Monday, August 21, 2017

Still more about grids ,,, and a 'play test'.

The portable wargame in action:
Soviet combined arms assault...
More later...

Part One:  Thoughts on 'offset square' grid system

After considerable thought, I have come to the conclusion that trying to bring diagonals in to a square grid game system isn't worth the candle. But I do have some thoughts on the offset squares (rectangles) grid system.  Since when this notion first occurred to me, back in 1990, I always envisaged a field of offset rectangles as a simplified field of hexagons - hexes. For mine, that meant the cells were rectangular, rather than square - in fact it never crossed my mind to make them square - with an aspect ratio of 1.155/1 (or 1/0.866).
Demonstrating 60-degree fire arcs on an 'offset square'
grid.  Note that (a) the squares are rectangles, (b) the long
axis of the rectangles is aligned with the long axis of the page.
No one is going to be so exact, of course, but it seems to me that an aspect ratio of 7:6 (1.167/1)or 8:7 (1.143) would be a good approximation. Somewhat inconveniently, 1.155 lies half way between 1.167 and 1.143. In these diagrams the cells are 21mm across by 18mm high - a 7:6 aspect ratio. Incidentally, I would recommend anyone adopting this scheme to align the rectangles with the long sides parallel to the long sides of the playing surface.

The point of this article is how are the cells to be treated. In the Bob Cordery's Portable Wargame, the 'offset' square cells are treated as such: having four sides. I tend to treat them as having six sides still: Two 'vertical' long sides; four 'horizontal' short sides (opposite pairs or which happen to be co-linear!).

I wanted to see what the effect would be on a unit's facing, and given a limited, 60-degree, arc of fire. In the diagrams, I have used 'tank' symbols to indicate facing. But I ask you to imagine them to be assault guns, with a firing range of 4 cells, and its traverse limited to 30-degrees either side of dead ahead. The first diagram shows the cells in range, depending on the facing: 'up-right', 'up-left' and 'horizontal' (I wish I could think of better terms!). You will notice, of course, the apparent asymmetry of the firing 'arcs' in the first two cases.
Note the lines drawn from the centre of the unit's 'square',
 through the centres of the left- and right-most squares
 of the arc, and its centre.  The lines describe two 30-degree
angles - a 60-degree firing arc overall.

But look at the arrowed lines. Passing through the centres of the cells along the extreme left and right of the 'arc' and straight ahead, they do indicate the practical symmetry of the '60-degree' arcs. I have placed the 30-degree angle of a set-square to demonstrate this (and to show that the 7:6 aspect ratio is quite accurate enough for our purposes).

The page flipped, and hexes sketched over the 'squares'
The symmetry of the arcs is much clearer!
To show further just how truly symmetrical those arcs of fire are in practical terms, I turned the piece of paper over. You can see how the ink soaked through to form a mirror image of the above. Then in pencil I roughly sketched in the hex-field.  You can see there that the firing arcs are indeed symmetrical.

Reverting to the original. I added some dots to indicate a 120-degree arc. The symmetries are much easier to discern and to understand. Even so, I believe the 60-degree arcs would better represent the limits of firing units lacking the 360-traverse capacity of tanks, say.

Part Two

Now we come to my version of the Portable Wargames 'Soviet Combined Arms Assault'. Well, the beginnings of it anyhow.  First off, I played it on my little 10x10-square table, set up on the kitchen table. The original hex-field map had to be adapted to my table, which tended to stretch it slightly in the up-down direction.  The extra square in width was occupied by a wide, fast-flowing river.

Kampfgruppe Fredrickson
The Opposing Forces:

German: Kampfgruppe Fredrickson (Oberst Willi Fredrickson)

- 1 Command Unit (mounted in light half-track) nominal SP = 6
- 2 Infantry Units (Rated average) @ 4SP (Strength Points) = 8SP
- 2 Machine-Gun Units (Rated Average) @2SP = 4SP
- 1 Infantry Gun Unit (Mountain gun in the original, Rated Average) @2SP
- 1 Anti-Tank Gun Unit (PaK40, Rated Average) @ 2SP
- 1 Tank Unit (PzIIIL, Rated Elite) @3SP
Total 8 units including the Colonel himself in his halftrack
SP = 25.
To this add 3 squares of field works @1SP, 3 minefields @2SP and 4 wire entanglements @1 SP brings the total SP to 38.
Exhaustion point: loss of 9SP (I have to admit, I am not clear whether the nominal SPs of field defences go towards the exhaustion point.  I was inclined to think not.).

Elements of 101 Mechanised Brigade

Russian: Lead elements of 101st Mechanised Corps, commanded by Col Pavel Strelnikov.

- 1 Command Unit, represents by a stand with a battle flag, accompanied by a jeep. SP=6 (nominal)
- 6 Rifle units (Rated Average) @4SP = 24SP
- 1 Field Artillery Unit (Rated Average) @2SP
- 1 Anti-Tank Unit (45mm/L66, Rated Average) @2SP
- 4 Tank Units (T34/76, Rated Average) @3SP = 12SP
Total number of units, 13
SP = 48; Exhaustion point, loss of 16SP.

Germans dug in and awaiting the Russian onslaught.
The Germans I set out as far as possible according to the original book scenario. As seen in the diagram. Oberst Frederickson parked his half-track within the works occupied by 1st MG Unit.  In this action, I tended to think of the units as companies, and so I'll describe them. That suggests that Col Strelnikov's force might have been the bulk of a Mechanised Brigade - most of the heavier support weapons having been left behind in the 'steady advance' of the previous days 'in the face of almost non-existent German resistance' (quotations from R. Cordery, The Portable Wargame, p80). In the above picture, the anti-tank obstacles stood in for minefields and were treated as such.

Russians approaching the forward defensive locations
of the German line.  Number 5 Company has reached the
re-entrant in the line of wire entanglements.

The were several changes I made to the scenario:
1.  Square grid instead of hex-grid:
2.  Strength Points instead of the 'Sudden Death' option.  I did, however, use the 'Going 
Solo' card system of activating units.  
3.  The infantry and machine gun units' strength points were indicated by the number of stands - 4 for the rifles, 2 for the MGs.
4.  I had the Russians advancing on a broad front...

To be continued... 


  1. Just a few comments about the first part of your post:
    - the ratio of the rectangles is 1/cos(30 degrees) to take into account the foreshortening along one dimension. But I guess you knew that already :-)

    - w.r.t. fire arcs: something I have used before is to count only half the firepower in hexes or squares that are only partly in the fire arc near the edges. It is a small correction to the discretized fire-arc, but games design wise, it is a bit of an ugly fix (YMMV).

    - if you want to use fire-arcs in multiples of 30 degrees, I think a hexgrid is the best solution. I know an offset square grid and a hexgrid are topologically the same, but I do feel the main orientations of the grid (whether hexes, squares ...) should also be reflected in the rules for fire arcs.

    1. Thanks for your comments, Phil.
      1. Yes, I knew that. cos(30 degrees) = 0.866
      2. You're right in that the arcs represented are actual wider than 60-degrees if you take into account the half-square overlap of every alternate square at the fringes. I'd be inclined to ignore that as not really requiring a 'fix'. Since grid systems lead to a fair bit of 'fudging', I reckon one more 'fudge' won't hurt!

      Having said that, though, I can see that if one allowed 2 units to occupy one square, and they faced different angles, the 'half effect' rule might well be desirable, to obviate 'double jeopardy' on those squares.

      3. You know, for more than 20 years I thought I was the only one who had come up with the 'offset rectangles' notion. From the very start, my 'brick pattern' was intended as a simplified hex field, and to be topologically the same.

      Of course, on the matter of arc, a hex field would be a whole deal simpler, but my whole idea was to avoid drawing up a hex field.

      As it transpires, I have since developed a quick(ish) method of drawing up a hex field, so that for my purposes at least, my 'brick pattern' is obsolete. I never did do anything with it. Enjoyed thinking about it though!

    2. On the matter of using the square orientation to determine fire arcs, I did notice that 'Cordery' system (p23 of 'TPW') also 'fits the 60-degree arc (you can see that by examining the above diagrams). But on the next page, the firing arc 'with the grain' is 120-degrees. At a range of 4 squares, firing 'across the grain', the arc covers 14 cells. 'With the grain', the 60-degree arc covers 12 cells, the 120-degree, 20 cells.

      That need not be a problem, particularly, though I tended towards trying as much as possible to 'equalise' the effects, whatever the facing. Hence my thoughts in the substantive article.

  2. Archduke Piccolo,

    I very much enjoyed your discourse about the merits of offset grid areas, and although I follow your reasoning, I still prefer standard square or hex grids.

    I look forward to reading your battle report ... and you are right about the SP value of defences that are lost or destroyed not counting towards the Exhaustion Point. The idea was done to ensure that troops in a defensive position were less likely to 'break' than any attackers.

    All the best,


    1. Thanks, Bob. You might be interested in Phil's comments above, and my responses. I agree with your preference for squares and hexes over the compromise represented by the offset 'brick pattern' as I originally called it.

      It is interesting how different people approach something like this. I always thought of it as a field of 'oblong hexes', simply because I had in 1990 no way to produce a hex field without drawing one, and that, I had found, was bally hard.

      As it transpired, a few months ago I found a good, reasonably quick method of hand drawing a hex field, which I posted on this blog. So I won't be using my 'brick pattern' either.

      All the same, I thought what I had to say might be useful for anyone who does (intend to) use the 'brick pattern'. There is one advantage with the oblong pattern: you can get more cells onto a given area. The only 'wastage' will be at the ends.

  3. W.r.t. drawing a hex grid:

    The error most people is to think that you have to draw hex by hex, adding to hexes already there.

    But the easiest way is to draw a set of parallel horizontal lines across the entire board, a set of parallel lines at a 30 degree angle left from the vertical, and another set of parallel lines at another 30 degree angle right from the vertical.

    That gives youa triangular grid as shown here:
    Then you draw in the hexagons, and erase any unwanted lines ...

    1. Of course that was the method that I first thought of, but I found it a lot easier to conceive than to achieve. Then I figured out this method:
      It is more complicated to describe, perhaps, but surprisingly quick and easy. That has become my preferred method of drawing a hex field.