# Vector movement rules in updated companion: questions and issues!

##### Banded Mongoose
Ahoi Travellers!

With the new (rather simple) vector movement rules in the newly updated Traveller companion I have some questions...

Specifically it does not seem that the rules account for momentum properly.....

For example: there is no description for how to apply negative thrust/ negative thrust at an angle.

Hey there! I wrote that chapter, so I can answer this.

I see that all my examples are starting with an initial vector of (0,0), and now I wish I'd included a multi-turn example. The key thing is that once you establish a velocity, that velocity will be maintained from turn to turn without the need to apply any further Thrust, but if you do apply Thrust in subsequent turns, that will add or subtract from your existing velocity vectors.

Let's use the three XY-grid examples on page 171, but instead of restarting from an initial vector of (0.0) each time, we'll apply those Thrusts one after the other:
1. On the first turn, from an initial (stationary) vector of (0,0), we apply 4 Thrust in the +X direction, resulting in a final velocity of (4,0). At this point, without applying any Thrust on subsequent turns, our momentum in the frictionless void of space means we'd continue at a velocity of (4,0) forever, or as long as combat continues (remember that these rules do ignore gravity wells from planets, stars, etc. But in order to demonstrate how to apply Thrust to an already-moving ship, we'll use the Thrust applied in the second and third XY-grid examples.
2. On the second turn of space combat, our pilot applies 2 Thrust in the -X direction, and 2 Thrust in the +Y direction. We just add those to our existing velocity, which is 4 in the +X direction and 0 in the Y direction. For the X direction, we had a velocity of 4, and we're applying 2 Thrust in the -X direction, so effectively we're subtracting 2 from 4, resulting in a net velocity of 2 in the +X direction. For the Y direction, we had a velocity of 0, and we add 2 Thrust in the +Y direction, so we add 2 to 0 for a net velocity of 2 in the +Y direction. Mathematically, this can be expressed as (4,0) + (-2,2) = (2,2).
3. On the third turn, the pilot applies 3 Thrust in the +X direction, and 1 Thrust in the -Y direction. Our existing velocity from the last turn is (2,2), and now we're adding (3,-1) to that so (2,2) + (3,-1) = (5,1).

Does that help?

I found this explanation at the Ad Astra website:

Hey there! I wrote that chapter, so I can answer this.

I see that all my examples are starting with an initial vector of (0,0), and now I wish I'd included a multi-turn example. The key thing is that once you establish a velocity, that velocity will be maintained from turn to turn without the need to apply any further Thrust, but if you do apply Thrust in subsequent turns, that will add or subtract from your existing velocity vectors.

Let's use the three XY-grid examples on page 171, but instead of restarting from an initial vector of (0.0) each time, we'll apply those Thrusts one after the other:
1. On the first turn, from an initial (stationary) vector of (0,0), we apply 4 Thrust in the +X direction, resulting in a final velocity of (4,0). At this point, without applying any Thrust on subsequent turns, our momentum in the frictionless void of space means we'd continue at a velocity of (4,0) forever, or as long as combat continues (remember that these rules do ignore gravity wells from planets, stars, etc. But in order to demonstrate how to apply Thrust to an already-moving ship, we'll use the Thrust applied in the second and third XY-grid examples.
2. On the second turn of space combat, our pilot applies 2 Thrust in the -X direction, and 2 Thrust in the +Y direction. We just add those to our existing velocity, which is 4 in the +X direction and 0 in the Y direction. For the X direction, we had a velocity of 4, and we're applying 2 Thrust in the -X direction, so effectively we're subtracting 2 from 4, resulting in a net velocity of 2 in the +X direction. For the Y direction, we had a velocity of 0, and we add 2 Thrust in the +Y direction, so we add 2 to 0 for a net velocity of 2 in the +Y direction. Mathematically, this can be expressed as (4,0) + (-2,2) = (2,2).
3. On the third turn, the pilot applies 3 Thrust in the +X direction, and 1 Thrust in the -Y direction. Our existing velocity from the last turn is (2,2), and now we're adding (3,-1) to that so (2,2) + (3,-1) = (5,1).

Does that help?
thanks Dave, helpful but still confusing...
First, let's forget about squares as a reasonable approximation for spacecraft movement, hexes or GTFO.

I understand that you add G's to existing vectors to get total velocity/ g rating.

It would seem that you are suggesting above that thrust should be split between various vectors ("-x, +y") however I am struggling to see how this would work, especially in a Hex environment.

1). For example if you are moving at 5g in the X direction and then apply 2g in the X direction you are now moving 7g in the X direction.
2). If you apply 2g in the -X direction you're now moving 5g in the X direction, easy enough.
3). What happens if you apply 2g in the -Z direction (there doesn't seem to be a way to calculate this)?

All right, hexes, I love it!

You're correct on points 1 and 2. And the same principle applies to hexes as in grids -- you're just adding or subtracting as needed. Using the 'Z' axis as defined in the chapter (namely, the roughly Northeast/Southwest diagonal axis on a two-dimensional hexagonal grid, not the up/down 'Z' axis used in the three-dimensional Cartesian coordinate system) is a little more complex, so first I'm going to answer the question: "What happens if you apply 2g in the -Y direction?"

When you're just using X (left-right) and Y (roughly Northwest/Southeast diagonal) axes on a hex grid, you can express any velocity in the same (X, Y) vector format. So if you start at (0,0), and apply 4 Thrust in the positive-X direction, your velocity will change to (4,0). At that point, if you apply 2 Thrust in the negative-Y direction, your velocity will change to (4,-2).

For the 'Z' axis, take a look at the "Using the Z Axis" section, and my personal recommendation is to use the second bullet point, translating 'Z' axis movement to X and Y equivalents -- any Thrust or velocity along the Z axis can be expressed as equivalent Thrust or velocity along both the X and Y axes simultaneously. So if you are starting at (0,0) on a hex grid, and apply 2 Thrust in the negative-Z direction, it's the same as applying 2 Thrust in the negative-X *and* negative-Y directions. Therefore, your new velocity would be (-2,-2). This may seem like you're applying a total of 4 Thrust (2 in the negative-X direction and 2 in the negative-Y direction, but that's just an artifact of how we count things for this third "axis".

Taking a more complex example, let's say you want thrust in the "South" direction, splitting the difference between the -Y and -Z directions. If you're starting at a velocity of (0,0), how do you apply 1 Thrust in the negative-Y direction, and 1 Thrust in the negative-Z direction? First, translate that negative-Z thrust into its X/Y equivalent, which will be (-1,-1). Then add the negative-Y thrust to that, resulting in (-1,-2). Taking a look at the X/Y/Z 3-axis diagram at the top left of page 172, you'll see that (-1,-2) (1 hex in the -X direction, 2 hexes in the -Y direction) will put you 2 hexes due "South" of the starting point.

So now let's say your velocity is (-1,-2) and the next turn you decide to apply 4 Thrust in the +Z direction. First translate that Z Thrust into X and Y equivalents, making it (4,4). Then add that to your existing velocity of (-1,-2), and your resulting net velocity will now be (3,2).

Not everyone finds vectors easy to understand, which is ok. As a structural engineer vectors are my meat and drink, but my geotechnical engineer friend struggles with them. On the other hand, she is much better at calculus than I am.
Vectors are definitely best understood with diagrams.
Is there a good YouTube introduction to vectors that anyone can share?

After multiple turns using the vector movement it will be easy for the resultant movement vectors to get very large, making the plotting on the game table difficult.
If this is the case, and assuming that there are no “fixed points” in the vicinity (asteroids, etc), it is good to remember that your ship’s velocity is essentially only relevant to your opponent.
If you both have a velocity of X=200 then you are not actually moving relative to each other.
So, a tip: if the ship movement vectors are all getting too large, take the smallest one away from all vectors. Or some other arbitrary vector - it does not matter as long as all ships have the same change.
For example, ship A has a movement vector {23,35} and ship B has {18,25}.
Take {B} from {A} and you get {23-18,35-25} = {5,10} = new vector for ship A
Ship B’s vector will now be {0,0}
And the table is now small enough again.

It's true that vectors can get quite large, so that's a nice tip! Of course, that can also get complicated if you have a large number of ships and/or missile salvoes in flight.

Here's a video that might be helpful in introducing vectors:

After multiple turns using the vector movement it will be easy for the resultant movement vectors to get very large, making the plotting on the game table difficult.

I've used JumpDave's vector-based combat rules on a fairly large hex grid and they worked well. We had it scaled out over 100 hexes IIRC. If the ship's start leaving a field that large, you can kind of just reset the encounter and arbitrarily determine when and how it restarts, if necessary.

After multiple turns using the vector movement it will be easy for the resultant movement vectors to get very large, making the plotting on the game table difficult.
If this is the case, and assuming that there are no “fixed points” in the vicinity (asteroids, etc), it is good to remember that your ship’s velocity is essentially only relevant to your opponent.
If you both have a velocity of X=200 then you are not actually moving relative to each other.
So, a tip: if the ship movement vectors are all getting too large, take the smallest one away from all vectors. Or some other arbitrary vector - it does not matter as long as all ships have the same change.
For example, ship A has a movement vector {23,35} and ship B has {18,25}.
Take {B} from {A} and you get {23-18,35-25} = {5,10} = new vector for ship A
Ship B’s vector will now be {0,0}
And the table is now small enough again.
It is generally quite comical watching people new to the concept, go screaming toward one another to engage, only to go flying off the map edge ;-)
Like a game of conkers using 50' strings

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