Minecraft Physics

Here is a great video showing some physics in the game Minecraft.

Similar to Angry Birds, this is a great world to explore physics. Why? Mostly because you can set up your own experiments. That is exactly what is done in this video. Essentially they do the following:

• Build a canon to launch blocks.
• Measure the horizontal distance the block travels when shot at an angle.
• Find the time of flight for the block.
• Make a block tower at the midway point to find out how high the block goes.
• Use this to estimate the vertical acceleration.

Ok, since I don't have Minecraft (and I am afraid to play it), let me instead do a quick double check of the calculations in the video.

Vertical Acceleration

To start, I will just go with the statement that each block is 1 meter long. Really, I have no idea about this. I know what Minecraft is, but that is about it. So, if the launched block takes 2.25 seconds to fall from a height of 43 blocks (meters) then I can write the following for the motion in the vertical direction:

In this case, the starting y-position is 43 meters and it ends at 0 meters. At the highest point, the vertical velocity is 0 m/s. Putting in these values:

This is slightly different than the value from the video. I guess they used a time of 2.3 seconds instead of 2.25 seconds. No problem there. However, I am still not satisfied. Just as a quick check. If the length of the block was 0.5 meters, the starting position would just be 21.5 meters. This would give a vertical acceleration of 8.5 m/s². That is a bit closer, but really I am not satisfied.

Video Analysis

Don't pretend like you didn't know this was coming. The robot creator of that video (I am guessing it was a robot based on the voice) clearly intended me to do this analysis. Why else would he set the virtual camera perpendicular to the motion of the projectile? Perfect for – video analysis with Tracker. This is a little difficult since I can only see the projectile block (or what appears to be the block) for a few frames.

First, here is a plot of the horizontal position of the block. I could clearly mark the start and the end of the motion along with some points right before it gets to the highest point. This is what that would look like.

What is going on here? For projectile motion with zero air resistance, this should be a straight line. Well, my first guess is that there could be some perspective issues. Let me check that. I know the tower is supposed to be 43 blocks high and the range is 97 blocks. When I started the analysis of the video, I used the tower to scale the video. Now, measuring the range, I get 119 blocks and not the 97 blocks stated in the video. I am sure they can count blocks, so there must be some perspective issues.

Here is the data that is just near the center of the video (where the perspective issues shouldn't be too bad).

If this motion does indeed have a constant horizontal velocity, it should be around 40 blocks per second. Now what about the vertical motion for these points?

Using just these points, I get a vertical acceleration of -39.8 blocks/s² (leaving it in units of blocks just in case a block is not 1 meter). What if I include both the starting and ending points to find the vertical acceleration?

So, a vertical acceleration of -19.5 blocks/s². Basically, I have no clue what is going on here. Here are some ideas:

• The object I marked on the screen is not actually the block, but just a reflection off the block. I think this actually might be the case since it doesn't seem to be near the highest point around the half way in time point. What are those things called - oh yeah: lens flare.
• I don't think the problem is a perspective issue. For the few points I have, they are close enough to the center to give good data.
• Maybe objects in Minecraft don't have constant vertical acceleration. The video showed a short example of a block on a piston (which I will analyze below) that didn't appear to have the correct motion.

The more I think about it, the more it seems like I was looking at the motion of a lens flare. If that's what that was, I am going to feel really stupid.

To redeem myself, I am going to look at the motion of that block on the piston. At least I can do that, right?

Here is the motion of the block on the piston. I am not sure about the time scale - but this seems to be the part before the video was slowed down. Let me assume that the time is correct.

This shows an acceleration of -20.6 blocks/s². Also, the block just stayed in the air for a little bit after the piston was lowered. It was about 0.1 seconds before the block started to move. Maybe this is the same world as Wiley Coyote.

Suggested Experiments

So, things aren't looking too great. What can you do? I say 'you' because I don't have Minecraft and I don't plan on playing it. Here are some suggested experiments to further explore what is really going on here.

• Repeat the experiment in the video, but with a different number of explosive blocks. This will (in theory) give the projectile block a different initial velocity. If Minecraft uses real world projectile motion (without air resistance) then you should find the same vertical acceleration of the block. Actually, try a whole bunch of different launches with different explosions. That's what I would do.
• Can you launch the block at different angles? I really don't know the answer here. Assuming you can, this would be another way to check the acceleration.
• What if you zoom in on the part of the block's motion so that you can see the block near the top of the trajectory. If so, you could use video analysis to find the acceleration.
• Is it possible to shoot a block straight up?

That should keep you busy for a while. Let me just say that I suspect the projectile behaves like a Earth-based world projectile motion object. If I had to guess, the acceleration is not -9.8 m/s² but something else. Also, base on the motion of the block on the piston I suspect that weird things happen at low speeds.

I guess the funny thing is that I originally planned to put together a post that essentially said "hey, look at this cool Minecraft physics video". Seems like I failed.