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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).

Zip line diagram. This example shows a 255 meter zip line that is hung between two trees. The launch platform is 16 meters high and the landing platform is 11 meters high. The vertical drop from the launch point to the lowest point on the line is 16 meters and the horizontal distance is 214 meters. 

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.


D i s t a n c e ( d ) = h o r i z o n t a l   d i s t a n c e 2 + v e r t i c a l   d r o p 2
2
2
Distance


Step 2: Approximate Acceleration

A c c e l e r a t i o n   ( a ) = g × s i n ( θ ) l o s s r e m e m b e r : g = 9.81 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.

s i n ( θ ) = v e r t i c a l   d r o p d i s t a n c e ( d )


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.


Graph showing loss according to rider weights in pounds. An outline is included to indicated the loss value for a 130 pound rider.     

So, for a rider of 130 pounds, acceleration can then be calculated as: (enter the values of  sin(θ) and  loss below)

A c c e l e r a t i o n   ( a ) = g × s i n ( θ ) l o s s


Acceleration =

Step 3: Calculate Maximum Velocity

M a x i m u m   V e l o c i t y ( V m a x ) = 2 × a × 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 =