## Friday, July 22, 2016

### Brief Notes On A High Energy Event

I have been interested in analyzing the Drebuchet technique in the context of EVE's motion model for some time.  I was pleasantly surprised to find that the Rooks & Kings YouTube channel had a helpful clue along these lines. In this video, RnK explains how this technique works, and show some applications.  The essential idea is to take advantage of a ship being ejected from a POS shield to bump ships with tremendous energy.

My interest in analyzing the motion of ships in these conditions is that POS shield ejection represents a new physical interaction that is not yet modeled in my notes.  I've modeled the effect of ships bumping ships, as well as ships bumping immovable objects, but what is the equivalent bump of changing a POS-shield password?

Normally, I would try to measure the energy of the POS shield by seeing how far ships are flung.  What is their final resting distance from the starting position?  While this might be easy to do conceptually, it is much easier if someone takes the data for me.  Furthermore, the bump data from this video will provide a way to double-check any other measurements I make in the future.

On with the data -- The video below has a clue at the 5:28 mark that can help me to determine how much energy is in a POS shield ejection.

Is there anything more satisfying than a titan moving at 20km/s?  A couple things to note about this.  First, the narrator explains that the dreadnought is put in siege mode prior to ejection with the POS password change.  This means that during the event, the mass of the bumping ship is +900% or 10x the nominal mass.  Second, even though there is no explicit image showing the alignment of the bump dread and the titan target, I am going to assume alignment is perfect.

 Figure 1: Thanks to the velocity overlay, the Avatar velocity can be read.  It appears that the maximum is near 20km/s for this bump event!  Furthermore, note they have used a Naglfar Dreadnought to bump this titan.

You can see that the moment when the bump event occurs, where the Titan accelerates from stationary to 20km/s instantaneouslyWe know the mass of both objects and we know the velocity of the Titan immediately after the collision.

As a matter of perspective, the energy change required to accelerate a titan to 20,000m/s is approximately 2 x 1017 joules, which is a remarkable energy.  Consider that the energy released by a one megaton nuclear weapon is approximately 4 x 1015 joules.  So the POS shield energy delivers at least the energy of a 50 megaton warhead all to one object.  That would be a lot of energy, but keep in mind that we are looking at the energy of only one of the two ships, and unless the mass of the bumping ship matches the mass of the target ship, there will be residual energy reflected in the bump ship as well.

Fortunately, we know the masses of the objects as well as one of the final velocities, leaving the velocity of the bumping ship before and after the bump event as unknowns.  All collisions in EVE are elastic, so we also have two equations -- one for conservation of momentum and one for conservation of energy.   I'm not including the equations here but you can review them in Part III of my notes or in the posts on bumping with mass-matching techniques.

### Two Equations, Two Unknowns -- You Know What To Do

I solve for both the before bump and after bump velocities of the siege-mode dreadnought.  I find the velocities before and after the bump, respectively,
$\Large v_1(0^-) = v_2 \frac{m_2 + m_1}{2m_1}$
$\Large v_1(0^+) = v_2 \frac{-m_2 + m_1}{2m_1}$

I'll assume that the Dreadnought is in siege resulting in the masses as follows:

• m1mSiegeNaglfar = 1.1 x 1010 kg
• m2mAvatar = 2.2 x 109 kg
The velocity of the bump ship before and after the bump are,
• v1(0-) = 12000 m/s
• v1(0+) = 8000 m/s
Prior to striking the titan, all of the energy is in the Naglfar, meaning that we can revise our calculation of the total POS shield energy from the motion of the one ship at that time, prior to the collision.  I find the total energy is 8 x 1017 joules, equivalent to a blast from 200 megaton warhead

Putting this in the context of being bumped by other ships, it would take all of the energy from over 700 thousand 500MN stabbers to deliver this much energy in a single bump, which isn't even realistic.

If you left the titan to drift to a stop, it would come to a rest at τVMAX = 81.4s x 20,000m/s = 1,600km.  Because a siege-mode Dreadnought has 10x the time-constant as non-siege-mode, the bump distance should be almost 6000km.  Indeed, the POS password is mightier than the sword.

### Always More Questions

You can have a lot of ships inside a POS shield.  Do they all get the same energy?  Or is there an equivalent bump mass that the POS shield delivers to the ships.  Like characterizing matter with high energy particle collisions, the POS shield could be characterized by looking at the resting distance of launching ships with a spectrum of masses.

#### Acknowledgement

Thank you to Rooks and Kings for posting their technique with quantitative information, making it possible for EVE physics to move forward.

1. The other base question is whether ejection velocity is constant for all ships regardless of mass or is energy constant?

Although it would be a lot less fun mathematically it would probably be easier and much more accurate to just go on SISI, get a dreadnought and a POS, eject it and find its initial velocity. Like I said, that does kind of take all the fun out this though.

1. Andrew,

I agree that there is much more data to study on this subject. SISI is a good place to study this, and it sounds as though RnK have actually taken a great deal of data. I'm hoping to publish additional analysis when I get a chance.

Santorine

2. This does segue into a really fun mathematical question that's always bothered me about Eve:

Ships in eve slow down and stop without any apparent need for reverse thrust. I've always assumed (although this may be explained somewhere way back in the lore) that the ships somehow converted their kinetic energy into another form of energy such as heat which was then radiated into space; just like how a car's brakes convert kinetic energy into heat. My question is: assuming 100% efficiency energy conversion and a perfect black body radiator- because in space there is no conduction/convection- how large of a radiator would it take to dissipate the kinetic energy of a Titan traveling at 20km/s in 1600km?

Then again, radiating the heat into space is extremely wasteful. What if we wanted to capture that energy and reuse it? What size of an electric storage medium (capacitor, battery, inductor etc.) would be required to store that energy? How does it compare to the Titans existing capacitor?

3. Do a blog on align time mechanics plz! Love the blog man!

1. Thanks for reading. I did a little work on align time, but only the basics. See, the thing about align time is that we all know how it works when starting from stopped. I think the work would be to, first, confirm that the model works for alignment starting from all angles. That should be easy to calculate and measure. The second step is to see how alignment time is affected by external forces, such as bumping. That is a more relevant case for player combat situations. And that is a tricky experiment to run carefully. I'll add it to the list of to-do's.

Regards,

S. Santorine

4. Do a blog on align time mechanics plz! Love the blog man!

5. [This was Lord Maldoror's comment from reddit post. I put it here for completeness, but I still need to respond on reddit. https://www.reddit.com/r/Eve/comments/4u33ae/thanks_to_rnk_i_have_measured_the_energy_in_pos/]

Great read and a very interesting blog (presently reading through the other articles too).
Another relevant aspect when considering POS shield energy is the location of the Drebuchet relative to the tower centre. The "deeper" inside the shield and the closer to the tower centre, the greater the velocity of the Drebuchet at the moment it exits the shield. This is also of course why we approached the centre of the tower before Starbursting our Pantheon fleets when required.
This raised several questions during initial testing, years ago, e.g.:
Does this mean a Large Tower has more potential POS Shield Energy than a small tower (yes) and if so, is there greater energy "deeper" inside the shield, or can we attribute it simply to a constant force acting over a greater distance to increase the acceleration of the ejected object and produce a higher exit velocity?
If so, can we use different distances to tailor different Drebuchet results?
Somewhere I have a graph plotting tactical uses for what we called different Drebuchet "loading strength". So, for example:
1) Fulcrum needs a titan bumped entirely off grid. Maximum Power! After all, that vessel needs to be impossible to catch by any interdictor class ship that could possibly pursue it. So the dread is fired from ~0km to the tower structure and exposed to the expelling force for ~26km of acceleration (server tick is a factor in this too, the server only appears to provide acceleration at specific steppings but that's another subject).
2) We need RR Archons separated but not entirely off grid. They aren't in siege like dreads or in triage, so they might just jump out and jump back in if they go 'too far'. We want some of them 90+ km from the others but still broadly in reach of our tacklers and bubbles. For that the Drebuchet's "bow string" is weakened a little (Hooke's Law is a precarious thing around POSes but somehow archery nomenclature worked its way in) and the dread is fired from around ~12km from the tower, IIRC.
I'll see if I can find the original data, I have it somewhere. It records the distance from the tower (in steppings of 2km) of the sieged dreadnought vs. its exit velocity (as best I could capture at 120fps recording) and its speed upon exiting siege. The latter is very reliable to record since at that point the speeds are more in realm of a few thousands metres per second. (On that subject, it's interesting that in the boiling pot of Eve physics, as the Drebuchet dread exits siege and thus loses mass instantly, it's velocity drops rapidly)
Anyway, I'll see if I can find those numbers. We also have them for the Sun and other objects. Then we could ask - is the Sun simply a bigger POS (deeper inside = greater exit velocity) and we have a universal Eve constant for such ejections, or does it actually exert a greater constant force across it's radius?
With these new grids I'm really into bumping things as far as possible, e.g. 300 carriers jump in, drop fighters and bounce to the edges of the grid by some questionable physics which I'll get into some other time, and unleash their dark arts from the far corners, like Papedipupi's carrier work in WoWS.