Spell: Blade Barrier (Math Error?)

So, the one day I was reading through different spells and I came across what I believe to be a simple math error in the effect of one:

Blade Barrier
6th-level evocation

…You can choose to make the wall up to 100 feet long, 20 feet high, and 5 feet thick, or a circle up to a 30-foot radius and up to 20 feet high and 5 feet thick…




We can ignore the height and thickness for this purpose as the only variable difference in volume between the two is length.
100 feet long vs. 30-foot radius.

I base the following critique on the premise that the desire is for the circle and line to have the same volume. For the purpose of volume I am going to simplify it and just refer to squares, even though they have no volume they will work for my purpose here.

100 foot long wall takes up 20 squares if they are 5-foot squares (100 / 5 = 20).

The 30-foot radius circle has a circumference of 188.5 feet (2 * pi * Radius = C)…(2 * 3.14 * 30 = 188.5). It would seem obvious already that the listed dimensions of the circle are wrong. But let’s look at the grid squares occupied.

Referring to Fig-1, a circle with a 30-foot radius occupies 28 squares.

My first impression is that the mistake made was that the Diameter was intended to be 30-feet which would make the radius 15-feet.

A 15-foot radius circle has a circumference of 94.2 feet (2 * pi * Radius = C)…(2 * 3.14 * 15 = 94.2). And since 5-foot increments are the only increments that make sense to use if the effect may need to be utilized on a gridded battle-map, then this would make sense. However, if we look at how this circle fleshes out on a grid then we will see that 20-foot radius is, in my humble opinion, the most appropriate with staying true to the original premise.

Referring to Fig-2, a circle with a 20-foot radius occupies 20 squares.
    A 20-foot radius circle has a circumference of 125.7 feet (2 * pi * Radius = C)…(2 * 3.14 * 20 = 125.7)

Referring to Fig-3, a circle with a 15-foot radius occupies 12 squares.

Shape                              Space   
100-foot line                    20 squares
30-foot radius circle         28 squares
20-foot radius circle         20 squares
15-foot radius circle         12 squares 

So even though, mathematically, it seems like the spell should be corrected to have up to a 15-foot radius; my opinion would be that it should be defined as having a radius of up to 20-feet.

Thoughts?
Hard to argue with good math.  A second possibilty is to make the wall 200ft rather than 100, or 40 ft high rather than 20.  Since volume can go in either direction.  A 30ft radius is really pretty big for a wall-spell though, so I would probably go with the 15ft radius.  I know that you lose some volume, but a circle can be used as all-around protection OR used to trap enemies.  The circular arrangement gains extra tactical viability, so I would err on the side of less volume.  Secondly, squares are not an assumed measurement in 5e, so using the per-foot translation is more viable even if it changes the total number of squares.

Still,  I appreciate the math, and you are correct to point this out.  It is clearly an oversight on their part.  The spell list generally needs a lot of work.  1st level spells should do more damage than cantrips.
It's probably just something they didn't consider. I'm sure they meant radius, though. Circles in D&D have always been given by radius as long as I can remember. Sounds like a 20 ft radius would be the best.
Well, I'm glad that other people appreciate the point being brought up. Didn't know if it'd seem like I was being too nitpicky.

There are some spells that I really like what they did with though. I don't know what they were like in 4th but some of these are definitely more interesting than they were in v3.5.
> Blink
> Color Spray
> Dimension Door
etc.

In general I like the direction of having spells with the possibility of less than desirable outcomes. 
...Secondly, squares are not an assumed measurement in 5e, so using the per-foot translation is more viable even if it changes the total number of squares...



While I think we agree for the most part and I do not have a definitive case to argue against squares not being an assumed measurement in 5e (yet); I would wager that 5-foot squares will be the default mode of visually describing tactical combat on the battlemap when the final version is released.

We do know at least:

How to Play, page 7
Movement
... When precision is important, such as during a battle, you spend your speed in segments of 5 feet, unless told otherwise ...

Also it seems like almost anything with a significant distance is rounded to the nearest 5 foot increment.

Another big clue that squares, while not explicitly stated are implied is from:
DM Guidelines, page 11
Creature Size
...For example, eight Medium creatures can surround a fellow Medium creature...
Also, the size chart would match up very well with a squares as a measurement.

Plus, I'm sure wizards wants to end up making money on this release. So they'll want as many mini's sold as possible. Myself being an impulsive spender and user of battlemaps; I WILL purchase some.
Remember, 3rd edition books never gave any distance in "squares," but its combat rules standardized the 5 foot square grid anyway, and they sold plenty of miniatures. Taking us out of the game world to talk about meta-measurements like squares in game isn't the right way to go, in my opinion. Anyone who can do any of the other simple math in D&D can divide by five.

For the game I'm starting in a couple weeks, I'm going to try using a battlemat with hexes.  I know it won't work so well for rectangular shaped areas, but I want to see how things go with it in irregularly shaped areas.  For rooms and most hallways, I'll probably fall back on dungeon tiles.

Remember, 3rd edition books never gave any distance in "squares," but its combat rules standardized the 5 foot square grid anyway, and they sold plenty of miniatures. Taking us out of the game world to talk about meta-measurements like squares in game isn't the right way to go, in my opinion. Anyone who can do any of the other simple math in D&D can divide by five.



If you mean that things like Race Speeds (in the Races chapter) or in Spell Desriptions never referred to squares, then you're probably right and ignore the last paragraph of this response.

I agree with you in regards to limiting the talk about squares for most chapters. My ideal PHB would be designed to read as a Scientific and Historical study of the game world (e.g. Races would be described as though they're being explained by a zoologist or anthropologist [i.e. Dwarves for ex. would have their scientific name listed as something like Homo-Dvergar (Old Common dvergar, sing. dvergr)).

I do believe it could be explained in the DM Guide(lines) without taking away from the game world.

v3.5 definitely did give specific references to squares though. I opened up a randomly selected page from Chapter 8: Combat of the v3.5 PHB and on page 147 there are two diagrams that specifically explain movement in terms of squares. There is also Table 8-3 which gives different speeds in squares... Actually, paging through Chapter 8 - it's littered with talk about squares.

For the game I'm starting in a couple weeks, I'm going to try using a battlemat with hexes.  I know it won't work so well for rectangular shaped areas, but I want to see how things go with it in irregularly shaped areas.  For rooms and most hallways, I'll probably fall back on dungeon tiles.


I so far have been using the Hexgrid battlemap in the Playtest I'm running. I just assume that the square grid is so ingrained in the battlemap culture that to talk about critiques in terms of hexes would be more off-putting.

You hit the mark, I've found that for areas with square corners and straight lines that the hexgrid is bothersome. The two things that I really prefer about the Hexgrid map (which may not be enough to keep using it) are:

1. You never have to count with a mixture of 1 or 2 squares or 5 or 10 feet (Not a very big deal).

2. Area Weapons in shapes like Cones and otherwise never have to change shape based on the direction of the attack. 
My ideal PHB would be designed to read as a Scientific and Historical study of the game world (e.g. Races would be described as though they're being explained by a zoologist or anthropologist [i.e. Dwarves for ex. would have their scientific name listed as something like Homo-Dvergar (Old Common dvergar, sing. dvergr)).


However, the required time and effort to achieve this would probably just be a waste. Eh, maybe never mind on that last point.  
My ideal PHB would be designed to read as a Scientific and Historical study of the game world (e.g. Races would be described as though they're being explained by a zoologist or anthropologist [i.e. Dwarves for ex. would have their scientific name listed as something like Homo-Dvergar (Old Common dvergar, sing. dvergr)).



That would be the coolest thing ever! But then people who think the Knowledge (Science) skill is useless would rail against it.

My ideal PHB would be designed to read as a Scientific and Historical study of the game world (e.g. Races would be described as though they're being explained by a zoologist or anthropologist [i.e. Dwarves for ex. would have their scientific name listed as something like Homo-Dvergar (Old Common dvergar, sing. dvergr)).



That would be the coolest thing ever! But then people who think the Knowledge (Science) skill is useless would rail against it.


I also think it would be ideal. When I was thinking about how it would work I came up with the following, general ideas to make it work:

1. The rules would have to read more like laws (both physics laws and societal laws).
2. As previously mentioned, Race descriptions would read more like a zoologist/anthropologist scientific description (including scientific names and name origin).
3. Classes would have to be presented more like Academic/Trade/Spiritual areas of study.
4. Skills... I'm not sure exactly what you'd do with them. Maybe you'd define them more so than explain how to use them. As an example let's take Climb:

Climb (Defined as I would have
it)
Climb: (verb) 1. To scale an incline subject to a level of difficulty that is related to the sheerness, slipperiness, degree of incline, terrain, or other characteristics of the surface: to climb up a mountain face. 2. A test of Strength to hold or lift oneself: he relied on his skill of climbing to pull himself up over the ledge. 3. A test of Dexterity to avoid falling from a precarious perch: she used her climbers reflexes to grab a hold of grip before tumbling of the hillside.

Climb (Explained at present)
Climb
You can use the Climb skill when you're attempting to scale a sheer or slippery surface, avoid hazards while climbing, or stay on a vertical surface while something is trying to knock you off. You'll most often use your Climb skill to modify a Strenth check you make to keep your hold, or sometimes to a Dexterity check to avoid toppling from a precarious perch.


5. I think that if it were presented this way; the PHB would need to be provided with at least a small portion of the world described. A basic map, names of some cities and towns, average populations, patron deities, official language(s), banner, laws, etc.
> This would fit in with WotC desire to include more flavor and story into this edition.
> I also think this would be found to be very useful to DM's starting up Campaigns.
> I know there have obviously been resource materials that provide a lot of this but I think having a bit more in the PHB in this manner would give the world a little more life to the average player.

I would love to hear what other people think about this. Maybe I'm in the minority here, but I'm curious.

I think EVERY instance "Radius" should be changed to "Diameter"

Look at Fireball, 20 ft Radius, meaning 40 ft Diameter

Lets see you realistically manage to use that in combat
I think EVERY instance "Radius" should be changed to "Diameter"

Look at Fireball, 20 ft Radius, meaning 40 ft Diameter

Lets see you realistically manage to use that in combat



really?

The math doesn't really change, but the reason they have used radius is that burst spells tend to "radiate" naturally.
A fireball explodes from a single point and radiates 20ft outward.  So anything within 20ft of the targeted point gets scorched.
An aura radiates out from a creature. 
Furthermore, any spell effect radiating out from a creature ignores the space they occupy.  So an Antimagic field has a diameter of 25ft.  but it only "radiates" 10 ft. out from the caster.