# Best way to visualise impact distance against launch speeds and angle

I am modelling the trajectory of a projectile, incorporating atmospheric drag.

I am calculating the distance from the launch point for when the projectile impacts the ground.

I have generated this impact distance data using the Monte Carlo method (a range of randomly selected speeds and angles), so I have impact distances with corresponding launch speeds and angles.

What is the best way to visualise these data? What graph would be the best to use? I am currently using a 3D graph to explore the 3 variables, but I was hoping there was a better alternative.

• What might be "best" depends on your needs (such as the uses to which the display or displays will be put), the preferences of your audience and various other things we have no way to judge. We may be able to suggest some good visualizations, but how could we know if they're 'best' for your needs? – Glen_b -Reinstate Monica Jan 25 '15 at 0:12
• Are the results themselves (given the inputs launch speed and launch angle) fixed or is there a random component? – Glen_b -Reinstate Monica Jan 25 '15 at 0:13
• @Glen_b The results are fixed depending on the inputs. (ie same result each time with the same inputs). Would you be able to suggest some good visualisations to try out? – Spiruel Jan 25 '15 at 12:22
• When you say the inputs are 'randomly selected' can you elaborate? Are both variables from a continuous uniform distribution? Or are the points selected from some discrete set? Or something else? How will the visualization be used? e.g. will people be trying to read values off it? – Glen_b -Reinstate Monica Jan 25 '15 at 16:52

For such a smooth function, I suggest a contour plot with a sequential color map. Your dense, rainbow-colored scatter plot simulates this effect, but the colors are not evenly spaced or perceptually ordered.

Given your angle/speed locations are plentiful and random, you may not need to show the explicit points.

You can have as many contours are you want, but if you need to see the individual colors, here's a scatter plot with a sequential color map for comparison.

I've found a visualisation that I'm happy with - able to present 3D data 2 dimensionally.