dropping water from a height and plotting the spread

Question

Im working on building a basic model which simulates the spread of water when dropped from a firefighting helicopter. To make a start I just want to plot the spread of water dropped from a fixed point.

I decided to treat the volume of water as discrete particles that fall from a height h, and at an angle $\Theta$ which is normally distributed around an estimated mean (not sure yet what to set mean to yet, 90 degrees? since its dropping from a fixed point). Ive coded this scenario in R: The first plot is what my code produces The second plot is what I am trying to achieve (think about how water disperses if you drop it on the ground) can someone help me figure out how to plot the second graph with each data points x, y coordinate as a function of $\theta$. Thankyou in advance.

Answer 1

Dividing by $\sin$ is obviously wrong, because $|\sin x|\le 1$ for all $x$, so the absolute value of the result will never be less than drop_ht. If you draw the triangle, you will see that

x_coord1 <- drop_ht * tan(drop_angx)
y_coord1 <- drop_ht * tan(drop_angy)

is the true result of your model.

But this shows you that your model is flawed $-$ if the rnorm function is a normal distribution, then your model blows up when drop_angx or drop_angy is close to $90^\circ$. I would be more inclined to treat x_coord and y_coord as being normally distributed, with a standard deviation that depends on drop_ht somehow.