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Horizontal falling objects?
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<blockquote data-quote="The Sigil" data-source="post: 146791" data-attributes="member: 2013"><p><strong>Physics...</strong></p><p></p><p></p><p></p><p>As stated by others, this assumes that all energy is transferred to the victim... but when I saw this question, I thought of a different way of trying to figure it out that stays within D&D's abstract system (I think)...</p><p></p><p>Assumption:</p><p>Falling damage (from objects falling on characters, not characters falling to the ground) is essentially due to an object with a given mass smacking into the character at a given speed. In other words, I assume that if a character takes 1d6 hp of damage from a given object dropped from a height of ten feet, I can make some relations.</p><p></p><p>The object takes 0.791 seconds (g=32 ft/s^2=9.8 m/s^2) to fall from the release point to the character. At the time of impact, the object is moving at a speed of 25.3 ft/s (v=at).</p><p></p><p>Assumption:</p><p>An object moving at a given speed which hits a character from any direction, falling or not, inflicts the same amount of damage.</p><p></p><p>In other words, if an object inflicts 1d6 hp of damage by falling 10 feet onto my character (it is moving at 25.3 ft/s when it hits), it seems to me that if somebody threw the same object at my character horizontally (instead of vertically) at a rate of 25.3 ft/s, it would inflict 1d6 hp of damage, the same as though it had fallen on me.</p><p></p><p>F=ma, E=1/2 mv^2, and other strict physical equations for treatment of how Force/Energy are applied are not needed with these assumptions, all we need are the equations relating distance, velocity, acceleration, and time.</p><p></p><p>We can easily reverse-engineer the height from which the 50-ton object was dropped by calculating the time it would take for it to achieve the listed speed of 6.5 mph. 6.5 mph is equivalent to 9.53 ft/sec. Since v=at, and we know v (9.53 ft/s) and a (32 ft/s^2), we can find t (0.297 sec).</p><p></p><p>(This leads also to the consequence that since a round is 6 seconds long, the object has a move of ~60 feet... meaning that if the PCs run/sprint, moving 4xtheir base move, most medium-size PCs who are not too heavily encumbered should be able to beat this thing in a footrace... and a PC with no equipment should be able to move at least twice as fast as the object).</p><p></p><p>Now that we have the value of t, we can find the equivalent height from which it was dropped (d=0.5at^2)... the answer is 1.42 ft.</p><p></p><p>Now, I simply reference the SRD to see how much damage a 50-ton object does if dropped from a height of 1.42 feet... hmmm...</p><p></p><p><em>For each 200 pounds of an object’s weight, the object deals 1d6 points of damage, provided it falls at least 10 feet. </em></p><p></p><p>This tells me that I should prepare to do a freaking lot of damage... 50 tons comprises 500d6 points of damage...</p><p></p><p>But, we are given the caveat that the object must fall at least 10 feet, and our equivalent "fall" was only 1.42 feet.</p><p></p><p>Thus, by the rules, the 50 ton weight moving at 6.5 mph inflicts *no* damage (didn't fall far enough to "get started").</p><p></p><p>I would of course add a "common sense" corollary - a 50-ton weight smushes you up against something "immovable" (such as a wall), you get squished flat (dead), with a Ref save allowed to "get out of the way" first (a "save or die" situation).</p><p></p><p>Seems to me this is the simple way to handle it without trying to figure out exactly how many Joules of energy are in a d6... ;-)</p><p></p><p>--The Sigil</p></blockquote><p></p>
[QUOTE="The Sigil, post: 146791, member: 2013"] [b]Physics...[/b] As stated by others, this assumes that all energy is transferred to the victim... but when I saw this question, I thought of a different way of trying to figure it out that stays within D&D's abstract system (I think)... Assumption: Falling damage (from objects falling on characters, not characters falling to the ground) is essentially due to an object with a given mass smacking into the character at a given speed. In other words, I assume that if a character takes 1d6 hp of damage from a given object dropped from a height of ten feet, I can make some relations. The object takes 0.791 seconds (g=32 ft/s^2=9.8 m/s^2) to fall from the release point to the character. At the time of impact, the object is moving at a speed of 25.3 ft/s (v=at). Assumption: An object moving at a given speed which hits a character from any direction, falling or not, inflicts the same amount of damage. In other words, if an object inflicts 1d6 hp of damage by falling 10 feet onto my character (it is moving at 25.3 ft/s when it hits), it seems to me that if somebody threw the same object at my character horizontally (instead of vertically) at a rate of 25.3 ft/s, it would inflict 1d6 hp of damage, the same as though it had fallen on me. F=ma, E=1/2 mv^2, and other strict physical equations for treatment of how Force/Energy are applied are not needed with these assumptions, all we need are the equations relating distance, velocity, acceleration, and time. We can easily reverse-engineer the height from which the 50-ton object was dropped by calculating the time it would take for it to achieve the listed speed of 6.5 mph. 6.5 mph is equivalent to 9.53 ft/sec. Since v=at, and we know v (9.53 ft/s) and a (32 ft/s^2), we can find t (0.297 sec). (This leads also to the consequence that since a round is 6 seconds long, the object has a move of ~60 feet... meaning that if the PCs run/sprint, moving 4xtheir base move, most medium-size PCs who are not too heavily encumbered should be able to beat this thing in a footrace... and a PC with no equipment should be able to move at least twice as fast as the object). Now that we have the value of t, we can find the equivalent height from which it was dropped (d=0.5at^2)... the answer is 1.42 ft. Now, I simply reference the SRD to see how much damage a 50-ton object does if dropped from a height of 1.42 feet... hmmm... [i]For each 200 pounds of an object’s weight, the object deals 1d6 points of damage, provided it falls at least 10 feet. [/i] This tells me that I should prepare to do a freaking lot of damage... 50 tons comprises 500d6 points of damage... But, we are given the caveat that the object must fall at least 10 feet, and our equivalent "fall" was only 1.42 feet. Thus, by the rules, the 50 ton weight moving at 6.5 mph inflicts *no* damage (didn't fall far enough to "get started"). I would of course add a "common sense" corollary - a 50-ton weight smushes you up against something "immovable" (such as a wall), you get squished flat (dead), with a Ref save allowed to "get out of the way" first (a "save or die" situation). Seems to me this is the simple way to handle it without trying to figure out exactly how many Joules of energy are in a d6... ;-) --The Sigil [/QUOTE]
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