Everyone loves a good chase or Ben Hur moment, but handling any kind of high-speed encounter poses a significant challenge to the DM and the players: speed.
Most things are just too darn fast. Your average character moves 80 ft. per round on foot (16 spaces double move at a run). If a round is roughly 6 seconds, the maximum speed for a character is 9 miles per hour. The average horse’s top speed is 37 mph. Assuming that’s a double move at a run, the horse travels 64 squares per round. And that’s a horse, on the ground. You would think the air speed of a dragon would be even faster.
A high speed race or pursuit is going to leave your grid very quickly and redrawing the terrain every round will bog down your game. So what’s the DM to do? There are two possible solution, one proposed by d20 modern and a homebrew I’ve developed with some buddies.
Big squares
If all the action is taking place at speeds in excess of 10 mph, consider scaling the field. Instead of each square representing a 5×5 foot area, have it represent a 10×10 foot area or greater if everyone is galloping, flying, or sailing at great speeds.
Even at 10×10, that fast horse is covering 32 big squares for a double move at a run and about 12 big squares as a standard move.
The pursuit
Big squares are useful for scaling fast battles, but what if all the action is happening in one direction at a constant high speed? Your grid is only going to go so far before you run out of spaces, no matter how big your squares are.
For a chase, you might want to consider using relative distance. If all combatants move at the same speed in a single direction every round, their distance from each other wouldn’t change, so don’t move them on the grid. Instead, use miniatures to represent significant parts of the terrain (like obstacles) that the players would move farther from or closer to in the course of their move.
As obstacles appear at the end of the grid the players will have to think carefully about sparing some of their forward movement to side-step and avoid logs, pits, debris, and anything else that might trip up their progress. Attacks will have to be well placed to keep ahead of the pursuers or to keep up with the pursued if it double moves. Powers that pull push and slide become a lot more useful, and knocking a combatant prone turns into an effective way to remove an enemy from combat.
Now go forth, play, and give your players an encounter they won’t see coming.
I started Dungeon Mastering with secondhand AD&D materials in 1996 and have run a vast number of D20 campaigns, from cliche' medieval adventures in a kingdom made of Lego bricks to fighting zombies and the mob in the mid 1930s. I try to make the gaming experience as enjoyable, fast-paced, and easy to play as humanly possible. 
What sort of damage would you suggest for a character that gets knocked prone, and removed from combat, during a high speed chase (eg. a full-speed horse)?
When characters are brought to an abrupt halt from high speed, I typically rule that they take 1d10 damage for every 10′ they traveled or would have traveled that turn. A character knocked prone from a vehicle or steed can make an acrobatics check to reduce the damage, just like from a fall.
So that’s 32d10 for falling off a horse at top speed. Ouch.
That’s why getting knocked prone is pretty much the end of you in a high speed pursuit. Not only are you unlikely to catch up, but you’re probably too injured to continue.
Items that reduce falling damage or slow a fall are invaluable for any rider (see purple dragon’s ring).
Great timing! I’ve been trying to figure out how to manage a chase between two mine carts on a rollercoaster ride along old mine rails. This will work perfectly. I can even simulate two different tracks that diverge at points and join together again later. Excellent!