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.