- #1

- 10

- 0

I am attempting to create a spreadsheet that models the flight path of a sphere. My model should consider air resistance, but I've opted to ignore magnum. As a resource to help me, I'm using this page, but I have ran into some trouble. I have the velocity and position defined recursively as:

$$v_x(n+1)= v_x(n)+a_x(n)Δt$$

$$v_y(n+1)= v_y(n)+a_y(n)Δt$$

$$x(n+1)=x(n)+v_x(n)Δt+a_x(n)(Δt)^2$$

$$y(n+1)=y(n)+v_y(n)Δt+a_y(n)(Δt)^2$$

The acceleration has given me some trouble, though. I tried defining acceleration as it the page seemed to indicate:

$$a_x(n)=-(D/m)v_x(n) \sqrt{{v_x(n)}^2+{v_y(n)}^2}$$

$$a_y(n)=-g-(D/m)v_y(n) \sqrt{{v_x(n)}^2+{v_y(n)}^2}$$

When I used this to finish my spreadsheet, I noticed that the vertical velocity was always positive, an obvious error. It is very possible that I have made an error unrelated to the acceleration equations (I am a novice at best at mechanics and Excel), but I saw this as the most likely candidate. The [erroneous] spreadsheet I currently have is attached.

What is causing these incorrect values? If there is any additional information I can give to help, let me know, and I will be happy to do so. I'd hate for all of my work to be wasted, so any help you can give is very much appreciated. Thank you for your time and for your assistance.

$$v_x(n+1)= v_x(n)+a_x(n)Δt$$

$$v_y(n+1)= v_y(n)+a_y(n)Δt$$

$$x(n+1)=x(n)+v_x(n)Δt+a_x(n)(Δt)^2$$

$$y(n+1)=y(n)+v_y(n)Δt+a_y(n)(Δt)^2$$

The acceleration has given me some trouble, though. I tried defining acceleration as it the page seemed to indicate:

$$a_x(n)=-(D/m)v_x(n) \sqrt{{v_x(n)}^2+{v_y(n)}^2}$$

$$a_y(n)=-g-(D/m)v_y(n) \sqrt{{v_x(n)}^2+{v_y(n)}^2}$$

When I used this to finish my spreadsheet, I noticed that the vertical velocity was always positive, an obvious error. It is very possible that I have made an error unrelated to the acceleration equations (I am a novice at best at mechanics and Excel), but I saw this as the most likely candidate. The [erroneous] spreadsheet I currently have is attached.

What is causing these incorrect values? If there is any additional information I can give to help, let me know, and I will be happy to do so. I'd hate for all of my work to be wasted, so any help you can give is very much appreciated. Thank you for your time and for your assistance.