Thursday, 24 July 2014

How far can you see on a hex map?

One of the key aspects of wilderness geography is being able to assess the lay of the land.  This is one thing that the traditional, top-down way of representing geography doesn't say much about.

If you walk north west from Nivereen, you'll emerge from the forest and be greeted by a view of the mountains across the valley.

That view might look something like this:

Or does it? Can we actually see the mountains from there?  What about if we climb the jagged hills to the west of the forest spur?  How far can we see then?

How far is the horizon?

It turns out that the main obstacle to seeing faraway landforms - besides atmospheric interference like fog or rain - is the curvature of the earth.  A consequence of this is that the viewer's altitude is a key factor in how far they can see. (If you go high up enough that you're in space, for instance, you could see nearly half the planet!)

Wikipedia has a wonderful page on the horizon that gives us all the info we need.  The few equations we need aren't that complicated:

Distance to Horizon (miles) = 1.22 x sqrt( observer's height in feet )
Distance to Horizon (km) = 3.57 x sqrt ( viewer's height in meters )

For a hypothetical, 6' tall viewer, this puts the horizon around 3 miles.  (As Steamtunnel pointed out, this is one argument in favor of using 6-mile hexes: an adventurer in the middle of a hex could see right to its edges.)

A 6' tall adventurer standing on top of a 30' town wall, however, could see further, about 7 miles.  An adventurer at the edge of a plateau, 200' above the plains below, could see 17.5 miles - quite a bit further.

Seeing Faraway Tall Things

Most of the time our adventurers are not looking at flat, featureless plains. The more interesting question is stuff like: how far away can I see that tower?  Can I see the mountains?

It turns out the answer is unexpectedly simple: all you need to do is know the horizon distance for the viewer's altitude, the horizon distance for the target's altitude, and then add them together.

So if I'm on the town wall, and I want to know how far away I could see a 100' tall wizard's tower, the answer is:

1.22 x [ sqrt( 6' ) + sqrt( 100' ) ] = 15.2 miles

Now, this is the distance at which we could just barely see the very tip of the tower - we probably wouldn't be able to pick it out of the grass.  Let's say we need to be able to see at least half the tower to recognize it, that gives us:

1.22 x [ sqrt( 6' ) + sqrt( 50' ) ] = 11.6 miles

On a hex map of six miles, we'd be able to make out the tower a full 2 hexes away.

The Meaning of Altitude

A key point I've glossed over so far is how to work out 'altitude'. This isn't elevation above sea level, but the height above the prevailing terrain.  If you're on a plateau 2000' above sea level, that doesn't help you see further along the plateau.

Only add the plateau to your height if you're looking down off it. If you're looking along the plateau, it doesn't count (because it will be the earth-curved plateau itself that eventually prevents you seeing further).

A Linear Approximation

Now of course, taking square roots at the table while juggling all the other GM duties is too much to ask, but I have a simplification that works well enough for the distances we care about:

6 miles + 1 mile / 50' of height

So if you're on a 200' cliff, looking down across a plain to see a distant tower or mature forest (50' to its halfway point), you can see it 11 miles away.

From flat plains, foothills (say, 1000' tall, resolvable when you can see the top half - so 400') could be seen 14 miles away (8+6).

From that same vantage point, large mountains (6000' above the plains, 3000' to the midpoint) could be seen 66 miles away.

Flying on a griffin at migratory altitude (e.g. 5000'), you could see those same mountains from 166 miles away.  (At this point, most likely the limits of atmospheric clarity would be involved, even in very clear air.)

If you climb the tallest tree in the forest, putting you 10' above the canopy, you could see the top 50' of the strange rock spire formation (that protrudes 100' above the trees) from 8 miles away.  (The top of the trees, here, is the altitude baseline.)

A Simple Legend

To help during play, I might work out a simple legend for various terrain types on my hex map. This just takes the height divided by 50', then by my hex width to work out a "visible-distance contribution".

Here's a simple legend for a 12-mile hex map with five types of terrain:

Mountain Peaks (5000-6000'): 8 hexes
Mountain Slopes (2500'): 4 hexes
Foothills (1000'): 2 hexes
Treetops (100'): 0 hexes
Rolling Lowlands (15'): 0 hexes

To use this, work out the height of the viewer and the target over the prevailing terrain, add those together, and add a free half-hex.

In the foothills, looking across more foothills toward distant mountain slopes?  4.5 hexes  (8-4 + 0 + 1/2)

In the treetops, looking to see where the foothills start?  2.5 hexes (2 + 0 + 1/2)

If you're on a mountainous slope (4) looking out across a vast, rolling flood plain (0) to a massive mountain range on the far side, you could make out the peaks (8) from 12.5 hexes away.

Easy peasy!

Wednesday, 9 July 2014

Spanish Translations Continue

Over at La Torre de Ébano, Hugo Gil keeps pumping out the Spanish translations of the adventures!  These have been quietly collecting on the Spanish adventures page, but I haven't mentioned them in the main feed.  Spanish typically has more letters than the equivalent English, so the dense layout is certainly giving Yugan a run for his money. :)

Saturday, 5 July 2014

The Circle of Wolves

The latest adventure has landed, The Circle of Wolves. Like the Raid Mirror, it's two pages, and still a tight fit!

This is decidedly an adventure for a powerful adventuring party. It starts off simply - a werewolf on the loose, but there's potential for almost open-ended levels of pain if several more Leádstæf escape.

When you run this, consider letting the players get stuck in before the Vinteralf arrive. The hermit, the ghost, and the members of the circle are all potentially friendly, at least initially, and Hyngran has plenty of destructive potential, especially if a PC or two gets bitten.

It's important not to play the Vinteralf as if they're here to save the day while the PCs watch - they're not!  They're meant to be potentially sympathetic antagonists: they start out rather pathetic, and perhaps they solicit the party's help in finding the hermit. Perhaps the party discovers them incapacitated with fever. And after all, they're trying to save their homeland from the Leádstæf.

Once they get rolling, however, they're extremely destructive. They're not above befriending the party and turning on them once they have what they need. Remember that they've given up everything they care about to come on this mission, they're not going to get squeamish about a few blubberless southerners. Or will they?

Graphic Files

Once more, thanks to everyone who's been supporting this project, it's been really fantastic.

Wednesday, 2 July 2014

Thursday, 19 June 2014

The Raid Mirror

Here's adventure #9, The Raid Mirror.  This started out as an experiment for a June freebie, which is why it's such a different format!

It has a Dungeon World "front" style, meaning that it's a bunch of terrible badness that can happen if the PCs don't act to change the course of events.

Download it, kill your PCs, and tell me about it!

Graphic Files

As usual, everything is free for non-commercial use under CC-BY-NC-3.0.

Monday, I showed the art for Circle of Wolves - well, I find myself in an unusual situation in that I'm ahead of myself on maps!  This one is coming down the pike, the first two-map two-pager, following an idea that Shane King gave me.  Here's the exterior view:

I still love drawing rocks

Monday, 16 June 2014

Crossing the Page Break

With all of your support, I've reached my last milestone (at least, of the ones I've thought up!)  That means - yep - I cross the page break, and everything from now on is going to be two pages.

When I got the notice, I was halfway through a little experiment - a freebie for June that is structured like a Dungeon World "front". Rather than describing an adventure-packed location, it describes an unfolding threat large enough to eventually impact the PCs, wherever they are.

It started from a question - what would happen if a pack of orcs got hold of a mirror of scrying and teleportation? Probably not much, I'm sure they'd be content to keep on hunting from their cramped, stinking orcnest. 
The Orcnest Tirru-Stryggal
They certainly wouldn't start extorting everyone within three hundred leagues, under threat of sending in a pack of orc commandos into your bedchamber in the middle of the night.  Then the nestlord starts pounding silver nails into his head and things get really bad.

Since the art's all done for the orc adventure and I'm not always by a computer to work on layout, I've started on the art for adventure 11.

The Circle of Wolves
A large clearing in an escarpment-riven forest, a convergence of ley lines gives off magical power. Over the years it has attracted worshippers, monument builders, madmen, and once a sorcerer-king.  But all that's in the past now, and it's just a creepy stone circle off in the forest.  Except that people have started to turn up half eaten.

I seem to enjoy drawing rocks!

Sunday, 1 June 2014

The Coming of Sorg

Here's the next one in the series!  This is a bad place that's going to get a whole lot worse unless the players do something about it.

Here's the link to the high-res art!  Like the adventure it's cc-by-nc.

In the spirit of the old B2 module, this is a place with enough goons to overwhelm most parties (especially in systems with flatter PC power growth) unless the players are able to cultivate some allies or sew dissent.  The 'factions' are definitely divided against one another, but it's going to take some intervention from the players to get things moving.

For tone, my mental image is of a fantasy version of WWI trench warfare. Groups of cultists are lurking everywhere, but most of them are frightened, hungry or exhausted, pinned down by the emanations and trying to muster the courage to act.  There are puddles of water, mud, bits of gore from previous kills, and every now and again a half-ethereal emanation goes screaming overhead, looking for an easy kill.  Real end of the world stuff.

This is an opportunity for you to bust out that random NPC reaction table. The PCs and any given group of the cultists might want exactly the same thing, but trust isn't easy to come by in this sort of environment. On the other hand, even the most wicked of cultists might be glad to see apparent reinforcements!

A few notes: the staircase isn't meant to be a big 'fuck you' to prepared parties! Unless your group goes for that sort of thing, be sure to raise their hackles first by describing what it's like to mount a staircase with all those broken and defaced statues looming over it.  I imagine most PCs will react pretty strongly to any wastage, so there's no need to deplete anyone.  Cultist allies, too, may warn the PCs, and a party with some experience should have no trouble making their own alternate way up through magic or climbing.

Sorg's emanations aren't invincible - they're just immune to "normal" weapons. Blessed, silver, or magical weapons will hurt them just fine.  You may wish to adjust this, depending on your system. Mid-level Burning Wheel or Torchbearer parties, for example, won't have much along these lines, while 8th-level Pathfinder PCs will be packed with it.

Also note that other than the scrolls in the archive and the possibility of a boon from Deel, there's no mention of treasure. If your system requires players to haul out a lot of treasure, by all means add some, particularly in the Ruined Archive (a little), the Brewmaster's House (a little more), and the High Temple (plenty).

How To Hook It In

A place like this is bad for the neighbours. Many of the cultists are former thieves and similar unscrupulous sorts, and the Blighted Order would have been a thorn in the side of any nearby community, much like a bandit camp.  After Sorg's arrival, a number of them would have fled outright, winding up picking pockets in taverns or - if they've cash to spare - drinking away their trauma and telling tall tales.

Nearby patrols, too, would have noticed the sudden drop in bandit activity, a welcome relief.  That's until the emanations start showing up, picking off fishermen and wood-gatherers, before finding more populous places to feed.

Hope you enjoy it! Don't forget to check out the others in the series! If you like these adventures, consider supporting the project on Patreon!