Effect of Altitude on Ray Range & Cover (or, blasting from buildings)

[Quidam]

Your spiderwalking warlock is perched on the side of a building (b) facing an alley (a) and wants to hit someone below with his eldritch blast (c).

His blast has a range of 60ft. How far down the alley can he reach? Depends on how far up the building he is (assuming it's vertical).

a^2 + b^2 = c^2

5ft up: a^2 + 5^2 = 60^2, 59.8ft down the alley or 11 squares.
10ft up: a^2 + 10^2 = 60^2, 59.2ft down the alley or 11 squares.
15ft up: a^2 + 15^2 = 60^2, 58.1ft down the alley or 11 squares.
20ft up: a^2 + 20^2 = 60^2, 56.6ft down the alley or 11 squares.
25ft up: a^2 + 25^2 = 60^2, 54.5ft down the alley or 10 squares.
30ft up: a^2 + 30^2 = 60^2, 51.9ft down the alley or 10 squares.
35ft up: a^2 + 35^2 = 60^2, 48.7ft down the alley or 9 squares.
40ft up: a^2 + 40^2 = 60^2, 44.7ft down the alley or 9 squares.
45ft up: a^2 + 45^2 = 60^2, 39.7ft down the alley or 7 squares.
50ft up: a^2 + 50^2 = 60^2, 33.1ft down the alley or 6 squares.
55ft up: a^2 + 55^2 = 60^2, 24.0ft down the alley or 4 squares.
60ft up: a^2 + 60^2 = 60^2, 0ft down the alley or the square directly below him.

Looks like the sweet spot is 20ft up- out of reach yet still hitting things 55' away. Interesting to see how far you can get even 55ft up.

Please let me know if I've miscalculated. I'll leave the eldritch spear table as an exercise for the student.

 

[Quidam]

Hm. Got me thinking. Is there an easy way to determine who has cover from you? If you're 50' up a wall shooting into the melee below, it's unlikely your targets receive cover from the other combatants.

Let's see. A medium sized combatant takes up a 5' cube. The most cover an enemy would get would be from someone adjacent to them. In order to deny them that cover you need to be higher up than they are far away from the base of the building.

If you're 10ft up looking down an alley, your allies give more cover than if you're 30ft up. There's got to be a relatively simple equation to determine how far a medium creature will grant cover based on how far above them you are and how far away they are, but I don't feel like crunching it right now.

Any math monkeys already done it?

 

[frankthedm]

Even at 50', most times medium allies will be granting cover to adjacent foes unless they are directly below you. You might be lucky if the DM uses "varying degrees of cover", but you allies will be in trouble if the "striking cover" rule varient is also used.

 

[mvincent]

a^2 + b^2 = c^2

Note that in D&D you don't need to use the Pythagorean theorem to calculate the hypotenuse for 3-D combat.

In D&D: c=a + 1/2b (where b is the smallest leg) because the rules say:
"When measuring distance, the first diagonal counts as 1 square, the second counts as 2 squares, the third counts as 1, the fourth as 2, and so on."

 

[Ilium]

Note that in D&D you don't need to use the Pythagorean theorem to calculate the hypotenuse for 3-D combat.

In D&D: c=a + 1/2b (where b is the smallest leg) because the rules say:
"When measuring distance, the first diagonal counts as 1 square, the second counts as 2 squares, the third counts as 1, the fourth as 2, and so on."

Wow. I never realized you get this result by counting distance per the RAW. But this is the exact calculation I use as a "close enough" approximation. I originally got it from Star Frontiers, of all places.