The Road to Whiterun (...AKA The Math Behind All This)

So, OK, there's no real magic behind all this...just console commands. Three simple console commands which nevertheless open up a vast world of things to be measured. player.getpos x tells our friend Magnus how far east or west he is, player.getpos y tells him how far north or south he is, and player.getpos z tells him the altitude of his position, i.e. how far above sea level. That's it. (Oh, and for all you amateur Skyrim cartographers out there who didn't know this already...you hit the ^ button to enter console commands).

Well - it's not quite as simple as all that. Warning - there's math ahead, and quite a bit of it - but I promise, it's just this once!

The first thing the Cartographer needs to do is figure out how to measure any given distance from a to b. Let's start easy: if he's heading due north or south, he takes a getpos y reading at one point, walks to the next, takes another reading, and subtracts the larger from the smaller to get the distance he's covered. If he's facing due east or west, he does the same with getpos x. Pretty straightforward, huh?

The trouble is, Skyrim's roads are a pesky bunch and simply refuse to just run in straight lines along the four cardinal directions. Which means we have to bust out the old Pythagorean Theorem from ninth grade geometry:

 

I just lost most of my readership, didn't I.

So, Magnus takes readings at one point, walks the distance c, and takes readings again at the second. a is the difference between his getpos y values and b is the same for his getpos x values. Let's keep things simple and say a=3 and b=4; 3² + 4² = 25, the root of which is 5 - the total distance walked. Basically, he has to walk (or run) in a straight line as far as he can given the curvature of the road, note the distance, turn, walk another straight line, note the distance, etc. etc. ad infinitum. Of course, having to crunch those numbers every few seconds would likely drive poor Magnus over the brink of madness; fortunately for him (and me), if you Google "hypotenuse calculator", there's a handy little widget thing--ah, I mean, the Imperial Surveyor's Guild has a magic spell for that too. Um. Yeah. Gotta keep this little project lore-friendly, right? Alternatively, you can just imagine Magnus wandering along with a spike and a rope.

With all of the theoreticals out of the way, it's time for Magnus to turn to his first assignment - the little road that leads up to the gates of Whiterun, its "driveway," so to speak. He begins right outside the city's sole gate and immediately takes all three measurements:

Since the road curves pretty much straight away, that's not going to be much of a grand First Distance Ever Measured in the Province of Skyrim, but nevertheless, he walks it dutifully, turns right (northwards) to face further along the road and takes his readings again.

Ignore that top z value, it's just left over from the first set of measurements.

Magnus finds the difference for both x and y values: 1,137.31 for the former and a paltry 22.01 for the latter. But take a look at the compass in the first image; we're heading almost due west, so a negligible value for y (north/south) was to be expected. Plug those two numbers into the Magic Pythagoras Spell (8 magicka per second) and Magnus gets a total distance of 1,137.49.

But his job is not done yet. After all, what about that z value? Skyrim can be a pretty vertical land at times, and on a really steep stretch of road (which this, admittedly, is not), up to the Throat of the World for instance, it could make quite a difference. Anyways, all Magnus has to do is take that 1,137.49 and plug it into the same Pythagoras Spell with the difference between his z-values - 190.75 - and he gets his final distance: 1,153.17.

But that number doesn't mean a whole lot, because we still have to translate it into meaningful units. Those used in the game don't have any inherent meaning (let's say it's the diameter of a fly amanita stalk), but fortunately, there is an official "conversion rate" - one fly amanita stalk is equal to 1.428 cm, or roughly 70 to the meter. An Imperial Magnus may be, but he is no lover of the Imperial system - nevertheless, he can also grudgingly tell you that one FAS = 0.5625 inches, or 21 1/3 to the foot.

Long story short? Magnus' measured distance of 1,153.17 FAS (don't worry, you won't be seeing much of that "unit" anymore) is equal to 16.46m or about 54 feet.

Basically, from here to that gate. Looks about right, don't you think?

The rest of the job is just rinse and repeat. Magnus measures a total of 7 straight-line distances before arriving at the junction with the main road, between Whiterun Stables and Pelagia Farm.

 Add up those seven lengths and you get the total length of the road, a whopping 227.58 meters or 746 feet and 8 inches. The first stretch of road ever measured in Skyrim! Magnus congratulates himself on a job well done and takes a moment to gaze majestically up at the Throat of the World.

Because one day he's going to have to measure the road up to that sucker too, and won't that be fun?