Among Us - Travel Distance

One of the methods that didn't make it into my Among Us seminar paper is distance measuring. Instead of the exact, I used graph distance. Since given the states of the latter one, they aren't compatible.

What Unit Would Our Speed Be?

We define speed as the distance something moves within a specific time frame. In Guild Wars 2, we could convert between in-game units and meters.^[1] However, Among Us doesn't have this to my knowledge. So, alternatively, we need to abstract this by creating a custom unit. We could choose rooms per second, players per second, and so on, but I've decided on the standard vision per second. Thus we can measure rooms in vision distance. Furthermore, if a room's wall distance is higher than one, players can't see it whole within their vision sphere. 

Measurement Of Movement Speed

Ill. 1: The approach to measuring velocity given
 crewmate vision ~GreenyNeko

To measure the velocity, we create a lobby with four instances. While you can do this with friends, it also works using Bluestacks instances. We use the recommended settings for the room (which we can consider as the standard settings). For the measurement, any map with a big room where you can walk in linearly will do. I decided to use the cafeteria of the Skeld. We place one of the players in the middle, and the other player will walk into the vision cone on one side and out on the other side, as demonstrated in the image on the right. A decent way to measure the velocity is to record the player's movement from the stationary player's view and then check how many frames have passed between entering and leaving the vision bubble. With the first frame at 78 (=1.3s) and the last at 335 (=5.5833s) the resulting speed is one player vision in 4.28333s or 1 crewvision / 4.28333 seconds = 0.23346cv/s.

Measuring The Map

Skeld with most distances measured ~GreenyNeko

Now having the player movement speed, we can use it in combination with the time it takes to get from one point to another to determine the distance of walls and hallways. These tools allow us to measure the whole map and use the data to approximate how long it takes us from one spot to another. The image on the left shows the result for the Skeld map. We can do this for the other maps, but I'll leave it at Skeld for this post. When we sum up the horizontal and vertical distances, we get the total distance approximation from one point to another. However, since players can walk diagonally, the sum is an overestimation of the shortest path.

Conclusion

An example of this would be the distance from navigation to the reactor.

Given:

Navigation to Weapons:	0.307cv+0.074cv/2+0.218cv+0.144cv+0.189cv	= 0.894cv
Weapons to Cafeteria:	0.116cv+0.125cv*2+0.237cv+0.198cv	= 0.801cv (guessing missing distances)
Cafeteria to Upper Engine:	1.012cv+0.237cv/2+0.77cv	= 1.9005cv (including the button)
Upper Engine to Reactor:	0.397cv/2+0.339cv+1/3*0.498cv	= 0.7035cv

In total that's 0.894cv+0.801cv+1.9005cv+0.7035cv = 4.299cv 

This would take a player 4.299cv / 0.23346cv/s = 18.414s. With a quick check on mobile and approximately reaching around 18s (Well 20s minus getting stuck twice and starting/stopping the timer), our calculation isn't too far off. We can do this for each room and enter the distances into a graph. Alternatively, we can take an already created graph and sum the distances for it.

^[1]https://www.greenyneko.com/2018/01/guild-wars-2-velocity.html

Guild Wars 2: Mount Speed

Which is the fastest mount? Well quite simple. The beetle when you move on the ground and the griffon if you can use it. Well, if you use the abilities. I've always wondered which is faster if you don't use your abilities. Also, some mount engage abilities have quite an insane forward motion. Lastly, to crown it all I already did a calculation on the movement speed and it would be interesting to compare that to the mount speed.

Procedure

Screenshot of the Gilded Hollow bridge in Guild Wars 2

To find these things out, as with most things we will need to find a place that fits our experiments and is measurable. You can compare this to the DPS benchmarks done by Guilds like Snowcrows, except that we're doing speed benchmarks instead of DPS. The velocity is calculated via the distance laid back in a certain time frame. The only way for us to measure the distance is by using the skills and abilities that have a radius given. To have accurate values we need a straight flat track with a clear start and a clear end. This turns out to be harder than one would expect. Back in the old post, I used the World vs World bridge, that's found south of the alpine borderlands. Unfortunately, it's not possible to use mounts aside from the Warclaw, so we need to find another one. The bridge in Lornar's Pass near Durmand Priory one of my ideas. It reaches a total of  4890 units. Another idea I had is the Guild Hall. If I could get the rights to build I could make myself a bridge that's as long as I want. That's when I saw that there was a bridge already in the Gilded Hollow. I went there first to measure the width and it turns out that from the stairs the entrance of the building is 7905 units. I couldn't come up with a longer bridge without building myself - which again would require the rights to build in a Guild Hall, which I don't have.

Screenshot showing the
small bumps on the Gilded Hollow
bridge in Guild Wars 2

Unfortunately, the bridge in the Gilded Hollow Guild Hall is not perfect. It does have a long-distance, it is straight there's a clear beginning and a clear end to use and it's flat. Well mostly, since it does have three small bumps in it. While these do not stop your movement directly they do have a tiny slow effect. Given this, our calculations do have a small inaccuracy. Testing this with walking results in hardly if any change of speed. Thus I'm gonna ignore it for these test cases. Another issue is the dive/flying ability of the griffon. I tried to use the high buildings near the bridge beginning pointing towards the middle of the Guild Hall and used Commander with markers on the map to determine the track and try to fly as accurately as possible. This turned out to be harder than expected so I would take the griffon results with a grain of salt. They may be accurate enough but there could be deviations of up to 0.50 seconds I would say.

The Actual Experiments

The actual experiments aside from those issues are quite simple. We move from point A to point B and whenever we move over point A or point B we respectively start and stop the timer. For the timer, I use my smartphone app again. keep in mind having to manually start and stop the timer results in a short delay due to the reaction time. I did not calculate in my own or the average human reaction time into the calculation so again values may vary by ~0.6 seconds or so. I performed this experiment on each of the eight mounts there are. Experiments were run on normal walk speed meaning not using the ability of the mount, Spamming or repeatedly mounting and using the engage ability and lastly using the mount ability and testing a few mechanics respective to it, such as double dive or the roller beetle speed after the boost.

The Result

I will represent the result in a table again. The table is sorted by time. Each mount has it's own color per row to allow an easy distinction which behaviors time belongs to which mount. The type of behavior is explained by the note. The time is given in seconds and milliseconds where one second is equal to 100 milliseconds. Calculation of the units per second is done by taking the bridge's length in units (7905 units) and dividing it through the measured time (e.g.4''21''') which will then yield the result (e.g. 7905u / 4.21s = 1877.67u/s). The m/s use the conversion of units to meters which is units multiplied by 2.52cm / 100 = 0.0252m. (e.g. 1877.67u/s * 0.0252m = 47.32m/s). I've omitted the conversion from u/s to feet/s to mph. I have also recalculated the walking speed with the mount name being "None" to be able to compare the mounts to the normal walking speed without boons.

Mount Name	Note	Time	u/s	m/s	km/h	mph
Griffon	Ability (One boost)	4''21'''	1877.67	47.32	170.34	106.26
Griffon	Ability (Double boost)	4''03'''	1961.54	49.43	177.95	111.01
Rollerbeetle	Ability	4''72'''	1517.27	38.24	137.65	85.86
Rollerbeetle	Rolling (After Ability)	5''75'''	1374.78	34.64	124.72	77.80
Griffon	Ability (flight)	6''47'''	1221.79	30.79	110.84	69.14
Raptor	Ability	8''60'''	919.19	23.16	83.39	52.02
Jackal	Ability	9''41'''	840.06	21.17	76.21	47.54
Rollerbeetle	Engage Spam	10''06'''	785.79	19.80	71.29	44.47
Skyscale	Ability (Charge)	10''31'''	766.73	19.32	69.56	43.39
Skimmer	Engage Spam	11''20'''	705.8	17.79	64.03	39.94
Jackal	Walking	12''65'''	624.9	15.75	56.69	35.36
Warclaw	Ability	12''80'''	617.58	15.56	56.03	34.95
Griffon	Ability (Flutter)	13''11'''	602.97	15.19	54.70	34.12
Raptor	Walking	13''18'''	599.77	15.11	54.41	33.94
Skyscale	Ability (Flight)	13''27'''	595.7	15.01	54.04	33.71
Rollerbeetle	Rolling	13''41'''	589.48	14.85	53.48	33.36
Bunny	Walking	13''72'''	576.17	14.52	52.27	32.61
Skimmer	Ability	14''00'''	564.64	14.23	51.22	31.95
Skimmer	Walking	14''37'''	550.1	13.86	49.91	31.13
Warclaw	Engage Spam	14''37'''	550.1	13.86	49.91	31.13
Warclaw	Walking	14''44'''	547.44	13.80	49.66	30.98
Jackal	Engage Spam	14''71'''	537.39	13.54	48.75	30.41
Raptor	Engage Spam	15''33'''	515.66	12.99	46.78	29.18
Griffon	Walking	15''82'''	499.68	12.59	45.33	28.28
Skyscale	Walking	15''87'''	498.11	12.55	45.19	28.19
Griffon	Enage Spam	16''37'''	482.9	12.17	43.81	27.33
Bunny	Engage Spam	16''88'''	468.31	11.80	42.49	26.50
None	Walking	20''11'''	393.09	9.91	35.66	22.25
Skyscale	Enage Spam	20''15'''	392.31	9.89	35.59	22.20
Bunny	Ability	22''15'''	356.89	8.99	32.38	20.20

Conclusion

#1 Majestic Griffon

So, as you can see the griffon seems to be the fastest way of traveling if you can get one or two dive boosts in.

#2 Roadorolla-Beetle Da

The roller beetle is the fastest if you can't use the griffon and even after only one boost you have a decent constant movement. 

#3 Rapping Raptor

If both of these do not apply, the raptor is next on his third place. Though it comes short when you have to move uphill.

#4 Jackal with it's Portal

 Moving uphill I'd probably advise the jackal as it's ability is more dependable in an uphill scenario.

It's really awesome to see that using the roller beetle you could basically roll around the streets of some countries such as Germany. even though cities only allow 50km/h at maximum and the highway often has a limit of 100 or 120km/h. Then again if you had the mounts from Guild Wars 2 aside from some people sexting Asura's or whatever we would have portals and waypoints. I would definitely pay 1€ to teleport to university or work to port back for 1€. Worth it!

Oh, by the way. I heard there is actually 3rd party software that shows the current speed and you could basically take that. The thing is that from talking to someone who uses it the values might vary depending on the direction. Like for example a griffon with a downward motion has a faster vertical movement that gliding straight and some ground tracks you roll with your roller beetle aren't even or maybe you're in a curve or not moving straight. All these aspects can have an effect as you travel more distance in a zigzag than a straight line.

Guild Wars 2: Tyria's Gravity

Finally, Tyria's gravity has been calculated. Now we can compare to other planets' gravities and maybe draw some new conclusions from it? Anyways we left off by figuring out that Guild Wars 2 does indeed seem to have gravitation.

Next Steps

So, if we assume Guild Wars 2 does indeed have gravity - where things seem to point to - then we can calculate it. Calculating gravity is the same as acceleration. Acceleration is often related to F = m * a. Unfortunately, we know neither F nor m. There's another formula as well though. Acceleration is the change of velocity over time. So, basically a = ∆v / ∆t. Next up is another problem. We don't know the velocity of our character. It's not shown in any kind of way in Guild Wars 2. This means we need to calculate it as well. For this, we have a formula as well. The time it took to get from a position to another or the distance passed in a time frame. That's v = ∆x / ∆t.

The Experiment

Okay, so what we need to do is calculate the velocity at two different points of time that are still related to each other (e.g. different points of time in one fall). To get the velocity we need to calculate how long we take to fall a certain distance. We obviously need some way to tell the time, a watch could do this, however, the fall speed is too great to use a stopwatch this rapidly. Thusly I'm gonna record the fall on video and use the footage and frames to measure the fall speed. As a distance, I'm gonna use the Necromancer's staff traps that provide a 240 unit radius or 480 unit diameter. As a drop, I'm gonna use the one at the Kormir High Road.

To do the experiment I need to start the recording drop down while placing my marks on the wall and then get up as fast as possible, position the camera and jump down. It only took me one try even though it sounds quite stressful.

Analysis of the Footage

Next up, we're gonna analyze the footage. Specifically, we want to mark the two frames that meet the respective points well enough. Then we take the time between those.

As a reminder to calculate the gravitation we use the formula a = ∆v / ∆t with ∆v = v₂ - v₁ with v = ∆x / ∆t with ∆x = pos₂ - pos₁ and ∆t = t₂ - t₁

If we combine everything to a big formula we get: 
a = ((pos_2v2 - pos_1v2) / (t_2v2- t_1v2)) - ((pos_2v1 - pos_1v1) / (t_2v1 - t_1v1)).

Screenshot pos₁ of v₁

The first mark or first velocity v₁ we reach pos₁ after about 30 seconds of the fall. When using Vegas Pro 15 - which was available last year during a Humble Bundle :P - the time is given in hours, minutes, seconds and 1/30th of a second using the format HH:MM:SS:ss. We convert the next smaller unit to seconds by dividing it through 30 and multiplying the result with 100. E.g. 30 / 30s = 1s or 9 / 30 = 0.30s. This point in time in the video is t1 is 29:24, so 29s + 24 / 30s = 29.80s. The second position pos₂ is reached at 30:08 which is 30s + 8 / 30s = 30.27s. This means that ∆t = t₂ - t₁ so 30.27s - 29.8s = 0.47s. We already know the distance as it is the diameter of the staff mark which is

Screenshot pos₂ of v₁

480 units. Now we can calculate the velocity via v₁ = ∆x / ∆t. So our first velocity v₁ is 480u / 0.47s = 1021.28u/s. 

Screenshot pos₁ of v₂

Now on to the second one. We reach this point t₁ in the video at 31:01. That's 31s + 1 / 30s = 31.03s. The second point t₂ at the end of the mark is reached at 31:13 equivalent to 31s + 13 / 30s = 31.43s. Calculating the delta for v₂ we get ∆t = 31.43s - 31.03s = 0.39s.

With this we can calculate the velocity v₂ which is 480u / 0.39s = 1230.77u/s.

Screenshot pos₂ of v₂

At this point I must mention the difference between the first delta time and the second delta time is ∆t = 0.47s - 0.39s = 0.08s. Since my Guild Wars 2 runs at ~30 frames per second and my recording at 60 frames per second we are still limited to the ~30 frames per second from Guild Wars 2. One frame thus, as represented by Vegas Pro is 1/30th of a second. This means that one frame is equal to 1 / 30s = 0.1s. This means the difference between the two delta's could just as well be a measurement error and thus would require more research.

For the rest of the post, I'm gonna assume this is not a measurement error as such I'm gonna continue.

The Finale

Now that we have the two velocities and we can calculate the acceleration. As a reminder, we're gonna calculate the acceleration using a = (v₂ - v₁) / (t₂ - t₁). For t₂ and t₁ we're gonna use the start points pos₁. Filling out the variables we get a = (1230.77u/s - 1021.28u/s) / (31.03s - 29.80s) = 209.49u/s / 1.23s = 170.32u/s². Now to convert this to something that's more familiar to us and less useful for theorycrafting (heh :D) using the conversion from units to metric and to feet:

in metric: 170.32u/s² * 2.52cm/u = 429.21cm/s² | 429.21cm/s² / 100 = 4.29m/s²

in feet: 170.32u/s² * 0.083ft/u = 14.14ft/s²

in mph: 14.14ft/s² / 5280ft/mile * 3600 = 8.64mph

I have a small little book with formulas and data in it that helps students in exams. Let's look at which planet would equal this gravitation. 

Earth with a g-factor of 9.81 is well known. the nearest ones below are Merkur with 3.7 and Mars with 3.71.

Thus we've got us a planet with a little higher gravitational constant than Merkur or Mars.

Now if someone can do the drop with 60 frames per second it would be appreciated. Until disproven... I rest my case. Have a good day/night. 

Guild Wars 2: Fall Speed in Tyria

Since the post about the velocity in Guild Wars 2, I wanted to make one about the gravitation as well as the mount speed. Honestly, I just remembered the one about the mount speed while I started writing this haha! Anyways I sat down and sought a nice position to do my calculations.

Calculating Gravitation

There are a few ways to calculate gravitation. First things first we need to make ourselves clear that for our purposes gravitation is nothing more than a force that causes acceleration. One way to calculate acceleration is with the formula F = m * a. We don't know the weight or mass of our character nor if different races and character sizes play a role. Thus we need a different way. Another option would be
a = Δv / t. For this formula, we only need the velocity and the time. To get the velocity we can use the formula v = d * t. We can get the distance d using in-game measurements. For the time we can use a mobile phone or some other way to use a stopwatch. To get the velocity delta we need two spots, one with a long fall and one with a shorter fall or one that is long enough to perform two calculations on it.

Finding the Right Spot

An ideal spot would feature the following attributes:

• vertical wall
• nothing in the way during the fall
• easy to measure

I've decided to scout Divinity's Reach for spots and have decided for the one at the Plaza of Kormir and the other one is further up the Kormir High Road.

Guild Wars 2 Screenshot: Fall distance at Plaza of Kormir

Guild Wars 2 Screenshot: Fall at the Kormir High Road

Measuring the Walls

Guild Wars 2 Screenshot: Measuring Concept,
Plaza of Kormir

To measure the walls I used the skills and skill markers. Originally I've been using the Scourge Summon Meat Scepter- err I mean Flesh Worm is 1/4 of the staff mark and 1/3 of the shade radius. This means it has a 60 unit radius. The only issue that was left is that the indicators are a little bit off on some walls. The first wall took about one staff mark, one shade and half of the worm indicator. This is a fall of 480 + 360 + 43 = 883 units.
shades which feature a 180 unit radius and the staff trap skills which feature a 240 unit radius instead. Doing some experimentation I figured out that the indicator of the Summon Meat Scepter- er... Flesh Worm has a 60 units radius.

The second wall doesn't fit into a picture and was much harder to measure due to the marks disappearing after a certain time. It was 5 marks high and a little bit more than the Summon Flesh Worm indicator. This makes a distance of 480 * 5 + 120 + λ. For my calculations, I've set λ to 15. This gives me a distance of 480 * 5 + 120 + 15 = 2535 units.

Thought Process

If Tyria has gravity, the velocity at the longer fall should be higher than the velocity at the shorter fall. Both drops have a distance delta of 2535 - 883 = 1652 units. 

Possible Outcomes Include

a) The velocity of the first drop is significantly lower than the velocity of the longer second drop.

In this case there is an acceleration thus enabling us to further research. When we would do calculations on another planet or place in real life this would be the obvious result. In the case of game development games may not necessarily have acceleration and use a fixed fall speed.

b) The velocity of the first drop and the velocity of the longer second drop are similar enough.

There may always be errors in these empirical calculations. Errors during measurement specifically. Nonetheless if they're equal enough this means the falling speed is constant and the acceleration is strong enough to reach the terminal velocity in an instant.

c) The velocity of the first drop is significantly higher than the velocity of the longer second drop.

Honestly, I have no idea what's going on if this would be the case.

Measuring the Fall

 All we have to do at this point is to place our character, prepare the stopwatch and throw ourselves into our demise. Don't forget to start the stopwatch when the character starts to fall.

Due to the high chance of errors from reaction time I made 10 attempts. This table features all attempts and their resulting velocity in units.

Measurement	Short Drop (883 units)	Velocity (883 units)	Long Drop (2535 units)	Velocity (2535 units)
1.	0.97s	910.31u/s	2.51s	1009.96u/s
2.	0.91s	970.33u/s	2.39s	1060.67u/s
3.	0.97s	910.31u/s	2.53s	1001.98u/s
4.	0.87s	1014.94u/s	2.67s	949.44u/s
5.	0.88s	1076.83u/s	2.66s	953.01u/s
6.	0.82s	939.46u/s	2.62s	967.56u/s
7.	0.93s	949.46u/s	2.56s	990.23u/s
8.	0.96s	919.79u/s	2.67s	949.44u/s
9.	0.90s	981.11u/s	2.51s	1009.96u/s
10.	0.85s	1038.82u/s	2.61s	971.26u/s

Next up we take the average of the velocity which is 973.84u/s for 883 units and 986.35u/s for 2535 units. Now let's convert them to values that tell us more. For this, I'm using the same conversion I've used in all my posts. (1 unit = 2.52cm; 1 unit = 0.083ft)

883 unit velocity is

• 973.84u/s * 2.52cm/u = 2454.08cm/s which is 2454.08cm/s / 100 = 24.54m/s
• 973.84u/s * 0.083ft/u = 80.83ft/s

1260 unit velocity is

•  986.35u/s * 2.52cm/u = 2485.60cm/s which is 2485.60cm/s / 100 = 24.86m/s
• 986.35u/s * 0.083ft = 81.87ft/s.

Conclusion

I'm gonna call it a day here. The values seem to fall into either case a or case b. Now the question is whether or not it's a measurement error or if there is gravitation. Though if there is gravitation we can calculate it by finding a drop that's high enough on which we can do two separate time stops at two different points. That sounds difficult but it might work and even easier if done on video. So I'm gonna look into that in the next days. Until then.. stay tuned and maybe you find something else from me that's interesting. ^^

Guild Wars 2: Which Height is Deadly?

A few days ago I somehow ended up talking about falling damage with someone. He mentioned that it is known at which falling height (in-game units) it is deadly. What a snarky little detail. Wouldn't it be interesting to know how much it is in a more common unit? Well, let's do that and see what we can deduct from it!

In-Game Falling Death Data

On the page, for falling damage on the official Guild Wars 2 wiki, we can find a nice little graphic that shows how much %-health you lose respectively to which height you fall from. Due to copyright, I can't post it here so I have to describe it. It shows the %-health loss in a step of 10 starting from 0% and going to 180% and the distance in in-game units with a step of 100 going from 0 to 1500. It marks anything starting with 1500 as deadly even with fall damage reduction trade and 1250 units or higher as deadly without falling damage trait.^[1]

Conversion

A long time ago I already did a conversion from units to meters and feet. I'll leave this link to the post so you can check on it if you don't remember.

The conversion was 1 Unit is equal to 2.52cm or 0.083ft.

Now we just have to put in the numbers and do the calculation...

a) with falling damage reduction: 1500units * 2.52cm/unit = 3780cm or 37.8m.For feet it's 1500units * 0.083ft/unit = 124.5ft

b) without falling damage reduction: 1250units * 2.52cm/unit = 31.5m.For feet it's 1250units * 0.083ft/unit = 103.75ft

Well... that sounds ridiculous. I don't have anything to compare it to though. So let's see for a real-life equivalent to compare.

Most Reliable Resource

Looking through the interwebs there are a lot of stories about huge falls and indecisiveness of accurate numbers. Though according to a paper of NASA the fatal speed seems to be 16m/s on hard surfaces.^[2] Assuming the acceleration due to gravitation a to be 9.81m/s² and the formula being V = a * t. The total time of the fall would be t = V / a, thereby 16m/s / 9.81m/s² = 1.63s. 

To calculate the distance of the fall we have to put this into the following formula: d = 1/2 * g * t²

Thus our falling distance is 1/2 * 9.81m/s² * (1.63s)² = 13.03m. (14.75ft)

Can We Calculate the Gravity on Tyria?

To do that we would need to know how long it takes to fall a certain distance or how long it takes to fall 1250, additionally it wouldn't be accurate enough compared to simply calculating the falling speed and acceleration between reaching two points during a free fall.

Nonetheless, it's still interesting to see that it takes twice the height in Guild Wars 2 to die compared to real life. Float away Sapient Beings, float away! 

^[1] https://wiki.guildwars2.com/wiki/Damage#Falling_damage

^[2] https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19930020462.pdf

Minecraft: Player Velocity

Still, remember Minecraft? The blocky game that sold minions? I've decided to do some theorycrafting on a different game this time. Just to throw something into the mix. Since I've been very hyped about velocity in the past days.

The Same Like Before

No! Let's do it differently! Well... we're still forced to do the calculation the same basically. The easiest way to determine the velocity is by using the formula in physics. Velocity equals the distance done per second. So the easiest way would be to determine the distance and the time and calculate velocity that way. I still wanna do things differently than before so instead of using my stopwatch I'm using Minecraft's features.

Getting the Value of the Variables

This is some common knowledge but if you didn't know yet you know now. In Minecraft, each block has a size of 1-meter times 1 meter. Using this we can easily determine the length of a distance by counting blocks. It's as easy as it sounds. For the time we're gonna do something different. The best way to get the time is by using the in-game time system. Minecraft has a day and night cycles that are 20 minutes long or 24000 ticks. Using the time command we can determine the current amount of ticks of the day:

  /time query daytime  

However, this will probably return some number between 0 and 24000 depending on what time of day it is. So we need to reset this count to a value that makes it easy for us to calculate the difference. Of course, we could use the query command twice and subtract to get the value but that makes things more complicated. Using this command we can reset the ticks of the day back to 0:

  /time set 0  

Building the Experiment

The next step is building the experiment. For this, we will build several blocks in a straight line and place redstone signals to the start point of the measurement and to the endpoint of the measurement. I did this for a normal line for us to walk and run on and another one for minecarts on a boosted railroad. counting the blocks between both results in 41 blocks or 41 meters in my case.

For our detection mechanic, we're gonna use a classical tripwire trap using string and tripwire. Once something walks upon it these tripwires will set off a redstone signal. We're going to use this signal to power the first command block that is going to set the time to zero ticks. At the end of the path, we place another one of these that will send a redstone signal to the other command block which will query the current time. This way we can determine the time it took us from the first tripwire to the second tripwire.

For the mine carts, we're going to use a detector rail instead. Detector rails send off a redstone signal when there's a  minecart on them. Just like the tripwires, the first detector rail will send a redstone signal off to the first command block resetting the number of ticks to zero. Another detector rail at the end will send off a redstone signal to a command block that will query the current amount of ticks that have passed.

And Now The Best Part About Experiments

Nothing is better than executing the experiments. Even though it's more fun when things blow up.

So for our player movement and riding movement, we simply run over the first tripwire until we reach the other tripwire. So let's see how long it takes me to walk this. It took me 195 ticks to walk this. How much time are 195 ticks? Using the Minecraft Wiki we know 1000 ticks equal to 50 seconds. That means 1 tick is 50 / 1000 = 0.05 seconds. So in our case 195 ticks are 195 * 0.05 = 9.75 seconds. So we did 41 meters in 9.75 seconds. That's a movement speed of  41m / 9.75s = 4.21 m/s.

Next up let's run our stretch. This time I got 150 ticks. Going through our calculation again we have 150 * 0.05 = 7.5 seconds. So we did 41 meters in 7.5 seconds. Now we're running with a  41m / 7.5s = 5.47 m/s.

Let's Move On With Riding

First the most fabulous of all the ridable animals. The Pig. Get a pig, put on a saddle, get out the stick with a carrot and off we go. This amazing gracious animal maxes out at an unbelievable time of 346 ticks. That's a whole 346 * 0.05 = 17.3 seconds. So the pig puts on a surprising amount of 41m / 17.3s = 2.37 m/s.

Let's better go into the opposite direction of the movement speeds. Spawning a horse and taming it we can run our stretch taking a time of mere 73 ticks or 73 * 0.05  = 3.65 seconds. That's a whole 41m / 3.65s = 11.23 m/s.

Now it also would be interesting to know if the other horse types have the same or nearly the same speed so let's check them out.

Going with a mule the time I reached was 127 ticks or 127 * 0.05 = 6.35 seconds.  So the mule did me a 41m / 6.35s = 6.46 m/s.

The donkey gave me a time of 114 ticks or 114 * 0.05 = 5.7 seconds. So it did a 41m / 5.7s = 7.19 m/s.

I also figured out pressing the run key must do something on mounts and well... the times are the same. So aside from changing the camera view and looking fancy holding the run key does not increase your speed at all.

Last Animal: The Mine Cart

What do you mean the mine cart is not an animal? I bet one can somehow craft together a theory explaining mine carts to be animals, but that's not our topic. Let's check out our minecart track, time and speed. I've built some more boosters before the first signal for the mine cart to reach the maximum speed before the first detector rail. So I'll take back at the beginning and place the cart there. Let's see what the times gonna be.

It's 105 ticks. That's 105 * 0.05 = 5.25 seconds over a distance of 41 meters. We got 41m / 5.25s = 7.81 m/s.

Bonus Experiment: Ship

Decided to add an additional bonus experiment. The concept is the same as without first track but on water now. 

We have to start a little earlier than our first checkpoint to reach maximum speed before. We need to do this to prevent the acceleration to inflict an error on our time. I made sure it's again 41 blocks so let's see what the time is.

It's 106 ticks. Nearly the same as the mine cart. That's 106 * 0.05 = 5.3 seconds over a distance of 41 meters. So that's 41m / 5.3s = 7.74 m/s.

No, mph?

Yes, no mph. Instead, you get this bonus experiment with the ship. If people really, really want me to do mph here I'll do it but for now, bare with what you get. It's not that hard to be like "7.74 m/s in mph" on google. :P