Do It Yourself Flying in DnD
A Little DIY Math Shows What Your Flying Spells Can Do
Copyright © 2002 Simon Woodside
http://www.simonwoodside.com/dnd/
Why Flying is Important
In the real world, people don't fly. So, we don't all have a really clear picture of what the world looks like from the air. But in D&D, your characters can fly without the aid of airplanes and other fantastic gadgets. They can use levitate and fly spells.
In this article I try to demonstrate, with examples, why flying has such a big impact on your campaign ... and give you some Do It Yourself formulas to figure out how high your character can go, how far they can see, and how much land area they can overlook.
In the Old Days They Did Not Have Airplanes
Medieval maps, being based on inadequate observation and the most rudimentary navigational tools, are barely recognizable to us today. D&D is based on a roughly 12th-century technology level, and in those days they didn't even have the compass or the clock (to measure longitude). They didn't have any way to get high enough for a good perspective on the land they were mapping.
In addition, warfare took place firmly on the ground. Military tactics focused on the edges of groups of troops, holding the line, and charging through it. Castle walls 30 ft. high were enough to stop a host of knights. Big rivers halted armies, horses, baggage trains, and siege engines, until they found a ford or a bridge.
If you make the same assumptions about your own world, here's some food for thought: flying magic lifts your character up to where they can see lots of land and rain fire into the middle of enemy forces.
The Basic Math Of Visible Distance
Some math is necessary in order to calculate the results of flying magic. In order to demonstrate the effects of flying, we must calculate how far people can see when they are on the ground or in the air. We will assume that the world is the same as the earth (a ball about 24, 860 miles around). The visible horizon is the apparent boundary between earth and sky, visible in all directions. The visible surface is all the land within that boundary.
A NASA website (http://www-istp.gsfc.nasa.gov/stargaze/Shorizon.htm) describes how to calculate the distance to the horizon. Their formula is in metric units, so I have converted it to imperial. It is D = 1.223 x sqrt(h) where h is the height in feet. The result D is in miles.
Given the formula for the area of a circle, the visible surface is pi times the distance to the horizon squared (that is, πr^{2}).
At the end of the article is a simple tutorial that shows how to use your calculator or Microsoft Excel to find the numbers for your own characters.
Fliers Make Great Maps
Here are two examples, one using levitate and one using fly, that show what a flying spellcaster can do to improve their kingdom's map.
Example One — Halka Makes A Good Map
Halka, a 3rd-level wizard, learns the levitate spell, and she wants to find out how high she can go. On a clear day she levitates upwards at the maximum rate, which is 20 ft. per round, or 200 ft. per minute. After 15 minutes, she reaches a height of 3000 ft. Then she immediately stops and levitates back down at the same speed, reaching the ground just before the 30 minute time limit expires.
According to the formulas provided with this article, Halka was able to attain a peak visible distance of 67 miles using her spell. At that height, she can see 14,000 square miles of land, which is enough to see all of Massachusetts and quite a bit of Connecticut and New Hampshire as well.
Later, when she's gained a level, Halka is able to spend some time hovering at 3000 ft. She carries up a charcoal pencil and a canvas, and sketches out the rivers, valleys, roads, and towns of the kingdom. Like an aerial photograph, her carefully traced lines are a good match for the real features.
Example Two — Iagel Makes an Even Better Map
Iagel is an ambitious 5th-level sorcerer who hears about Halka's experiment. She thinks she can outdo the wizard by a substantial margin. As she attains 6th level, she learns to fly and casts it. Iagel flies up at the fastest possible rate, 45 ft. per round, for 48 minutes, and then immediately dives back down at 180 ft. per round. She lands back where she started 12 minutes later.
Iagel is pleased as she substantially outperforms the lowly Halka. At her peak, she achieves a height of 21,600 ft. She didn't fly quite as high as the highest mountain in the world, which like Mount Everest is about 29,000 ft. high. But she topped the local peak, similar to Mount McKinley, by a thousand feet or more. Her view was outstanding — the horizon was 175 miles away. At that height she saw 96,000 square miles of land, which is more than England, Scotland, and Ireland put together!
Of course, she may also experience altitude sickness without the aid of a new spell such as endure high altitude.
Fliers Rain Fire From the Skies
Map-making isn't the only use of the fly spell. It can also be used for making war. The following two examples using fly illustrate a simple way to destroy an enemy army that isn't expecting an aerial attack.
Example Three — Iagel Spots Invaders
The local king recognizes Iagel's flying ability and starts to pay her substantial sums to be his aerial agent. One of her patrols hits paydirt: she spots an invading army of orcs.
Example Four — Iagel Battles An Army
The king, once informed, sends out a force to repel the orcs. The force includes Iagel, flying above the king's army. From the ground she appears as a small figure, that could be mistaken for a bird.
Iagel flies at a height of 600 ft. over the invading orcs. At that height, she's safe from many attacks, including missile weapons, and short- and medium-range spells. However, it's not so high that she can't cast long-range spells down on her foes (since she's 6th level, long range is 640 ft.: 400 ft. + 40 ft. per level).
Her foes, the orcs, are tightly packed on the ground because they are expecting a charge from the king's cavalry. They stand one to each 5 ft. square. As Iagel utters her words of power, she unleashes a fireball on her foes. A ball of flame 20 ft. in radius explodes at the impact point, dealing 21 hit points of damage to each of the 50 orcs caught in the blast radius.
This only represents a small part of the humanoid army, but fortunately Iagel is joined by the king's Lord High Wizard, a 10th-level mage. He starts to cast the eight fireballs he has memorized today. About a minute later, 400 more orcs are down. The spell-casters leave the heavily injured enemy to run before the king's regular forces.
If Both Sides Have Fliers
If both opposing sides have spell-casters, flying monsters, or some other way to threaten each other from the air, the tactical situation changes in many ways that I won't examine here. Still, the fliers from both sides continue to threaten the land forces while they remain in the air, not otherwise engaged. Hit-and-run tactics, invisibility, and blink are just a few ways to evade aerial enemies.
How To Respond as a DM
In my opinion, fliers present an extreme danger to the integrity of a medieval-style campaign. The ability for moderately low-level spell-casters to affect travel and warfare so dramatically means that the enemies must respond in kind, leading to a magical arms race. I'm not interested in finding out where that goes. My solution is to limit all flying spells to a maximum of 30 ft. from the nearest surface or object. The spells remain useful for a variety of purposes without allowing any of the unbalanced examples here to develop.
Some might choose to go the other route and have their NPCs embrace flying magic to the full extreme.
Please tell me what happens, either way, by emailing me at sbwoodside@yahoo.com .
Links
The NASA site has much more information about how we see the world. The address http://www-istp.gsfc.nasa.gov/stargaze/Shorizon.htm is a good place to start.
For picture of medieval maps, try http://www.britannia.com/history/herefords/ mapmundi.html which has a good overview.
Do it Yourself Section
This section details how to find the maximum altitude, visible horizon, and visible surface for your own character. You will need a calculator with a square root (√x) button and a square (x^{2}) button. Or, you can copy the formulas below into Excel.
Find Your Maximum Altitude
With levitate: Your maximum altitude with levitate is 1000 ft. per level. You spend half of the spell duration going up, and half going down.
With fly (light or no armor): Your maximum altitude with fly is 3600 ft. per level. Since fly climbs much more slowly that it descends, you spend 80% of the spell duration going up, and 20% descending.
With fly (medium or heavy armor): Your maximum altitude with fly is 2400 ft. per level. Since fly climbs much more slowly that it descends, you spend 80% of your time going up, and 20% descending.
DM fudge factor: Beware of running out of time in midair. Warm updrafts can lift you higher than you intended to go, or crosswinds that knock you out over the sea can lead you to drown.
Find Visible Horizon
Once you know your altitude, calculate your visible distance with this formula:
1.223 x √altitude
On most calculators, enter your altitude, press the square root button (√x), press the multiply button (x), enter 1.223, and press the equals button (=).
You must enter your altitude in feet, and the resulting number is the number of miles to the horizon.
Find the Visible Surface
Once you know your visible horizon, calculate your visible surface with this formula:
3.1414 x (horizon)^{2}
On most calculators, enter your horizon, press the square button (x^{2}), press the multiply button (x), enter 3.1415, and press the equals button (=).
You must enter the visible horizon distance in miles, and the resulting number is the number of square miles that are visible below you.
Microsoft Excel
Instead of using a calculator, you can more easily calculate these figures in Microsoft Excel by copy-and-pasting the following formulas. You must include the = sign first. Change the number in bold to match your level, maximum altitude, or horizon.
To find your |
Bold number is |
Copy this to Excel |
Maximum altitude with levitate |
level |
=1000*(3) |
Maximum altitude with fly (light or no armor) |
level |
=3600*(6) |
Maximum altitude with fly (medium or heavy armor) |
level |
=2400*(6) |
Visible Horizon |
altitude |
=1.223*SQRT(3000) |
Visible Surface |
horizon |
=PI()*POWER((67), 2) |
Complete Calculations for Verification
This section is included for readers who want to verify my math. Otherwise, you may be inclined to skip it unless you want grade 10 math flashbacks. For the calculations here I used the NASA formula as given on their site, which is 112.88 x sqrt(h) with h and the result in km (although the formula used in the article is equivalent, as you can verify).
Example 1: Using levitate to make a better map
200 ft. per minute x 15 minutes = 3000 ft.
3000 ft. = 0.9144 km (convert to km)
112.88 x sqrt(0.9144) km = 107.94 km (apply NASA equation)
107.94 km = 67.1 miles (convert to miles)
Example 2: Using fly to make an even better map
This is an algebra problem in two variables (h and t)
let h be the maximum height achieved
let t be the time spent moving directly upwards
let d be the duration of the spell (which will be10 minutes x level)
Also, movement upwards is at 450 ft. per minute, movement downwards is at 1800 ft. per minute.
Thus we have two equations:
(1) 450t = h (for upwards travel), and
(2) 1800(d - t) = h (for downwards travel)
Now, set the left hand side of (1) = the left hand side of (2):
(3) 450t = 1800(d — t) = 1800d — 1800t (expand the brackets)
(4) 2250t = 1800d (add 1800t to the left hand side)
(5) t = (0.8)d (divide both sides by 225)
In the given example, d = 60 minutes. Substituting that into (5) gives t = 48 minutes. Thus, 48 minutes must be spent moving directly upwards, followed by 12 minutes of moving downward.
The height achieved is given by either (1) or (2). Using (1), we get h = 450(48) = 21,600 ft.
Now apply the NASA equation:
21,600 ft. = 6.583 km
112.88 x sqrt(6.583) km = 289 km
289.62 km = 179.96 miles = about 175 miles
Now calculate the surface area:
πr^{2} = π(175)^{2} = π(30625) = 96,211 square miles = about 96,000 square miles.
Example 3: Battling orcs
The radius of the fireball is always 20 ft., so using πr^{2} we have π(20)^{2} = 1256.637 square ft.
Each orc takes up a 5x5 square of 25 square ft.
1256.637 / 25 = 50.265 = about 50 orcs.
At 6th level, a fireball deals 6d6 hit points of damage. Each die averages 3.5, thus 6(3.5) = 21 hit points of damage are dealt on average.