Supposed you try launching a party member across a 500 feet wide and 50 feet deep gap with a trebuchet. however, something goes horribly wrong and he's launched straight down into the pit (let's just say he was stuck in the bag until it reached the end). this would launch him at about 3X the speed of a normal fall (150 feet per second instead of 55 feet per second). Does he still take only 5d10 falling damage (1d10 per 10 feet), or does he take more like 15d10 damage because he lands at triple speed?
[RPG] Is falling damage affected by falling speed
dnd-4efalling
Related Solutions
Keep in mind that human terminal velocity peaks around 53-56m/s — about 170-183 ft/sec— or about 1100 ft/round. It should take, at 32ft/sec (which is close enough for this), it's about 5.7 sec.
ragdoll Mode Terminal Velocity calcs \begin{array}{crrrl} S1 & 16\text{ ft} & 32\text{ ft/s} & 192\text{ ft/r} \\ S2 & 64\text{ ft} & 64\text{ ft/s} & 384\text{ ft/r}\\ S3 & 144\text{ ft} & 96\text{ ft/s} & 576\text{ ft/r}\\ S4 & 256\text{ ft} & 128\text{ ft/s} & 768\text{ ft/r}\\ S5 & 400\text{ ft} & 162\text{ ft/s} & 972\text{ ft/r}\\ s6 & 574\text{ ft} & 183\text{ ft/s} & 1098\text{ ft/r}&\textit{ terminal velocity} \end{array}
So, since terminal velocity is hit during turn 1 half that is the distance covered in turn 1. Turn 1 should then be to about 550 feet, and each turn thereafter another 1100 feet.
Now, peak recorded speed was about 125mph in random posture, or about 210mph in bullet posture for about 308 ft/sec.
so, if the character's in bullet mode:
Bullet Mode Terminal Velocity calcs \begin{array}{crrrl} S1 & 16\text{ ft}& 32\text{ ft/s}&192\text{ ft/r}\\ S2 & 64\text{ ft}& 64\text{ ft/s}&384\text{ ft/r}\\ S3 & 144\text{ ft}& 96\text{ ft/s}&576\text{ ft/r}\\ S4 & 256\text{ ft}& 128\text{ ft/s}&768\text{ ft/r}\\ S5 & 400\text{ ft}& 162\text{ ft/s}&972\text{ ft/r}\\ S6 & 576\text{ ft}& 194\text{ ft/s}&1164\text{ ft/r} & \textit{exceeds ragdoll TV}\\ S7 & 784\text{ ft}& 224\text{ ft/s}&1344 \text{ ft/r}\\ S8 & 1024\text{ ft}& 256\text{ ft/s}&1536\text{ ft/r}\\ S9 & 1296\text{ ft}& 288\text{ ft/s}&1728\text{ ft/r}\\ S10 & 1600\text{ ft}& 300\text{ ft/s}&1800\text{ ft/r} & \textit{terminal velocity}\\ S11 & 1900\text{ ft}& 300\text{ ft/s}&1800\text{ ft/r}\\ S12 & 2200\text{ ft}& 300\text{ ft/s}&1800 \text{ ft/r} \end{array}
So, a little physics: falling like a ragdoll: 550' in round 1, 1100' each round after.
Falling in speed suicide dive: 550' in round 1, another 1600 in round 2, and another 1800 per round in rounds 3 and later...
For simplicity, make it 500 and 1000 in ragdoll, and 500, 1500, and 1800 for diving.
Also note the 4E DMG says 500 feet in round 1, which is about 50' short, but could be covered by not being in ragdoll, but parasol, or by a 28' per second per second gravity.
References:
http://hypertextbook.com/facts/JianHuang.shtml
http://answers.yahoo.com/question/index?qid=20080412205510AAEu62v
In this section, it says
This rule is helpful to a flier that is knocked prone but is still conscious and has a current flying speed that is greater than 0 feet. The rule is designed to simulate the creature flapping its wings furiously or taking similar measures to slow the velocity of its fall.
Meanwhile, the rules for flying say:
If a flying creature is knocked prone, has its speed reduced to 0, or is otherwise deprived of the ability to move, the creature falls, unless it has the ability to hover or it is being held aloft by magic, such as by the fly spell.
... so, there are different ways to knock a flying creature out of the air. Note that the prone condition doesn't reduce your speed — and it's clear that that's the case that the new optional rule really applies to. In that situation, the creature can't fly and falls, but can flap or take whatever measures. The rule notes that if the fall continues for more than one turn (that is, more than 500 feet), a "prone" creature with a fly speed can recover. Other more powerful means which reduce the target's flying speed to 0 still mean a dangerous fall.
But, also note that Earthbind is not one of these more dangerous situations, since it explicitly gives a soft landing:
An airborne creature affected by this spell safely descends at 60 feet per round until it reaches the ground or the spell ends.
(The text does not specify "no damage", but it's implied by "safely" — and note that this is the same rate that Feather Fall provides.)
So, to directly answer your question: being prone has no effect on the calculation. As the optional rule says, subtract the creature's flying speed from the distance fallen and then calculate damage as normal (1d6 bludgeoning damage per 10 feet) for the remaining distance.
Best Answer
You are absolutely and entirely outside rules territory from the moment you've decided to fire someone out of a trebuchet and into the ground, so only loose inferences from the rules are going to help us here. But let's see what it gives us to work with.
Forewarning: if you're after real-world simulation in D&D 4e, you've come to the wrong town. The designers consciously eschewed real-world simulation in order to just make a fun and well-balanced game, so 4e runs on simplistic game logic that laughs in the face of our Earthen physics. 4e has squircles for instance: consider that the circle is defined as a shape where every side is equidistant from the center, and that this perfectly describes a square room of any size as far as a walking PC is concerned. Instead of attempting to draw real-world physics out of D&D 4e—which 4e will either directly contradict or simply not help you with—use the game logic, leave the calculator aside and use your time to beat stuff up and do fun things instead.
You have some parts of this conclusion wrong.
First, there's nothing that makes him fall faster. You have a trebuchet, but we don't know how fast he's actually traveling: D&D 4e doesn't exactly have specific rules for trebuchets that I'm aware of, unless you'd like to point us to them.
Second, the speed of a normal fall is 500 feet per round, at the end of the creature's turn (Rules Compendium, p209, High-Altitude Falls). Since a round is 6 seconds, that's actually 83.33 (recurring) feet per second, and nobody ever falls faster than this. That's far less than the falling speed of a skydiver (who is trying to fall slowly), so we can assume accurate simulations of Earth physics and wind resistance are to be left well aside: things work differently here.
So. Your orc hits the ground normally, and takes the normal amount of fall damage.
If they hit the wall instead, we don't know if they're really traveling fast enough to even simulate it with an equation that works from 500 feet/second of fall damage. You're in house rule territory, and we've established D&D 4e doesn't really care about what physics has to say about falling, so make a judgement call with a small portion of fall damage, or decide your character survives it fine because they might as well.
Alternately, whilst I would not advise against firing D&D 4e characters out of trebuchets on account of how awesome that is, I would at least just advise saying they succeed and skipping this trouble.
Unless they're an enemy NPC, in which case I advise they die hilariously.