tag:blogger.com,1999:blog-3092603842974378319.post4930178966957657155..comments2024-01-24T11:36:17.328-08:00Comments on Explore: Beneath & Beyond: Low Ceilings RevisedJoe Nuttallhttp://www.blogger.com/profile/02395295081337987607noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-3092603842974378319.post-15510772258064379482015-09-19T05:39:16.689-07:002015-09-19T05:39:16.689-07:00"I like that you included formulas. Did you d..."I like that you included formulas. Did you do that for the determination of difficulty for ranges?"<br /><br />Thanks. Yes I used formula for the difficulty for ranges, but not in the blog post.<br /><br />"Isn't 7ft+6ft = 13ft which would mean a six foot tall person couldn't throw an axe 50' with a 10' ceiling?"<br /><br />In this case yes: the thrower's max range is 60' and the ceiling is 10', which from the table reduces the Max Range to 40'. But it depends upon the max range for that thrower - another thrower with a max range of 80' would not hit the ceiling.<br /><br />"The height at release is a simplification"<br /><br />Yes, I could model it more closely as you outline, but I think the loss of head room with an axe is roughly cancelled out by the fact that the max range was from a flatter angle than 45 degrees. That is, the axe with a max range of 80' has a higher initial velocity than a bow with a max range of 80'.<br /><br />"It should be possible to check those initial heights by measuring an actual throw." <br /><br />You could do some experiments, but they'd be tricky to do as you'd need to measure initial velocity and angle and max height and range, and you'd need someone capable of throwing the axe very fast!<br /><br />"So rather than 4' as we need to go higher. "<br /><br />Note it's not 4' release height in the table, it's 4'+ and all heights up to 8'. The values are actually for 6'.<br />If you want more accurate results, then the area it falls down most is not having a column for a 15' ceiling. I tried that but the table becomes massive and unwieldy.<br />Joe Nuttallhttps://www.blogger.com/profile/02395295081337987607noreply@blogger.comtag:blogger.com,1999:blog-3092603842974378319.post-53205558679915522792015-09-18T23:58:36.272-07:002015-09-18T23:58:36.272-07:00I like that you included formulas. Did you do that...I like that you included formulas. Did you do that for the determination of difficulty for ranges?<br /><br />"A: To achieve max range, which it looks like those throwers are at, you have to throw at 45 degrees. In this case the projectile reaches a height of one quarter the range, which would be 15ft in that video (plus 6ft for the thrower’s height). Reduce the distance only slightly, and if you throw with the same velocity, you can reduce the angle massively, and hence the maximum height. At a range of 50ft the max height is only 7ft (+6ft)."<br /><br />Hi Joe, isn't 7ft+6ft = 13ft which would mean a six foot tall person couldn't throw an axe 50' with a 10' ceiling? <br /><br />The maximal height for the axe is going to be equal to the height at release plus the rise of a ballistic (not straight line) throw. <br /><br />The height at release is a simplification, really we need the height of the center of momentum at release. For a bow that is where the arrow is on the draw which is about shoulder height. For an axe I think it would be a bit higher than a bow, maybe a bit below head height. And for a javelin higher still, above head height, I imagine. It should be possible to check those initial heights by measuring an actual throw. So rather than 4' as we need to go higher. In addition the axe rotates around it's center of mass which is, I imagine, closer to the head. So you need to add in something over half the length to the axe to the distance as well. So I think for axes and javelins we are looking at adding 6' or more to the h of the throw itself. <br /><br />Also note that a big person/creature still needs not to hit the ceiling with the top of the axe or javelin while swinging above their head. That means an 8' tall critter will hit the ceiling with their axe or javelin, maybe even with their hand without a weapon in it.<br /><br />I like the fact that shorter creatures like dwarves will have a range advantage underground over taller creatures like humans.Gaston's_Hathttps://www.blogger.com/profile/02776970532947597692noreply@blogger.comtag:blogger.com,1999:blog-3092603842974378319.post-35331446761326594552015-09-18T05:59:03.901-07:002015-09-18T05:59:03.901-07:00Just been playing the Saxophone and thinking some ...Just been playing the Saxophone and thinking some more about this. I'm modelling the range as being able to hit the middle of your opponent - that means I'm saying at the extremes of the range you can't hit the top half of your opponent (you'd hit the ceiling). So perhaps at the furthest extent of range (in this case 40'-50') you should have an extra -3 penalty to hit. If this causes you to miss you'd say it hit the ceiling, so it adds flavour.Joe Nuttallhttps://www.blogger.com/profile/02395295081337987607noreply@blogger.comtag:blogger.com,1999:blog-3092603842974378319.post-84271950217938206022015-09-18T01:12:04.650-07:002015-09-18T01:12:04.650-07:00During my run this morning I was wondering about a...During my run this morning I was wondering about an axe-specific effect for the length of the axe reducing head height and hence max range. If you threw entirely flat, a throwing angle of zero, then max range would decrease a lot – thrown from it would go from 80’ to 27’. But even a slight angle of 10 degrees, rising only 1 foot, would go 41ft. This would be enough to drop the range one category. However I then recalled that the axe (like the knife) at max range is thrown at a far flatter angle than 45 degrees, and hence its velocity for a particular max range is much higher than other projectiles, which would lead to the opposite effect – a lessening of the effect of low ceilings. When I ran the calculations this raises the range back to 50ft, cancelling out the first effect!Joe Nuttallhttps://www.blogger.com/profile/02395295081337987607noreply@blogger.comtag:blogger.com,1999:blog-3092603842974378319.post-13093514429505987042015-09-17T22:45:05.640-07:002015-09-17T22:45:05.640-07:00You wouldn't be trying not to hit the ceiling,...You wouldn't be trying not to hit the ceiling, you'd be throwing it as hard as you could at the target - you'd purely be trying not to aim it too high a part of their body. Mostly hitting the ceiling would be aiming too high and would simply be missing what you aimed at.<br /><br />You *could* increase your height by one foot when you're throwing an axe to compensate for its length, but not unless you're also making a distinction between people who are 5'5'' and 6'5''. It doesn't affect other thrown items like your example of a ball. The overhand motion is why I've assumed you're throwing from your height (it's slightly lower for bows).Joe Nuttallhttps://www.blogger.com/profile/02395295081337987607noreply@blogger.comtag:blogger.com,1999:blog-3092603842974378319.post-16061044372472216892015-09-17T19:18:31.445-07:002015-09-17T19:18:31.445-07:00My point was more about thrown items; I was also t...My point was more about thrown items; I was also trying to point out that you can't assume these people will somehow throw or shoot within an inch of the ceiling perfectly. The tendency to hit the ceiling or overcompensate in trying to not hit the ceiling will have an effect, even if the shot is within range. When you also consider the objects are not points in space but actual physical objects, the length of the axe for the period of the time it is travelling perpendicular to the ground will reduce the height you can throw. When you combine the overhand motion and the length of the axe and some cushion space, there is not much height left to a 10’ ceiling.Thiles Targonhttps://www.blogger.com/profile/02928790313150694394noreply@blogger.com