Table 1: Original and adjusted slope gradients for each difficulty rating Traditional Ranges Adjusted Ranges

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1 1 Summary Nothing beats a day spent skiing. Except, of course, a day spent designing slopes for skiing. As winter looms closer, some wealthy investors are considering purchasing Wasatch Ranch in Utah. The investors would like to transform the mountain into one of the top ski resorts in North America to be used every winter. The investors have expressed interest in making Wasatch Ranch a location for a future Winter Olympics. Their representative, Ms. Mogul, has asked us to create a preliminary model of a ski resort. The model would include potential slopes and trails to fulfill the guidelines of a ski resort and possible Winter Olympics location. She has recommended plenty of slopes of varying lengths, totaling at least 160 kilometers. The distribution of trails should be about 20% green circles, 40% blue squares, and 40% black diamonds. We were asked by Ms. Mogul to plan the development of a ski resort on the property of the Wasatch ranch that could serve as a location for a future Winter Olympics. Our conceptual resort will be split into four main areas: a main area in the western region of the property, two smaller sister areas to the south, and a family-friendly area to the north. (See Appendix, Figure 9.) In designing this possible resort, we took a variety of factors into account. First, we assumed that rivers could not be crossed anywhere on the mountain except at locations with base lodges. We intentionally placed these lodges near both rivers and primary roads, which could be developed to support an influx of traffic. One of the guidelines was a wide variety of lengths of slopes. We achieved this guideline by placing the tops of our ski lifts at peaks of varying distances from the base lodges. Our resort will require the construction of 9 lodges and 24 lifts. (See Appendix, Figure 1, 4, 6.) The lodges and the lifts eventually became the central factor of each of the sections of the resort. The trails were ultimately designed around the placement of the lifts and the lodges so that the trails did not pass over any of the rivers. At each of the peaks accessed by the chairlifts were one or more main slopes. These slopes typically went from a peak to a base lodge. Off of these main slopes, a plethora of other trails could be traced. We then determined the difficulty ratings of each of the trails and the slopes on the mountain. We did this by measuring, on a topographical map, the shortest horizontal range per 40 vertical feet. We then took the vertical rise over the horizontal run and multiplied by 100% to get the percent gradient of the steepest part of each slope. Because our terrain was steeper in general, we adjusted the ranges for the slope gradients so that they more accurately reflect each trail s difficulty relative to other trails in the park. After this adjustment, 15% of the total length of trails is rated as green circles, 39% is rated as blue squares, and 45% is rated as black diamonds. In this proposed resort, there will be a total of 151 slopes and trails that span approximately 164 kilometers. This ensures that there are plenty of trails to choose from because the number of trails is close to the average trails of the North American ski resorts. The lengths of the main slopes also vary widely and interestingly, with a range of about 1.4 kilometers. When we compared the North American resorts with the resort of Wasatch that we designed Wasatch placed third.

2 2 Memo Dear Ms. Mogul, We have surveyed the terrain in the Wasatch ranch and have created a preliminary model of a ski resort. We think there is a lot of potential in this region, and we would highly recommend that you buy this ranch. The recommendations for the paths of the slopes and trails are included at the end of this document. While deciding upon the specific trails and slopes, we kept your guidelines in mind. Our main resort, which hosts the most trails, will be located mostly on the west side of the property. In addition to this main resort, we suggest three sister zones at nearby peaks. There are two to the south of a similar difficulty as the main area. Because these two and the main ski areas are both challenging, we suggest a fourth sister zone (affectionately called Kiddie Land by members of our team). This one, north of the main area, will be more family-friendly, with easier and safer trails. As we were dividing up the land for the slopes we quickly realized that a good portion of the mountain has a steep slope. To fulfill your requested percentage of each difficulty level more trails had to be added in the north where there was less of an incline. Generally, the terrain becomes more difficult as one moves west. While this terrain could be daunting to some beginners, it may also attract seasoned experts, lending the resort more attention and prestige, which will be helpful for its prospects as a Winter Olympics venue. Even with Kiddie Land, much of the park s terrain is very difficult. We thus adjusted our difficulty rating system 2 percentage points above the traditional slope gradients. Table 1: Original and adjusted slope gradients for each difficulty rating Rating Traditional Ranges Adjusted Ranges Green Circle 6% to 25% 8%-27% Blue Square 25% to 40% 27%-42% Black Diamond 40% or more 42% or more With the current adjustments, about ~15% of the total length of the slopes are rated as green circles, ~40% are rated as blue squares, and ~45% are rated as black diamonds. If desired, the values could be adjusted to better fit your desired percentages of 20% greens, 40% blues, and 40% blacks. In ranking our proposed ski resort against others in North America, we gathered data about the number of trails in each of the other resorts. Unfortunately, no data could be found from the Canadian ski resorts, but perhaps with more time, this could be investigated further. Thus, our ski resort was ranked against the other resorts in the U.S. only. We ranked based on a point system with 2 criteria. The first was a ratio of lifts to trails. (Having a high ratio indicates more ski lifts and less queuing time.) The second was average trail length. (Having a low average length means the trails are kept interesting.) Each of the ski resorts were ranked in these two areas, with the resort in first place receiving 12 points, the second receiving 11, and so on. We

3 3 scored first in the ski lift competition and 6th in terms of average trail length. This gave us 19 points overall, putting us in 3rd place out of all the American ski resorts given. While this ranking is not all-encompassing, it indicates that this resort is good for guest satisfaction. In conclusion, we would fervently suggest that you purchase this ranch and construct a ski resort according to this model. It will be an amazing long-term investment! Here is a map of the middle slope for your reference. If you have anymore questions about the designs of the other slopes then feel free to contact us for a follow up or more information. Sincerely, team 7408

4 4 Given Variables Wasatch Ranch 13,000 total acres on Wasatch Mountain property 5,500 skiable acres on Wasatch Mountain property 11 mile ridgeline 4750 foot drop top to bottom 24 peaks 15 bowls North American and Olympic Ski Areas (Refer to Appendix Table 1) Base elevation Peak elevation Skiable acres Slopes total The distribution of green, blue, and black trails Number of lifts Olympic Ski Areas (Refer to Appendix Table 2) Base elevation Peak elevation Slopes Total The distributions of green, blue, and black trails Number of lifts Trail Classifications Green Circle: 6%-25% slope gradient Blue Square: 25%-40% slope gradient Black Diamond: 40%+ slope gradient

5 5 Assumptions Because the prospective buyers of the property are wealthy and have expressed interest in making this a possible Olympic venue, money will not be much of a constraint. Trees can be chopped down anywhere to make the trails. On the mountains, it is not feasible to make a ski trail cross streams and rivers. However, it is assumed that at the base lodge location, rivers can be diverted underground. It was observed that the primary roads entered in yellow on the map, provided on mapright.com, were undeveloped dirt roads (Mirr). It is assumed that some of these roads could be developed as a way to get to the ski area, but they cannot be crossed. The other roads can be abandoned and covered with snow, allowing trails to cross over them. It can be assumed that snow will cover the roads completely because the mountain receives over 400 inches of snow (Wasatch Peaks Ranch, 2017). It is assumed that main slopes typically span from the top of a ski lift to the bottom. Ski trails will branch off of the main slopes. Ski slope should be viable for non-olympic as well as Olympic use. When calculating our data and using the given data, main slopes were included in the total number of trails. Hypothesis The trials that are created will not perfectly fit the difficulty ratio on the first iteration; through the implementation of multiple iterations the trail variation will get closer to the desired ratio. Analysis and Model Development Brainstorm To design a mountain with the optimal variation of trails we determined the usable area. To gain a better understanding of the skiable area we found a map of Wasatch Mountain (Mirr). When we analyzed the map we discovered that rivers and roads covered many parts of the mountain. In fact, the yellow roads depicted on the map appeared to cover the whole span of the mountain. Based on the assumption that roads could be either developed or overridden, we created trails over some of the yellow roads. Next, we determined the process of drawing and calculating the slopes of different ski trails. The problem stated that the percent slope of a ski trail determined the difficulty rank of that trail. On the topographic map each line or loop goes by 40 feet. Using the virtual map a line could be drawn and the distance could be determined. However, to calculate the steepest part of the trail only one vertical drop of 40 feet was needed. The percent slope of the line could be

6 6 determined by dividing the rise (the vertical drop) by the run (the horizontal difference between the 40 foot vertical difference). First Model To start planning out possible locations for ski trails we split the topographic map into sections for each person. We began collecting data separately in the various locations and recording the slopes as each trail was added. The data would be used at the end to determine the rank of each of the trails. The separation of the area proved to be an inefficient way of collecting data. The plan was not successful because the methods varied greatly. We determined that we needed to develop a better way to keep each section of the mountain together as a whole. Second Model From the first attempt we determined that the area of the topographic map should not have been handled separately. A new strategy was attempted by creating trails in each of the labeled quadrants. The trails were added down the diagram for each section. However, there was still a flaw in this system; the trails were still scattered all around the quadrants and did not make any logical sense with the data. The data from this trial was also more difficult to keep track of because we did not put a system in place to keep track of any of the lengths of the lines. Final Model From the previous two attempts of creating the slopes we concluded that we needed a system to keep track of the data as the lines were being configured. To keep track of the data we created an excel that kept the running total of the kilometers of trails because it was given that we needed to include a total of at least 160 kilometers of trails. The trails also had to be made more consistent and connected with each other. To ensure that the slopes were connected the lodges and possible chair lifts were placed first for each of the sections that the total area was divided into. After the chair lifts and the lodges were determined the main slopes for each section were then connected from the lodges to the ski lifts. As the slopes were drawn using the interactive map the lengths of each ski trail and the horizontal length between the steepest vertical drop were recorded on the excel. These steps were repeated for four sections of the map to create slopes over the entire ranch. As the slopes were recorded and the percent of the data were calculated the excel was programed to highlight percent higher than six and less than 25 in green, the percent higher than 25 but lower than or equal to 40 in blue, and the percent higher than 40 in black. The highlights signified, based on the givens, the difficulty level of each of the trails.

7 7 One weakness of our model was our failure to consider specific elements of each trail in their difficulty ratings. We simply used the ranges of slope gradients provided for each rating as hard cutoffs. In the future, some of the trail ratings could be revised to fit a wider variety of criteria. (Refer to appendix for visual a model) Analysis One of the guidelines the team was given was that the main slopes should have great variance in length. In order to find this we did a few tests to measure variance in our data. First, we took the range of lengths of our main slopes. The longest slope was feet and the shortest main slope was This range came out to 4,488 feet, but the other data we were using was given in kilometers, so we converted this to km and it came out to be km. To further show the variance, we found the standard deviation of all of the trails. We know that the guideline was focused on main slopes, but we thought that the variance of the trails is also an important factor. The standard deviation came out to be.604 km. Using these two measures of variance together, but focusing mainly on the main slopes value as that is what was asked, we decided that the variance in main slope length was great enough to pass this checkpoint. Another guideline that was important to Ms. Mogul, so it was important to our team, and that was that there are plenty of trails. First we had to define what plenty of trails actually means. We decided to base it off of the given data for North American resorts. At first we were considering using the mean of the data, but due to a few resorts who had too many trails comparatively and became outliers, we decided that a median value might be more accurate. The median for the North American data set was trails in each resort. Our resort came out to have 151 trails. To determine if our resort could be considered to have enough trails, we first found the standard deviation of the number of trails for the North American resorts, which came out to be Our value is within one standard deviation of the median, so we decided that Wasatch fits the guideline, Plenty of Trails There were multiple comparisons to be made between our model of Wasatch Ranch and other potential guidelines. The first comparison to be made was with the original guidelines, provided by Ms. Mogul, referred to as target in table 1. The original guidelines suggested that 20% of the trails should be green, another 40% blue trails, and the final 40% black trails. To determine the percent of leveled trails in our model, we divided the total kilometers of each level by the total kilometers of all the trails combined. (refer to figure #). This comparison showed that our model did not completely match the guidelines given. Our percent of green trails, 13.49%, and blues trails, 33.72%, were both less than the target percentages of green and blue. However, our percent of black trails, 52.80%, exceeded the target percentage. In order to get more of an understanding of what our data actually means, more comparisons were made. We compared our data to the North America data and found the following. We decided that the most efficient way to compare our data to the North American ski resorts was to compare the average percentages for each difficulty level. This was calculated by taking the average number of kilometers for each difficulty level across the North American

8 8 resorts provided, then we divided that by the average total number of kilometers. Our percentage of green trails and blue trails were both less than the green and blue trails for the North American data set, which were 19.25% and 43.88% respectively, while our percentages of black trails was larger than the North American percentage which came out to 36.87%. Due to the somewhat concerning differences between our model values and the target values, we decided to look into where we could rearrange the difficulties. We decided that the most accurate representation of the distribution of the difficulties in our resort was to shift the percentage boundaries up by 2 %. This means that trails with slopes of 27% and under would now fall into the green circle category, slopes between 28% and 42% are now considered blue squares, and any slope that is steeper than 42% is a black diamond. Before the shift, our distribution of levels was off which meant that the rankings were not doing a good job of discerning which trails were actually hard compared to others. The shift resulted in 7 of the easiest black diamonds falling into the blue category which greatly helped our ratio. In addition to these changes, 4 blues were now considered to be greens. This means that following the shift, the percentages reflected the relative difficulty level of the trails more accurately. The percentage for the green trials rose to 15.08%, the percentage of the blue trails sky rocketed to 39.76%, and the blacks fell to 45.16%. % Trail Types Iteration 1 Boundary Shift 100% 100% 80% 80% 60% 60% 40% 40% 20% 20% 0% Wasatch North American Resorts Olympic Target 0% Wasatch North American Resorts Olympic Target Green Blue Black Green Blue Black The important thing to look for in these graphs is the improvement in similarity from the left graph to the right graph. After the shift, there is a substantial improvement in the ratios for Wasatch. We were also asked to rank our proposed ski resort amongst other existing North American ski resorts, specifically the ones we were given. We decided that an important part of a ski resort is the guest experience, and decided to weigh aspects of that heavily. An important part of the guest experience that we could quantify with the data we were given and the data we found was the number of ski lifts to the number of trails. If there is a high ratio of ski lifts to trails that means that it is less likely that a guest will have to wait in line to get to their

9 9 destination. We found this for our proposed resort by dividing the total number of lifts by the total number of trails. We decided that the higher the resultant value is, the lower the congestion of riders making the guest experience a more positive one. We found that for the Wasatch Ski Resort, this ratio came out to be approximately 0.16 ski lifts per each. We then researched the number of trails for each of the resorts we were comparing to (Mountain Info). However, it proved to be rather difficult to find information regarding the number of trails in the Canada based ski resorts. We compared our ratio and found that we surpassed all of the other resorts in this aspect of the guest experience (Table 4). Another aspect of the guest experience that we thought was important was how enjoyable the trails are. While some people will certainly disagree, we made the assumption that most guests will not enjoy staying on one trail for long periods of time. Thus, we decided that it is more interesting and therefore should help a ski resort in rank, if the resort has a relatively low average length for its trails. We found the value for our proposed resort by dividing the total amount of kilometers by the total number of trails. We found that our trails on average were approximately 1.09 kilometers long. When comparing this value to the other resorts, we found that Vail, Whistler Blackomb, and a few other resorts were better in this regard judging by our standards. We found that we placed sixth in this part of the competition. Using these aspects of guest experience, we tried to rank which resorts were the best in the areas we tested. Out of the North American groups we were given, only 13 had enough information about their ski areas for us to rank them. Based off of that, we gave the team that did the best in each of the heats 12 points, second place received 11 points, so on and so forth until last place received 0 points. Wasatch came in first in the ski lift ranking and sixth in the optimal trail length ranking, meaning the ski resort received 12 points and then 7 points, adding up to 19 points. Only Vail and Whistler Blackomb received more points than that, so for this ranking system, Wasatch would place in third out of the existing ski resorts in North America that were compared. Solution and Extensions The suggested slopes and trails are able to fulfill the requirements of plenty of slopes, varying length of main slopes, difficulty distribution, and the 160 plus kilometers. An extension would be to consider the Olympic data more significantly. There was a small amount of Olympic data therefore most of the calculations determined provided skewed results. If more data was found about other Olympic locations then Wasatch could have been compared with them. However, the fact that Wasatch ranked third of the North American results might play a part in the ability of the resort to host the Olympics. References

10 10 Mirr, K(n.d.). Retrieved November 09, 2017, from (n.d.). Retrieved November 09, 2017, from ABOUT PARK CITY MOUNTAIN. (n.d.). Retrieved November 09, 2017, from info.aspx Cowan, J. (2001, December 16). How Steep Is Steep? Retrieved November 09, 2017, from Lifts & Trails. (n.d.). Retrieved November 09, 2017, from mountain/current-conditions/lifts-and-trails#sm.00b8vyn81cl0eae11cb11lsh0ulrw Mountain Info. (n.d.). Retrieved November 09, 2017, from mountain/about-the-mountain/mountain-info.aspx Mountain Info. (n.d.). Retrieved November 09, 2017, from mountain/about-the-mountain/mountain-info.aspx Mountain Info. (n.d.). Retrieved November 09, 2017, from mountain/about-the-mountain/mountain-info.aspx Mountain Stats. (2017, October 19). Retrieved November 09, 2017, from Piste. (2017, August 30). Retrieved November 09, 2017, from Trail Map Winter Jackson Hole Resort. (n.d.). Retrieved November 09, 2017, from Wasatch Peaks Ranch. (2017, November 09). Retrieved November 09, 2017, from

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12 12 Appendix Table 1: The table below shows the given data for the North American ski resorts. Table 2: The table below shows the given data for the Olympic ski resorts.

13 13 Table 3.0: The table below shows the data for the proposed Wasatch Ranch. Each length that was recorded was found and the percent slope was calculated. The column of length is color coded for the green, blue, and black trails. Table 3.1: Continuation of the Wasatch data

14 14 Table 3.2: Continuation of the Wasatch data Table 3.3: Continuation of the Wasatch data

15 15 Table 3.4: Continuation of the Wasatch data Table 3.5: Continuation of Wasatch data

16 16 Table 3.6: Continuation of Wasatch data Table 3.7: Continuation of Wasatch data Table 3.8: Continuation of Wasatch data

17 17 Table 4: The table below shows the number of lifts per a trail for each of the mountains in North America. Figure 1: The figure above shows the northern area of trails that were designed. The lifts are not shown because only one lift was used. This area is known as the children s area.

18 18 Figure 2: The figure above shows the lifts and the base lodges for the middle section of the area. The base lodges are squares and the triangles are the lifts. Figure 3: The figure above displays the main slopes of the middle section of the area. All the main slopes meet at the ski lift or the base lodge.

19 19 Figure 4: The figure above displays all the trails in the middle section of the total area. Figure 5: The figure above shows the lifts and the base lodges for the third section of the total area.

20 20 Figure 6: The figure above displays all the trails that connect the lifts and the lodges from figure 5. Figure 7: The figure above displays the lifts and the lodges for the southern section of the mountain.

21 21 Figure 8: The figure above displays all the trails in the southern section of the data.

22 22 Figure 9: The figure above demonstrates the overview of all the trails throughout the mountain.

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