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

[AnotherDilbert]

1. explain without shouting what we actually draw on the game board according to the rules.

This is an example play surface:


It shows the positions and velocity vectors of two ships and a missile.
The distance between the objects can be determined by measurement with a ruler.

2. if the "vectors" are velocity vectors then you do not know the positions of ships

The points, the origins of the velocity vectors, shows the position of the ships.

3. if the "vectors" show position - which they must to allow for weapon range- then they are displacement.

No, the vectors shows the speed and direction of travel, from the position they currently occupy.


Each ship or other object has a position, represented by a miniature or marker:

LBB2'81, p26:
4. Units: Starships and space vehicles are individually represented by spacecraft miniatures, or (if necessary) by counters or markers. Because spacecraft miniatures are almost certainly oversize for the scale in use, each should be marked with a spot or point to designate the exact true location of the ships in play.

Each ship has a vector, showing it's velocity:

LBB2'81, p27:
Each ship has a vector, which expresses that ship's velocity as a line (arrow) o f a specific direction.

We change the velocity vector with acceleration vectors:

LBB2'81, p26:
3. Thrust: Maneuver drive thrust is measured in Gs (gravities) expressed as a vector of both length and direction.

Distance and direction - a displacement vector.
Not force, not acceleration, not momentum, not velocity - direction and distance is displacement. QED

https://www.britannica.com/science/vector-physics

vector, in physics, a quantity that has both magnitude and direction. It is typically represented by an arrow whose direction is the same as that of the quantity and whose length is proportional to the quantity’s magnitude.

For example, displacement, velocity, and acceleration are vector quantities, while speed (the magnitude of velocity), time, and mass are scalars.

https://www.britannica.com/science/velocity

velocity, quantity that designates how fast and in what direction a point is moving.

https://en.wikipedia.org/wiki/Vector_(mathematics_and_physics)

In mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector[1] or spatial vector[2]) is a geometric object that has magnitude (or length) and direction.

Vectors play an important role in physics: the velocity and acceleration of a moving object and the forces acting on it can all be described with vectors.[7] Many other physical quantities can be usefully thought of as vectors. Although most of them do not represent distances (except, for example, position or displacement), their magnitude and direction can still be represented by the length and direction of an arrow.

https://physics.ucf.edu/~roldan/classes/phy2048-ch3_sp12.pdf




A vector is something with a direction and magnitude (length).
Displacement, velocity, and acceleration can all be described as vectors.

Note that the very next sentence proves the authors didn't understand the physics of it since they then say.

Of course LBB2, Encyclopædia Britannica, Wikipedia, and University of Central Florida are all plain wrong, it couldn't possibly be that you have misunderstood something, even just slightly?

 

[Spinward Flow]

1. explain without shouting what we actually draw on the game board according to the rules.

The sum of all the vectors accumulated each turn determines where the ship goes.

2. if the "vectors" are velocity vectors then you do not know the positions of ships

Um ... the system is turn based?
The only way you don't know the position of the ships is if you throw away the map.

3. if the "vectors" show position - which they must to allow for weapon range- then they are displacement.

Vectors show the change in position (from "here" to "there").

Note that the very next sentence proves the authors didn't understand the physics of it since they then say.

What an arrogant thing to say.



Let's make this as incredibly dirt simple as possible. If comprehension still eludes you after this explanation, Abandon All Hope that education can be effective.

Let's say that a ship wants to accelerate continuously at 1G in a single direction ... call the direction Spinward.
For every increment of time that passes (let's call them "turns"), the ship keeps accelerating, increasing its velocity to Spinward.
Every "turn" the ship moves "faster and faster" in a Spinward direction, because it is accelerating continuously.

Starting point: 0 (at rest)

So in turn 1, the ship accelerates at 1G to Spinward.
For the purposes of our illustration, that means the ship adds a vector of +1 to Spinward in turn 1.
Move the marker on the (stationary) map 1 hex to Spinward from the starting point.

In turn 2, the ship accelerates again at 1G to Spinward.
For the purposes of our illustration, this means that the ship adds ANOTHER vector of +1 to Spinward in turn 2.
By adding the vector from turn 1 (+1 to Spinward) plus the vector from turn 2 (another +1 to Spinward), the resulting vector in turn 2 will be +2 to Spinward.
Move the marker on the (stationary) map 3 hexes to Spinward from the starting point.

In turn 3, the ship accelerates again at 1G to Spinward.
For the purposes of our illustration, this means that the ship adds ANOTHER vector of +1 to Spinward in turn 3.
By adding the vector from turn 1 (+1 to Spinward) plus the vector from turn 2 (another +1 to Spinward) plus the vector from turn 3 (another +1 to Spinward), the resulting vector in turn 3 will be +3 to Spinward.
Move the marker on the (stationary) map 6 hexes to Spinward from the starting point.

In turn 4, the ship accelerates again at 1G to Spinward.
For the purposes of our illustration, this means that the ship adds ANOTHER vector of +1 to Spinward in turn 4.
By adding the vector from turn 1 (+1 to Spinward) plus the vector from turn 2 (another +1 to Spinward) plus the vector from turn 3 (another +1 to Spinward) plus the vector from turn 4 (another +1 to Spinward), the resulting vector in turn 4 will be +4 to Spinward.
Move the marker on the (stationary) map 10 hexes to Spinward from the starting point.



So over 4 turns, adding +1 each turn to the movement vector that compounds over time, does not result in a progression of:
0, 1, 2, 3, 4

Instead, because of acceleration, the progression of position on the map is:
0, 1, 3, 6, 10

This is because the velocity in the Spinward direction is continuously increasing by +1 each turn.

Acceleration = +1, +1, +1, +1 (constant over 4 turns)
Velocity = 1 Spinward, 2, Spinward, 3 Spinward, 4 Spinward (linear increase over 4 turns)
Position = 1 Spinward, 3 Spinward, 6 Spinward, 10 Spinward (exponential increase over 4 turns)



1, 1, 1, 1 acceleration causes 1, 2, 3, 4 velocity causes 1, 3, 6, 10 positions at end of turn.

Basically ... THIS:

Of course LBB2, Encyclopædia Britannica, Wikipedia, and University of Central Florida are all plain wrong, it couldn't possibly be that you have misunderstood something, even just slightly?

UNPOSSIBLE!

 

[RogerD]

Position, velocity and acceleration are all vector quantities, relative to a frame of reference that we can choose arbitrarily. On a game table, the position vectors are relative to someplace on the table. You can't add a position to a velocity or an acceleration to a velocity DIRECTLY, but since we work in turns (fixed units of time), we can express each of these in terms of position in a future turn. That is the brilliance of the Mayday system that they made it easy to represent the vector and the acceleration in terms of position using multiple markers and the turn sequence.

Inaccuracies arise from there being no integration over time - acceleration is treated as an impulse at the beginning of a turn. Those can be compensated for via house rules, but there are additional inaccuracies when in a gravitation field (which you always are, just a question of how strong/significant). Orbital mechanics are too hard to deal with in a game setting, likely even with computer support - it probably just wouldn't be fun.

 

[AnotherDilbert]

By setting the scale of 1 Hex equal to the "Thrust Vector" for 1 turn at 1G, they completely removed the all THRUST VECTORS from the plotting and calculations on the game map. After the Velocity and Gravity vectors determine a new movement position, the ship's THRUST may simply change the position 1 hex in any direction for each G of Performance (select any hex within 2 hexes for a 2G ship). That was a VERY elegant solution in my opinion that greatly simplified the game mechanics and improved playability.

Just like LBB2 with hexes of 100 mm?

The direction of Gravity vectors was simplified to the 6 directions of a Hex face from the infinite number of degrees in the LBB2 fractional degree system, which further sped the application of gravity vectors in game play (they just stepped in increments of a whole hex in easy to identify directions.) Conforming movement to discrete hexes made it more like a chess board [knight moves one forward and one diagonal] and less like a HS Geometry test [now get out your protractors and draw the following three vectors ...].

We have the same vectors, we just draw them with markers, rather than pencil?

I believe in concept Mayday was very like LBB2, but in execution Mayday was very much improved.

Or made worse, I have a slight problem with being forced to conform to arbitrary limitations (hexes).

In physics I can move any length in any direction I choose, in LBB2 I can move in any length in any direction I choose (good), in Mayday I can only move some arbitrary distance steps in some arbitrary direction steps (bad).

 

[AnotherDilbert]

Distance and direction - a displacement vector.
Not force, not acceleration, not momentum, not velocity - direction and distance is displacement. QED

https://www1.grc.nasa.gov/beginners-guide-to-aeronautics/what-is-lift/

Lift is a mechanical aerodynamic force produced by the motion of the airplane through the air. Because lift is a force, it is a vector quantity, having both a magnitude and a direction associated with it.

Is NASA also completely wrong?

 

[mike wightman]

I have quoted many times.

A vector quantity has magnitude and direction.

Now the bit that appears to be difficult to grasp.

You can represent this quantity as an arrow, the length of the arrow represents the magnitude.

If you are drawing displacement vectors then the length is distance travelled.

If you are drawing velocity vectors the length represents distance/time.

You can not mix and match vectors - you can not add a velocity vector to a diplacement vector.

Now in LBB2 combat we draw the positions of ships, we draw their movement. The rules confuse this by mixing up displacement vector and velocity vector.

I repeat - a 1g ship moving from rest for 1000s moves 5,000km, but only changes velocity by 10km/s

Which of those is actually drawn on the table so we can measure range to target?

 

[mike wightman]

Time to dig out the rules

2. Space: A playing surface is required, representing space as a two-dimensional
surface at the scale of 1 :100,000,000; one miilimeter equals 100 kilometers.* Three
meters equal one light-second. Planetary template disks may be produced to show.
the presence of worlds and the effects of gravity.
3. Thrust: Maneuver drive thrust is measured in Gs (gravities) expressed as a
vector of both length and direction. While direction is variable, the length of the
arrow is represented at the scale 100 mm equals 1 G (1,000 seconds acceleration at
1 G will produce a velocity change of 10,000 km, or 100 mm in scale, per turn).**

Can you spot the error or do you want me to point it out?
*so on the playing surface we are measuring and plotting distance.
** 1000s of acceleration at 10m/s^2
hmm
velocity change is 10km/s not 10,000km/s
displacement should be 5000km
they are confusing displacement with velocity

 

[McPerth]

Please, be polite and stop doing personal references to each other's education level (or to answer them). I would hate to have to begin infract or close the thread

 

[AnotherDilbert]

Now the bit that appears to be difficult to grasp.

You can represent this quantity as an arrow, the length of the arrow represents the magnitude.

If you are drawing displacement vectors then the length is distance travelled.

If you are drawing velocity vectors the length represents distance/time.

You can not mix and match vectors - you can not add a velocity vector to a diplacement vector.

Look at the title of this tread "V=AxT and S=0.5xAxT^2"

dd(t)/dt = v(t) <==> d(t) = ∫v(t)dt

and for constant velocity:

d(t) = ∫v(t)dt = vt


We turn a velocity into displacement by integrating over time, and for constant velocity that is simply multiplying by time.
https://openstax.org/books/universi...g-velocity-and-displacement-from-acceleration
(Sorry, that is not a reference to someones education, it's an appeal to authority greater than a random guy on the internet, i.e. me.)


Yes, LBB2 assumes velocity is constant during the turn:

LBB2'77, p37:
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.

Now in LBB2 combat we draw the positions of ships, we draw their movement. The rules confuse this by mixing up displacement vector and velocity vector.

I repeat - a 1g ship moving from rest for 1000s moves 5,000km, but only changes velocity by 10km/s

Which of those is actually drawn on the table so we can measure range to target?

As I have shown repeatedly, but you have apparently not yet bothered to read:

The ship moves from P₀ to P₁ (100 mm), with a velocity vector representing the velocity gained from accelerating by 1 G during a turn of 1000 s = 10 000 m/s = 10 km/s, drawn to scale as [100 mm], as it represents a speed of 10 000 km/turn.



As I said yesterday:

Acceleration is measured in m/s², not m/s.
You get change in velocity over a time by integrating over time (=multiplying with time for constant acceleration), thereby turning it into a change of velocity, measured in m/s the dimension of velocity.



So, the velocity vector starts at the new position, and points 1 Gturn in the direction of travel.
The velocity vector give both position and velocity, as they always start in the current position of the ship.

Like this:
View attachment 3616

Yes, LBB2 will give an inexact answer as all acceleration "this game assumes, for simplicity, that all acceleration is instantaneous, and occurs at the beginning of the movement phase of the turn". LBB2 says P₁ is 100 mm = 10 000 km away from P₀, and P₃ is 200 mm away from P₁ and 300 mm away from P₀.

Constant acceleration 1 G [100 mm/turn/turn], starting velocity 0 m/s [0 mm/turn].
Turn 1: Velocity is 10 000 m/s [100 mm/turn] the whole turn, so we have travelled 10 000 m/s × 1 000 s = 10 000 km [100 mm].
Turn 2: Velocity is 20 000 m/s [200 mm/turn] the whole turn, so we have travelled 20 000 m/s × 1 000 s = 20 000 km [200 mm] this turn, for a total of 30 000 km [300 mm].


If we were exact P₁ would be 50 mm = 5 000 km away from P₀, and P₃ would be 150 mm away from P₁ and 200 mm away from P₀.

d(t) = ½at²
d(0) = 0 km
d(1 turn = 1000 s) = 5 000 km [50 mm in scale].
d(2 turns = 2000 s) = 20 000 km [200 mm in scale] totally, 15 000 km [150 mm] this turn.

We plot the position and velocity vector of the ships, so we can measure the range directly on the playing surface:

This is an example play surface:


It shows the positions and velocity vectors of two ships and a missile.
The distance between the objects can be determined by measurement with a ruler.

 

[AnotherDilbert]

Time to dig out the rules

2. Space: A playing surface is required, representing space as a two-dimensional
surface at the scale of 1 :100,000,000; one miilimeter equals 100 kilometers.* Three
meters equal one light-second. Planetary template disks may be produced to show.
the presence of worlds and the effects of gravity.
3. Thrust: Maneuver drive thrust is measured in Gs (gravities) expressed as a
vector of both length and direction. While direction is variable, the length of the
arrow is represented at the scale 100 mm equals 1 G (1,000 seconds acceleration at
1 G will produce a velocity change of 10,000 km, or 100 mm in scale, per turn).**

Can you spot the error or do you want me to point it out?
*so on the playing surface we are measuring and plotting distance.
** 1000s of acceleration at 10m/s^2
hmm
velocity change is 10km/s not 10,000km/s
displacement should be 5000km
they are confusing displacement with velocity

1 G (~10 m/s²) for 1000 s is 10 000 m/s = 10 km/s.

While direction is variable, the length of the arrow is represented at the scale 100 mm equals 1 G (1,000 seconds acceleration at 1 G will produce a velocity change of 10,000 km, or 100 mm in scale, per turn).

10 km/s over a 1000 s turn is 10 000 km, i.e the velocity is 10 000 km/turn.

 

[mike wightman]

I am well aware of what you keep drawing, but the vector arrow we draw on the table is a displacement, a position change, not a track of velocity.

Or are you claiming that all acceleration is instant at the start of the turn?
A ship goes from 0 to 10km/s instantly and then coasts for 1000s?

This sentence is just plain wrong:

"1 G will produce a velocity change of 10,000 km, or 100 mm in scale, per turn", it should say
"1 G will produce a displacement of 10,000 km, or 100 mm in scale, per turn.

That is the only way to reconcile what you are claiming.

How can a 10km/s velocity vector be 100mm in length when 100mm is:
a - defined as a displacement not a velocity
b - defined as 100mm = 10,000km

More quotes -

Maneuver drive uses thrust to accelerate a ship in a specific direction for a specified distance.

That is displacement, not velocity.

This direction and distance is expressed as an arrow (a line in one direction) called a vector. Vectors determine
how far, and in what direction, a ship can travel.

Once again how far and what direction is a displacement.
But one again the authors mistakenly then conflate this with velocity in the very next sentence

Each ship has a vector, which expresses that ship's velocity as a line (arrow) of a specific direction

which contradicts what has just been defined.
Then immediately it changes back to using the term vector for displacement

A ship's vector determines the direction and distance a ship will travel in the
next turn, provided it is not changed by voluntary acceleration or by gravitational
effects.

One turn of 1g acceleration produces a velocity change of 10km/s - this produces a displacement of 5,000km (50mm) the first turn, and 10,000km (100mm) on subsequent turns.

 

[mike wightman]

1 G (~10 m/s²) for 1000 s is 10 000 m/s = 10 km/s.



10 km/s over a 1000 s turn is 10 000 km, i.e the velocity is 10 000 km/turn.

How can a ship go from 0 to 10km/s instantly?
And we draw the 10,000km as 100mm.

 

[RogerD]

I actually think we are violently agreeing with each other here, there is just some confusion on terms going on.

I am well aware of what you keep drawing, but the vector arrow we draw on the table is a displacement, a position change, not a track of velocity.

I think the argument here may be because it is both. The tail of the arrow is chosen to be drawn at the position of the ship. The units of the graphical velocity vector are chosen such that it is equal to displacement for the special case of a time interval of one turn.

How can a ship go from 0 to 10km/s instantly?

It can’t. It is a simplification for ease of game play. There are rule quotes to that effect cited above.

This sentence is just plain wrong:

"1 G will produce a velocity change of 10,000 km, or 100 mm in scale, per turn", it should say
"1 G will produce a displacement of 10,000 km, or 100 mm in scale, per turn.

The ‘per turn‘ in the first sentence makes it a velocity since velocity is distance per unit time and a turn is a time unit equal to 1000s. Your version is correct also.

How can a 10km/s velocity vector be 100mm in length when 100mm is:
a - defined as a displacement not a velocity
b - defined as 100mm = 10,000km

There are 3 scales here.
displacement 100mm = 10,000km
velocity 100mm = 10km/s
acceleration 100mm = 10m/s^2
With one turn = 1000s, all these scales work together as the rules describe, given the simplification about acceleration.

 

[AnotherDilbert]

I am well aware of what you keep drawing, ...

Why do you keep asking?

1. explain without shouting what we actually draw on the game board according to the rules.
2. if the "vectors" are velocity vectors then you do not know the positions of ships
3. if the "vectors" show position - which they must to allow for weapon range- then they are displacement.

...but the vector arrow we draw on the table is a displacement, a position change, not a track of velocity.

Not according to LBB2:

LBB2'81, p27:
Each ship has a vector, which expresses that ship's velocity as a line (arrow) of a specific direction.

The position of the miniature representing the ship is a displacement (e.g. from the original position). We don't care what the original position was, so we don't draw a vector from the original position to the current position, it's not important.

Or are you claiming that all acceleration is instant at the start of the turn?
A ship goes from 0 to 10km/s instantly and then coasts for 1000s?

Yes, LBB2 explicitly says so:

LBB2'77, p37:
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.

That is the simplification LBB2 has chosen as a basis for its movements system.

This sentence is just plain wrong:

"1 G will produce a velocity change of 10,000 km, or 100 mm in scale, per turn", it should say
"1 G will produce a displacement of 10,000 km, or 100 mm in scale, per turn.

That is the only way to reconcile what you are claiming.

10 000 km per turn is a velocity.
10 000 km once and then stop is a displacement.

How can a 10km/s velocity vector be 100mm in length when 100mm is:
a - defined as a displacement not a velocity
b - defined as 100mm = 10,000km

10 km/s = 10 000 km/turn = to scale 100 mm/turn.

How can 10 km/s be a velocity, when 10 km is a distance? The hint is in the unit "km/s", distance per time.

Once again how far and what direction is a displacement.
But one again the authors mistakenly then conflate this with velocity in the very next sentence
which contradicts what has just been defined.

No, all vectors are not displacement:
https://en.wikipedia.org/wiki/Vector_(mathematics_and_physics)

Vectors play an important role in physics: the velocity and acceleration of a moving object and the forces acting on it can all be described with vectors.[7] Many other physical quantities can be usefully thought of as vectors. Although most of them do not represent distances (except, for example, position or displacement), their magnitude and direction can still be represented by the length and direction of an arrow. The mathematical representation of a physical vector depends on the coordinate system used to describe it.

One turn of 1g acceleration produces a velocity change of 10km/s - this produces a displacement of 5,000km (50mm) the first turn, and 10,000km (100mm) on subsequent turns.

Not according to the LBB2 system, it's an explicit simplification:

LBB2'77, p37:
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.

 

[atpollard]

Thread closed for a brief rest period.

(... so we can all review the rules of the board, read our favorite Physics text book and try to locate and play a copy of "Triplanetary".)

 

[atpollard]

Thread reopened

[FYI ... marching orders are to put a stop to the "personal attacks" and "trolling" ... so stick to rules and facts moving forward.]

 

[BackworldTraveller]

Anyone want to add the in effects when Speed approaches 300,000km/s or the local G starts to get very, very big?

Or what happens when the magnetic field in the space traversed is huge?

OK - Not really relevant to most of traveller and awkward to draw on a 2D surface

 

[atpollard]

Anyone want to add the in effects when Speed approaches 300,000km/s or the local G starts to get very, very big?

Or what happens when the magnetic field in the space traversed is huge?

OK - Not really relevant to most of traveller and awkward to draw on a 2D surface

I always thought a fun “what if” was to just take the TRAVEL Rules as written and apply the “magic MD” to interstellar travel. What if a species never invented Jump Drive but found that the Gravity Manipulation of the MD had no Speed of Light limitations? So a very large ship built for an infrequent, but very long journey might cross parsecs using only a MD and constant acceleration.

 

[mike wightman]

You would need to carry an awful lot of fuel for the power plant

Depending on which canon you go by STL speeds of 0.9c are achievable with regular m-drives.

Here is what it would look like:

 

[Condottiere]

Ramscoops.