While I was ranting about Why I think hills are horrible in wargames rules, I found two rules had a clever solution for dealing with line of sight on hills using geometry. I’d already thought of a similar approach, also using geometry. I call the two approaches “Parallel crest” and “Perpendicular crest”. Both solutions are clever. Which one is better?
A tiny bit of geometry
To use these methods to find implicit crests based on the peak, you need a tiny bit of geometry. The key concepts are parallel and perpendicular.
A parallel line is side by side with the original line and is the same distance from the original line along its entire length. Because of this, parallel lines never meet
A perpendicular line is a straight line at an angle of 90° to original line. Because of this the two lines must cross each other at right angles.
Parallel crest
Both Volley & Bayonet and Blitzkrieg Commander IV (BKC4) use implicit crests to affect visibility. These implicit crests are calculated during the game based on the relative position of the observer and the centre of the hill (the peak). The two systems use different language but the rule is the same I’ll reproduce them here:
This is the V&B version:
Each hill is assumed to have a crest line, which runs down the centre of the hill perpendicular to the line of sight [facing] of a unit. The crest line is the point at which the line of sight of a stand on a lower elevation is blocked. (p. 32)
Just to be really clear, where V&B says “perpendicular to the line of sight” it actually means “perpendicular to the straight ahead facing of the unit”. I had to check the diagrams to be sure. The net effect is that V&B is talking about a line parallel to the front edge of the unit.
BKC4 is a bit clearer about the whole parallel thing:
To determine LOS to and from high ground, calculate the crest-line of the terrain feature as and when required during the game. To do this, draw an imaginary line across the centre of the high ground, parallel to the front base edge of the unit on lower ground. This line will be the crest line in relation to that unit, with any troops forward of the line being within LOS, and those behind it bing out of sight. (p. 14)
Different words. Same system. Enemy are visible on the slope rising up to the implicit crest and hidden on the dropping slope on the far side of the implicit crest.
Perpendicular crest
Before I wrote Why I think hills are horrible in wargames rules I was already toying with a rule using a implicit crest line perpendicular to line of sight from unit to unit. But I thought I’d blog about published rules before I shared my own thoughts. However, in a comment on my previous post, Dr John D’Alton suggested the same perpendicular approach. It goes like this…
Imagine a line of sight (LOS) from the observer to the target. The implicit crest is a line perpendicular to the LOS and passing through the peak of the hill.
The LOS is what is appropriate for the set of rules because we have choices about where we draw the LOS. Tilly’s Very Bad Day goes to/from centre of the unit. But in the examples of this post I’ve drawn LOS from the observer to the target, using the centre of the front edge of the unit in both cases.
Comparing parallel and perpendicular crests
I have a few side by side comparisons of the parallel and perpendicular approaches to implicit crests. In all cases the blue infantry is trying to observe the red cavalry. A few examples are there to show how to exploit one of the approaches or the other. And I have also reversed a couple of examples to test where the approaches are reciprocal i.e. when blue can see red, red can also see blue.
I’ve rated each of the approaches in each of the examples as plausible, implausible, or wrong. I might question the result of the method with an “implausible” result, but “wrong” is down right weird. An example of “wrong” is where line of sight is not reciprocal i.e. blue can see red but the reverse is not true.
Example 1
The first example has the red cavalry visible to the blue infantry using both the parallel solution and the perpendicular solution. In fact the implicit crest lines are very close together in this example, with the parallel crest being slightly closer to the observer.
Parallel: Plausible
Perpendicular: Plausible
Example 2
In the second example the blue infantry cannot see the red cavalry. This is true whether using the parallel crest or the perpendicular crest. Again the parallel crest is closer to the observer in this example, but the two implicit crests are further apart.
Parallel: Plausible
Perpendicular: Plausible
Examples 3
Example 3 shows how to exploit the parallel approach. In the example the Blue player has used a pivot to exploit the situation from example 2. The perpendicular crest has remained unchanged. In contrast, the pivot means the parallel crest now reveals the rear of the hill including the red cavalry.
Parallel: Wrong
Perpendicular: Plausible
Example 4
The fourth example shows that visibility is not reciprocal using the parallel approach but is when using the perpendicular approach. The example reverses the positions of the units in example 3. In either approach the Blue infantry on the hill cannot see the red cavalry on the flat. So far so good.
The problem is that, example 3 showed the red cavalry can see the blue infantry using the parallel approach. This lack of reciprocality is because there is a different implicit crest for the two units involved. And that is pretty weird given the geography is unchanged. In contrast the perpendicular method is always reciprocal; for any two units, there is only one implicit crest.
Parallel: Wrong
Perpendicular: Plausible
Example 5
Example 5 flips to an oval hill. Both the parallel crest and perpendicular crest are plausible and block line of sight. In this case the parallel crest is closer to the observer.
Parallel: Plausible
Perpendicular: Plausible
Example 6
In example 6 the Blue player tries to exploit the situation in example 5 by moving the unit sideways and further away from the hill. The parallel crest is unchanged but the line of sight does not cross the implicit crest (i.e. on the hill) so line of sight is not blocked. Similarly the perpendicular crest also exposes the red cavalry. Actually, looking at the scenario, this seems reasonable, with the blue infantry sufficient far from the hill to see around the curved slopes.
Parallel: Plausible
Perpendicular: Plausible
Example 7
I included this example because it looks like the red cavalry should be visible, and they are with the parallel crest, but they are hidden with the perpendicular crest. This one I’m not sure about.
Parallel: Plausible
Perpendicular: Implausible
Example 8
Example 8 and 9 are another pair. The blue infantry on the flat can see the red cavalry using the parallel crest but not with the perpendicular crest.
Parallel: Implausible
Perpendicular: Plausible
Example 9
This is another example where I reversed the positions, in this case example 9 reverses the observer/target of example 8. Not surprisingly the perpendicular crest is unchanged. However, this time the blue observer cannot see the red cavalry, regardless of whether the parallel or perpendicular crests are used. The red cavalry can see the blue infantry using the parallel crest.
Parallel: Wrong
Perpendicular: Plausible
Observations and conclusions
The summary is:
| Example | Parallel crest | Perpendicular crest |
|---|---|---|
| 1 | Plausible | Plausible |
| 2 | Plausible | Plausible |
| 3 | Wrong | Plausible |
| 4 | Wrong | Plausible |
| 5 | Plausible | Plausible |
| 6 | Plausible | Plausible |
| 7 | Plausible | Implausible |
| 8 | Implausible | Plausible |
| 9 | Wrong | Plausible |
| Example | Parallel crest | Perpendicular crest |
| Plausible | 5 | 8 |
| Implausible | 1 | 1 |
| Wrong | 3 | 0 |
I think the perpendicular crest is a clear winner. Using the combination of observer position, target position and the peak gives more plausible results than using just the facing edge of the observer and the peak. The perpendicular approach also avoids results that are just wrong i.e. where units observing each other have different implicit crests hence visibility.
References
Chadwick, F. and Novak, G. (1994). Volley & Bayonet. Game Designers’ Workshop (GDW Games).
Chadwick, F. and Novak, G. (2008). Volley & Bayonet: Road to Glory. Test of Battle Games.
Fry, M. (2019). Blitzkrieg Commander, [4th ed.]. Pendraken Miniatures.
Hiya, great diagrams! If you compare #7 with numbers 1-3, but making the oval hill more circular, they are effectively the same except the units are closer, BUT still on a real hill like that LOS is indeed blocked because there is an effective crest at the perpendicular line. So I am not sure why #7 is rated “implausible”? is it because the units are closer? if so then 1-3 with moved-closer units suffer the same problem. I think you got it right overall 🙂 This is indeed the only way to avoid gaming the orientations/positions.
re Example 7
It just looks wrong. If the oval hill had a ridge line across the length, the unit would be sitting across that virtual ridge line. So, visually, it seems odd that in the perpendicular approach the unit is hidden. The parallel approach, in this example, does not have that problem.
I think there’s a more complicated but possibly necessary ingredient; the military crest.
As I understand it this is below the physical crest, but near enough for an observer from that unit to see over. The unit is invisible to the enemy until they cross the physical crest.
Perhaps the military crest should extend for an inch or so either side of the physical crest and produce a dead zone.
In your testing examples, some should fall into this dead zone.
I’d also argue some of the problem examples follow from our modelling of hills. A round hill would have multiple crest lines all around. A ridge would have one running along it’s length but if rounded at the end, more than one at this edge.
Modelled realistically, it would be obvious, but we have to make do with reduced scale charicatures.
Just my fourpenneth….
Neil
Neil, what is the effect of the “dead zone”? In the back of my mind I was thinking of special rules to cope with near the crest. Perhaps you’re ahead of me.
I’m puzzled by what “A round hill would have multiple crest lines all around” means. I look at a real round hill and see one crest line, the virtual crest crossing the peak. I call it a “virtual” crest because if I move 20 metres around the hill, there is still only one crest, but its location shifts as my point of observation changes, and continues to shift as I walk further. As I see it there is no fixed crest line on a round hill.
I suspect that more realistic modelling would make the situation more complicated, not less. I’m struggling to find a good system for just two shapes of hill. 🙂
Steven,
I would see the “dead zone” as providing cover and so either making the unit invisible or harder to see / spot. The reverse slope being the side of the hill away from the enemy.
I’m thinking here of say a French unit crossing the crest of a hill to discover a British unit previously invisible; so even if (as in some of your examples) there was a theoretical line of sight over the crest, if the unit was close to the actual crest, it would still be hidden. If further down the slope, then possibly slightly visible from a flank.
Or if on the military crest in front of the actual crest, then invisible until close up; I recall reading something in the Spanish American War (but may be mis-remembering) something to do with digging trenches on the actual crest, not military crest.
https://en.m.wikipedia.org/wiki/Military_crest
So less visible as not silhouetted against the skyline.
The round hill is difficult to express clearly. You had an example where by judicious positioning, a unit was visible. The hill had a single crest line drawn across it. I would argue it should have multiple crest lines – which is like you say when you talk about it moving depending on your viewpoint- the point being until you get to the top of that hill the only other way to see a unit is by being on the same physical slope as them.
Not sure that expresses it any better.
Neil
Thanks Neil, that helps.
I like the link on “Military Crest”. I’ll keep that in mind.
So the “dead zone” is an area of limited visibility, where the reverse slope makes the target invisible. Got it. This is probably covered by a phrase along the lines of “any part of the stand is across the crest”.
British tactics in the Peninsular are much on my mind as they relied on hills and crests. As I understand it, they deployed about 30 yards down the reverse slope then hammered the French when they came over the crest. And the British favoured ridges.
I think a rounded hill – a dome in my language – has an infinity of crests. That is why I resist drawing pre-defined crests lines on them. There is no single crest line; nor are there a predefined set of crest lines. There is an infinite number. This is exactly whey I’m exploring geometric solutions to the visibility problem. So for a particular observer and target I can determined if the hill blocks line of sight, or not.
And…visibility would be rightly mostly to front and side, more often than not done not by the entire unit but by a few officers standing out on horse/ skirmishers. In which case sideways orientation should not have an impact. Again it mopight vary with ground and time scales.
I have to say with all these rules that I personally have always had an issue with “moving” crests of any kind, never mins the geometric exercise in the midst of a battle.
For purposes of fun and quick resolution of Line of Sight, but an actual crest line on the hill (all the way across, only partially, of any length). A but if string or yarn would do.
A unit’s base that is on the hill and overlapping the crest is on the hill top and can see and be seen by everyone. A unit’s base that is on the hill but not on the crest line can be seen by any unit that can draw a line from the front center of its base to the front center of the opponent’s base (even if the opponent is rear-facing, just draw it to the center front). If that line crosses the crest line, no los. If it does not, there is line of sight.
You can even have multiple crest line without any great difficulty. But more importantly to me, the crest lines are fixed, and not some amorphous thing that a defender, by moving around the hill can change where the crest of that hill is. Military leaders have to do the opposite and figure out where the crest actually lies and adapt to it.
However, if the desire is not to have to work with crest lines on the table, I think your approach is a good one!
Chris, to my eye, my “dome” hills do not have an actual, fixed crest line. The effective crest line is entirely dependent on the position of the observer. I could impose artificial crest lines on my “domes”, but that seems unnecessary. Ditto for the end of the ridges.
I think military leaders were conscious of this and knew that deploying “behind” the crest is relative to the approach route of their enemy.
I really love your insightful thought into all these matters, Steven! I was remiss in not thanking you for your blog and your posts which I have followed for several years now.
I know that you have dome hills in your collection, but I was wondering how common they are as actual features? In my experience – and no, I don’t have much – most hills are irregularly shaped with irregular cresting points and almost never are a nice, smooth pi ratio and that’s what I meant with my comment.
Militarily, certainly you want to be on the hill facing the enemy, but I always though that the crest line of a hill (or more commonly crest line of a ridge) was a geographical fix point or feature, not at all reliant upon the relative position of the enemy . . . but I think now that perhaps I am thinking more along the line of long, gentle hills and long(er) gentle ridges and perhaps I am the one that is out-of-sort.
My immediate thinking was the various hills and ridges around the Battle of Gettysburg, one of the few battlefields I have visited. The “hills” and “ridges” and “crest lines” there are mostly slow, gradual rises to higher elevation until the ground drops off behind the top of the hill, and the arrangement of the landscape is very much dependent on prohibiting the enemy from assaulting the ends of the ridge, which would provide no real defensive benefit other than “being uphill” and “being able to see all around you on the battlefield” . . . both important to be sure, but those “ends” or “flanks” of the ridge would not be useful for concealing oneself from enemy or protecting against defensive firing.
In any case, thank you so very much for your commentary and insightful analysis. You have clearly thought about these facets thoroughly and I appreciate you perspective!
Chris, thanks for the nice words on the blog.
Even my simple wargaming collection of only two types of hill (dome, ridge) is not simple to simulate effectively.
Having said that, ridge lines are easy. I think this is why most wargaming rules focus on “predefined crest lines”. Draw a line on the hill. All good.
This post is about the not so easy situations of my two types of hill. I focus on domes here, with a peak and rounded slopes. But the same problem/solution applies at the ends of ridges, where there is no ridge line and only rounded slopes. What to do when there is no clear ridge line?
There is a point where reality and wargaming separate. People who want more realistic hills go for geo-hex solutions where contour lines can be lovingly crafted. Of course they have to tackle the issue of visibility and I don’t know how they’d do that because I’m not one of those geohex 3D types.
I use scatter terrain as part of my general “cartoon” approach to wargaming. Simple, robust, easy to store, and good enough for a game. I suspect the majority of wargamers are like me, using scatter terrain. And for those wargamers the majority type of hill is a dome. So I want rules that deal with domes. Whether or not they exist in reality, they exist on table. Often.
As it happens domes exist for real. I’ve walked over some and historical battles also featured them. The battle of Maipo, for example, features a large triangular dome. The hill exists and was significant in the battle. I’ll also cite Vargas Swamp even though the battle was fought at the end of a massive ridge. The ridge was kilometres long and because it is so long the battle was fought on the rounded slopes at the end. Effectively this was steep but continuous slopes leading up to a peak where the Royalists had their HQ. In my abstraction this behaves like half a giant dome.
This is all about wargaming with abstractions. Most of my gaming is at 1:1000 scale and at that scale a lot of detail just evaporates. So I’m not modelling every single undulation on the hill, I’m modelling the presence of a hill that generally speaking has a peak and rounded slopes. That is close enough and good enough for a game.
Nor do I bother modelling every contour line. I simulate the key heights that make a difference to the battle and that I can represent using my collection of wargaming domes and ridges.
It is horses for courses and some people will seek more precision. My mate Chris would model every single contour line. I know as I saw his 1:300 scale set up for Battle of the Rapido river (January 1944). Amazing; should be in a museum. Just not what I’m going for.
You mention Gettysburg, and waterloo is another one of those battlefields with “mostly slow, gradual rises to higher elevation until the ground drops off behind the top of the hill”. Standing where the French deployed there is no visible hill. Only if you walk to where the British deployed and look back you realise there is a rise at all. Luckily I’m not attempting to fight Gettysburg or Waterloo. If I did, the scale of the game might mean I ignore most of the hills and ridges and only simulate the key terrain, perhaps with a stand alone crest line borrowed from my Crossfire terrain.