Vector Movement In Space Games

A Critical Look At Three Systems

The Editor

There are several games about combat between spaceships out there. Perhaps surprisingly, none have been wildly successful, but a great variety exists nonetheless. Speaking in broad terms, these games and their players can be divided in two categories: Those just looking for a little fun blowing up the Death Star and those looking for realism.

Aargh! I'm going to fall off the edge of space! For a number of reasons, realism isn't such a hot item in Hollywood portrayals of space combat (or their portrayal of pretty much anything else), which leads to the popular image of space combat being something like WWII battleships in space. Consequently, most of the rulesets out there try to capture the silver screen feel.

But a vocal subgroup of space miniatures gamers is looking for more realism, and realism in this context usually means more realistic movement system (these same people typically accept lasers, particle beams and FTL at face value).

One manifestation of this quest for realism is the 3-D movement system, in various incarnations. Sort of obvious, but actually of less use than in traditional air warfare games. But we'll ignore that for now and concentrate on the other big thing in space combat realism.

Namely, vector movement. The attempt to apply Newtonian physics to space games (as if they somehow did not apply to movement anywhere else). Vector movement, ah, the ultimate in realism, elevating space games to a completely new level, a veritable nirvana of frictionless gaming...

Except that I'm not too thrilled about it.


Because I didn't sleep through High School Physics.

Elementary Physics

What we're talking about is Newton's three laws of motion. As the point I'm about to make is about High School Physics, I'm ignoring a lot of stuff here to present a very simplistic model.

The first law states that an object in motion continues in motion unless force is applied. As there is virtually no drag (read: external force slowing movement) in space, in practical gaming terms this means that speed builds up.

The second law states that force equals mass times acceleration. The important bit here is that force maintains acceleration, not velocity - a radical departure from classical Greek thinking, but in practical gaming terms it means the same thing as the first law.

The third law is actually the one that makes rocket engines and therefore space travel as we currently know it possible. Consequently, it is ignored by pretty much all game systems. So shall we, for the time being.

Does this directly relate to gaming? Not really. What we are really interested in are two basic formulas of kinematics.

Velocity under constant acceleration: current velocity equals initial velocity plus acceleration times the time spent accelerating. Or

v = v0 + a * t

Simple enough. However, enter the realm of higher mathematics with this one:

Distance traveled under constant acceleration equals initial velocity times time traveled plus one half acceleration times time squared. Or

d = v0 * t + 0.5 * a * t^2

That's it. Simple really, isn't it? Let's see how certain game systems handle this.

In This Corner...

Renegade Legion: Interceptor

Another fleet lineup. The space combat system of the ill-fated Renegade Legion line originally published by FASA, then by Crunchy Frog, then FASA again and now probably no one... but the nice armor system was resurrected in Crimson Skies, except the original boardgame version of that is out of print too...

As typical, the vanilla movement system is pure Hollywood, but optional rules exist for vector movement. The game is played on a hex map, which makes turning somewhat granular.

Attack Vector

Originally known as ΔV, published in 2003 by Ad Astra Games. It is designed from ground up to be a vector game unlike most of the competition. However, Attack Vector also uses hexes, which introduces a certain amount of granularity.

The results here are based on a pre-publication version of ΔV, which the publisher was kind enough to send me.

Full Thrust

When Full Thrust was originally published by Ground Zero Games, it was firmly in the Hollywood realm, and quite rightly so. But after demands from fans and a couple of unofficial variant systems on the web, an optional vector movement system was published in Fleet Book 1.

As a pure tabletop game, Full Thrust does not suffer from granularity quite to the same degree as hex-based systems.

The Tests

Looks like a vector game. We'll take three simple test cases and see how each of these rules handles it, and what results you would get if you applied your knowledge of High School Physics to the same problem.

The basic unit of time is one game turn. This makes the calculations even easier without really compromising anything - we are talking in somewhat abstract terms here anyway.

All test results are based on the rules as printed. Errata, FAQs, Internet discussions etc. that do not come with the rulebook when picked up from a random game store shelf are not considered.

A note to algebra purists: The following calculations are presented in a slightly informal way with many of the variables replaced by specific numbers. This is done to make this easier to understand for general audiences, not to imply that the cases aren't general in nature.

Test 1: Acceleration

Let's start with a simple one-dimensional case. Yes, you heard me right, 1-D. Just constant acceleration of one unit for a couple of turns. We are interested in three things:

Constant acceleration in straight line
Game TurnVariable Game System
InterceptorAttack VectorFull Thrust High School Physics
1velocity11 11
distance11 10.5
total distance11 10.5
2velocity22 22
distance23 21.5
total distance34 32
3velocity33 33
distance35 32.5
total distance69 64.5
4velocity44 44
distance47 43.5
total distance1016 108

Note: Attack Vector numbers halved for this chart. See below for an explanation.


As you can see, all systems model current velocity just fine. However, looking at distance traveled during each game turn and the total distance traveled, we are beginning to see differences.

The Attack Vector numbers look a bit funny until you realize each hex is actually half a unit, a necessary tweak to show half-unit movement on a discrete hexmap. Then it all clicks into place and the numbers are actually exactly correct. Attack Vector numbers are halved in the chart for comparison purposes.

But in case of Full Thrust and Interceptor, the problem is systematic and cumulating.

In fact, Full Thrust and Interceptor are not modeling constant acceleration at all, but something completely different. The full effect of the acceleration is applied at the start of each turn, instead of gradually over the time period.

Test 2: Stopping

Note the counters. This was also an attempt to use the FT vector system. I did not particularly like it, for reasons I'm planning to unveil in an article. The previous test might seem like small potatoes, but consider this example:

You are cruising along peacefully, when suddenly a giant foot descends from heaven and blocks your path.

Conveniently, you are travelling at velocity that equals your one turn's acceleration, which just happens to be one (two in case of Attack Vector). The foot is directly in front of you (distance zero). Assume that switching the thrusters to braking takes effectively no time.

Interpreting the previous results slightly differently, we get the following results:

Emergency brake
Game System
InterceptorAttack VectorFull Thrust High School Physics
Final velocity00 00
Collision with footNoYes NoYes


How convenient for Full Thrust and Interceptor players! If the designers of these games would only sell this technology to car manufacturers, they'd be millionaires!

Attack Vector pilots must actually invest in some seat belts and airbags, as their game manages to replicate High School Physics in this respect.

Test 3: Turning

This is a Grendel model I believe. Another of my misguided attempts at funky camo schemes. Many people think that the important thing about vector movement is that your guns don't have to point the way you're going. But any old tank can do that.

No, the really important bit is that your traction is zero. This becomes especially important when you want to change the direction you're going, i.e. actually turning your course instead of just pointing your nose.

Mathematically, it would be easiest to calculate a 90-degree turn because the vectors would be orthogonal. However, hex-based systems handle everything in increments of 60 degrees (one hexside), so we're going to choose a test which gives our hexbound contestants a sporting chance.

Twist and Shout

Or rather turn and burn. We'll assume that the ship is coasting at speed equal to four turns' acceleration, with nose pointed 120 degrees to right.

At the start of the test, the ship begins to apply thrust in the direction its nose is pointing, and continues this for some time. The following picture shows the position of the ship at the end of each turn.

Again, we'll halve the Attack Vector numbers to scale it to match the others.


Well, Interceptor is clearly in a class of its own. This isn't really vector movement at all, it's basically Hollywood movement with spinning-while-coasting added.

Which, incidentally, is pretty much what Babylon 5 space combat actually looks like.

Another interesting thing is what happens to Attack Vector. After spending many painful moments plotting drifts and calculating vector changes, the hex grid granularity actually pries the Attack Vector apart from the real one.

Full Thrust actually handles pretty well. The velocity vector is correct, but the faulty displacement handling makes the turn tighter than it should be.

Another fleet lineup. Finally, it should be noted that all of the tested rules exaggerate the turning ability. Pure coincidence or cutting corners to improve playability?

It would be easy to extend these calculations for Full Thrust and High School Physics. In fact I've done so. Unfortunately, for Attack Vector it would mean a boatload of tedious counting of hexes... The extended numbers can be downloaded as an Excel sheet.

Test 4: Turning and Acceleration

"Hey, you said three tests! Not fair!", I hear you say. Well, yes. Let me explain why there is no fourth test.

The logical progression here would to be to apply thrust and turning the same time. But solving these cases would require differential equations, which I believe is slightly out of the realm of High School Physics. It'll be the first thing they'll hit you with when you go to a real school, though...

Like the fourth child, that's it for this one's airtime.

To give credit where credit's due, Attack Vector can handle a fair approximation of this.

In The Good Old Days

For some reason, every game we play tends to disintegrate into a closeup brawl. If you are old enough, you might remember classic video games such as Asteroids and Lunar Lander. I loved these games. The thing that made them fun was that they were based on a simple Newtonian movement model. Incidentally, these games used vector graphics, but that's not really related to our issue here. Goes to show all vectors are not created equal, though.

When I'm thinking of even semi-realistic space movement, I'm thinking of these games. They demonstrate the basic principles so clearly and intuitively.

Lunar Lander

In Lunar Lander, your job is to apply thrust gently to ease the lunar module down without making a new crater in the pock-marked lunar surface.

Sounds simple, doesn't it? Ok, there's a time limit in form of limited fuel, but still... Then why is your lunar module going up instead of down?

Because you overcompensate. You apply thrust until you see the module slowing down to a crawl. But the problem is that your perception of speed is based on the distance you saw the module travel on screen. As we saw earlier, the distance traveled under constant acceleration does not match the change in velocity. In fact, it's exactly half.

So, when you apply enough thrust to cancel out the accumulated downward velocity, you are actually turning the velocity vector 180 degrees, to straight up! The gravity is actually the only thing that saves your bacon from being flung to outer space.

That's what makes Lunar Lander hard. That's what makes it interesting. And that's what the lesser vector system utterly fail to handle.


Spin to correct heading, apply correct thrust, repeat. Sounds simple enough.

Btw: I hate those lassos too. While not Pac-Man, Asteroids was a raving success. And no small wonder, the game is a blast.

Why is it fun, even more fun than Lunar Lander? Because you never have enough time to do things neatly. The ship turns so painfully slowly when an asteroid is zooming in on you... you end up hitting the thrusters even though you're not quite heading in the right direction... or worse yet, hitting thrusters and trying to turn at same time - a tactic that almost inevitably ends in the spiral of doom.

There is a very good game design reason the teleport button kills your inertia too...

Asteroids shows you in very clear terms how hard it is to change your course in space and what sheer madness turning and thrusting at the same time results in.

Inevitably, when I'm considering a space game, I remember these two classics. If the game claims realism, these are the benchmarks I measure it against.

And, for the most part, they fail to do even what a simple computer game from early eighties did, nevermind even skimming the more advanced stuff.


The results are pretty clear. Attack Vector is the only game of the three presented here that has any claim to presenting realistic space movement.

Does that mean I like it? Not really. It is far too complex for my current tastes. I gave up phased movement with Car Fleet Battles.

However, when something is touted as realistic and I can poke holes in using only my vague recollection of High School Physics, I feel my intelligence has been insulted. These systems are not realistic, so the question turns to are they fun. In my humble opinion, they do not bring anything to the games besides additional complexity.

If you really want realism, go with something like Attack Vector. If you just want to play, use the Hollywood movement systems.


P.S. Incidentally, the new Car Wars is much simpler than what I used to play.

P.P.S. Besides, in full realism you can't do sound effects, where's the fun in that?

Sucks! (4) Sucks by 4 votes Rocks by 30 votes (30) Rocks!


Attack Vector dating maxxon Oct 23, 2003 10:37

In all honesty, I should mention that my pre-publication copy of deltaVee(Attack Vector) is dated July 18th, 2000.

Ken Burnside from Ad Astra tells me the game has evolved much since (unlike the other contestants). I believe that if this article makes Attack Vector sound like a game you'd like to play, the new edition will deliver more of it.

Attack Vector dating and evolution. burnside Oct 23, 2003 21:10

I'm actually amazed, having looked at the old file from July 18 2000, that Mikko was able to follow enough of the game to get as favorable an impression as he did.

It has been mucn streamlined, and now works in 3-D....including 12 point facing on a hex map (which will still have the hex grain error Mikko compained of). We do show the integral of fuel mass over dry mass of the ship when calculating total delta V; running at nearly empty tanks doesn't increase your max thrust rating because the fuel fractions we use result in changes below the granularity of the game. You do get some "extra" fuel dots for having nearly empty tanks, though.

We now have physically correct pivots and rotations, handled in clean charts that are pretty easy to use. We know how much energy goes into a damage point, and what the armors are made of. We know the aperture size and wavelength of our lasers in the game, and all sorts of crunchy engineering details that, well, are there in sidebars to show how the rules came to be, but which the player doesn't need to know to play it.

Every physics problem someone has given us, we've solved and put into mechanics in the game. There are a few engineering implausibilities...but very few people will be offended that we have engines capable of pushing 5,000 ton frigates around in whopping quarter g increments without melting.

While we have phased movement, we have only 8 phases per turn, and the decision making is all simultaneous. I've seen 3-D 7-on-7 squadron/fleet actions running at 10-20 minutes per turn, with upwards of 1000 individually tracked missiles in flight...all because we tossed I-Go/U-Go in favor of "OK, everyone place future position marker. OK, everyone, check off your order boxes. OK, reveal fire. (resolve fire) OK, reveal long orders. (turn on engines, begin pivots, set persistent rotations...) OK, resolve thrust, move to future position marker. Anyone need to re-do their movement grid? No? OK, regenerate power. Segment 2. Place future position marker..." It literally takes about as long to play out a segment as it does to read that paragraph out loud twice.

We try to minimize special cases. We try to make everything flow logically from the rules.

I actually prefer board games to computer games for this kind of simulation. A boardgame will give you a better understanding of what's going on. There's a bit of time to think...and compared to asteroids, there's a bit less granularity.

One thing that makes AV:T somewhat different is that you shouldn't even TRY to do precise maneuvers. This results in iterative hex counting and sucks the fun out of the game. Instead, decide roughly what vectors you want by the end of the turn, and keep it as a guideline for the maneuvers you want to perform. As people do other things the maneuvers you make won't match that guideline...but in the end you fly by the seat of your pants.

To see the complete Sequence of Play and other play aids, go to

Weee Paul Brown (guest) May 01, 2013 08:52

Thanks for this article dude. Found it very informative from a science-based perspective.

Though I wouldn't mind if one day you took it to round 4 and did the double equation thing :)

The fourth test maxxon May 02, 2013 08:30

I'm glad you liked it.

The first thing with the fourth test is that only Attack Vector models it at all and then only because it has phased movement. Then you could argue that an Attack Vector phase is actually equal to a turn in other games and the comparison starts to get messy.

Assuming starting from standstill (an odd concept in a space game, but let's go with it for now) with realistic physics you would see the ship spinning in a fairly tight but slowly widening circle. A bit like a car doing donuts. Due to the discrete handling in games, the ship will be to travel a fair bit farther before any canceling thrust can be applied, thus creating a rapidly expanding spiral. Many won't be able to make a full circle before falling off the table (the edge of space, another interesting concept, perhaps for another article).

And the other thing is that I haven't actually needed or used differential equations for anything in the past couple of decades, so I'm a tad rusty with actually solving them.

And, as I said, differential equations are beyond high school physics, I think.

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