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Calculating Trajectory – A Few Notes In Case You Ever Find Yourself Near a Giant Slingshot

Written by mike on October 18th, 2010

Not every episode of Catch It Keep It involves saving falling objects – but as the title of the show indicates, it does happen from time to time. And when an object is launched through the air, it helps to know how to track the trajectory of it.

There are a number of calculators available online, ranging from simple three-field layouts to impressively complicated, with every ballistic variable definable. But when you need to, sometimes you just have to get down and dirty and crunch some numbers. For CIKI, I built my own spreadsheet based off various trajectory formulas that allowed me to get the specs and graphs I needed – handy when launching an object off the roof of our workshop, for instance.

Ehow has a pretty simple breakdown of calculating trajectory. It requires some easy trigonometry (get your money’s worth from your calculator and use the Sin/Cos/Rad functions). This will give you a good start.

1. Break the initial velocity into its vertical and horizontal components. You will already need to know the angle at which the object was fired and its initial velocity. For this example, an archer fires an arrow at 30 degrees with a velocity of 150 ft/sec.
V0x = 150*cos(30) = 130 ft/sec
V0y = 150*sin(30) = 75 ft/sec
2. Choose a value for time and calculate the horizontal distance at that time. It’s best to start with zero and work your way through the trajectory incrementally. For this example, the value is calculated at
t = 1.
x = V0x*t = 130*1 = 130 ft
3. Calculate the value for vertical distance at the same time interval. The value for gravitational acceleration in English units is 32.2 ft/sec^2.
y = V0y*t – 0.5*g*t^2 = 75(1) – 0.5*32.2*1^2 = 58.9 ft
4. Plot the horizontal and vertical values on a sheet of graph paper. Choose another time value and calculate another set of coordinates. Continue until you have enough points to define your trajectory.

Joe, the engineer challenged to find the landing spot of the Big Green Egg for his team, was awesome. He pulled out all the notes you could use to check and re-check, given the data and measurements they pulled from the demonstration. I really enjoyed spending a few days with him.

Where will it land?

The hard part is adding in other elements (launch height, air resistance, rotation); things get a bit trickier. With so many variables, the safest bet was always to eliminate as many as possible by trying to take trajectory calculations out of the equation altogether… Giant butterfly nets are always a good thing to have near a giant slingshots.