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.
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.
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| Guild Wars 2 Screenshot: Fall distance at Plaza of Kormir |
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| Guild Wars 2 Screenshot: Fall at the Kormir High Road |
Measuring the Walls
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| Guild Wars 2 Screenshot: Measuring Concept, Plaza of Kormir |
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
- 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. ^^
