Rules Only: V=AxT and S=0.5xAxT^2

[atpollard]

So I was looking at the basic MOVEMENT rules and attempting to change the scales ... you know, what if a turn was 100 seconds instead of 1000 seconds or 100 minutes. That got me to trying to figure out the length of a 1G THRUST vector (you know, how far will a thrust of 1G for 1 "turn" change the movement vector.

That led me to discover what others before me must have discovered (after 40+ years, I cannot be the first to observe this).

So let us set 1G at 10 m/s/s for simplicity of math and start with the 1000 second turn common in most CT Movement/Combat Rules (LBB2/LBB5):

• 1000 seconds at 10 m/s/s = 10 x 1000 = 10,000 m/s velocity = +10 km/s = 10,000 km/turn change in velocity
• 1000 seconds at 10 m/s/s = 0.5 x 10 x 1000^2 = 5,000,000 meters = +5,000 km = 5,000 km/turn change in displacement

So let us set 1G at 10 m/s/s for simplicity of math and use the 100 minute (6000 second) turn from Mayday:

• 6000 seconds at 10 m/s/s = 10 x 6000 = 60,000 m/s velocity = +60 km/s = 360,000 km/turn change in velocity
• 6000 seconds at 10 m/s/s = 0.5 x 10 x 6000^2 = 180,000,000 meters = +180,000 km = 180,000 km/turn change in displacement

So the ship will MOVE only half of its increase in VELOCITY from the thrust accelerating it.
LBB2:81 states a 1G Thrust will produce a 10,000 km (100 mm) vector [which is correct for final VELOCITY, but doubles the actual DISPLACEMENT].
MAYDAY allows a 1G thrust to produce a 300,000 km (1 hex) vector [which is correct for final VELOCITY, but doubles the actual DISPLACEMENT].

So let's talk about it ... (I know it inspired lots of immediate thoughts in my mind).

 

[atpollard]

First Thought:

I wonder if there are other MOVEMENT RULES?
I was never big on space Combat or detailed movement. The ships carried heroes from one adventure to the next ... they were background setting for most of my games. So I am only getting around to finding all the details about them now.

[I think that is because my first few attempts at the Traveller Book vector movement went so badly that it left a bad taste for Starship Movement rules in general.]

 

[atpollard]

Second thought (first useful thought):

It is interesting that the movement works if the acceleration is instantaneous at the start of the turn. That harkens back to classic Orbital Transfer assumptions where the Impulse is instantaneous and the velocity is constant ... burn and go. It makes one wonder if they had REACTION ROCKETS in mind in 1977 when they were creating the rules?

Perhaps, it was just a simplification that was viewed as acceptable inaccuracy for the sake of playability.

 

[Spinward Flow]

So the ship will MOVE only half of its increase in VELOCITY from the thrust accelerating it.

Congratulations, you have discovered that D=1/2AT² ... which can be found in any basic physics textbook on the subject of Newtonian Motion.

One of the fundamental problems that you're going to run into is that Distance IS NOT Velocity IS NOT Acceleration.
When there is No Drag Force (because, vacuum of space) ... constant thrust (acceleration) does not equate to constant velocity or even a constant speed.

Acceleration is what a crew can control directly.
Velocity (with a direction, so it's a vector) is a RESULT of that acceleration.
Distance traveled (in any direction) is a compounding result of the velocities up to that point in time (keyword: compounding).

So you've got what you can directly control ... that yields two different independent results that you're (as a pilot or navigator) attempting to "balance" in order to reach your destination "on time and on target" without overshooting, undershooting or flying off in the wrong direction entirely.

Or to put it another way ... Orbital Mechanics and "space maneuvering" is so far removed from our everyday terrestrial "friction and drag" experiences that it's akin to the difference between thinking in 2D versus thinking in 3D. The mental gymnastics involved are NOT intuitively obvious if you aren't already well acquainted with basic Newtonian Motion physics.

For starters, everything moving in space "moves in curves that are actually straight lines" ... because Gravity has universal reach (not just 100 diameters worth!).

If you want to "break your brain" on the subject of Orbital Mechanics ... here's just a teaser that scales up from planetary motion to galactic motion to "local region of the universe" motion ... because Reality is way more interesting (and complicated) than simplistic rules or tabletops suggest it can be.

 

[Grav_Moped]

Orbital Mechanics

Forward takes you up
Up takes you back
Back takes you down
Down takes you forward

This really screwed with piloting the first orbital rendezvous until they figured it out.

Edit to add:

"East takes you Out, Out takes you West, West takes you In, In takes you East. Port and Starboard bring you back". (From Larry Niven's The Smoke Ring, though it may also have been used in The Integral Trees as well.)

 

[kilemall]

For completeness sake, Brilliant Lances does Mayday like moves with hexes 30000 km, I don’t recall the time scale.

I’ve done a lot of work on having 100 minute impulses with a view towards energy allocation of HG EPs towards vee/evade and weapons. Have to decide on a lot of variables and what exactly you are modeling.

 

[AnotherDilbert]

Perhaps, it was just a simplification that was viewed as acceptable inaccuracy for the sake of playability.

Presumably so. And it's only 2D, not 3D, a massive simplification.

They did note that this is inaccurate in LBB2'77:

LBB2'77, p37:
Optional Acceleration Effects: The vector movement system used in this game assumes, for simplicity, that all acceleration is instantaneous, and occurs at the beginning of the movement phase of the turn. For those who wish a greater degree of realism, note that, if acceleration occurs evenly during the movement phase, initial movement (i.e., during the turn acceleration is applied) will only be half that of the added vector (D = ½at² for constant a). Full effect of the new vector will be felt only on succeeding turns. This also applies to the force of gravity.

Also, it is assumed that the acceleration is constant, both in strength and direction, during the turn. That might be true of drive acceleration, but rarely gravity, as the ship moves in relation to the gravity well. To fix that you would have to integrate the acceleration over the turn.

For starters, everything moving in space "moves in curves that are actually straight lines" ... because Gravity has universal reach (not just 100 diameters worth!).

Yes, and nothing stops, it keeps moving, rotating around something. You can't park your ship in space and expect it to stay still.

 

[AnotherDilbert]

I wonder if there are other MOVEMENT RULES?

CT Traveller Starter one dimensional vector movement:

CT Starter, B1, p40:
_ _ Ships move in range bands, each about equal to 10,000 kilometers. They may move forward or back, but no side-to-side movement is allowed. Ranges are determined by counting the number of range bands between any two ships; for example, ships in adjacent range bands are at a distance of 1.
_ _ Every ship has a velocity, either forward or backward, which equals the number of range bands it moved in the previous turn. (Initial velocities are determined by the referee.) Each turn, a ship may change its velocity by up to its maneuver drive rating and then moves a number of range bands equal to its new velocity. For example, suppose a ship with a maneuver drive-6 is moving forward with a velocity of 4 range bands per turn. During its movement phase, it could speed up to 10 range bands per turn forward, change to 2 range bands per turn backward, or anything in between.

This is the same as LBB2, but in one direction only. It's much simpler and faster in execution, actually playable...

 

[mike wightman]

The only way to do it properly is to track velocity and displacement separately.

Displacement is what you draw on the map, your velocity could be recorded on your ship card.

But for the vast majority of rpg cases Starter range bands work just as well as anything else.

 

[atpollard]

Congratulations, you have discovered that D=1/2AT2 ... which can be found in any basic physics textbook on the subject of Newtonian Motion.

1. rude much?
2. see post #2.

 

[atpollard]

The only way to do it properly is to track velocity and displacement separately.

I was thinking that it might be possible to do GRAPHICALLY by adding an extra step to the existing Vector Movement System.

P0 = Starting Position of the ship.
V0 = Starting Velocity Vector.
Vt = Thrust Vector
Vg = Gravity Vector

[all of these are calculated exactly per LBB2 rules.]

• P0 + V0 yields P1 [hypothetical next point based on current velocity]
• Apply Vg to P1 to get P2 [temporary calculation point]
• Apply Vt to P2 to get P3 [temporary calculation point]
• Create Vf from point P0 to point P3 [THIS is the ships new V0 for next turn]
• Draw a temporary line from P1 to P3 and place point Pf at the midpoint [This is the final position that the ship will move to and becomes point P0 for next turn.]
• Draw the actual MOVEMENT vector (Vm) from P0 to Pf and move the start point for Vf to Pf (without changing bearing or length).
• Pf becomes the new P0 and Vf becomes the new V0 for the new turn.

The extra step is adding a line from P1 to P3 and moving the Vf to the midpoint of this line.
I THINK that this will yield the same results as creating half length displacement vectors for Thrust and Gravity to calculate the position of Pf [as LBB2:77 suggests].

I still find the vector movement too fiddly and counterintuitive for actual play, but the goal in this post was just improved accuracy within the existing framework.

 

[atpollard]

Also, it is assumed that the acceleration is constant, both in strength and direction, during the turn. That might be true of drive acceleration, but rarely gravity, as the ship moves in relation to the gravity well. To fix that you would have to integrate the acceleration over the turn.

Mayday "sort of" attempted to deal with that when it applied Gravity per HEX that the ship passed through (effectively adding several small Gravity Vectors together).

One of the things that started me wondering was the thought that if the TIME and DISTANCE scale were reduced (in Mayday) then Gravity could be applied "per Hex" with smoother results than the one big vector at the midpoint from LBB2.

 

[AnotherDilbert]

One of the things that started me wondering was the thought that if the TIME and DISTANCE scale were reduced (in Mayday) then Gravity could be applied "per Hex" with smoother results than the one big vector at the midpoint from LBB2.

Yes, of course. The smaller the time steps, the more accurate the estimate.

But if we can fire at 500 000 km or even potentially out to the 900 000 km tracking range with low accuracy, it's not much point moving in increments of 100 or 1000 km.

Changing the scales means changing a lot of other things...

 

[AnotherDilbert]

The extra step is adding a line from P1 to P3 and moving the Vf to the midpoint of this line.
I THINK that this will yield the same results as creating half length displacement vectors for Thrust and Gravity to calculate the position of Pf [as LBB2:77 suggests].

Yes, sure, but:

Now do that for every missile in play...

I still find the vector movement too fiddly and counterintuitive for actual play, but the goal in this post was just improved accuracy within the existing framework.

Yes, and we don't need it even more fiddly?


We need computer support to do this, and then it doesn't matter how fiddly the system is.

 

[Spinward Flow]

rude much?

One of my personal catch phrases is ... it only hurts because it's true.

There's a rather astonishingly wide variety of contexts in which that catch phrase of mine applies ... even when I wish it didn't (or shouldn't).
This just happened to be yet another one of them.

 

[kilemall]

For completeness sake, Brilliant Lances does Mayday like moves with hexes 30000 km, I don’t recall the time scale.

I’ve done a lot of work on having 100 minute impulses with a view towards energy allocation of HG EPs towards vee/evade and weapons. Have to decide on a lot of variables and what exactly you are modeling.

Sorry, I meant 1000 seconds broken into 100 second impulses. The idea was to make it more roleplay and less mini wargame, and player agency in making tactical choices in an emotionally engaging time scale.

 

[infojunky]

Ok, short history lesson, Book2 is based on Marc's mechanics from Triplanetary (1973). Which uses the simplified vector system.

Note D=1/2AT2 was a option in Book2.

Now I have assumed a shorter scale for years, Mostly to get more Terrain on the field, Planets should feel bigger. The High Port and/or other orbital elements being on the table.

Different editions of Traveller have a love/hate relationship with Vector movement. Book5 and MT dispensed with it entirely.

Right now I am enamored with a version of Fullthrust's cinematic movement. I am a big fan of miniatures on the table as well.

 

[atpollard]

Yes, sure, but:
View attachment 3611
Now do that for every missile in play...



Yes, and we don't need it even more fiddly?


We need computer support to do this, and then it doesn't matter how fiddly the system is.

The only difference is ...

1. do we move Vf to P3 [RAW]
2. or move Vf to Pf [proposed change]

You still have to do it for "every missile in play" (which is what makes it generally unplayable for most people).

 

[mike wightman]

On the playing surface you have to track displacement because you have to know where stuff is so they can interact.

If you plot velocity vector then you can not get range to target without doing a bit of maths.

another issue is vectors are straight lines whereas the actual movement is curved,

 

[AnotherDilbert]

The only difference is ...

1. do we move Vf to P3 [RAW]
2. or move Vf to Pf [proposed change]

You still have to do it for "every missile in play" (which is what makes it generally unplayable for most people).

I meant, "Yes, sure" your method enacts the optional rule in LBB2'77.
"but", it's more fiddly for very little gain.

Do we use the optional rule? Well, that's up to each Referee?

My take is: If we want to make the vector system usable, we have to make it simpler...