Published Oct 8th, 2016, 10/8/16 1:45 pm
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Alright, while originally I had written this all up in proper physics paper format, I figured the planetminecraft forum probably wasnt the best area to actually post such a paper. As such I have rewritten this to be much more readable and understandable to the average reader, even if they may not understand the math.
Gravity Blocks:
So in order to begin this experiment I decided the easiest way to determine gravity was simply to do a drop test.
The Process:
Essentially to start off I took an average of the amount of time it took for sand to fall from varying heights, fortunately for me the first distance I tried (6 blocks) was almost exactly what I needed.
Upon taking an average of 10 drops from this height (keeping in mind it actually needs to be 7 blocks up because the bottom starts at 6) I managed to get almost exactly 1 second (.98 seconds) , and taking into account that it went a little over and a little under after all my tests, id say rounding to 1 second isnt completely unfair.
Once we had this information all we had to do is plug the numbers into some Kinematics equations:
d=(Vi+Vf)/2t
-6=(0+Vf)/2*1
-6=1/2Vf
-12=Vf
Note:
Just to keep thoughs who havent taken any basic physics in the loop
d=Displacement
Vi=Velocity Initial
Vf=Velocity Final
T=Time
Alright so with that I concluded that the gravity of blocks in minecraft was about -12m/s^2 (speeds up 12m or blocks every second)
However anyone who knows anything about this would repremand me for simply doing on distance and calling it a day, so in order to confirm my theory I simply used what information I had and concluded that if my information was correct that it would obviously take 2 seconds for the block to fall 24 blocks.
So after going and preforming another 10 drops and taking the average time I got 1.99 seconds average for a block to fall 24 blocks, which I assume despite the .01 difference can be pretty much regarded as 2 seconds.
So just for the math incase anyone cares although it is essentially the same as the last:
-24=(0+Vf)/2*2
-24=(1/2Vf)2
Vf=-24
Vf/2 = 12m/s^2
Terminal Velocity:
The idea behind this was simple, essentially we were doing the same thing but taking an average time of how long it takes to fall from 256 to 1 (the farthest possible distance)
After another 10 trials I found the time was almost consistantly 8.91 seconds.
Doing this math we can find how fast you can fall at maximum speed:
-256=(0+Vf)/2*8.91
-256=(1/2Vf)8.91
-256=4.445Vf
Vf = -57.46m/s
So In minecraft you can fall at a maximum velocity of -57.46 m/s, meaning you reach terminal velocity in just under 5 seconds...Thats Fast!
This however wasnt the weirdest thing I can across when doing this smallscale study...
Player Gravity:
So naturally I assumed that player gravity would be pretty darn close to block gravity when I started, and only really decided to do one trial just to make sure...And boy was i wrong.
So because it was the last one I had setup and the easiest to compare I decided to use the 256 block drop test as a player to check the terminal velocity just to see how it compared.
Strangely after 256 blocks I didnt get 8.91 seconds or even close for that matter, i instead got 5.68 seconds.
Time for some more math:
-256=(0+Vf)/2*5.68
-256=(1/2Vf)5.68
-256=2.84Vf
Vf=-90
So based on this, not only did players excellerate much faster than blocks, but they also had a much higher terminal velocity.
So off I go to try to find a fairly exact drop distance in order to calculate and find that
14 blocks is pretty much perfectly 1 second and do the math from there
-14=(0+Vf)/2*1
-14=(1/2Vf)
-28=Vf
So basically the gravity was 28m/s^2 after many trials more trials from varying heights. Keep in mind however that I found this number to be slightly more inconsistant sometimes dropping as low as 14m/s^2 or even 7m/s^2, these results however only occured once and hence may have been the result of human failure or simple lag problems.
Disclaimer:
These Experiments were most likely highly effected by human failure such as how accurate I was able to be on the timer as well as problems with the game itself, such as lag or other unnoticed errors. As such these numbers should be taken only as an approximate or an average and not an exact.
If you repeat these experiments on slower of faster computers than mine you may get different results, and I would be interested to see them in the comments.
Conclusion:
The acceleration due to gravity of all falling blocks in minecraft is about -12m/s^2
Terminal velocity for these blocks is 57.46 m/s
Players on the other hand seem to be much more highly effected by gravity
Acceleration due to gravity for players is -28m/s^2
Terminal Velocity is about -90m/s
Gravity Blocks:
So in order to begin this experiment I decided the easiest way to determine gravity was simply to do a drop test.
The Process:
Essentially to start off I took an average of the amount of time it took for sand to fall from varying heights, fortunately for me the first distance I tried (6 blocks) was almost exactly what I needed.
Upon taking an average of 10 drops from this height (keeping in mind it actually needs to be 7 blocks up because the bottom starts at 6) I managed to get almost exactly 1 second (.98 seconds) , and taking into account that it went a little over and a little under after all my tests, id say rounding to 1 second isnt completely unfair.
Once we had this information all we had to do is plug the numbers into some Kinematics equations:
d=(Vi+Vf)/2t
-6=(0+Vf)/2*1
-6=1/2Vf
-12=Vf
Note:
Just to keep thoughs who havent taken any basic physics in the loop
d=Displacement
Vi=Velocity Initial
Vf=Velocity Final
T=Time
Alright so with that I concluded that the gravity of blocks in minecraft was about -12m/s^2 (speeds up 12m or blocks every second)
However anyone who knows anything about this would repremand me for simply doing on distance and calling it a day, so in order to confirm my theory I simply used what information I had and concluded that if my information was correct that it would obviously take 2 seconds for the block to fall 24 blocks.
So after going and preforming another 10 drops and taking the average time I got 1.99 seconds average for a block to fall 24 blocks, which I assume despite the .01 difference can be pretty much regarded as 2 seconds.
So just for the math incase anyone cares although it is essentially the same as the last:
-24=(0+Vf)/2*2
-24=(1/2Vf)2
Vf=-24
Vf/2 = 12m/s^2
Terminal Velocity:
The idea behind this was simple, essentially we were doing the same thing but taking an average time of how long it takes to fall from 256 to 1 (the farthest possible distance)
After another 10 trials I found the time was almost consistantly 8.91 seconds.
Doing this math we can find how fast you can fall at maximum speed:
-256=(0+Vf)/2*8.91
-256=(1/2Vf)8.91
-256=4.445Vf
Vf = -57.46m/s
So In minecraft you can fall at a maximum velocity of -57.46 m/s, meaning you reach terminal velocity in just under 5 seconds...Thats Fast!
This however wasnt the weirdest thing I can across when doing this smallscale study...
Player Gravity:
So naturally I assumed that player gravity would be pretty darn close to block gravity when I started, and only really decided to do one trial just to make sure...And boy was i wrong.
So because it was the last one I had setup and the easiest to compare I decided to use the 256 block drop test as a player to check the terminal velocity just to see how it compared.
Strangely after 256 blocks I didnt get 8.91 seconds or even close for that matter, i instead got 5.68 seconds.
Time for some more math:
-256=(0+Vf)/2*5.68
-256=(1/2Vf)5.68
-256=2.84Vf
Vf=-90
So based on this, not only did players excellerate much faster than blocks, but they also had a much higher terminal velocity.
So off I go to try to find a fairly exact drop distance in order to calculate and find that
14 blocks is pretty much perfectly 1 second and do the math from there
-14=(0+Vf)/2*1
-14=(1/2Vf)
-28=Vf
So basically the gravity was 28m/s^2 after many trials more trials from varying heights. Keep in mind however that I found this number to be slightly more inconsistant sometimes dropping as low as 14m/s^2 or even 7m/s^2, these results however only occured once and hence may have been the result of human failure or simple lag problems.
Disclaimer:
These Experiments were most likely highly effected by human failure such as how accurate I was able to be on the timer as well as problems with the game itself, such as lag or other unnoticed errors. As such these numbers should be taken only as an approximate or an average and not an exact.
If you repeat these experiments on slower of faster computers than mine you may get different results, and I would be interested to see them in the comments.
Conclusion:
The acceleration due to gravity of all falling blocks in minecraft is about -12m/s^2
Terminal velocity for these blocks is 57.46 m/s
Players on the other hand seem to be much more highly effected by gravity
Acceleration due to gravity for players is -28m/s^2
Terminal Velocity is about -90m/s
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I find it really weird that gravity blocks and the player have different gravitational accelerations. I mean, more than double!
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