Exploration

If you guys don't like these hard and crunchy mechanics of travel, we can change these rules.

Travel Pace
While traveling, you can move at a normal, fast, or slow pace. A fast pace makes you less perceptive, while a slow pace makes it possible to sneak around and search an area more carefully.

Forced March. It's assumed that players travel for 8 hours in a day. You can push on beyond that limit at the risk of exhaustion. For each additional hour of travel, each character must make a Constitution saving throw at the end of the hour. The DC is 10 + 1 for each hour past 8 hours. On a failed saving throw, a character suffers on level of exhaustion.

Mounts and Vehicles. For short spans of time (up to an hour), many animals move much faster than humanoids. A mounted character can rode at a gallop for about an hour, covering twice the usual distance for a fast pace, but after that the mount will need to rest.

Characters in wagons, carriages, or other land vehicles choose a pase as normal. Characters in a waterborne vessel are bound to the speed of the vessel, and don't suffer penalties for a fast pace or gain benefits from a slow pace. Depending on the vessel and the size of the crew, ships might be able to travel for up to 24 hours per day.

Special mounts, such as a pegasus or a griffon, or special vehicles, like a broom of flying, allow you to travel more swiftly.

Difficult Terrain
Travel speeds in the table above assume relatively simple terrain: roads, open plains, or clear dungeon corridors. But adventurers often face dense forests, deep swamps, rubble-filled ruins, steep mountains, and ice-covered ground--all considered difficult terrain.

You move at half speed in difficult terrain--moving 1 foot in difficult terrain costs 2 feet of speed--so you can cover only half the normal distance in a minute, an hour, or a day.

Hex Map
We're using a hex map for wilderness travel. A hex map is made out of tessellating hexagonal cells.

Our hexagons are 6 miles across on the short side and 7 miles across on the long side. The edges of the hexagons are 3.5 miles long.

The island that our adventure takes place should take roughly a week to get to any coastline from its center... and since most of it will be difficult terrain, the radius should be like, 18 hexes...

TODO: Figure out map stuff.