Tinker is a hero in the popular game Dota 2. He has a spell called 'March of the Machines' that creates a stampede of little robots in a rectangular area. The robots do damage on impact of an enemy unit. Basically this can be considered a vector field and enemy units are surface area. We want the maximum flux in order to optimize damage.
If you're really interested in what this looks like:
https://www.youtube.com/watch?v=AmXRvkaYhIE
Anyways, you often end up in static situation where enemy units aren't moving in this common pattern. It makes sense that a diagonal march will provide the most damage:
A vertical march would have one enemy 'shielding' damage from the one behind it (depending on if it were downwards or upwards). A horizontal march does negligable damage to the bottom due to way less surface area being hit.
What kind of confuses me is once things start moving. The common advice is(artwork not mine):
Things tend to run roughly single file so you can assume the stuff running through the march is a wall of surface area. My intuition always made me think that when things are running through march, going fully perpendicular would maximize damage. The sadder part is I've taken vector calculus before, so I've encountered a great deal of this stuff. But this is certainly the area where my brain had a melt down! I'd love to see a mathy justification for this angled approach being optimal.
