spellcasting – I need help with distance scaling in a homebrew RPG – from “your body” to “the whole planet” in 10 simple steps

Square Cube Law

When we increase the range os a spell by a simple value, we increase its area of effect by the square and the volume of effect by the cube. Or rather:

$$R$$ $$A=pi R^2$$ $$V=frac 4 3 pi R^3$$

Energy density is defined as energy per volume. So our power scale should follow the Volumetric scaling, not a linear one. From one step to the next, you increase the energy needed by the third potence.

Self

A typical human body has about a weight of 100 kilos if we are rather broad. A human body also has a density of 1 ton per cubic meter, so a human is 1/10th of a cubic meter or $1 times 10^{-1} text m^3$. That’s, if condensed into a sphere, one of about 30 cm radius. $$frac V pi frac 3 4=R^3$$ $$R=0.287 text{ meters}$$

Planet

Mother earth has a volume of $1.08 times 10^{21} text m^3$.

Scaling the difference

We want to stretch between $1 times 10^{-1} text m^3$ and $1.08 times 10^{21} text m^3$ in 10 steps. That’s -1, 0 and 1 to 21, so 23 numerals for the exponent to scale the volume. Let’s try to get a nice progression, with a factor 1 in front.

  1. $10^{-1} text m^3$ – That’s the volume of our human, so self
  2. $10^{0} text m^3 = 1 text m^3$ – a 1x1x1 meter cube, or anything you can easily touch with one arm.
  3. $10^{1} text m^3 = 10 text m^3$ – Anything within 1.3 meters, or about 2 steps
  4. $10^{3} text m^3$ – Anything within 6.2 meters – about a small building or large room
  5. $10^{6} text m^3$ – Anything within 62 meters – or almost a Manhattan city block (technically that’d be 80.5 meters)
  6. $10^{9} text m^3$ – Anythign within 620 meters – about 8 blocks or a city quarter or village
  7. $10^{12} text m^3$ – Anything within 6.2 kilometers – or if you’d stand in the center of Manhatten, almost the whole of the peninsula. So let’s round that to Town.
  8. $10^{15} text m^3$ – Anything within 62 kilometers – or about the size of an average county or shire or halfway to space
  9. $10^{18} text m^3$ – Anything within 620 kilometers – or whatever is within an about a single European country if you are centered in it.
  10. $10^{21} text m^3$ – Anything within 6203 kilometers – or a sphere as big as earth centered around you. This sphere encompasses a whole continent. Yes, it means you affect less than half the planet, and only a small fraction of the distance to the moon, but this compromise keeps the scaling somewhat nicely.

The scaling here is clearly logarithmic, with two distinct areas: the “short” ranges (steps 1-3) and then the Magnitude steps from 4 to 10. This allows to differentiate better on the low end, and then proceeds into a smooth large scale, offering useful intermediate steps.

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Why this scale?!

So, why did I choose this scale, which focusses on the low end?

First of all: game usability & realism

Most spells that a typical player character could or should use need to be in distances that are within sight or useable in what accounts for typical combat ranges. These paradigms are fit up to somewhere between steps 6 and 7, depending on the weapons involved – a typical military rifle is useful all within step 6, while modern artillery would go up to 7.

The typical engagement distances of armies over time are rather short, so a focus on the short end for spells is best to model typical spells and have a difference in ranges available that allows separating between short and medium range combat spells. Some examples:

  • Spear infantry was limited at 15 feet or about 4.5 meters. That’s Range step 4.
  • Archery in the middle ages was used at ranges of about below 300 meters, so inside the range step 6.
  • modern infantry combat doesn’t go further than 500 meters usually, and in urban areas is often quoted to be below 50 meters even. Artillery, especially naval one, can stretch that.
    • in fact, the typical engagement range in WW1 was 50 to 250 meters
    • in WW2, the typical long engagement range for tanks was 500 to 800 meters while infantry fought well shorter at below 300 meters. The longest tank hit recorded was 2.5 kilometers… on a stationary target.
    • the longest ever navel artillery hit was 24 kilometers, which makes that the absolute maximum distance we can assume any engagement will happen unless missiles or drones are involved. That is a third of range step 8.
    • Drones are generally used on the same side of the planet to keep latency short by reflecting signals of one satellite only. This is pretty much Range step 10.
    • Modern ICBMs have ranges that are double the range of our step 10 – 12000 to 16000 km. They can hit literally any target on the planet but spend hours in flight. We are in the same order of magnitude though, so that’s just a little adjustment of factor 2 or something if you really want to have spells that far

Magic-propagation speed calculation

The scale also has the benefit of being roughly multiples of 60. So it can be used to quickly calculate speeds from the distances. Say our fireball with range step 5 takes 60 seconds to get to that far point, and for math sake, we round to the closest 10. 60 meters/60 seconds means it travels at 1 meter a second, or rather sluggishly and can be dodged. If the range was step 6, that’s 600 meters/60 seconds, so in the area of 10 meters a second – Olympic runner speeds! And if it takes step 6 but only takes 6 seconds, we are at 100 meters per second, that’s the speed of a longbow arrow or about half the speed of a slow bullet or a quarter of a heavy arquebus.

Look over the plate: other systems

Let me pull out GURPS. GURPS is notorious for cramming everything in spreadsheets. Including this list for range increments from 3rd edition, and I bold roughly equivalent distances to our distances above:

  • 1/10″ – 1/5″ – 1/3″ – 1/2″ – 2/3″ – 1″ – 1.5″ – 2″ – 3″ – 6″ – 12″ – 1.5′ – 2′ – 1yd – 1.5yd – 2yd – 3yd – 4.5yd 7yd 10yd 15yd 20yd 30yd 45yd 70yd 100yd 150yd 200yd 300yd 450yd – 700yd – 1000yd – 1500yd – 2000yd – 3000yd – 4500yd – 7000yd/4 mi (~6 km) – 10000yd – 10mi – 15mi – 20mi (~30 km) – 200mi – 2000mi – 20000mi – 200000mi

Those are horrible fine segments, and the modifier progression in that thing goes from -15 to +49 with 0 on the 2-foot step. But for the far distances (where GURPS goes with half my proposed distances but adds another increment in the end), the distances I propose show up, making them at least useable for a simulatoric standpoint.

The picture of putting the focus on the engagement ranges of combat however shows itself in various Fantasy RPGs:

In my decade-and-half of being the GM for various The Dark Eye groups, the longest engagement range ever wanted was 550 meters from the weapon used – a heavy trebuchet. Most TDE spells have a range well below 100 meters, even there are very few spells that have a range of as far as the eye can see or continent. I only know of one instance where such a spell was used in combat at distances further than about 100 meters – and it was aimed at a target the size of a house. Any spell that I witnessed to be used at a longer range was either a communication or clairvoyance spell. In this I am not counting any trans-planar spell: the distance to hell is one step through the invocation/banishment pentagram. As a result of the costs and targeting needed, most combat magic in this system is actually pretty close to mundane ranged weapons when it comes to their ranges, even though the efficiency/impact of the spells can be much higher.

Pathfinder 1e and D&D 3.5 have only very few spells that have ranges that are longer than half a kilometer (those exceptions are generally clairvoyance, communication, or translocation spells). Most combat spells are even limited to less than about 100 meters. Generally, magic can be (and is) treated as just another type of ranged weapon in Pathfinder, even if area-effect spells are common.

Shadowrun also fortifies this experience: Shadowrun imposes no range limit but the (optically redirectable) line of sight (and ability to see its target) of the caster. However, in the last 12 years of playing Shadowrun the longest spell directly cast by any caster I witnessed was about 250 meters using binoculars, and most spells were flung even below 50 meters. In fact, I remember only very few casts of spells further than 50 meters, unless a spirit sent on a mission was involved. As far as I witnessed, even as magic in this system is allowed to be super-long-range, generally it was used at ranges where close-combat weapons are used – and often as a replacement for such.

Mage the Ascension uses one of the magic disciplines as the limiter for distances in its rather freeform magic system, on a success scale: you need 1 to target something that you can see, 2 allows you to reach a very familiar place (like you home) no matter how distant, 3 a familiar place (your buddy’s home), 4 gets you to a place you have been once (like the capitol), 5 can get you somewhere you have only been described or seen on a photo and 6 gets you anywhere on earth you can imagine, even if you have no idea what is there. But yes, Mage is a really poor limiter in magic ranges, as it is very free in casting magic (and only clobbers you over the head with paradox for it).

What steps should I take if I am getting involved in topic disputes on Quora?

What steps should I take if I am getting involved in topic disputes on Quora? – Web Applications Stack Exchange

2013 – Steps in a Process & Coloring them (SP2013)

I came across an example of a process with a current stage image (should be attached to the thread).

Sample Workflow

Basically there would be 4 or 5 stages: Initial / Assigned / Being Processed / Completed.

Each of the stages would have (almost like a flowchart diagram) a progress image with an arrow showing the current state and they would be colored.

For example:
Current Stage – White box / Green Outline
Completed Stage – Green Box / Black Outline
Pending – Yellow Box / Gold Outline
Cancelled – Red Box / Red Outline
etc.

As the list item gets updated, the workflow images would get marked and colored for the stages.

How could this be accomplished? Would it be as simple as having a column for each stage? And if so then would the coloring of each stage come from CSS?

Thanks

tokens – Steps to create a geofield view proximity search for unrelated content

I am using geofield, leaflet maps and views to try to create a view of nodes of a content type B within a specified proximity distance of an origin specified in another content type A. A and B do not hold references to eachother. Content types A and B are not related and they do not hold entity references to each other so I cannot rely on views relationships to access fields from B in the context of A.

A and B both have geofield locations: A has field_origin and B has field_position.
Content Type A actually has three fields: field_view (type: viewfield) field_origin (type: geofield) and field_distance (type:decimal). I do not want to define a relationship between origin nodes (type A) and proximity nodes (type B).

This was my starting point but there are too few detailed steps to reproduce it and I think it assumes that the origin node has a relationship with the proximity nodes: https://www.drupal.org/project/geofield/issues/3149688

I cannot find a way to configure a proximity filter using either exposed or contextual filters to compare the origin of A against the position of B’s.

I hope this is possible as I dont want to have to set up fixed one-many relationships between A and B so I can keep the views truly dynamic.

tokens – Views admin UI: Steps to create a geofield view proximity search for unrelated content

End goal:
I am using geofield, leaflet maps and views to try to create a view of nodes of a content type B within a specified proximity distance of an origin specified in another content type A. A and B do not hold references to eachother. Content types A and B are not related and they do not hold entity references to each other so I cannot rely on views relationships to access fields from B in the context of A.

Bit more detail… A and B both have geofield locations: A has field_origin and B has field_position.
Content Type A actually has three fields: field_view (type: viewfield) field_origin (type: geofield) and field_distance (type:decimal). I do not want to define a relationship between origin nodes (type A) and proximity nodes (type B).

This was my starting point but there are too few detailed steps to reproduce it and I think it assumes that the origin node has a relationship with the proximity nodes: https://www.drupal.org/project/geofield/issues/3149688

I cannot find a way to configure a proximity filter using either exposed or contextual filters to compare the origin of A against the position of B’s.

I hope this is possible as I dont want to have to set up fixed one-many relationships between A and B so I can keep the views truly dynamic.

Bluetooth headphone volume buttons make big steps

When I change music volume using the volume buttons on my bluetooth headphones, each click moves the volume 2 or 3 volume steps (compared to when I change volume using the volume buttons on my phone itself). This often means that it jumps right from too loud to too quiet, so I have to dig out my phone to get the volume to a comfortable level.

I’ve already tried Developer Options > Disable absolute volume, which didn’t seem to make any difference. I’m using a Pixel 2 (stock Android 11) with Soundcore Life Q20 headphones.

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