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 Post subject: AVT & Orbital Mechanics
PostPosted: Wed Sep 07, 2005 5:42 pm 
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http://www.adastragames.com/discus/messages/28/65.html?1124081111




Ken Burnside
Posted on Thursday, December 25, 2003 - 12:17 pm:

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I think, thanks to a customer who works for the Air Force, and sent me a declassified briefing, that I've got the first three clues on how to make orbital mechanics work for AV:T.

First, I want to see if I can get it to work at all (damn the record keeping) then sort for simplifying assumptions.

This is THE last major gap in the model, and makes 3-D look easy. (It builds directly from 3-D...)

The first clue is that I use a frame of reference that combines two of the common ones used by planetary scientists and folks orbiting satellites....and tosses out some of each, since we're eyeballing ship to ship combat rather than space to ground.

The orbit inertial frame of reference is the standard picture of a ball with a hoop around it. Your orbiting body travels in the hoop around the ball. Eccentricity is shown by changing the hoop from a circle to an ellipse.

The orbital-MAP frame of reference puts yout perspective on the object orbiting. From your perspective, you're standing still, and the planet is moving underneath you. Think of that circle in the previous explanation as expanding into a ribbon. The ribbon's width is the map.

If you're at rest to the map, you're in a circular orbit of a given semi-major axis and period. A is prograde, D is retrograde, up is directly away from the center of mass of the planet.

I'm in an orbit that's roughly 210 miles up, with an orbital period of 44 turns (5632 seconds) (this is roughly Space Shuttle orbit parameters.) This is 340 km from the surface of the planet, which is 17 hexes over the ground, and roughly 11 hexes over the atmospheric "don't go there" zone. The Van Allen Belt is 4000 km, which is 183 hexes above me, and can be looked at (sort of) as another "don't go there" zone for now.

We're going to do a 1 hex/turn velocity change == 1 G for 1 segment (16 seconds). This is an orbital energy change of 0.15625 kips (km/sec).

If I read this right, if I thrust in "up", I'm directly changing the eccentricity of my orbit, but not changing its period. I need to know what turn and segment I hit apogee on, because in 22 turns from that time I'm hitting perigee. If my apogee goes above 28, my perigee goes below 6, and I hit the atmosphere (which is a Bad Thing).

If I thrust prograde (direction A), I have added 0.15625 kips to my orbital energy; my orbit is still circular, but it's now marginally above the map frame of reference, which means that from the frame of the map I'm starting to drift in direction D, since higher orbits are slower. If I thrust directly retrograde (direction D), I'm decreasing my orbital energy by 0.15625 kips, and my altitude with regards to the map is permanently lowered, and I start drifting in A.

If I thrust in 30 degrees "up" from A, both my orbital energy (semi-major axis) increase and my eccentricity increase, with a ratio between the two that's about a 7:4 ratio over a whole turn of burning (if I thrust at 1 g for a whole turn, I'll burn 8 fuel dots -- 1.25 kips -- and get the equivilant of 1.09375 kips in prograde acceleration, and 4 dots (0.625 kips) in changing the eccentricity.) If I thrust at 60 degrees up, it's a 4:7 split with orbital energy and eccentricity as the first and second terms of the ratio.

If I thrust in direction B/C, I'm changing the inclination of my orbit south, and not changing any of its other orbital parameters. Changing the inclination just changes which direction is prograde on the AVID.

If I thrust in direction B, I've got a 7:4 split, dividing the energy between inclination adjustments and prograde acceleration. Thrusting in A/B uses a 4:7 split. Thrusting in A/B+ puts a 7:4 split between "plane of the map" and "eccentricity", with the stuff in the plane of the map being further subdivided in a 7:4 split between prograde acceleration and inclination change.

(Hmm. Which gets resolved first, inclination or prograde acceleration?)

What I don't know is how to convert the energy in orbit changes into map movement. If you thrust enough prograde, you eventually gain a full hex of altitude and a drift

(And this is going into some future supplement, not the core box).

If this becomes playable, we get to have the "battle in the ring fragments of NR/NB" for fun.


Ken Burnside
Posted on Friday, December 26, 2003 - 12:13 pm:

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It looks like accelerating prograde gets you an elliptical orbit. You need an equal burn on the other side of the orbit to make it a proper circular burn. (It's actually not an equal burn, but calculus is about four steps past what's fun in a game.)


Alden E. Moore
Posted on Friday, December 26, 2003 - 08:28 pm:

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For those of us whom need to do some serious catching up, how about a list of basic texts and possibly websites to provide the actual science principals behind the game? Best kind of game is one that makes you want to learn!


Ken Burnside
Posted on Friday, December 26, 2003 - 10:23 pm:

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Alden, I'm not sure there's a list I can give, but...

I started from A Step Farther Out, which, in one of its essays, covers the basics of the rocket equation. The rest of the math behind the movement engine came out of a used college textbook on kinematics.

The formulas for lasers I pulled off of a web site, then found that a friend (Eric Henry) had put them into a spreadsheet.

Let's see. Armor models and laser pulse times came from assorted discussions with Anthony Jackson, who built much of it from energy of vaporization, which is on the periodic table. Ditto for energy per mole for heat storage for heat sinks.


Ken Burnside
Board Administrator
Username: Admin

Post Number: 705
Registered: 10-2003
Posted on Friday, November 26, 2004 - 11:21 pm:

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Brent Werness has provided an Orbital Mechanics Paper with a possible solution (or refinement of our idea above) for an orbital mechanics solution set for AV:T.

It starts with the non inertial rotating reference frame of a circular orbit, and gives us some numbers for judging game scale effects. The short form is that it's a lot closer to flat space than we'd expected, if this is done right.

If it isn't, I'd like to know why and how (it goes a bit beyond my comfort zone with math).

First, I'd like some peer review on the math.

If it does check out, Brent and I know where to go from here for making the lookup tables...


Jeff Abbott
Junior Member
Username: Jabber

Post Number: 31
Registered: 05-2004
Posted on Tuesday, November 30, 2004 - 09:43 am:

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Ken,

I'll take a look at it if you want.

I studied this stuff in college (BS/MS in Astro Engineering), although that was a long time ago. I've also played with some of it since.


Ken Burnside
Board Administrator
Username: Admin

Post Number: 706
Registered: 10-2003
Posted on Tuesday, November 30, 2004 - 02:44 pm:

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Jeff, please do. More eyes are always better.



Brent Werness
New member
Username: Brent_werness

Post Number: 1
Registered: 11-2004
Posted on Tuesday, November 30, 2004 - 06:44 pm:

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While doing a quick review of the math myself, I found that one of my approximations was not valid, so I'm going to type up a fixed version of the document as soon as I can. However, my life suddenly got rather busy so don't expect the fix for a couple of weeks.


Ken Burnside
Board Administrator
Username: Admin

Post Number: 713
Registered: 10-2003
Posted on Tuesday, November 30, 2004 - 07:40 pm:

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Sure thing, Brent.


Ken Burnside
Board Administrator
Username: Admin

Post Number: 738
Registered: 10-2003
Posted on Wednesday, December 08, 2004 - 11:48 pm:

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Brent has sent the latest revisions of the Orbital Mechanics proposal in.

PDF of the Math and Rules and a spreadsheet to derive the values needed for the lookup tables in the more complex form of the rule.

Warning -- calculus involved in the derivations; the rules are presented later on as bullet items.


Brent Werness
New member
Username: Brent_werness

Post Number: 2
Registered: 11-2004
Posted on Thursday, December 09, 2004 - 01:31 pm:

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I'd be good if others could check my work and make sure there are no longer little errors hiding anywhere. But also it'd be good to get play testers to try out scenarios with the rules as described near the end of the document. I can probably answer any clarifying questions anyone has on either of these two topics.


Anthony Jackson
Intermediate Member
Username: Anthony

Post Number: 107
Registered: 10-2003
Posted on Thursday, December 09, 2004 - 01:45 pm:

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I'm having a little trouble parsing the math at the moment, though the basic scheme looks fairly close to what I determined. Compare this to one of my old archived messages

There's also some discussion below that which is possibly relevant. You rotated the map by 90 degrees, but otherwise I think we're going in the same direction.


Ethan McKinney
Senior Member
Username: Emckinney

Post Number: 418
Registered: 10-2003
Posted on Thursday, December 09, 2004 - 02:35 pm:

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I take it that there's a typographic error in the formula following 3. Cylindrical Coordinates (on the first letters of "observed" and "real" were subscripted).

The equations following 4. Derived Rules refer to four axes: z, y, r, and chi. I'm afraid I can't work out what directions these all are or how you can have four axes.

In the second option for avoiding the "moving slow" effects, are keeping separate totals for r and chi, or are you summing r and chi (probably by adding their vectors together rather than adding their magnitudes together)?

In the bullet points at the bottom of page 4, is the presumed direction of orbit A?

If that's the case, the third bullet point doesnt' make sense to me, because A and F are adjacent vectors, not reciprocals. If velocity in A moves you to a higher orbit, velocity in D should move you to a lower orbit.

The fourth bullet point makes no sense at all. Velocity in + moving you retrograde in orbit, that's OK. Velocity in minus should produce thrust in A, moving you forward in the orbit, shouldn't it?

Does the first bullet mean that if you're "off to one side" of the notional orbital path represented by the map, you get thrust moving you back toward the path? And then you'll eventually "slingshot" across the path and begin building velocity in the other direction, and so on?

In the second bullet, being high means you move ever higher, while being low means you move ever lower?

On the page six, I have absolutely no idea what step 1 means.

In step 2, you get positive acceleration in the A direction and "negative" acceleration in D?

I get the feeling that the rules on page six are supposed to be layered on some other rules from earlier in the paper, but I don't know which one. It would be most helpful if you could put all the rules used in the game onto a separate page, with no commmentary or formulae.


Brent Werness
New member
Username: Brent_werness

Post Number: 3
Registered: 11-2004
Posted on Thursday, December 09, 2004 - 04:08 pm:

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Ok, you found a slew of confusing typos.

Those were supposed to all be subscripts as you identified.

In your next error, simply a mind blanking on my part yielded me typing z instead of r. That section should refer entirely to chi, r, and y.

In your next comment, I think stems from me not being overly clear. The idea is this: on some play aid their would be two boxes containing numbers, one associated with the chi direction and one associated with the r direction(in game terms the A/D axis and the +/- axis). At the begining of each turn you add your ships current velocity to the velocity listed in the box(vector wise with a velocity 1 in A meaning +1 and a velocity of 1 in D meaning -1 etc.) Whenever, the total in that box exceeds the value I dub the "critical velocity" (3.5 in this section) in magnitude, you do what is necicary to reduce (either add or subtract the critical velocity) the value in the box. If it exceeded it in the positive, you subtract off the critical velocity as many number of times as is required before the value in the box drops below the "critical velocity". For each time you subtracted off the critical velocity, you gain, in this example, a thrust of 0.5 in the positive direction.

Next comment, I assume all orbits for this document have prograde pointing in A.

Next, you are exactly right it should read D not F.

Next, you are exactly right again. The last plus sign on the 4th bullet of page 4 should read A not +.

You are correct. The 1st rule on page 4 does produce that behavior. Think about it like this. Thrusting to the side like that will slightly change the direction of the orbit, but not eccentricity or energy(when talking in normal orbital mechanics terms). So you'll get an identical orbit which intersects you origional orbit both at the point you thrusted and at a point half way arround the planet. In between those two points it will gently sinusoidally oscilate side to side over the path. That is what modeled here.

That is again indeed what the 2nd rule says. Again it is useful to think about a simple case. Higher orbits have lower orbital velocities than lower orbits. So, if in the game's reference frame, you are stationary in a lower orbit, you will have too low of velocity to keep the craft in a circular orbit. Hence the craft will go further down. The reason this isn't a problem is because the velocity based rules are is a sense a lot more powerful than the position based ones. So as you fall you gain velocity in the - direction, which will cause acceleration in the A direction, which in turn will cause acceleration in the + direction. If your ship didn't have too low of energy, it will enter an eliptical orbit. If the energy was too low, it will simply crash.

On the step 1 of page 6, I'm simply refering to the adding of velocities to the play aid I described earlier as a method of getting arround the ability to use low velocities to sneak by rules.

I don't see A or D mentioned in step two. The + refers to map direction + (the up direction). And a negative acceleration in + is a positive acceleration in -.

I'm sorry about the typos and vagueries. I'll try to update the document to fix those quickly.


Ethan McKinney
Senior Member
Username: Emckinney

Post Number: 420
Registered: 10-2003
Posted on Thursday, December 09, 2004 - 06:06 pm:

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I see. I completely misunderstood step 2 on page six. I thought it was referring to the summed velocity in step 1, which is in A or D. It's quite confusing to sum the velocities in the first step, then not use the result until step 5.

Step 2 does need have the reference to starting at "0 hex" removed. It should read, "Starting at height -71 on the chart, read down the column to the first value less than your ship's height. Use this row to find the values for all remaining steps."

Note that you have to turn the table upside down (highest values at the top) for the table to work. Otherwise, a ship at height thirty looks at the first entry, -71, and uses that row, indicating that it's entered the atmosphere and been destroyed.

Along with this change, change -71 to -infinity, so that if a ship somehow starts a turn at -120, it's not below the lowest value on the table.

For the 150 and -71/-infinity rows, remove the values in the middle three columns. The ship is destroyed, so there's no need for orbital information.

In theory, you need some sort of a wrapping provision in the B/C and E/F directions, should a ship thrust so much that it ends up in a polar orbit. I'm not confident how useful that is, though.

I'm still not clear on the mechanics of the "summed velocities." Am I correct that we're doing all this only one a game turn rather than once per segment?

Let's suppose that I start with a zero in the chi box. During the turn, I thrust so that I now have a velocity of 11 in A. At the start of the next game turn, I add this to the zero, so my chi value is now 11. I subtract 3.5 from this three times, leaving 0.5 in the chi box and adding 1.5 to my velocity in +.

During the next game turn, I build up a velocity of 5 in D using thrust. Adding a -5 to the 0.5 in the chi box, I get a -4.5 (4.5 in D). I subtract 3.5, leaving -1 in the chi box and adding a velocity of 0.5 in - to my ship, which cancels part of the velocity in +, leaving the ship with vectors of 6A, 1+.

Is this right?


Brent Werness
New member
Username: Brent_werness

Post Number: 4
Registered: 11-2004
Posted on Friday, December 10, 2004 - 11:05 am:

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You've got it. I've changed arround some of that table stuff on my own last night, similar, but not identical to what you stated I should do. I'm going to try to get that up today. I also tried to clerify all of the rule situations you described. But it seems that you have it down correctly. On the topic of side to side wrapping, trying to add that seems to me to be difficult. First off, if you go off the top you appear flying downwards from the top someplace else on the map. In addition, I just don't know how to do it properly mathematically. I have a hunch as to what the resulting forces would look like, but I really don't know.


Ken Burnside
Board Administrator
Username: Admin

Post Number: 741
Registered: 10-2003
Posted on Friday, December 10, 2004 - 11:52 am:

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Brent:

Please put the rules to be used in the beginning, and the math justifications in the back. What's happening with some folks is they see the differential equations, and immediately stop reading.

When stating a rule, it's better to list "do X, and Y happens" rather than "If you want Y to happen, do X." Actions lead to consequences, and rules that are structured that way greatly enhance comprehension.

Try the following outline:

Rules Text (what a player needs to do)
Mathematical Justifications
Unresolved Issues.

If there's any game terminology you don't grasp, say so in Unresolved Issies so that people who know the game terminology but not the forces involved, can try and help.

If there are things (like the inability to transit to a polar orbit) that you don't know how to do, put them there -- so that the next wandering innocent who hits this topic can extend from it if you hit a wall.

I find that the case numbering system I use is quite handy for structuring thoughts. If you have your rulebook handy and the time, I recommend tackling that. (If not, I may sic Ethan on it. He's very good at finding the gaps in rules.)




Jeff Abbott
Junior Member
Username: Jabber

Post Number: 32
Registered: 05-2004
Posted on Sunday, December 12, 2004 - 01:14 am:

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Brent,

Very nice. This new version addresses my main issues with the previous version. I ran some simple simulations using these equations, and the behavior looks reasonable. I think that it is unstable (the velocities and distances keep growing), but only noticable over several orbits.

On your table, why do you show the ship destroyed if it reaches the Van Allen belts? They do increase the radiation environment, but its not nearly high enough to be instantaneously lethal (or even lethal within a few turns). Over the time period of a battle, they would be survivable.

Also, your wrap distance is too small. The radius of a 75 hex altitude orbit is about 390 hexes, so the wrap should be at about 2450 hexes.

-- Jeff


Ethan McKinney
Senior Member
Username: Emckinney

Post Number: 423
Registered: 10-2003
Posted on Sunday, December 12, 2004 - 11:17 am:

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The reference point is in the middle of the map, so once you get half the circumference away from it, you reappear half the circumference away in the opposite direction. The values are correct, at least within 5%.

Brent, would you need a different table for each planet, based on gravity and diameter? Do you have a spreadsheet to generate those values quickly?



Jeff Abbott
Junior Member
Username: Jabber

Post Number: 33
Registered: 05-2004
Posted on Sunday, December 12, 2004 - 04:11 pm:

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OK, so the wrap distance extends either direction from the reference point. I got it now. Thanks.

The table should be different depending upon planet.

-- Jeff


Brent Werness
New member
Username: Brent_werness

Post Number: 5
Registered: 11-2004
Posted on Sunday, December 12, 2004 - 10:44 pm:

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The table needs to be generated for each planet. The excel spreadsheet posted with this new version of the rules does the required computations to make the table. The table is shightly unclear as to its meaning, which could be the cause of the instabilities in the orbit. I've sent a (rules only) new document to Ken. Its the rules section of the new vesion of the document I'm working on, and it should be much more clearly worded. (Note: the exact limits on each or the ranges in the range column should be concidered kind of +/- 1 for the moment, I didn't go back to the unrounded numbers to see which way the endpoints should go) He'll probably upload it fairly promptly.


Edit: As for the ships being destroyed when they reach the van Allen Belts: I did it that way because in my early discussions with Ken, he stated that we should concider that as a max for the time being.

(Message edited by Brent Werness on December 12, 2004)


Brent Werness
New member
Username: Brent_werness

Post Number: 6
Registered: 11-2004
Posted on Monday, December 13, 2004 - 02:16 pm:

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Since Ken is currently unavailable to put up the file: Here


Ethan McKinney
Senior Member
Username: Emckinney

Post Number: 424
Registered: 10-2003
Posted on Monday, December 13, 2004 - 03:33 pm:

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Nice job, Brent! Looks fairly doable for anyone crazed enough to want to fight in orbit... I've got to run through it and see if any of the ships have enough delta-V to actually boost out of orbit.

Now all you have to do is figure out if there's any effect on projectile weapons (obviously there is, but I'm not sure if it's enough to have a game-scale effect) and solve the polar problem. Oh, and the altitude-range distortion issue.

The polar problem boils down to "the poles of the planet should be single hexes, but they're about 2,500 hexes long in this system." I'm not sure if this is a real problem or not, since you obviously pick an "A" direction that roughly follows the orbits of the ships in the game, so it's likely no one ever gets near the "poles." Are you familiar with icosohedral planetary maps? They only roughly approximate a spherical planet, but they do make the poles the correct size.

Altitude-range distortion occurs because the hexes on the map are treated as constant-diameter cylinders, but are really cones extending out from the center of the planet. Not a huge problem, but it should be noticeable for long-range weapons.


Claudio Bertinetto
Junior Member
Username: Claudio

Post Number: 25
Registered: 10-2004
Posted on Tuesday, December 14, 2004 - 02:10 am:

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Since I'm the one "crazy enough to want to fight in orbit", what would the design parameters be on a specialized, purpose-built orbital combat warship? Aside from lots of armor to withstand 8MRLS fire, plenty of Delta Vee, and all-laser armament?

The requirement is for a frigate-class ship that would carry part at least of the Drop Brigade's pathfinder battalion to its optimal launch position, and duel with planetary ZD to cover them on the way down.


Sylvester Wrzesinski
New member
Username: Xveers

Post Number: 1
Registered: 11-2004
Posted on Tuesday, December 14, 2004 - 03:39 am:

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Hmm... I'm pretty rusty on my physics 12 materials, but don't you simply break orbit by increasing your velocity (and thusly increasing your orbital distance) until the gravitational forces are too weak to hold you in your orbit (and thus you break orbit in a particular direction)?

Or am I just a notch too rusty/missing something obvious and logical?

PS: I wouldn't mind playing a few orbital engagements. It's always more interesting to fight for the last few hundred klicks than the thousands in between...


Bryn Monnery
New member
Username: Bryn

Post Number: 9
Registered: 10-2004
Posted on Tuesday, December 14, 2004 - 07:47 am:

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Pathfinder Bn? Now US Marine Divisions get ISTR a coy of Force Recon, British 3 Commando and 16 Air Assault (nee 5 Airborne) each had a specialist platoon (although the Airborne Pathfinders are structured like a mini-SAS squadron, with 2 16-18 man troops)


Claudio Bertinetto
Junior Member
Username: Claudio

Post Number: 26
Registered: 10-2004
Posted on Tuesday, December 14, 2004 - 11:29 am:

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I've used the term inappropriately. The Drop Brigade does have a specialist Pathfinder/recon company, and these would go in well ahead of the main drop. I actually meant the Brigade's lead battalion, which is still equipped as light infantry/hardsuits, as opposed to the heavy armor oprevalent in the rest of the Brigade. There are two such units, but one would very likely remain in the home system.

In either case, there is a need for a specialist ship to carry these units to their launch orbits. I'll post a description on the Shipbuilding thread, as the main requirement is definitely that of carrying shuttles and drop-capsules.


Eric Finley
Intermediate Member
Username: Eric_finley

Post Number: 122
Registered: 11-2003
Posted on Tuesday, December 14, 2004 - 11:56 am:

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I'll echo the congratulations; I've read the file, and it's good work. A note of caution, however, is that these parameters fall, for the most part, into the "small perturbations" region as far as AV:T combat is concerned.

The parameters I'm used to in most combats mean that they'd be virtually unchanged, if done in orbit. The biggest effect is to increase your "bingo" fuel requirements, so as to have enough to stabilize your orbit after the fight... but the increase is small compared to what it takes to (say) move around in a solar system.

So to me, the upshot of these numbers is essentially to serve as a mathematical proof that, to first order, AV:T combat in orbit is unchanged. And even the second-order effects are comparatively small. Only under some unusual circumstances (very low fuel) do these changes become really important. Sure, we can set those up... but in general propellant is cheap, so they'll be historical oddities at most.

Not to detract from the work; just trying to help put it into perspective with regards to the larger game.


Ken Burnside
Board Administrator
Username: Admin

Post Number: 744
Registered: 10-2003
Posted on Wednesday, December 15, 2004 - 09:26 am:

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Brent: Good work, keep it up.

It will make an interesting scenario or three I suspect.


Jeff Abbott
Junior Member
Username: Jabber

Post Number: 34
Registered: 05-2004
Posted on Thursday, December 16, 2004 - 12:36 am:

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Eric,

I think the effect will be a bit more significant than "small perturbations." Gaining one hex/turn of acceleration in the +z for every 3.5 hexes travelled in the +x direction can result in a significant amount of curvature to your course, and will certainly add to the complexity of close approaches. The effect of acceleration due to displacement in the Z and Y axis are much less important.

Brent,

The effect of velocity in the +x on acceleration in the +z is really driven by the how much slower or faster than circular orbital velocity the spacecraft is moving. It should therefore probably include the velocity component in the B or F directions. Since all velocity vectors in the x-y plane are reduced to components in adjacent directions, this is easy to do. In terms of the rules, step 1 is changed to something like "Add any velocity components in the A, B, and F directions to the value in the 'A Sums' box, and subtract any velocity components in the C, D, and E directions from the value in the 'A sums' box." Your equations currently view all velocity/displacement in the Y axis as being normal to the X axis, and all velocity/displacement along the X axis as being in direction A, and doesn't properly account for the fact that we are actually on a hex grid.
I'm not sure I'm expressing this well - let me know what you think.

-- Jeff


Ethan McKinney
Senior Member
Username: Emckinney

Post Number: 427
Registered: 10-2003
Posted on Thursday, December 16, 2004 - 07:41 am:

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It's slightly more complex than that, since you have to take the vector sum (Pythagorean formula gives the magnitude) to get the true velocity perpendicular to gravity. (Well, the difference from the circular orbit velocity, anyhow.)

Of course, any vector in a y-direction (B, C, E, F) adds half its magnitude to the appropriate x-direction. The amount of the vector in the y-direction is about 86% of the total (B, C, E, or F). Then you square the totals in the x-direction and y-direction, sum them, and take the square root. Sounding scary yet?

But here's the rub: all the ships are presumed to start with a very large orbital velocity. You'll find that the orbital velocity is in the range of 50 hexes per turn. That's going to dwarf most vectors generated by thrust, making the contribution to the magnitude of the vector sum minimal. You need to have a velocity in one of the y-vectors of at least 10 before there's any effect at all (thanks to rounding and the resolution of the game).

That said, we should probably add half of the y-vector to the x-vector to get a more accurate result.

I think.


Jeff Abbott
Junior Member
Username: Jabber

Post Number: 35
Registered: 05-2004
Posted on Sunday, December 19, 2004 - 01:37 am:

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Ethan,

I agree. The velocity in the Y axis can, in most cases, be ignored, and it's too much of a pain to worry about just for the extreme case of someone thrusting to 20+. However, the component of vectors in B, C, E, of F that contribute to in-track velocity (50% of the magnitude) can be significant, and is easy to account for. So, word the rule like "Add the velocity in the A direction, plus 1/2 of any velocity in the B or F directions to the value in the 'A Sums' box, and subtract the velocity in the D direction, and 1/2 the velocity in the C or E directions from the value in the 'A sums' box."

-- Jeff


Brent Werness
New member
Username: Brent_werness

Post Number: 7
Registered: 11-2004
Posted on Monday, December 20, 2004 - 12:37 am:

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What Jeff just said is 100% accurate. That should be added to the rules immediatly.

On the note of making the map sperical, I don't believe an icosahedral map will work. I personally can't really imagine a way to make the map fully spherical, nor do I believe it removes all that much from the game. In order to make a good projection, we want our "flattened" spheres of equal altitude to both preserve the areas of the hexes, and the angles involved. This is a known to be impossible problem in the exact. So this would make it we'd need to do some sort of approximation. In addition, the velocities would now become coupled. So we could no longer simply keep track of the 'A sums' and '+ sums'. We'd have to unload more math on the players. I just don't see it as a good idea.

The Altitude-Range distortion is a more tractable problem. In addition, there is a related issue that involves passing between bands when near the wrapping distance. For the second issue, imagine this thought experiment. Start your ship with 0 velocity out at the wrapping distance - 1, with every other dimension centered. Now drift down until you hit the bottom of the band and pass into the next one below you. Since the lower level's wrapping distance is less, you will now wrap and have a dispacement away from the wrapping distance of about 100 hexes, but you shouldn't. You should end up 1 hex behind the your new wrapping distance. I'm having a hard time seeing how to fix this cleanly. I have a feeling once that is solved, the weapon distance issue will be resolved as well.

~Brent


Richard Leclercq
Member
Username: Hardlec

Post Number: 80
Registered: 07-2004
Posted on Monday, December 20, 2004 - 09:45 pm:

--------------------------------------------------------------------------------
I'm sorry I haven't thought to post this link before:

http://www.cardfaq.org/

Long version: In OshKosh WI is the Air Museum. One of their exhibits was a case of model airplanes, made out of card stock.
There are hundreds of models available, some crude, some sophistocated, of model aircraft, cars, castles, etc. Most are either pre-printed or "send-us-money-to-download."
(I have assembled a few "285" scale buildings for military miniatures)
I have seen spheres that can be "printed" cut and glued into a pretty accurate globe.
My problem is: I can assemble the published versions, but I can't design my own. (I can do 2-D deck plans, and sculpt, but I can't draw to save my life.)

For some of the several people who read this and actually have the skill to use it, CardFaq can point you in the right direction to make 3-D globes. As for how to balance a "Tee" on a globe, well, there are actually several ways to do this. Considering how light everything is, a little dab of "blue-tack" is usually enough.



Ethan McKinney
Senior Member
Username: Emckinney

Post Number: 700
Registered: 10-2003
Posted on Sunday, August 14, 2005 - 11:45 pm:

--------------------------------------------------------------------------------
Brent, please contact me ASAP. I'm trying to turn your work into real rules for the first issue of Nexus Journal and I need clarifications. Deadlines loom!


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