Movement Types and Limits Series - Translational and Rotational Movement [Part 1/23]

Having gone through several hundred profiles for the various Factions the average Move Value for an Infantry company/formation is about 6" and the average for a Cavalry company/formation is about 10". I want to go through a few of the various move types and which are applicable and how they can consume the distance comprising the Move Value - it may actually surprise you how short of a distance 6" really is … and the real kicker that we immediately noticed was that we were moving our formations WAY farther than their allowed Move Value within their profile would permit (so effectively we were cheating).

** WARNING: My Physicist Nerd side is really going to come out in this post - consider yourself warned! **

War of the Ring is a tabletop war game that is played within a 3-dimensional Cartesian (rectangular) Coordinate Axis Frame typically measured in inches or millimeters. This is the first step in defining and describing motion (namely the Move Phase) within the game. For example, we can specify the initial position of a formation to be the starting position for a Move and can relocate the formation by one of three motions: 1) Translational Motion of the Formation, 2) Rotational Motion of the Formation, or 3) Reconfiguration of the Formation into a new Organizational Structure. All of these motions will consume some portion of the formation's Move Value unto its maximum value and once attained with prohibit further movement (of course the exception to this rule is Heroic Moves, On the Double! Moves, and other Movement adjusting special rules [e.g., Shadowstride]).

I have noticed that even though the models and playing field are inherently 3-dimensional the game effectively takes place within the 2-dimensional plane (as if looking down from above); and the zenith (up or +y-axis) - nadir (down or -y-axis) axises typically does not consume any portion of the formation's Move Value (i.e., zenith and nadir movements are effectively "free" - which is interesting considering there could be some substantial variation of zenith/nadir directed movements over the course of the game). Let's go through a few of the movements and specify their ability/inability and how they consume the formation's Move Value.

MOVEMENT TYPE 1: TRANSLATIONAL MOVEMENT

The first type of movement we want to investigate is translational movement. This type of movement is moving in a straight line in a constant direction without any change to the formation's heading. For example, a formation comprised of 4 companies of Cavalry units could be oriented on the battlefield with a North (-z-axis) Heading. The desire may be to move this company via a translational movement to the West-North-West direction (approximately 30-degrees off of the -x-axis) while maintaining its Northern Heading. This may look something like the image to the right. Note that the maximum distance defined by the unit's Move Value for the 2x2 Cavalry Formation is shown via the blue line and the pink lines show the limit for bows (1/2 the Move Value of the formation).

As long as the movement is strictly translational and not rotational, the formation can move up to its maximum Move Value along that straight line. In fact, and measure made from the original position the final position would be precisely the same for all companies within the formation.

MOVEMENT TYPE 2: ROTATIONAL MOVEMENT

The next type of movement we want to discuss is rotational movement. This is a little more complicated since this requires the overlay of a Polar Coordinate Axis Frame on top of our Cartesian Coordinate Axis Frame. The angles of Azimuth and Elevation provide rotational components for the company in 3-dimensional space with the radial distance being defined as either: 1) the quarter cross-sectional distance of all the companies within the formation from the formation's center point or 2) the formation's horizontal length rotating about one of the two front corners of the formation (called "wheeling" in Warhammer Rulesets).

         

Again, since the game effectively takes place within the 2-dimensional plane ; and the zenith-nadir  axis is the only axis which is rotated about. That means that any elevation angles do not consume any portion of the formation's Move Value (i.e., the formation could be "leaning" up against a rock formation and the elevation required to get into that position does not cost extra move distance).

For example: The two companies on the left here of Erkenbrand's Riders have a slight elevation to them. The far left company has an elevation along the +z-axis of about 15 degrees and the next formation to the right of it has an elevation along both the -x-axis and +z-axis. However, this would be effectively equivalent to all three companies laying flat on the table from a Move Value perspective.

The Math for calculating the distance traversed by the rotation is the same regardless of the case that is employed (the only variation is the length of the radial arm); however, considering the impact of rotation by the two means available it is interesting to see which provides the most conservation of Move Value and which provides the most tactical advantage (thusly impacting the strategy of using Heroic Moves or On the Doubles!).

I will start with a formation comprised of a single company to get the idea across and then show how it applies to a formation of more than one company.

CASE 1 - Rotating about the Center of a Formation



For this case, the center of the formation would be right in the middle of the only company in the formation. The size of a standard infantry base is 110mm x 60mm - so that would imply 55.0mm in from the edges and 30mm in from the front and back. For this type of rotation, the center of the formation does not move - it becomes the pivot - and the formation rotates about that pivot. using the geometry above we can calculate the traversal distance for this company when it rotates.

** WATCH YOUR UNITS (lol - no pun intended) **

3.28034 cm = 3.28034 cm * (1"/2.54 cm) = 1.29147"

Let's take a look at the Minas Tirith Warriors and see what the means for a formation comprised of a single company.

Since they have a Move Value of 6", this means that rotating the company by 30-degrees would use up 1.3" of their 6" Move; meaning they could translate by only 4.7" more after the rotation is complete.

CASE 2 - Rotating about the Front Corner of a Formation ("Wheeling")

For this case, one of the two front corners of the formation would the pivot point for the rotation of the formation. in the image to the left we have chosen the front right corner of the formation to be the pivot point. Having played with both types of rotation, this one is definitely the easier of the two to execute while participating in the game. Trying to rotate platforms with models that just don't want to stay standing is difficult enough - but trying to find the "center" that is required by CASE 1, above, is it quite difficult to keep track of it (the center) as bases are being repositioned. However, that being said - running the math shows us that this type of a rotation is actually more expensive to execute.

This distance corresponds to a measure of 2.2676" for a single Infantry company of warriors comprising the entire formation. That would mean only a remainder of 3.7324" for any other movement anticipated to apply to the formation.

In fact, if we "go in reverse" and try to figure out the maximum rotational distance that could be traversed by a formation comprised of a single infantry company with a Move Value of 6" ... you may be surprised what we discover:

You are seeing that correctly - if we rotate a formation comprised of a single company by just under 80-degrees via "wheeling", we have used up the entire Move Value of the formation for the Move Phase!

To make matters worse, the radial distance for the "wheeling" movement only gets worse for larger formations. For example - look at this 3x2 formation comprised of 5 companies of warriors:

Just the geometric values for the circle alone have to take into consideration a radius that is 3 companies wide = 33 cm. Following the same equation above for the maximum wheeling distance that can be traversed by this formation, we find it comes out to just 26.46-degrees (and then the entire Move Value for this formation has been consumed). The only way around this is to have smaller formations (not good for getting destroyed quickly) or performing heroic actions to increase the Move Value for the formation for that turn (just as bad, because that could effectively consume some precious Might that a hero may need later in the game).

Long story short: I think the mass majority of WotR players actually only consider translational motion as counting against the Move Value (which is incorrect). In fact I have seen players make dramatic rotations of very large flat formations where the edge company in the formation moved upward of 6x its normal Move Value (not even doable with the best special rule in the game).

** This Post is getting a little long ... let's save Reconfiguration Movement for the next post! **

MOVEMENT TYPE 3: RECONFIGURATION MOVEMENT

LINKS TO OTHER PARTS OF THE WFMC PROGRESS SERIES

• WotR Formation Movement Calculator - Work in Progress [Part 1/11]
• WotR Formation Movement Calculator - Update ... Progress still being Made [Part 2/11]
• WotR Formation Movement Calculator - WFMC Continuing to Come Together [Part 3/11]
• WotR Formation Movement Calculator - Formations Look Like REAL Formations and Groundwork for Reconfig Costs Put in Place [Part 4/11]
• WotR Formation Movement Calculator - Load Previous Data & Reconfig Costs/Restrictions [Part 5/11]
• WotR Formation Movement Calculator - Fixed Expended Move Costs Round-to-Round and Added Color to the Reconfiguration Combo Box [Part 6/11]
• WotR Formation Movement Calculator - Movement Modifier Checkboxes Work Properly and Zoom Capability [Part 7/11]
• WotR Formation Movement Calculator - Implementing the Options for Rotation [Part 8/11]
• WotR Formation Movement Calculator - Calculating the Translation Distance for Vanilla WotR Rules of Movement [Part 9a/11]
• WotR Formation Movement Calculator - Calculating the Translation Distance for Vanilla WotR Rules of Movement (Continued) [Part 9b/11]
• TBD [Part 10/11]
• TBD [Part 11/11]

LINKS TO OTHER PARTS OF MOVEMENT TYPES AND LIMITS SERIES

• Movement Types and Limits Series - Translational and Rotational Movement [Part 1/23]

• Movement Types and Limits Series - Reconfiguration Movement of Infantry Formations Comprised of 2-3 Companies [Part 2/23]
• Movement Types and Limits Series - Reconfiguration Movement of Infantry Formations Comprised of 4 Companies [Part 3/23]
• Movement Types and Limits Series - Reconfiguration Movement of Infantry Formations Comprised of 5 Companies [Part 4/23]
• Movement Types and Limits Series - Reconfiguration Movement of Infantry Formations Comprised of 6 Companies [Part 5/23]
• Movement Types and Limits Series - Reconfiguration Movement of Infantry Formations Comprised of 7 Companies [Part 6/23]
• Movement Types and Limits Series - Reconfiguration Movement of Infantry Formations Comprised of 8 Companies [Part 7/23]
• Movement Types and Limits Series - Reconfiguration Movement of Infantry Formations Comprised of 9 Companies [Part 8/23]
• Movement Types and Limits Series - Reconfiguration Summary of Infantry Formations by Company Size [Part 9/23]
• Movement Types and Limits Series - Infantry Restrictions of Reconfiguration by Formation Name Summary [Part 10/23]

• Movement Types and Limits Series - Reconfiguration Movement of Cavalry Formations Comprised of 2-3 Companies [Part 11/23]
• Movement Types and Limits Series - Reconfiguration Movement of Cavalry Formations Comprised for 4 Companies [Part 12/23]
• Movement Types and Limits Series - Reconfiguration Movement of Cavalry Formations Comprised of 5 Companies [Part 13/23]
• Movement Types and Limits Series - Reconfiguration Movement of Cavalry Formations Comprised of 6 Companies [Part 14/23]
• Movement Types and Limits Series - Reconfiguration Movement of Cavalry Formations Comprised of 7 Companies [Part 15/23]
• Movement Types and Limits Series - Reconfiguration Movement of Cavalry Formations Comprised of 8 Companies [Part 16/23]
• Movement Types and Limits Series - Reconfiguration Movement of Infantry Formations Comprised of 9 Companies [Part 17/23]
• Movement Types and Limits Series - Cavalry Movement Example 1 from Page 33 of WotR Rulebook Analysis [Part 18/23]
• Movement Types and Limits Series - Cavalry Movement Example 2 from Page 33 of WotR Rulebook Analysis [Part 19/23]
• Movement Types and Limits Series - Cavalry Movement Example 3 from Page 33 of WotR Rulebook Analysis [Part 20/23]
• Movement Types and Limits Series - Reconfiguration Summary of Cavalry Formations by Company Size [Part 21/23]
• Movement Types and Limits Series - Cavalry Restrictions of Reconfiguration by Formation Name Summary [Part 22/23]
• Using WFMC to Verify Movement Examples [Part 23/23]