### Levitate And Fly: Going Over The Head Of A Medieval Campaign

### Introduction

In the medieval world, it was taken for granted that traveling was a dangerous and chancy endeavour. Even in the twelfth century, the Europeans lacked basic navigational tools like the compass (to find north) and the clock (to measure longitude). Maps were often guesswork and many of the landforms they depicted are hardly recognizable today (see

Brittania: Comparing Medieval Maps which has examples).

In addition, it was a ground-based world. Armies could assume that they had to send out land-scouts to find their enemies. Castles walls 30 ft. high were enough to stop a substantial siege. Seaports found out about new arrivals when they appeared on the horizon. People knew what they could see, and that wasn't very much.

Many D&D campaigns make the same assumptions about their own worlds. But some of the magic spells,

*levitate and fly* included, throw sand in the face of those assumptions. This article uses examples to show how these two spells affect map-making and army warfare in a medieval setting.

### The Basic Math Of Visible Distance

In order to demonstrate the effects of flying, we can use some math to 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 the surface of the world inside that circle.

According to NASA (

Distance to the Horizon) the distance to the horizon is 112.88 times the square root of the observer's altitude in km (that is, 112.88 x sqrt(h) km). We will convert km to miles with 1 km = 0.62 miles. According to the formula for the area of a circle, the visible surface is pi times distance to the horizon squared (that is, pi*r

^{2}).

### Example 1 - Using Levitate To Make A Better 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 given above, 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 2 - Using Fly To Make 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*.

### Warfare From The Air

Map-making isn't the only use of the

*fly* spell. It can also be used for making war. The following examples illustrate a simple way to destroy an enemy army that isn't expecting an aerial attack.

### Example 3 - Patrolling The Neighbourhood

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 4 - Battling Orcs

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 we will not examine here. Still, the fliers from both sides will 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.

### Some Ways To Respond As A GM

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 let me know what happens, either way, by emailing me at

[email protected].

### Appendix - Calculations Used In The Examples

**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:

pi*r

^{2} = pi(175)

^{2} = pi(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 pi*r

^{2} we have pi(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.

**Copyright � 2002 Simon Woodside. All rights reserved. **