Some Quick Hexcrawl Horizon Visibility Calculations

How far away can an object be before it dips below the horizon and is no longer visible?

For simplicity, treat the planet like a smooth perfect sphere, and ignore the atmosphere and any other obstacles.

Table of Examples

Assume that your eyes are 1.8 meters above the surface of an earth-sized sphere. From how far away can you see the tops of various objects?

Object	Object Height (m)	Visable Distance (m)	Vis. Dist. (miles)
The Ground Itself	0	4,800	3.0
Garden Gnome	0.5	7,300	4.5
Another Person	1.8	9600	6.0
A Male Giraffe	5.2	13,000	8.0
An Aspen Tree	16	19,000	12
Statue of Liberty (with base)	93	39,000	24
Great Pyramid of Giza	140	47,000	29
Statue of Unity (with base)	240	60,000	37
Burj Khalifa	830	110,000	67
Mount Everest	8800	340,000	210
Severe Thunderstorm	18000	480,000	300

The practical takeaways for hexcrawling are that if you're standing in the middle of a flat twelve-mile hex, then: 

• You can just barely see the top of someone's head if they're standing at the edge of the hex. (But there's probably a shrubbery in the way.)
• You can see the top of a mature tree standing in the middle of the neighboring hex. (If you use a telescope and there are no other trees in the way.)
• You can see the top of a giant robot from two hexes away. (Very important to know.)
• You can see storms and mountains from quite some distance. (Haze will be more important than horizon by that point. I don't know whether you'd actually be able to recognize a storm at 300 miles (25 hexes), but here are a couple anecdotes of people noticing thunderstorms from more than 120 miles (10 hexes) away under the right conditions.)

I've seen similar numbers before, but wanted to recalculate everything in a tidy little list for my own use. 

Calculator widget below

A Metric System for Faerun

In many tabletop roleplaying games, the round of 6 seconds, and the space or square of 5 feet serve as basic units of measurement for game mechanics. Just for fun, let’s try to actually construct a system of measurements using these as our base units for time and distance.

The self-imposed rules of the exercise are as follows:

• Derived units are expressed simply in terms of base units. (Coherence)
• Larger or smaller units use a consistent exponential power (Though I’m not sticking to decimal).
• And if possible, the resulting system should feel psuedo-medieval, be intuitive to a 21st century American, and be useful for rules of thumb in a tabletop rpg.

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321 Hero* Dice: A post about unusual dice anatomy.

This post briefly mentions HeroQuest. As such, we must begin by viewing the sacred liturgy. Once this is done, you may return for the rest of this blogpost.

The structure of the dice:

Several games use six-sided dice with the following properties:

• 3 of the faces share the same symbol, usually indicating a successful 'attack' result.
• 2 of the other faces share a second symbol, usually indicating a successful 'defense' result.
• The final singular face has its own distinct marking.

An example of what these dice look like. Photo credit to Eric on BGG.

What follows are some examples, and my thoughts about adapting these dice for RPGs.

Wizards in Rayon Stockings: Some worldbuilding notes on plastics.

How reasonable is it is include plastics in a psuedo-medieval fantasy world without fossil fuels? 

 

A better title might be "Alchemists in Rayon", because of course you can just wave your witchofingers and summon tupperware from the realms of chaos. But even restricting ourselves to low-magic fantasy, for many plastics, it's totally reasonable to throw them in. They'll probably just be rarer and considered high-quality objects instead of throwaway trash.

Clearly, the question on everyone's mind when they see this compilation of public domain witches is
"Where did they get those sweet leggings?"

Skip to the end if you just want a bulleted list of which plastics I thinks a witch might be able to brew in a cauldron. But otherwise, come with me on this scatterbrained journey into the world of organic chemistry.

 

Universal Magical Object Classification Guide

After witnessing an argument about the difference between artefacts and regular magical items, I've devised a foolproof and universal classification system:

I hope that this answers all of your questions.

Rpg Mechanics Stolen from Clearance Rack Boardgames

Here are a couple board games I picked up from clearance bins. They each have interesting mechanics which can be stolen and incorporated into tabletop rpg encounters.

Attack on Titan

BGG link. One-versus-all boss battle. Based on a show about fighting giant monsters called titans. 

I picked this one up because I like the designer's other work. The main problem it has as a board game is that the titan's side of things isn't very engaging. If the titan was automated, then it could be a satisfying cooperative dice-rolling puzzle thingy. 

But it had some really fun little ideas:

Climbing on the Beast:

First of all, the human characters move up and down these little cardboard standees. The ground counts as a space, as does each layer of the tower, and about half of the locations represent the humans climbing up the titan, shadow of colossus style. Some spaces allow you to do special actions, like firing the cannons from the tower, while others are places you need to maneuver to accomplish certain objectives.

This is just good fun.  And you don't really need a 3d prop to accomplish this effect. Just lay up some index cards indicating certain points-of-interest atop whatever giant monster is being fought.

Doors, Shores, and Parallel Zones: a guide to the boundaries between worlds

So you're jumping around between parallel dimensions.  But what's the crossover like?

Here's a quick taxonomy, sorted in increasing order of smoothness.

 

Doors 

(Also known as gates, portals, wormholes, cosmic glory holes, or rifts. )

An enclosed frame holding a flat region of warped space which is connected to a paired surface elsewhere in the cosmos. Any particle which passes through the frame is transported to the other world. (Some doors connect to an intermediary demiplane, and so resemble a tunnel.)

These are the most common and easiest-to-understand type of planar boundary, and most cross-dimensional spells work by opening these doors.

The defining characteristic of this kind of boundary is that local space is entirely normal close to the boundary and then experiences a discontinuity.

d6 doors found in the Plates of Flavor:

1. A small pond of cream found in the Plate of Sweets. Jump in and you'll pop out of a similar pond in the Plate of Meats. Unfortunately, the pond has a tendency to move around when no one is paying attention to it.
2. An elephant-sized peach pit lays in the deserts of the Plate of Seed. Small tunnels dot its surface, just large enough to crawl through. Most of the tunnels are shelter to vermin, but one opens out into a giant half-eaten peach in the valley of unripened fruit. 
3. The city of Everything Bagel, found at the center of the Great Buffet of the outer plates, is just riddled with doors. Nobody actually lives there except for the Lady of Propane. All the other people bustling about were just unfortunate enough to have a random portal open up connected to their refrigerator or shower drain or something like that.
4. If you dig deep into the crust of the pastry plains, sometimes you'll find a pocket of filling connecting to some other world. A custard pocket connecting to the plain of sweets. A pocket of garbage connecting to the prime material. Etc.
5. Dionysus has a big inter-dimensional portal that he just uses to dump half-eaten chicken wings.  No clue where the other end opens up.
6. Dump enough fish sauce into any whirlpool and it will briefly transform into a portal to the shallow sea.

Hyperbolic Shores

A transition into another world with noticeable spatial distortions, but no discontinuities.

For example, you're in the Boiling Oil Ocean, cruising around on your turnip barge. You see an island made of meat off in the distance, giant billowing fingers dressing its shores. After cruising around a bit, the island doesn't seem too large. But when you land and go to explore its interior, you find that it's infinitely large and in fact contains the entire Elemental Plate of Meat.

Meanwhile, from the Meat side of things, you approach a lake of oil. You can easily walk around the entire thing in a matter of hours, but can't see across to the shore on the other side. The lake, is in fact, the entirety of the infinite Plate of Oil.

Another common kind of shore are the ones that form in large book collections. As we all know, a dense enough concentration of knowledge can cause spacial distortions, making libraries and bookstores bigger on the inside or even connecting them to L-space. Because such distortions are noticeable, but locally continuous, they count as Shores.

Parallel Zones

Characterized by a transition to another world despite the lack of absolutely any sort of spatial distortion.

You know, that crazy fairy kind of stuff where you're walking in the woods down a path you've travelled many times before, but it's unusually spooky this time and then somehow you find yourself trapped in an endless twilight forest. And it turns out it's because the vice-archduchess of the fey or whomever wanted to look at your hat was lined with beaver pelt from a particular magical beaver is seeking its revenge. Okay, we're back. It's fine.

Mathpost: Coordinates on a tesselating hexagonal world.

Turn back now, if ye be looking for some narrative content. This be nothin' but a big wad of barely polished geometry.


Basic idea is that you live on a giant flat plane that loops. (As in this story) Go far enough in any direction, and you'll end up back where you started. Navigational systems evolve to meet the needs of the people using them. What kind of system of coordinates would be useful for navigating on a looping hex?

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Rectangular Coords

X: Y:

Hexline Offset Coords

A: B: C:

 Unit length is equal to the inner radius of the hex.

(X,Y) coordinates are the standard Cartesian kind.

(A,B,C) coordinates are "Hexline Offsets". Basically, choose 2 opposite edges of the hex perimeter, and draw parallel lines first through the origin and then through your point. The absolute value of coordinate is the ratio of (the distance between the point and the line through the origin) and (the distance between the center and the perimeter line)

Further Explanation 

More detailed unpolished explanation below.

Neither the images nor text were optimized, so everything is a bit too large.

Skeleton Post 2019

It's a bestiary with over 300 skeleton variants. 42 pages long.

Too late for Halloween, and just in time to be late for Day of the Dead. Click here for the download link. I'll be back again next year with even more skeletons.

Again, here's the download link (PDF)

Variants for GLOG mishaps and Dooms.

Here's a primer to GLOG wizard stuff if you have no idea what I'm babbling on about.

One of the things GLOG magic has going for it is the tension associated with powerful spells. You can always add more juice to a spell, but it drastically increases the risk of [bad thing] or [very bad thing] happening.

The standard way it works is that doubles give you a random 'mishap', while triples give you a predetermined 'doom'. Your mishaps and your dooms are tied to your school of wizardry.

But I want to simplify and generalize that system to make it compatible with classless play ala Knave or Into the Odd. Type1Ninja's excellent ruleset here is what I've been using. It make two changes. Firstly, there is a single class-agnostic mishaps/doom table. Secondly, the trigger mechanism is changed from matching die faces to simply checking for a 6, with a secondary stat which ticks down over time to make dooms more likely. It's good! But it doesn't quite make my soul sing.

Here are a few untested spitball mechanisms along the same lines.