Alex Walinskas The Math Behind Skiing Cost and Budgeting Predicting Snow Fall Vertical Feet Skiing can be costly, so it's important to incorporate math if you plan on budgeting. Inequalities can be used to calculate how many days you can end up skiing. If you are on a budget of $1,000, and you know that a hotel room is $200 a night, lift tickets are $80 per day, and rentals are $40 dollars a day, you can make a inequality to calculate how many days you can afford. Nearly all mountains have some kind of tracking system that monitors snow fall on the mountain and predicts snow fall. Predicting snow fall is a mathematical process. The equation temperature + wind speed= snow fall is roughly what weather services use to predict snow fall. Vertical feet is a common reference used by skiers that marks how many feet in total one has skied. Vertical feet can be found a number of different ways, but the easiest is to take all the runs skied, multiply each one by the number of times it was skied, and add the numbers together. 200H+80T+40R<1000 Vertical Drop Vertical Drop is a term used to describe how "tall" a mountain is. To find a mountain's vertical drop, you subtract the height at the top of the mountain from the height at the base of the mountain. Example: Vail has a peak elevation of 11,570 feet, and a base elevation of 8120 feet. To find it's vertical drop, you would find 11,570-8120, which is 3,450 feet. Vertical drop is important because the higher the drop, the more skiable land. Calculation of Comfortable Carrying Capacity CCC compares the amount of vertical transport capacity supplied by the lift system against the demand for vertical transport by skiing guests on a daily basis. It is found by taking vertical transport feet per day, and dividing it by Vertical Demand. Finding Vertical Transport Feet-Per-Day and Vertical Demand VTF and Vertical Demand are crucial for calculating Comfortable Carrying Capacity, which is used by ski resorts to make their lifts most efficient and comfortable. VTF is found by multiplying the vertical rise (seen earlier) of the lift, the hourly capacity (in people), and the number of daily operating hours. Vertical Demand is first found by predicting skier flow characteristics (based on multiple factors), and predicting the average descent time. This produces a "round trip interval" figure, which represents the average number of runs a typical skier would take on a particular lift. When multiplied by the vertical rise of the lift, you get Vertical Demand. VTF/Vertical Demand Constant Rate Constant Rate can be used often in skiing. The equation x=ky can be applied to feet, speed, and other factors. Example: Finding a constant rate going downhill. If the height of a run is .5 miles, and it takes you 5 minutes, with height directly impacting time, you would plug in .5=5k, where k would equal .5miles/5 minutes. You would be moving at constant rate of .5 miles per 5 minutes. Finding Slope Slope can be found by

the simple equation

y2-y1/x2-x1, which is

the same as rise/run.

To find the slope of a run, you would find two points going vertical, and two points going horizontal to find rise over run. Example If i want to calculate the slope of a run, I would choose random points down the run. Theoretically, I would have a edge on view of the mountain. I would measure my rise (-200 ft) and my run (50 feet), and divide rise by run (-200/50). Therefore, the run has a slope of -4.

Angles Every good skier is aware of

the use of angles in skiing.

Understanding everything from the degree of a run to the degree of a sharp turn is crucial for skiing well.

skis and "digging": when a skier makes a turn, their skis cut into the snow at a certain angle, and knowing how much to cut in is helpful in order not to fall.

runs: being able to judge the angle of a run is important for knowing if you're capable of skiing it, and knowing what type of turns to make.

Angles (continued) turns: in skiing, there are many different kinds of turns. every turn has an angle, and it can vary from acute to obtuse to the occasional 360 degree angle :)

body position: angles also come into play when a person positions themselves. it's important to lean forward at a slight angle, and a skier needs to know when and how much to angle the knees.

Thank you for watching :)

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# The Math Behind Skiing

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