Instructables
Picture of Trajectory Modeling

This is an example of how to model the simple trajectory of a potato discharged from a potato cannon. To do this you need to have the gravitational constant, velocity of the projectile as it leaves the barrel, and the angle between the barrel and the ground.

 
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Step 1: Finding Velocity

Picture of Finding Velocity
FF2.jpg

My first step is to find the velocity. I used the method of finding the distanced traveled per frames. Knowing the frame rate of the camera, the velocity can be calculated. In my case I calculated, as seen in the video, the velocity to be 60ft/s since it traveled 5ft in 5 frames while being filmed at 60 frames/s.

5ft * (1/5 frames) * 60 frames/s = 60ft/s

Step 2: Velocity in X and Y directions

Picture of Velocity in X and Y directions

Now we find the velocity in the X and Y directions. For the X direction,

Vx = Vcos(angle) = 60cos(30) = 51.96ft/s

And the Y direction

Vy = Vsin(angle) = 60sin(30) = 30.00ft/s

Step 3: Plug and Chug

Picture of Plug and Chug

Now we have:

Vx = 51.96ft/s

Vy = 30.00ft/s

g = -32.2ft/s^2 (gravitational constant)

y0 = 4ft (Height of end of the barrel above the ground)

Now we plug them into the trajectory formulas:

x(t) = (a*t^2)/2 + Vx*t + x0

y(t) = (g*t^2)/2 + Vy*t + y0

We know that there is no horizontal acceleration (a = 0) and we are starting at x0 = 0

So plugging in Vx, Vy, y0 and g gives us,

x(t) = 51.96t

y(t) = -16.1t^2 + 30t + 4

jakeframe5 months ago

You could take this experiment a step further by measuring the real world trajectory and using that data to calculate the air resistance.

showden (author)  jakeframe5 months ago

I actually started out doing that and creating my own drag coefficient model. But it got into differential equations with conflicting x and y equations. I think I messed up with the integration so I simplified it and didn't worry about the drag, haha. But I had it narrowed down to two equations and two unknowns after putting in the initial conditions, but something was off.

Migs5 months ago

Can you post your spreadsheets?

showden (author)  Migs5 months ago

Yes I can; should be up now.

Migs showden5 months ago

Thanks!