Calculations: Example
Let's see how we can predict the maximum speed of a rider using the information from Figure 5. For this example, we will assume a rider weight (including trolley and harness) of 578 N (or equivalently, 130 pounds).
Step 1: Determine the Distance Traveled
Please find the horizontal distance to the lowest point and vertical drop values from Figure 5 and insert them into the equation below. Click on the "Calculate" button to see the result.
Distance(d) = | ^{2} + ^{2} |
The correct answer is:
$$Distance~(d)= \sqrt{214^2 + 16^2}$$ $$d = \sqrt{45796 + 256}$$ $$d = \sqrt{46052}$$ $$d = 214.597 m$$ $$d \approx 215 m$$Step 2: Approximate Acceleration
First let’s find sin(θ). It can be calculated by dividing the opposite leg (vertical drop) by the hypotenuse (distance (d)). Enter the two values into the equation below to calculate sin(θ). For simplicity, enter whole numbers only.
= /
The correct answer is:
$$sin(\theta) = \frac{16m}{215m} = 0.0746$$Next, we’ll use the chart below to determine loss. The loss values have been derived through experimentation on the WVU Canopy Tour. In this example the rider is 130 pounds. Find the approximate value of loss in the chart and use it in the equation below.
So, for a rider of 130 pounds, acceleration can then be calculated as: (enter the values of sin(θ) and loss below)
The correct answer is:
a = 9.81 X 0.0746 - 0.45a = 0.732 - 0.45
a = 0.282 m/s^{2}
Step 3: Calculate maximum velocity
Since the values of all variables are now known, the maximum velocity (speed) of a 130 pound rider can be determined. Enter the values into the equation below to find out.
V_{max} = | 2 X X |
The correct answer is:
$$V_{max} = \sqrt{2\times(0.282)\times(215)} = 11.0~m/s$$Thus, knowing the distance of the zip line to the lowest point in the catenary curve, the vertical drop, and the weight of the rider, you can predict the maximum speed on the zip line.
In this example, a 130 pound rider will have a maximum acceleration of 11.0 m/s or 24.7 mph (see unit conversion chart at the right side of this page).
Navigation
Standard International (SI) to English Conversions |
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To Convert: | Multiply By: | To Get: |
---|---|---|
Length | ||
meters (m) | 3.28 | feet (ft) |
kilometers (km) | 0.621 | miles (mi) |
Mass | ||
grams (g) | 0.0022 | pound mass (lb) |
kilograms (kg) | 2.202 | pound mass (lb) |
Velocity/Speed | ||
meters per second (m/s) | 3.28 | feet per second (ft/s) |
meters per second (m/s) | 2.24 | miles per hour (mph) |
kilometers per hour (km/hr) | 0.621 | miles per hour (mph) |
Force | ||
newtons (N) | 0.225 | pound force (lb) |