I have a regular 20km x 20km vector mesh grid that I wish to use as the basis for a network dataset. Each line in the grid has a cost value representing travel time. I created this grid in a Lambert Azimuthal Equal-Area projection and each line segment is exactly 20km long when viewed in this projection. As the basis for a network dataset, I hope to use the grid to calculate shortest routes between two points on the grid. However, I've been told that equal-area is a bad choice for distance calculations, and I should use an equidistant projection instead.
Is the solution as simple as projecting my equal-area grid to an equidistant projection and recalculating my routes? Or do I need to create a new grid from scratch with an equidistant projection? If I need to create a new grid, is there a tool for doing so? (I converted the equal-area grid from a previous dataset that was in equal-area).
You can create a feature dataset with the right equidistant projection and then use the GP tool Create Fishnet to create a new grid feature class with the right properties. If you already have a feature class that has 20 km edges, it will only matter what projection it is in if you are going to project it to something else later. And yes, anytime you project the data, the actual length of lines can change.
However if your goal is to simply have a grid with exactly 20 km as a length value, you could either add some length field to the feature class and calc it to 20 and use that in the length attribute of the network dataset OR simply add an attribute length and set it's evaluator to a constant value of 20!