Example Problem
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).
Figure 5. Measurements for the last zip line on the WVU Canopy Tour. The drawing is not shown to scale.
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 boxes below. Click on the "Calculate" button to see the result.
$$Distance(d)=\sqrt{horizontal\text{}distanc{e}^{2}+vertical\text{}dro{p}^{2}}$$
^{2}  
^{2}  
Distance  
Step 2: Approximate Acceleration
$$Acceleration\text{}(a)=g\times sin(\theta )loss$$ $$remember:g=9.81\frac{m}{{s}^{2}}$$
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 boxes below to calculate sin(θ). For simplicity, enter whole numbers only.
$sin\left(\theta \right)=\frac{verticaldrop}{distance\left(d\right)}$


sin (θ) =  
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 box below.
So, for a rider of 130 pounds, acceleration can then be calculated as: (enter the
values of
sin(θ) and
loss below)
$$Acceleration\text{}(a)=g\times sin(\theta )loss$$


Acceleration =  
Step 3: Calculate Maximum Velocity
$$Maximum\text{}Velocity({V}_{max})=\sqrt{2\times a\times d}$$
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 boxes below to find out.


Max Velocity =  