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 Post subject: Thoughts on duel tactics
PostPosted: Tue Jun 24, 2008 7:56 am 
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Having recently bought a copy of AV:T, I think I've found one or two friends who will be willing to give it a go - at least once. So, in preparation, I've been doing a bit of thinking about maneuver and tactics in a two ship duel situation. So here goes, see what you think.

In a two ship situation, we can always think in terms of a reference frame in which our own ship is stationary, and the enemy ship is moving relative to us. This is effectively the process being followed when we work out the crossing vector in the kinetic weapons rules.

Note: in the rest of the discussion, I'll be using the term relative velocity/vector for the crossing vector in the kinetics rules. This is because I'd like to use the term crossing vector for a different concept. Sorry if this makes it a bit confusing.

Tactical Variables
There are really two key tactical variables that we are interested in when considering an encounter:

- Closest Approach Distance - how close the enemy is to us at the point of closest approach.
- Relative Velocity - how fast the enemy is crossing at the point of closest approach.

The closest approach distance determines how effective our weapons are likely to be and our choice here will be influenced by our weapon mix and the weapon mix of our opponent.

The relative velocity determines how long the enemy will spend at a particular range. Our choice here is likely to be determined by the time it takes for our weapons to cycle, and heat and power considerations.

Prior to the point of closest approach, there are two other variables that we are interested in:

- Crossing Vector - this is not the crossing vector from the rules, but the component of the enemy's relative velocity that is perpendicular to the line-of-sight between us and him. At the point of closest approach it is the same as the relative velocity, and at an extreme distance, it is likely to be small.
- Range - this is the current range to the target.

A bit of playing around with the maths, vectors and similar triangles suggests that:

Closest Approach Distance = Range x Crossing Vector (magnitude) / Relative Velocity (magnitude)

The fraction:

f = Crossing Vector (magnitude) / Relative Velocity (magnitude)

can be approximated (very approximately) by using the first bit of the kinetics rules calculations to determine the relative velocity (referred to as the crossing vector in the rules) and measuring the number of windows on the AVID from the bearing to the enemy to the relative velocity (called the course offset in the rules)

Code:
Course Offset              fraction
0                                0
1                                0.5
2                                0.9  (actually closer to 0.87, but this all rule of thumbish)
3                                1


So, from the kinetics calculations, we can work out roughly how close the enemy is likely to be at the point of closest approach. Note that these calculations will be fairly approximate, and unlikely to be much use at long ranges.

Maneuver Options
Ok, so that's a bit of an overview of our tactical variables and how to estimate them on approach. So what are our maneuver options, and how do they affect these variables.

- Thrust towards the enemy along the line-of-sight - This increases the relative velocity and will slightly decrease the closest approach distance.
- Thrust away from the enemy along the line-of-sight - This decreases the relative velocity and will slightly increase the closest approach distance.
- Thrust perpendicular to the line-of-sight in the direction of the crossing vector - This will decrease the closest approach distance and slightly decrease the relative velocity
- Thrust perpendicular to the line of sight in the opposite direction to the crossing vector - This will increase the closest approach distance and slightly increase the relative velocity.
- Thrust perpendicular to both the line of sight and the crossing vector - This will increase the closest approach distance slightly.

Pivot rates, relative thrust ratings and the use of kinetics will limit your ability to choose which of these options you want to take.

So that's about as far as I've thought through it so far. Next step is to try to think about what the optimal distances and relative velocities are for a Rafik and a Wasp when engaging each other.

Daniel


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PostPosted: Tue Jun 24, 2008 8:19 am 
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Very nicely done, Daniel.

If you can write this up as a longer piece, I have a spot for it in Nexus Journal #2. Please include fully worked up examples so I can flesh it out into an article with illustrations.

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 Post subject: Re: Thoughts on duel tactics
PostPosted: Tue Jun 24, 2008 9:12 am 
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I'd use "lateral vector" for your concept rather than "Crossing Vector." Using the same term for two different things is the surest way to irritate people by confusing them.

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 Post subject:
PostPosted: Tue Jun 24, 2008 4:11 pm 
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Ethan,
yep, using lateral vector makes sense. I was trying to think of another term to use, but it was late and I just wanted to get the thoughts down somewhere. Using the term lateral vector would allow me to use the expression "crossing vector" instead of "relative velocity".

Ken,
I can certainly do that.


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 Post subject:
PostPosted: Thu Jun 26, 2008 7:17 am 
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Ok, so I've built a little spreadsheet that recreates AV:T movement so I can demonstrate all of this stuff. Our basic scenario is as follows:

A Wasp facing direction A with 0 velocity.
A Rafik 30 hexes from the Wasp in direction A, with velocities 7 in direction D and 5 in direction E.

In this basic scenario, if neither ship thrusts, then the Rafik reaches the point of closest approach at the end of 20 segments (2 turns 4 segments) and is at a distance of 12 hexes

If the wasp thrusts at thrust 6 for 3 segments the point of closest approach occurs at the end of segment 16 and is at a distance of 10 hexes.

If the wasp pivots 180 degrees, then thrusts at 6 for 3 segments, the point of closest approach occurs at the end of segment 27 and is at a separation of 16 hexes

If the wasp pivots 90 degrees anti-clockwise (towards the side the rafik is passing on) the point of closest approach occurs at segment 22 and is at a separation of 6 hexes.

If the wasp pivots 90 degrees clockwise (away from the side the rafik is passing on) the point of closest approach occurs at segment 17 and is at a separation of 17 hexes.

If there is an easy way to post images on the forum, I can put up a graph from the analysis.

All, in all this is pretty close to what I've posted above. The thing that surprised me a bit was that thrusting away from the Rafik was almost as effective as thrusting away from the point of closest approach in terms of opening up the distance between the ships as they pass.

Daniel


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PostPosted: Thu Jun 26, 2008 2:17 pm 
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Daniel Marlay wrote:
All, in all this is pretty close to what I've posted above. The thing that surprised me a bit was that thrusting away from the Rafik was almost as effective as thrusting away from the point of closest approach in terms of opening up the distance between the ships as they pass.


With the vast mathematical insight afforded by my liberal arts degrees, I'm going to guess that you'd find it works that way only when the Rafik is on the sort of course you picked. If Rafik thrusts straight at Wasp, then thrusting away from the ship for a few turns will delay things but it won't change closest approach distance.
And if I've read your description correctly, you're assuming Rafik doesn't respond to Wasp's maneuvering.

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 Post subject:
PostPosted: Thu Jun 26, 2008 3:00 pm 
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Daniel Marlay wrote:
If the wasp pivots 90 degrees clockwise (away from the side the rafik is passing on) the point of closest approach occurs at segment 17 and is at a separation of 17 hexes.

...

The thing that surprised me a bit was that thrusting away from the Rafik was almost as effective as thrusting away from the point of closest approach in terms of opening up the distance between the ships as they pass.


Keep in mind that the 90 CW rotation does not cause the Wasp to thrust directly away from the point of closest approach, so you're not comparing the most efficient thrust direction to the "thrust away on LOS" tactic.

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PostPosted: Thu Jun 26, 2008 5:32 pm 
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Chris DeBoe wrote:
With the vast mathematical insight afforded by my liberal arts degrees, I'm going to guess that you'd find it works that way only when the Rafik is on the sort of course you picked. If Rafik thrusts straight at Wasp, then thrusting away from the ship for a few turns will delay things but it won't change closest approach distance.
And if I've read your description correctly, you're assuming Rafik doesn't respond to Wasp's maneuvering.


The case when the Rafik thrusts directly towards you is different, yes.

And yes the calculations do assume that the Rafik doesn't respond. What the example is really trying to do is get a handle on is what the maneuvre options are when you are engaging the opponent. Obviously a real game would involve maneuvre by both parties, trying to change the relative velocity.

The Wasp captain is probably going to want a very close pass with a high relative velocity to minimise the time he is exposed to the Rafik's MRLS and allow a longer time for cycling the lasers before the second approach.

The Rafik captain is likely to want a pass that occurs at a distance of about 10 hexes and is slow enough to allow him to get off two rounds of fire from the MRLS and to maneuvre quickly for another pass.

Having an understanding of which directions you need to thrust in to achieve these aims is a good thing when you are maneuvring and when you are trying to limit your opponents maneuvre through the use of kinetics.


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 Post subject:
PostPosted: Thu Jun 26, 2008 6:32 pm 
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Ethan McKinney wrote:
Keep in mind that the 90 CW rotation does not cause the Wasp to thrust directly away from the point of closest approach, so you're not comparing the most efficient thrust direction to the "thrust away on LOS" tactic.


That is true, but with the shallow angle of the line-of-sight to the relative velocity (its a bit less than 30 degrees in this example) the differences between thrusting directly away from the point of closest approach and thrusting away perpendicular to the current line-of-sight are minimal (and somewhat gobbled up in the approximation to realspace that is a hex grid).


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 Post subject:
PostPosted: Sun Jun 29, 2008 10:08 am 
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Just to clarify, your scenario has the Wasp pivoting immediately, then thrusting for only 3 segments (that was the part that I really missed), and then drifting until closest approach. Correct?

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 Post subject:
PostPosted: Sun Jun 29, 2008 10:19 am 
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Daniel Marlay wrote:
That is true, but with the shallow angle of the line-of-sight to the relative velocity (its a bit less than 30 degrees in this example) the differences between thrusting directly away from the point of closest approach and thrusting away perpendicular to the current line-of-sight are minimal (and somewhat gobbled up in the approximation to realspace that is a hex grid).


Have you checked this? If the Wasp pivots to C and thrusts for 3 segments, I estimated that the closest approach is now 20 hexes.

Three factors influence this:
  1. Thrusting in B/C has a small component in the opposite direction as the Rafik's vector, which makes the intercept happen slightly earlier, which means less time for the vector to increase the distance.
  2. The lateral vector is marginally greater.
  3. The hex grid distorts the range just a bit.


A 3-hex difference in final range is actually pretty substantial.

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