I did some more digging, and it looks like they may or may not have been touched in 1.3.1 (most likely was, but not listed)
The suspected changes was a bit of a nerf/buff (Rising force up a little, drag decrease down a lot)
Chute was actually nerfed more in 1.3.2
(65 damage/s from 50 dmg/s)
Mass changes happened in 1.2
I can't find anything prior to that, but I'm only checking the release notes (these forums and the old ones).
For the calculations, I did do a lot of simplifications, although I probably did take it a little too simple. The biggest fudging of numbers was with the drag, mostly because I didn't want to deal with it.
http://gunsoficarus.com/community/forumarchive/discussion/1069/questions-on-thrust-drag-the-affects-of-speed-and-more/p1Based on that thread, drag is a constant and mostly affects the top speed with a much smaller effect to acceleration.
For the other assumptions, it was based upon a number of things.
-Height doesn't play a role in acceleration/velocity (only at the floor/ceiling of the map do they take effect)
-Pilot input is always 100% (You're either pushing the button or not. We assume you're holding the button for the duration.)
-Mass has already been factored into the acceleration
-Drag is a constant (independent for each axis)
-Initial velocity is 0
-Drag is negligible for acceleration
-Balloon HP is always 100%
-Gravity does not play a role
Essentially I just used drag as a correlation to the terminal velocity. It's related, but not the by the factor I used. For the balloon health, we just pretend it's at 100%, because while it does play a big role, there's a lot of possible variations. Are they fixing it immediately? What tool? Do they wait until it's low and use a mallet, or just spam the spanner? Does no one fix it at all? For gravity, we can see that it does not play a role while the balloon is active. While the balloon is alive, your ship will not move up or down unless you tell it to. When damaged, you have difficulty moving both up and down. If gravity played a role, it would be easier to descend rather than ascend; and they would likely have different values in the in game reports.
This time around we'll toss in simplified drag and balloon health. We'll be using the numbers listed on the tool tip, although these are known to be inaccurate.
So we'll go ahead and use F=k1*a+K2*v^2 to find the acceleration. Ultimately this will be a function of time.
We assume 100% ballon HP and no tools being used.
As far as I can tell, drag is also independent for each ship. To find the drag coefficient we assume the ship is travelling at terminal velocity (the acceleration is equal to the drag, leaving a net force of 0, and the ship travelling at a constant velocity).
0=a-D*v^2 (using D for drag coefficient. It's the same as k2 and will be a constant)
Rearrange to get: D=a/(v^2)
Goldfish: 0.011259
Junker: 0.010308
Squid: 0.013841
Pyra: 0.009549
Galleon: 0.007776
Spire: 0.012976
Mobula: 0.025921
Now that we have some solid numbers, we can apply the tool effects more accurately. Of course things get kind of ridiculous at this point, since your velocity is based upon the acceleration/drag relationship at a certain time, which is based upon your velocity. Which is why I tossed out drag in the first place. Luckily we're just looking for maximum velocity, so time can take a back seat for a bit.
We'll just do hydrogen
(a drag reduction will actually be an increase, as we've put a negative sign in front of Drag)
a=a0*4.5 (a0 is the normal acceleration)
D=D0*1.6 (D0 is the normal drag, 60%=1.6)
0=a-D*vt^2 (where vt is the maximum velocity)
A +350% is the (original value + 350% of the original). Or more simply (1*Original + 3.5*Original), or 4.5*Original
A +60% is the original value + 60% of the original, or 1.6*originalvt=sqrt(a/D)
or
vt=sqrt(2.8125*a0/D0)
| Ship | Acceleration | Velocity | Drag | Hydro Velocity |
| Goldfish | 3.25 | 16.99 | 0.011259 | 28.493 |
| Junker | 3.00 | 17.06 | 0.010308 | 28.61 |
| Squid | 4.00 | 17.00 | 0.013841 | 28.51 |
| Pyramidian | 2.75 | 16.97 | 0.009549 | 28.46 |
| Galleon | 2.25 | 17.01 | 0.007776 | 28.527 |
| Spire | 3.75 | 17.00 | 0.012976 | 28.51 |
| Mobula | 7.5 | 17.01 | 0.025921 | 28.527 |
Which shows the velocities originally estimated were off by about 5%. I'd say that's fairly accurate all considering.
The most complex question is how long does it take to reach that maximum velocity? Since velocity is a function of the forces over time, and the forces are a function of the velocity. Essentially we'll do it in increments of 0.01 seconds. We'll factor in balloon damage, which will start at 0 and then each 1 second mark after that.
We start with
Vf=V0+a*t
and get
Vf=V0+(a*HP-D*V0^2)*t
Vf is the velocity at that time, V0 is the velocity of the last increment. We'll be using the previous increment to calculate the current increment for simplicity when it comes to drag. It won't be exact, but it will extremely close. The acceleration (a) is with the hydrogen active. We're starting a vertical velocity of 0.
| Ship | Actual Peak Velocity (m/s) | Time to Reach (s) | Distance Covered in 3 seconds (m) |
| Goldfish | 22.72 | 3.99 | 42.59 |
| Junker | 22.46 | 3.99 | 40.67 |
| Squid | 23.48 | 2.99 | 47.91 |
| Pyramidion | 21.93 | 3.99 | 38.19 |
| Galleon | 20.92 | 4.99 | 33.04 |
| Spire | 23.15 | 3.99 | 46.3 |
| Mobula | 24.90 | 2.99 | 60.91 |
These numbers are noticeably different than those originally posted which assumed ideal conditions. This situation is just about worst case scenario (no one fixing the balloon). This rapidly slows down the max acceleration which in turn reduces the top velocity leading to a smaller area covered. You can see the balloon damage playing a fairly large factor, as the max velocity often happens right before the next tick of damage, where the velocity starts decreasing.
When it comes to distance covered, the mobula is obviously king, followed by the squid and spire. Near the bottom is the galleon and pyra. To give an idea of how much distance that really is, we'll turn to our trig.
We'll use the gat/mortar as our standard
Gatling - Range 450m, Up angle 25 degrees, Down angle 50 degrees
Mortar - Range 400m, Up angle 40 degrees, Down angle 40 degrees (additional shell drop 7m/s
2)
At a close range of 50 meters: the gat can hit targets ~21 meters above level, while the mortar can hit targets ~39 meters above level.
At 100 meters: the gat can hit targets ~47 meters above level while the mortar can hit targets ~ 78 meters above level
So you can start to see the pattern where the farther you are, the higher up you can shoot. For the dodges players like to bring up when talking about hydrogen, those generally happen at extremely close ranges while you're already in an upward motion. Basically the best case scenario. Most other situations will result in only dodging a little damage from the sudden change before the gunners and enemy pilot adjust. The balloon damage reduces maneuverability quite drastically (especially when you remember that the damage is actually higher than listed).
((Numbers were taken from the in game reports))
