term used by engineering geology and describes the deformation of porous rocks. It is the area underneath the tip of the rod where the density is uniform. There is nearly no further densification in this zone. The compaction force is transferred to the outer side of the compacted zone and does not get any denser.

Figure 18: Schematic of the compaction zone (C) and deformation zone (D) (source: (Floyer and Jamieson 2006))

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2.5.3 Temperature The hardness of the snow is mostly influenced by its density and temperature. Tusima (1975) measured the following snow densities at different temperatures from 0 to -56 °C:

• New snow with density < 0.2 g/cm³ • Fine-grained compact snow 0.2 - 0.3 g/cm³ • Old fine-grained compacted > 0.3 g/m³ • Artificial compacted snow 0.43 - 0.69 g/cm³

He showed that the hardness of every snow type increases when the temperature decreases from 0 °C to -40 °C except the new snow where no change in hardness has been observed. But at temperatures below -40 °C the temperature has no influence on the hardness anymore. As already mentioned, the density and the temperature have the main influence on the snow hardness. Density is seen as an intrinsic property of snow and temperature is seen as a changeable variable (Tusima 1971). Tusima proposed that different snow types should be compared at a specific temperature of -5 °C. The influence of the snow temperature on the friction has been observed by Buhl , Fauve and Rhyner (2001). They observed that friction is the lowest at -3 °C and increased by decreasing temperature as well as increasing temperature up to 0 °C. They obtained these results in the laboratory and also in the field. The temperature can also be used to measure the wetness of snow because the snow is expected to be dry under a temperature of 0 °C (Techel and Pielmeier 2011). Also, the speed of sound is dependent on the temperature. Öura (1952) stored snow samples in a cold room and lowered the temperature. Afterwards the samples have been put outside and the sound speed was measured for eight hours. This data shows, that the speed of sound in granular snow is not influenced by temperature, but the speed in compacted snow increases when the temperature increases. 2.5.4 Acoustics When there is a lot of snow in the area near the Japanese sea, people have trouble understanding each other when talking. This is referred to as the quietness of the snow and shows that the snow absorbs a lot of the sound. In measurements from Iwase, Sakuma and Yoshihisa (2001) you can see that in a depth of just 0.5 m more than 90% of the sound gets absorbed at

Based on the Mid Sweden University template for technical reports, written by Magnus Eriksson, Kenneth Berg and 31 Measuring snow properties relevant to Mittuniversitetet snowsports & outdoor 10.06.2019 Development of measuring method to analyze snow properties a frequency higher than 50 Hz. The acoustic behavior of snow is interesting because the sound is induced into a material and the propagation is then the movement of the particles in this material. The acoustic properties are closely related to the mechanical properties of the material. Nor- mally also some properties get tested in the lab with acoustic experiments. Snow is a porous material and so this interaction gets very complicated because you have a solid framework and in between the pore fluid or air. The snow structure has a big influence on the acoustic behavior of snow. The acoustic measurement is a good indicator for the stress state and history of a material.

Snow as a continuous medium In earlier years some authors used to treat the snow in their experiments and calculations as continues material. This makes it easier to measure the medium but impossible to answer the important questions right because the theory and experiments vary too much. On the other hand, these acoustic techniques have been used to determine some properties of very bulk snow with a high density (Sommerfeld 1982). Especially the data collected from Johnson (1978). Although his calculations differ greatly to his experiment, his conclusion that two interacting modes of propagation exist in snow could be right.

Snow as a porous medium Öura (1952) was one of the first, who investigated the sound properties of snow, and he treated the snow as a porous material. He tested snow with a low density and his data did not correlate with later studies from Yamada, et al. (1974). The difference of these studies could be explained by Sommerfeld (1982) by the fact that the pore air has more influence on sound propagation at the snow with a density below 200 kgm-³. On the other hand, in the snow with a density over 300 kgm-³ the ice network is more important. In general, you can say, that the speed of sound is faster if there is less structure in the composited snow. It is expected, that “in a complicated structure the direction of air flow in the pores is less likely to be aligned with a given macroscopic pressure gradient in the sample. Thus, the effective inertia of the fluid flow increases with the increasing complexities of the structure” (Lee and Rogers 1985). Figure 19 shows the speed of sound in relation to the density of snow. The speed of sound in ice is marked as ci and the speed in air is marked as c0. At first, the speed decreases in low density snow but when the snow is denser than about 300 kgm-3 the speed of sound increases again.

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Figure 19: Speed of sound in snow over density (source: (Bogorodskii, Gavrilo and Nikitin 1974)) 2.6 Ski slope preparation When considering the mechanical properties of snow, the right preparation of the snow is an important aspect for the skier, for the casual rider as well as for the professional athletes. It is widely known that although it is the same surface, the slopes get an extra treatment prior to an important race. A good indicator for the durability of the slope is the density and it varies very strongly from new snow or a racetrack, and even in the different disciplines there is a difference. The densities for a few different conditions are (SLF 2018):

• New snow: 50-250 kgm-³ • Average ski slope: 480 kgm-³ • Downhill racing slope: 300-500 kgm-³ • Super-g racing slope: ~550 kgm-³ • Slalom racing slope: ~600 kgm-³

The density does get changed by natural influence when the snow just has the time to settle, but on the slope normally a professional grooming device gets used, and every day after the lifts get closed in a ski resort the caterpillar machines roll out and prepare the slopes for the next day. The first grooming devices date back to the year 1939. But the aim of these machines was easier gliding for sledges on the roads. Horses have been used to tow a heavy agriculture roller over the street. Then in the 1950s, the first proper grooming devices for ski slopes have been introduced. The machine was towed by a skier down the hill and had blades in the

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front to powder up the hard snow and then afterwards to compact the snow. A whole armada of skiers with these machines was used to flatten out a ski slope (Masia 2018). More or less the same principle is used with the modern high-tech caterpillar machines to prepare the track. 2.6.1 Common preparation An ordinary skier expects a flat surface in the morning, enough snow on every part of the track for skiing and long durability so that the muggles are not on the track after one hour of skiing. The first task during the night for the groomer is to flatten out the ski track. If there is not that much snow left to spread it equally, it is possible to ride on the track and also to spread the new machine-made snow on the slopes. To ensure longer durability during the day, the snow has to be processed and left overnight. The grooming of a ski slope is considered an art because you have to deal with a lot of things. At first, there is the weather because unless it is an indoor ski park, you cannot control the weather, the temperature and the condition during the day and during the night. These have a big influence on the behavior of the snow. As already mentioned before especially the temperature has a big influence on a lot of the snow properties. The temperature of the snow depends on the heat balance, which is the difference between gain and loss of heat energy. If it is positive, the snow temperature rises and at a certain point the snow melts. If it is negative, the snow temperature decreases. The heat balance is strongly connected to the radiation balance of the snow (Figure 20). The terrestrial radiation is the heat loss from the ground. It occurs during the day and during the night. This kind of radiation is long-wave radiation (λ = 10 µm). The solar radiation (red in this scheme) is the radiation originating from the sun, this is short-wave radiation (λ = 0.5 µm). On a sunny day, a part of the solar radiation gets absorbed by the atmosphere and then the rest gets into the snow, but 50-95% get reflected depending on the snow type in the first 2- 20 cm of the snowpack. On a cloudy day, a bit of the solar radiation gets absorbed by the atmosphere and 75% gets reflected by the cloud. Then about 2% get absorbed by the snow and 23% get then reflected again from the snow depending on the snow type and the remaining radiation gets reflected of the clouds again. The terrestrial radiation gets reflected 100% by the clouds. During a clear night, the terrestrial radiation can disappear into the atmosphere. At a cloudy night, 100% of the terrestrial radiation will get reflected by the clouds. The snow absorbs about 99% of this kind of radiation and so the long-wave radiation has a bigger influence on the

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Figure 20: Schematic of the radiation balance (source: (SLF))

Sintering The usage of grooming to harden the slope and to increase the durability on the next day is a combination of machine work and nature. At first the groomer prepares the snow, and afterwards the natural sintering process begins. By going over the snow with the big caterpillar machine the following things are taken into account:

• increasing snow density • producing rounder and smaller grains with a wide grain size distribution in order to maximize the contact points between the grains • possibly increase of the snow surface temperature

The sintering process describes the bonds between the grain that can occur by the melt/freeze process. In the course of sintering, the bonds between the grains get formed by evaporation and condensation of ice. The most important parameters for sintering are:

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• Grain shape • Grain size • Grain distribution • Density • Temperature

If the grains are small and round, there will be more bonds between the grains, and so the snow is harder. The best condition would be wide distribution of grain sizes but with the majority of small grains there are a lot of bonds between the grains. With higher density, the contact points increase, and when the snow temperature is warmer, the snow hardens faster (Fauve, et al. 2004). Guily (1991) investigated the difference between the modification of the snow structure. After the preparation, the snow needs some time to sinter and get hard. He showed that the groomed snow has a six times higher penetration strength compared to the ungroomed surface. But the grooming affects only the first 30 cm of the snow below the surface and depends on snow temperature and density. The time of the sintering is a really important factor when it comes to the hardness and the resistance after opening the slope again. In Figure 21 you can see the difference between 2 hours of sintering and 10 hours of sintering. The surface was weaker or less hard after 2 hours compared to the surface after 10 hours and the skier sunk down more and pene- trated the surface deeper. This also means that the slope is less durable, and the muggles will build faster when the track gets used a lot.

Figure 21: Effect of time on snow hardening by sintering; left = after 2 hours, right = after 10 hours (source: (Guily 1991))

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As already mentioned, the weather has a big influence on the grooming. In Figure 22 you can see examples when it is the best time to groom the snow to have a perfectly prepared slope. In A the scenario is an overnight cooling. In this case, you have to start preparing the slope after the slope is closed. If the temperature is rising like in scenario B, it is better to wait before the grooming starts, because warmer snow temperatures speed up the sintering process. In scenario C there is a wet snow layer at the snowpack, and if you start too early with the grooming, the water will get pressed out and forms an ice layer. This is very dangerous for skiers. If the wet snow will get groomed too late, the snow is already frozen. Big snow blocks will form, and the snow cannot sinter properly. As already mentioned, the machine-made snow is different from the natural snow, because it has a shorter time to freeze and has a higher density. If you prepare a slope with machine-made snow, you have to let the snow freeze completely first, otherwise it will build an ice layer on the snow surface. The reason for this is that sometimes the inside of the snow is not frozen yet (Fauve, et al. 2004).

Figure 22: Different scenarios when to groom the snow; A)(top-left) when the slope is dry and there is a temperature decrease overnight, B)(top right) cold snow ski run with evening warming, C) (bottom) wet snow with nighttime refreezing (modified source: (Fauve, et al. 2004)) 2.6.2 Additional preparation for races To hold alpine ski races, the slope has to be as hard as possible and have a durable surface and sub-surface to promote safety and fairness. Good mechanical preparation of the slope is the first step to create a perfect race surface. There are three major tasks for the groomer to prepare a good racetrack:

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• Building a hard fundament • Hardening the snow surface • Repairing the track during the race

For building the snow surface the machine-made snow is suitable because it has high mechanical strength and can be compacted better than the natural snow. Every layer that is going to be prepared should have a maximum height of 20 cm and the first two layers should be compacted with the machine and the front blade. The top layer should then be groomed with the machine, the front blade and the tiller for an optimal result. If it is possible, the slope should be groomed perpendicular at critical zones, like curves and compressions. This way the slope gets more homogeneous and harder. For an alpine ski race, it is not enough to just groom the snow, you also need to additionally harden the snow with water or chem- icals to ensure proper hardness and durability. With water treatment, the strength of the snow can get to a level of hardness that cannot be reached with normal mechanical treatment. Density and bonding between the grains get higher with adding water. During water treatment, the water gets injected with high pressure into the compacted snow with a nozzle. The amount depends on the snow type, 20 l/m² at fine-grained snow and 10 l/m² at coarse-grained snow. This process increases the snow density and the liquid water freezes at a snow temperature below 0 °C (SLF 2018). For this treatment to work, it has to have a temperature below 0 °C, a negative heat balance and a hard fundament on the slope. The only way to increase the snow strength above the freezing temperature is the use of snow hardening products, but it can be minimized with good mechanical preparation of the track. The most common snow hardening products are sodium chloride – NaCl, urea – CO(NH2)2 and ammonium nitrate –

NH4NO3. When applying the chemical snow hardeners, the main effect, that is used, is the melting point depression. When the salts get dissolved in the water, the melting point gets lowered. If the snow crystals get in contact with the salt, they start to melt. This process uses a lot of heat that is generated by the surrounding of the grain. The change from the solid state to the liquid state requires energy to break down the bonds between the ions and the salt molecules. If the salt molecule has a greater size and higher complexity, the energy consumption gets increased. But on the other hand, if the grain is smaller, the reaction happens faster. In Figure

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23 you can see this process. The heat flow is represented by the black arrows and you can see that the salt liquifies the snow crystals over time.

Figure 23:Model illustrating the dissolution of the salt (source: (Rixen and Schneebeli 2010)) There are many different products to harden the snow and they have different instructions on how to apply them and for which snow types. But in general, you can say that NaCl is faster and has a bigger heat flow than ammonium nitrate. This generates a higher solute concentration and infiltration, which can damage the snow structure and conclude in a weaker snow strength. The spontaneous dissolution of NaCl creates its own water and requires less humidity in the snow to react. Though ammonium nitrate needs more snow humidity than NaCl to have the same cooling effect, it seems like that the outcome after the use of NaCl is a lower snow strength. Because of the lower solute concentration and the slower infiltration rate of ammonium nitrate it can achieve a higher snow strength. On the one side, the NaCl is corrosive and can destroy nature, and on the other side, nitrogen-based fertilizers like urea and ammonium nitrate can have a positive influence in the vegetation growth if it is not used in too high amounts. With the increase of the temperature the rate of dissolution will increase and react faster and so the hardening process has a lower time (Campbell 2011) (SLF 2018). 2.6.3 Other usage of snow preparation Not only the snow on the ski slopes gets special treatment. In some regions like in the Arctic or Antarctic snow is the only available building material and to make sure these structures are reliable and stable often salt is used. By putting salt onto the icepack, the melting point gets lowered and then an increase of the strength of the snow is possible. This method is based on the fact that a eutectic mixture with sodium chloride

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lowers the freezing temperature to -21.2 °C. With this mixture it is possible to wet snow and strengthen it. The strength is dependent on the quality of the salt, compaction load, temperature conditions and other factors. It is important to choose the right salt and the proper quantity to strengthen the snow. The salt can be scattered on the snow or it can be applied as a solution. After treating the snow with salt, it should get compacted at a temperature above the eutectic point. The higher the temperature at compacting the higher the strength (Yarkin, Tyutyunov and Sadovskii 1972).

2.7 State of the art – measurement devices There are some testing devices to measure the hardness. Some of the following devices have been invented to measure snow hardness, but there are also devices to measure the hardness in other areas that are close to the snow hardness measurement and the ideas from these devices could get used to improve the current way to measure the snow hardness. 2.7.1 Kinosita-type hardness gauge A common way to measure the hardness of snow is with the device invented by Kinosita (1960) (Figure 24). It consists of a cylindrical base A, a rod B, a weight C and a stopper D. To measure the device gets placed on the snow, and then the weight gets lifted till it touches the stopper. The next step is to release the weight and it drops from a height ℎ onto the base. It will penetrate the surface and after that, you measure the depth 푑. With the sinkage depth you can calculate the resistance force as followed (Equation 7):

ℎ 퐹̅ = 푚 ∗ 푔 (1 + ) + 푀푔 푐 푑 Equation 7

After that you can calculate the hardness 퐻 when you know the base of the surface 푆 (m²) (Equation 8): 퐹̅ 퐻 = 푆 Equation 8: Hardness of snow

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Figure 24: Kinosita-type hardness gauge (source: (Hämäläinen and Spring 1986))

2.7.2 Gauges for testing sand in or for golf course sand bunkers In golf there are these so-called bunkers, where the turf or soil has been removed to be filled with sand and there are also very specific rules what a player is allowed to do and what not, if his ball lands in one of those bunkers. A player is prohibited to test the condition of the hazard, touch the ground of the bunker with the club or otherwise or touch or move a loose impediment lying in. This means a player has to play the ball without testing the surface from a sand bunker. The bunkers are highly main- tained and footprints are immediately ranked after the player played the ball, so everybody has the same conditions. But even with this mainte- nance and grooming sand traps differ highly from each other. There are a lot of factors that make it very unpredictable for the player to play the ball (Wood and Harman 2003):

• Sand grain size • Grain shape • Distribution • Density • Depth of the sand • Moisture content • Compactness

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These factors are similar to the fact of the hardness of the snow. The connection to the snow is that a lot of authors refer to dry snow as it has the same temperature as sand (F. P. Bowden 1953). The aim of this measurement device is to measure the hardness of the sand to give the players different conditions under which they can practice the golf shot. Another object is that they can measure and define the category of which the par- ticular sand trap is. In Figure 25 you can see different categories of the sand hardness and in Figure 26 there is a schematic drawing of the measurement device. It consists of a guidance tube, a spike and also a spring, so it possible to penetrate the sand with more force. There are two ways to measure. The first one is to measure without the spring and put simply just a weight on top of the spike and penetrate the sand. The other way is to measure with the spring and simply push down the device until the outer shell touches the sand surface. In both cases the depth of the penetration is measured to get the hardness.

Figure 25: Table of sand characteristics according to (source: (Wood and Harman 2003))

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Figure 26:Schematic drawing of the sand measurement device (source: (Wood and Harman 2003))

2.7.3 Soccer turf measurement There are new improvements and inventions of artificial soccer turfs every year. But these surfaces should not differ too much from the natural grass field to ensure safety for the users. To measure the soccer field turf, on hardness and resilience and have some limits, a device was created (Figure 27). It consists of a tube with ventilation holes on the side so the falling missile will not produce so much air pressure and therefore falsify the measurement. This device measures the force and the acceleration at the impact. A load cell is built into the missile to measure the force. To get the acceleration and to measure the acceleration at the impact an accelerometer is fixed inside the missile. The sensor is connected to a wireless transmitter who sends the data to a computer, where the data gets evaluated (Miles and Quarles 2005).

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Figure 27: Device to measure the hardness and resilience of a soccer turf (source: (Miles and Quarles 2005))

2.7.4 SnowMicroPen® The SnowMicroPen® (SMP) is a high-resolution snow penetrometer (Figure 28). The first version was invented by the WSL Institute for Snow and Avalanche Research (SLF) (Johnson and Schneebeli 1998) and currently the 4th version of this measurement tool is available at the market. It measures the bonding force between snow grains with high spatial resolution and high speed. It can measure up to a depth of 1720 mm with a penetration velocity of 20 mm/s. It has a spatial resolution of 4 µm and a layer resolution <500 µm. The SMP is a further development of the ram penetrometer. The problem with the ram penetrometer was, that it could distinguish between the snow layers but was not accurate enough, and it only registered the really hard snow layers (Grubler 1975). The SMP consists of a penetration tip, where a force cell is implemented, two pedestals and a long rod. First, the feet get placed into the snow and then the rod, with the penetration tip, drives with constant speed into the surface. It measures the force that occurs when penetrating the different snow layers. The data will then be saved on a SD card for further processing and it gets displayed on a monitor that is connected to the device. The device

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Figure 28: SnowMicroPen® 4 (source: (W. I. SLF 2014))

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3 Methods 3.1 Profile of requirements Before starting the construction of the new measurement device, a profile of requirements has been made. First of all, the tool should be waterproof, since it is measuring snow and can get wet. Also, it should not have parts where the snow can easily get stuck on and freeze. If this would happen, you would have to stop measuring and defrost the tool first, before you can continue measuring again. Another requirement is, that it should be as small and lightweight as possible and transportable since it will be car- ried around on the ski slope. It should at least be transportable with a snowmobile, either on board or dragged behind. Another demand for the device is, that it should get electronic data and not like in previous measuring devices that you have to measure by hand. This electronic data should be saved during the measurement, so you can transfer the data after the measurements onto a PC in the laboratory and evaluate it. Fur- thermore, it should be possible to change the impactor to different shapes, so you can measure the snow for different snow sports like for example for alpine and cross-country skiing, but also other sports equipment, that touches the snow surface. Additionally, you also have to collect other data that does not influence the construction but are really important for the analysis. You have to measure several other factors that influence the results of the snow measuring, like the weather conditions, snow crystal shape, snow density and also the snow wetness.

3.2 Setup and evaluation Since there is no system on the market that fits the requirements of the project, a new device to measure the snow hardness got developed. In the beginning, a device got created with the 3D-CAD program Creo parametric 2.0 (PTC Inc., Needham, USA). The model consists of a tube, a dropping body, later also called missile, rails and a top. This construction was very detailed, and it was decided to build the first prototype with simpler elements. The first prototype consists of a tube with 18 holes and a falling missile with all the sensors in it to analyze the hardness of the snow.

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To measure the surrounding factors like the air and snow temperature, an Arduino UNO (Arduino AG, Sommerville, USA) has been set up. It consists of a waterproof temperature sensor DS18B20 (Adafruit Indus- tries, New York City, USA), a temperature and humidity sensor DHT11 (Adafruit Industries, New York City, USA) and a barometric pressure sensor BMP388 (Adafruit Industries, New York City, USA). It has an organic light emitting diode (OLED) display (Adafruit Industries, New York City, USA) so you can follow the process of the measurement and the acquired data gets saved onto a microSD card as CSV-file for further processing. To measure the sinkage depth an Arduino UNO with ultrasonic sensor SFR-04 (Devantech, Attleborough, UK) and an IMU MPU6050 (Sparkfun, Niwot, USA) to calculate the angle of the slope has been programmed. This tool also has a display to follow through the measurement and saves the data on a microSD-card in CSV-format. To measure the snow hardness, an accelerometer ADXL377 (Analog Devices, Inc., Norwood, USA) and a load cell model 151 (Honeywell Inc., Morris Plains, USA) is used. These two parts are located in the falling missile. To acquire data from the accelerometer and the load cell they have been connected to a NI-USB6211 (Texas Instruments Inc., Dallas, USA) which again is connected to a PC with a LabVIEW-application Version 11 (Texas Instruments Inc., Dallas, USA) on it. The data gets saved with the Lab- VIEW-application as a LVM-file. In Table 2 a summary of all the sensor specifications is shown. For the evaluation of the acquired data, an application with a graphical user interface (GUI) got created with MATLAB 2017b (The MathWorks, Inc., Natick, USA). This application evaluates the distance measurements from the Arduino, as well as the surrounding data that got measured during the tests. It also evaluates the data from the accelerometer and the load cell inside the missile. Of all the data the mean values and standard deviation get calculated and can be saved into a local database. First anticipations have been made about how the results will look like in the soft and hard snow. These results have been drawn in Microsoft Excel (Microsoft Cooperation, Redmond, USA).

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Sensor Name Supply Volt- Accuracy Range age Temperature DS18B20 5V ±0.5°C -55°C -125°C Sensor Temperature DHT11 5V ±0.5°C 20-90%RH0 and Humidity -50 °C sensor Barometric Sen- BMP388 5V ±50 Pa 300 – 1250 sor hPa Ultrasonic range SRF-04 5V ~2 cm 26 – 1070 cm sensor IMU MPU6050 5V 16.4 ±2000 °/s LSB/(º/s) Accelerometer ADXL377 5V 6.5 mV/g ±200g Table 2: Sensordata

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4 Results 1 – Considered solution 4.1 Construction To suite the profile of requirements a construction has been selected that is very similar to the construction of the measurement tool for the soccer turf. For the construction the program Creo parametric 2.0 (PTC Inc., Needham, USA) has been used. In Figure 29 you can see the 3D-model of the device. It consists of a tube with ventilation holes on two sides at the bottom. These holes have been placed in a way the compressed air will be pressed out and does not increase the air resistance. On the bottom of the tube a pout is mounted for more stability. At the top it has some in- dentations so the top part fits perfectly onto his counterpart. The top is removable for better handling and easier carrying. At the top of the top part is a beam mounted, where the missile gets hocked in. So it can get released at the beginning of the measurement. On the inside of the tube rails are located, so the missile has a guided fall. The missile itself consists of a hollow cylinder with a smaller cylinder in the middle. Inside this small cylinder is the accelerometer placed and in the bigger cylinder it is possible to place some weights if it is necessary to penetrate the snow harder or to have the same weight with different impactors. On the bottom the cylinder is threaded, so it is possible to screw the load cell on and onto the load cell the impactor. The missile has little bumps on the side. These will be inserted into the rails, so the fall is guided, and the missile is not spinning around inside the tube. In the first step, it was decided to have a lot of different shaped impactors. You can see the 3D-models of the impactors in Figure 30. These shapes should represent different sport equipment or body parts. The test with each impactor cannot be compared to another impactor. The different shapes are a rounded cone, a regular cone, a ball, a plate, a pyramid and a wedge. During the first test phase, it has to be decided which kind of shape can give the best feedback about the snow properties.

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Missile Top

Rail

Tube

Figure 29: 3D-Model of the measurement device with a vertical cut in the middle

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A) B) C)

D) E) F)

Figure 30: Shapes of the impactors; A) Rounded cone, B) Cone, C) Ball, D) Plate, E) Pyramid, F) Wedge

4.2 Measurement devices inside the tube Inside the missile there is an accelerometer ADXL377 (Analog Devices, Inc., Norwood, USA) built-in to measure the acceleration during the hit on the ground and the deceleration due to the damping of the snow. On the side there is a Hall sensor (Littelfuse, Inc., Chicago, USA) mounted and it gets signals from the magnets, that are mounted on the inside of the big testing tube. With this sensor it is possible to calculate the velocity of the missile before the impact. A load cell model 151 (Honeywell Inc., Morris Plains, USA) is mounted on the bottom of the missile. It measures the force that is needed to penetrate the snow at the impact and also during the damping phase. It will give feedback about the hardness of the snow. All these sensors are connected to an ATmega32 microcontroller (Microchip Technology Incorporated, Chandler, USA). In Figure 31 the block diagram of the setup is shown. This block diagram was created using the program yED Graph editor 3.19 (yWorks GmbH, Tübingen, Ger- many). The load cell is also connected to an INA128 (Texas Instruments

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Inc., Dallas, USA) amplifier to get higher signals. On this board, there is a real time clock (RTC) DS1339 (Maxim Integrated Products, Sunnyvale, USA) for keeping track of the measurements. On board is also an USB bridge, to communicate with the PC and fetch the data live. To start the measurement a button, that is connected to the microcontroller has to be pressed. The LED shows the current status of the microcontroller. The live data will get loaded into a LabView-application (Texas Instruments Inc., Dallas, USA) and will be saved into an LVM-file. Later the data will get processed further in a MATLAB-application 2017b. The measurement will be started by releasing the pin at the top of the missile. Then the missile will fall and accelerate until it hits the snow. After the impact, the missile will get damped by the snow and decelerate. During all this time the data of the accelerometer and the load cell will get fetched and sent to the PC.

Figure 31: Block diagram for the sensors in the missile

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5 Results 2 – Actual solution 5.1 Construction Since the construction in 4.1 Construction is quite detailed, it was decided to do the first tests with a simpler construction that consists of a tube with 18 small holes on the side to let the compressed air out so the missile does not get slowed down. This tube has the same dimensions as the tube in the considered results part and consists of aluminum to save weight. It has a height of 1 m, a diameter of 0.3 m and a wall thickness of 2 cm (Figure 32).

Figure 32: Aluminium tube

In Figure 33 a 3D-model of the simple fall weight is shown. It consists of a hollow cylinder where the accelerometer gets placed and a wider cylinder around it where the weights can be placed to adjust the weight. On the bottom it is threaded so it is possible to screw on the load cell.

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Figure 33: 3D-Model of the simple fall weight

5.2 Measuring the ground distance To measure the inclination of the slope and the sinkage depth, a microcontroller has been set up. The setup consists of an Arduino UNO (Ar- duino AG, Sommerville, USA), a 1.3” OLED display (Adafruit Industries, New York City, USA), an IMU MPU6050 (Sparkfun, Niwot, USA), an ultrasonic distance sensor SFR-04 (Devantech, Attleborough, UK) a mi- croSD adapter (Adafruit Industries, New York City, USA), a status RGB- LED and a button to start the measurement. In Figure 34 you can see the connection of the sensors to the Arduino board. This circuit was created using the software Fritzing 0.9.3b (Friends-of-Fritzing, Potsdam, Ger- many). In Figure 35 you can see the block diagram of the circuit drawn in yED Graph editor 3.19 (yWorks GmbH, Tübingen, Germany). This whole circuit is mounted inside a 3D printed case with only two holes on the side for the ultrasonic sensor, a button to switch on the Arduino and another one to start the measurement (Figure 36). This case has been drawn in Creo parametric 2.0 and got printed on a Stratasys uPrint SE Plus (AIM SWEDEN AB, Frösön, Sweden) with P430XL material. To make it waterproof, but still see-through a Plexiglas is on top, so it is possible to see the display. This waterproof case gets mounted on a tripod with the ultrasonic sensor pointing towards the snow. When measuring the tripod gets placed over the area, where the measurement takes place. After switching on the Arduino, it starts to initialize the sensors. Then the program asks

Based on the Mid Sweden University template for technical reports, written by Magnus Eriksson, Kenneth Berg and 54 Measuring snow properties relevant to Mittuniversitetet snowsports & outdoor 10.06.2019 Development of measuring method to analyze snow properties to press the button to start the measurement. After pressing the button, the program starts and the LED changes its color from green to red. The measured data gets displayed on the OLED display and saved in a CSV- file on the microSD. The IMU sends the acceleration and the gyroscopic data, so the inclination angle of the ground can be calculated on the Ar- duino. Additionally, the temperature gets measured by the IMU, and it is possible to calculate the distance to the snow with the data from the ultrasonic sensor. You need the temperature (휗) to calculate the speed of sound (푐), because it varies at different temperatures according to the following Equation 9 :

푐 ≈ 331.5 + (0.6 ∗ 휗) Equation 9

To get the actual sinkage depth the measurement with the Arduino has to be conducted twice, once before the drop and another time after the drop test to calculate the exact depth. The Arduino measures 10 samples with a frequency of 2Hz. After the measurements, the data gets transferred to the PC and there it gets processed and evaluated further (5.6 Evaluation).

Figure 34: Circuit of the ground microcontroller

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Figure 35: Block diagram of the ground microcontroller

Figure 36: 3D-Model of the Arduino case

5.3 Measurement of the surrounding factors For the measurement of the air and snow temperature, humidity and altitude a similar setup as for the ground measurements is used. This device

Based on the Mid Sweden University template for technical reports, written by Magnus Eriksson, Kenneth Berg and 56 Measuring snow properties relevant to Mittuniversitetet snowsports & outdoor 10.06.2019 Development of measuring method to analyze snow properties consists of a pressure sensor BMP388 (Adafruit Industries, New York City, USA), a temperature and humidity sensor DHT11 (Adafruit Indus- tries, New York City, USA), a waterproof temperature sensor DS18B20 (Adafruit Industries, New York City, USA) and as before the 1.3” OLED display, a microSD adapter, an RGB-LED and a button. All these sensors are again connected to the Arduino and Figure 37 shows the circuit for these surrounding sensors on the Arduino. The whole setup gets mounted into a 3D printed case with outlets for the temperature sensors. The waterproof sensor has to be inserted into the snow and the air temperature sensor is also placed outside the case, to prevent an error by heating up the inside of the case due to the microcontroller. In Figure 38 the block diagram for the surrounding sensors is shown. In the beginning, the sensors are getting initialized. Then the user is asked to press a button to start the measurement. After that 10 samples of the altitude data, the air and snow temperature and the humidity data is collected with a frequency of 1 Hz, shown on the OLED display and saved in a CSV-file on the microSD for further processing. Likewise, there is an real time clock (RTC) DS1339 (Maxim Integrated Products, Sunnyvale, USA) mounted to the Arduino which adds a timestamp to the file at the end of the measurement and defines the start of the measurement.

Figure 37: Circuit for surrounding measurements

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Figure 38: Block diagram for surrounding sensors

5.4 Measurement device inside the tube Due to the different construction it is not possible to mount a Hall sensor on the missile since there is to less space in between the missile and the tube and it is not a guided fall without the rails. For this reason, it is not possible to measure the velocity at the end of the fall. The measurement devices, that are used in the missile, are similar to the sensors planed in the chapter “4.2 Measurement devices inside the tube” above. The acceleration is measured with an ADXL377 accelerometer (Analog Devices, Inc., Norwood, USA) and the force with a load cell model 151 (Honeywell Inc., Morris Plains, USA), but instead of an AT- mega32 they are connected to a NI-USB6211 microcontroller (Texas In- struments Inc., Dallas, USA). The NI-USB is then connected to a PC, where a LabView-application Version 11 is running on. In this case, the LabVIEW was chosen because it is more flexible and the PC can handle the amount of data during to the high frequency at the data acquisition. In Figure 39 a block diagram of the sensors in the missile is shown. Be- tween the load cell and the NI-USB, an amplifier is connected to amplify the signal. The amplifier is a bridge amplifier, but the exact one has not

Based on the Mid Sweden University template for technical reports, written by Magnus Eriksson, Kenneth Berg and 58 Measuring snow properties relevant to Mittuniversitetet snowsports & outdoor 10.06.2019 Development of measuring method to analyze snow properties been chosen yet because it has to be tested on snow to get the right amplification. The measurement starts when the pin is released, and the missile starts to fall down. Before it hits the ground, it passes an optical inter- rupter ITR8307 (Everlight Electronics Co., Lt, New Taipei, Taiwan) that is connected to the NI-USB and this sensor gives a trigger signal to start saving data. Then the LabVIEW- application gets the analog signals from the accelerometer and the load cell and saves it into a LVM-file during the hit on the snow and the deceleration process in the snow. The tests are executed at a frequency of 1000 Hz and the duration of the measurement can be decided by the user on his/her own. In the end, a time stamp is added to the file and it is possible to have alook at the recorded graphs. In Figure 40 you can see the design of the application. In the beginning, you can choose how many seconds you want to measure, and under which name the recording should get saved. When you start the application, the LED for primed lights up and the application waits for acquiring data until the missile passes the trigger and sends the starting signal to the PC. The data gets saved into two separated files, one for the acceleration data and one for the force data. This data gets then further processed in the MATLAB-application, see chapter “5.6.4 Evaluation of missile data”.

Figure 39: Block diagram of the sensors in the missile

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Figure 40: Front panel of the LabView-application 5.5 Manual measurement of the snow To measure the snow wetness and the snow density, manual measurements will be conducted. For the data acquisition of the snow wetness a hygrometer (Doser Messtechnik GmbH & Co. KG, Füssen, DE) gets used. It works as a denothmeter and measures with condensers. Before the measurements, this device gets calibrated with a calibration plate provided by Doser Messtechnik. For the measurement of the density, a core of snow gets drilled and measured in length. Afterwards it gets weighted with a scale and the density can be calculated with the volume and the weight. 5.6 Evaluation After the measurements, all the data gets transferred onto the PC and gets evaluated with an application written on MATLAB 2017b (The Math- Works, Inc., Natick, USA). This application has been created with a graphical user interface (GUI). With this application it is possible to evaluate all the collected data and display it in several plots.

5.6.1 Start page In Figure 41 you can see the start page, where it is possible to decide between the different data, that will be analyzed from the different micro- controllers. It is possible to choose between evaluating the data for the distance and depth measurements, the environment data or the data from

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the falling missile measurements. Additionally, you have access to a database, where you can access all your stored mean values and plot them or erase the databank. More information about the database is written in the chapter “5.6.5 Database”.

Figure 41: Main page of the MATLAB application

5.6.2 Depth evaluation In Figure 42 the page for ground measurements is displayed. First, the user has to enter the name and the number of measurements he/she wants to evaluate, later the two values are going to be taken as input to read the files into the program. Then the user has three options on how to evaluate the data. The first option is to show the single test he/she has chosen and display every data point of the distance, x- and y-angle in a plot to check

Based on the Mid Sweden University template for technical reports, written by Magnus Eriksson, Kenneth Berg and 61 Measuring snow properties relevant to Mittuniversitetet snowsports & outdoor 10.06.2019 Development of measuring method to analyze snow properties if there are any irregularities in the measurements. The second option is to calculate the sinkage depth for every drop. Here the mean value of each measurement gets calculated first and afterwards the distance from the beginning of the measurement gets subtracted from the distance of the end. So you get the depth that has been added by dropping the missile into the snow. Then you get a plot with the mean value and standard deviation of the sinkage depth of every measurement. For the angle you get a plot where you can see the mean value and the standard deviation at the beginning and the end of every single measurement. If the user chooses the last option to “Calculate mean”, first the data gets proceeded like in the last option. But in the end, an overall mean and standard deviation of all the measurements gets calculated and displayed in a plot (Figure 43 and Figure 44). Also, the user gets asked if he/she wants to save this data into the databank, and if he/she wishes to do so, he/she has to give this mean value a name under which it will be saved (Figure 45).

Figure 42: Distance evaluation of the MATLAB GUI

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Figure 43: Example plot for the mean value of the sinkage depth

Figure 44: Example plot for the angle measurement

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Figure 45: Pop-up windows for saving the data into the database

5.6.3 Evaluation of surrounding data In Figure 46 the screen for the evaluation of the environmental data is shown. First, the user has to enter the name and the number of the measurements he/she wants to evaluate. Here the user has two options about what to evaluate. He/She can choose again the button “Show single test” and every data point will get plotted. In one plot the air and snow temperature are displayed, and you can see a timestamp in the title when the measurement was taken (Figure 47). In a second plot the humidity and the altitude get displayed and you will find the timestamp in the title when the measurement started (Figure 48). If the user chooses the “Cal- culate” option, the mean values and the standard deviation of the selected set of measurements get calculated and plotted. One plot with a bar diagram of the air and snow temperature and the standard deviation gets shown and another plot with a bar diagram of the mean values and standard deviation of the humidity and the altitude (Figure 49 and Figure 50).

Figure 46: GUI for the evaluation of environment data

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Figure 47: Example plot for a single test air and snow temperature

Figure 48: Example plot for a single test of humidity and altitude

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Figure 49: Example plot of the mean values for air and snow temperature

Figure 50: Example plot of the mean values for humidity and altitude

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5.6.4 Evaluation of missile data Figure 51 shows the GUI for the evaluation of the accelerometer and the load cell in the missile. The user has many different options for what to evaluate and how. First, there are the buttons “show single test (filtered)” and “show single test (raw)” in the upper right corner. For these buttons the input gets done by a button click with the MATLAB implemented function “uigetfile”. The explorer opens and the user can manually choose which measurement he/she wants to see unfiltered or filtered. The chosen file then gets plotted in a graph. The shown data gets only converted from volts into g. For the other buttons the user has to input a valid name of a set of measurements and click a button. therwise the application gives back an error regarding if there has been no input-name or an incorrect input-name. If the user presses the “calculate acceleration” button, all the measurements with the same starting name get imported and processed. First, the data gets converted and filtered. Then the mean values of the trajectory of all measurements get calculated as well as the standard deviation and the maximum. In the end, everything gets shown in two figures. One bar-plot, that shows the mean maximum with the standard deviation and another plot that displays the mean trajectory of the acceleration during the impact and the deceleration due to the snow (Figure 52 and Figure 53). Afterwards the user has again the possibility to save the data into a database and can choose the name of this data. When the user clicks the “calculate force” button, the load data gets evaluated. Similar to the acceleration data also the name of the measurement set has to be in the input and the application imports all the files with that name. Then the data gets filtered and the mean values, the standard deviation and the maximum get calculated. Conclusively the load cell data gets plotted in two figures like the acceleration data and the user has the possibility to save it into the database. One plot shows again the maximum in a bar-plot and the other plot shows the force trajectory during the impact and deceleration (Figure 54 and Figure 55). The user also has the opportunity to evaluate the acceleration and load data at once if he/she clicks the “calculate all” button. At the end of this loop, the application shows the four plots with the maxima and the trajectories, and the user can choose individually if he/she wants to save the acceleration data, the load data or both. The two buttons for velocity and distance have already been implemented but are not working at the moment. They have already been implemented for later studies. This has been done, so it will not destroy the design of the application if they get implemented later.

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Figure 51: GUI for missile data

Figure 52: Example plot of the mean value for acceleration

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Figure 53: Example plot for the maximum acceleration

Figure 54: Example plot of the mean value for the force

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Figure 55: Example plot for the maximum of the force

5.6.5 Database To store the values of the different snow conditions and work with them in a later stage again, a local database has been set up. For this purpose, the software MySQL (Oracle Cooperation, Redwood City, USA) has been used. A local host address has been chosen to set up the databank called “snow”. This databank includes three tables:

• Mean and standard deviation of depth • Mean maximum and standard deviation of acceleration data • Mean maximum and standard deviation of force data

The database is connected with the MATLAB-application via an Open Database Connectivity (ODBC) driver. It is possible to store values after every evaluation into the database and also to have a look into the database to delete values and to plot the data. So it is easy to compare the different data sets of different snow conditions. Additionally, all the values of the acceleration and load trajectories get saved in a cell array in a MATLAB file. To delete a dataset the user just has to choose the dataset he/she wants to delete and then click on the “delete” button. The program then checks which lines have a tick and erases them from the list. It is also possible to delete the whole database (Figure 56). Additionally, the possibility is given to export the table by pressing the “Export data” button.

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Here the table gets saved with a “;” as a delimiter in a CSV-file for easier importing into Microsoft Excel (Microsoft Cooperation, Redmond, USA). As mentioned before, the user does not only have the opportunity to look at the values, it is also possible to plot the mean values. In case of the distance, a bar plot gets shown with the mean values, the standard deviation and for better understanding the name under which the measurement got saved. When the user accesses the acceleration data, two windows will pop up. In the first window all the mean values of the damping processes will be shown in a subplot, that arranges its size according to the size of the database as well as the according standard deviation to the saved evaluated set of measurements. In the second window, a bar-graph shows the maxima with the according standard deviation of the different sets of measurements. If the user decides to plot the force database, he/she also gets two windows. The first one shows the trajectories of the mean values and the maxima with the corresponding standard deviation get shown in the second one.

Figure 56: GUI for the database

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6 Results 3 – Anticipated results 6.1 Acceleration data Since the system could not be tested on snow an anticipation of the results has been conducted. In Figure 57 the expected results of acceleration measurements on hard snow are shown. It is expected that the hard snow stops the missile over a short duration of time. In Figure 58 you can see the expected outcome of the acceleration sensor on soft snow. Compared to the data of the measurements with hard snow it is expected that the deceleration happens slower. This means the missile will fall for a longer time and travel a longer distance. But both times the original acceleration will be the same due to the fall, just de deceleration will occur differently.

Hard snow Acceleration

Time

Figure 57: Expected diagram for the acceleration on hard snow

Soft snow Acceleration

Time

Figure 58: Expected diagram for the acceleration on soft snow

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6.2 Force data In Figure 59 the assumed results for the force on hard snow is displayed. It will raise immediately after the impact and rise until the snow is compacted. Afterwards it will get less again until there is only the pressure from the weight itself on it. Comparable to that the expected results of the force on soft snow are shown in Figure 60. The force should rise slower and the peak force will be less due to the softer snow. After the peak, the force is expected to fall slower so the whole process takes a longer time.

Hard snow Force

Time

Figure 59: Expected diagram for the force on hard snow

Soft snow Force

Time

Figure 60: Expected diagram for the force on soft snow

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7 Conclusion The simplified prototype is in production and as a next step the parts have to be fixed together and tested on known material to verify the accuracy of the collected data. Then it is possible to analyze the hardness of the snow with this tool. Due to the long Production time it was not possible to conduct real measurements. The setup for the environment sensors is working as expected, it is possible to measure the air temperature, the humidity, the altitude and the snow temperature simultaneously. The only sensor that is not completely accurate is the altimeter. But the altitude does not influence the measurement of the snow hardness. It only gives additional data on the location where the measurement took place. The setup of the second Arduino, which measures the inclination and the sinkage depth, works as well. But the distance sensor is not as accurate as expected. It is still accurate enough to use this kind of system because the alternative to this would be to measure the sinkage depth by hand and this involves a human error. The difference due to this error can even be higher than the error with this measurement system. The human error occurs when reading the scale and when placing the measurement tool into the snow because it might not be the deepest point where the depth gets measured. The inclination measurement with the IMU works and it is possible to measure snow on an inclined slope. You could implement these values into the evaluation. The MATLAB evaluation is running, and it is possible to evaluate the surrounding data, the distance and inclination data as well as the acceleration and load cell data. You can save it in the database and afterwards plot the collected data to have a better overview of the gathered knowledge.

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8 Discussion 8.1 Improvement of the construction The first prototype consists of simple elements and was quite heavy. To improve the construction in general it should be possible to reduce the weight by using thinner walls on the elements because the device is still durable enough if the tube and the missile have a wall thickness of about 1 cm. To reduce the weight even more and improve the outlet of the compressed air inside the tube during the fall, there should be more holes in the sidewall of the tube. Due to more holes, the air can easier exit the tube and will not get compressed by the missile. So far, the air can only exit in the last few centimeters of the tube and not on the top. As already described in the chapter “Results 1” the construction could have more features that provide a more accurate fall of the missile, hence a more accurate measurement. First, the rails on the side of the tube, this feature gives the missile fewer spots to glide on and allow a guided fall. So the missile will not start to spin during the fall. These exchangeable rails should be coated with Teflon to reduce the friction between the tube and the slider even more. The other part that has been left out in the first prototype compared to the considered construction is the top of the tube. This removable top would bring the advantage of a more accurate release of the missile and simplify handling while setting it up and pulling up the missile after the measurement. 8.2 Improvement of measurement equipment The equipment that got created and programmed works so far, but for the load cell the right amplifier still has to be chosen. It is possible to decide for the right amplification, if you measure with the actual measurement setup. The setup for the Arduino could be improved as well. So far only an OLED display is used to display the status of the measurement and you cannot give any input to the device except if you connect it to the PC. If you chance to a more advanced microcontroller and use a touch display it would be possible to give an input and change for example the name under which the data gets saved on the slope. Another improvement would be to connect the microcontroller to the internet and use an online database to save the data in. This would later save time when the user does not have to transfer the data from the microSD card to the PC to evaluate it.

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8.3 Acoustic implement For further improvement the system could use an additional acoustic measurement. The idea behind this is the side-scan sonar that is already used for soil by geologists. For this, legs could be mounted on the device and on the end of this legs a speaker and a microphone to receive the induced sound from the speakers. Small cases could be 3D printed and the sensors placed inside. To make it waterproof but not soundproof one side should be open and only closed by a thin rubber membrane, so it is still possible for the microphone to receive sound. With this measurement it should be possible to measure the density of the snow by calculating the speed of sound in snow. Then it is not necessary to do this manually. But first, a test has to be conducted to check if the data correlates with the data measured by hand. 8.4 Improvement of evaluation As already mentioned before in chapter “5.6.4 Evaluation of missile data” the buttons for velocity and distance evaluation are already implemented in the GUI of the accelerometer evaluation but do not work yet. For future studies, it could be helpful to implement the calculation with an integra- tion of the accelerometer data. These calculations must be done very care- fully since the accelerometer tends to drift. This drift error will be integrated two times. But it should be possible to calculate the velocity and the distance after the impact on the snow (the sinkage depth). In the next step, it should then be possible to calculate the force and omit the load cell because you can calculate the maximum impact force with the velocity and the distance traveled through the snow. With all this extra evaluation it would then be possible to measure the snow hardness with only the accelerometer inside the missile. The database could get improved as well since now half of the saved data gets saved into a database from MYSQL. The other data gets saved in a MAT-file. These tables have to be set up in a way that they contain long arrays to save also the trajectory and not only the maxima and mean values. This database is only a local database and you have to use the same PC for the evaluation all the time. But it would be helpful to have a connected database, since you cannot measure every snow condition in every location due to different weather condition. If different people would research on this topic a lot of data could get collected and compared.

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This evaluation program runs so far only on MATLAB because it uses a lot of implemented functions from this program. But it would be possible to create a standalone program using the “deploy tool” from MATLAB, so it is possible to run this evaluation on any PC. It has not been done so far, because if you use the “deploy tool”, you cannot work on the program anymore, just executing it and until this point, a few features are missing in the program code.

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9 Bibliography Abele, Gunars, and Anthony J. Gow. Compressability characteristics of undisturbed snow. Research Report 336, New Hampshire: Cold Regions Research and Engineering Laboratory, 1975. Ambach, W., and B. Mayr. "Ski gliding and water film." Cold Regions Science and Technology (Elsevier) 5, no. 1 (1981): 59-65.

Barnes, P., David Tabor, and J. C. F. Walker. "The friction and creep of polycrystalline ice." Edited by The Royal Society. Proceedings of the Royal Society of London (The Royal Society) 324, no. 1557 (1971): 127-155.

Bogorodskii, V. V., V. P. Gavrilo, and V. A. Nikitin. "Characterization of sound propagation in snow." Soviet Physics Acoustics 20, no. 2 (1974): 121-122.

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Based on the Mid Sweden University template for technical reports, written by Magnus Eriksson, Kenneth Berg and 83 Measuring snow properties relevant to Mittuniversitetet snowsports & outdoor 10.06.2019 Development of measuring method to analyze snow properties

Appendix • Addition 1 - Kinosita hardness gauge • Addition 2 – Soccer turf measurement • Addition 3 – Gauge for testing sand in or for golf course sand bunkers • Addition 4 – Drawing of the tube • Addition 5 – Drawing of the missile • Addition 6 – Drawing of the top • Addition 7 – Drawing of the rail • Addition 8 – Block diagram of the LabVIEW application • Addition 9 – Drawing of the Arduino Case

Added in an additional ZIP- folder: Arduino: • Addition 10 – new_disp_distance_datalogger …… distance sensor and IMU • Addition 11 – weather_complete………….. surrounding sensors MATLAB: Everything runs on MAINPage.m • Addition 12 – MAINPage.m…………………….………. main page • Addition 13 – Elevation_Distance.m…………...ground evaluation • Addition 14 – Environment.m…………... environment evaluation • Addition 15 – acc_force.m……… acceleration and fore evaluation • Addition 16 – delete_acc_database………….example for database • Addition 17 – Example codes for other parts of the GUI

Based on the Mid Sweden University template for technical reports, written by Magnus Eriksson, Kenneth Berg and Mårten Sjöström. Addition 1 – Kinosita hardness gauge

Kinosita hardness gauge

Based on the Mid Sweden University template for technical reports, written by Magnus Eriksson, Kenneth Berg and Mårten Sjöström. Addition 2 – Soccer turf measurement

Soccer turf measurement Patent No. US 6,925,858 B2

Based on the Mid Sweden University template for technical reports, written by Magnus Eriksson, Kenneth Berg and Mårten Sjöström. Addition 3 – Gauge for testing sand in or for golf course sand bunkers

Gauge for testing sand in or for golf course sand bunkers Patent No. US 6,536,263 B1

Based on the Mid Sweden University template for technical reports, written by Magnus Eriksson, Kenneth Berg and Mårten Sjöström. Addition 4 – Drawing of the tube

Drawing of the tube

Based on the Mid Sweden University template for technical reports, written by Magnus Eriksson, Kenneth Berg and Mårten Sjöström. Addition 5 – Drawing of the missile

Drawing of the missile

Based on the Mid Sweden University template for technical reports, written by Magnus Eriksson, Kenneth Berg and Mårten Sjöström. Addition 6 – Drawing of the top

Drawing of the top

Based on the Mid Sweden University template for technical reports, written by Magnus Eriksson, Kenneth Berg and Mårten Sjöström. Addition 7 – Drawing of the rail

Drawing of the rail

Based on the Mid Sweden University template for technical reports, written by Magnus Eriksson, Kenneth Berg and Mårten Sjöström. Addition 8 – Block diagram of LabVIEW-application

Bloch diagram of LabVIEW application

Based on the Mid Sweden University template for technical reports, written by Magnus Eriksson, Kenneth Berg and Mårten Sjöström. Addition 9 – Drawing of the Arduino case

Drawing of the Arduino Case

Based on the Mid Sweden University template for technical reports, written by Magnus Eriksson, Kenneth Berg and Mårten Sjöström.