Pondering Tanks 'At An Angle' and the 'Glancing Off' Effect

There is usually a mechanism in rule sets covering AFVs & anti-tank fire to determine whether front or side armour should be targeted. In simple terms, attackers want their AP rounds to impact the target AFV as close to perpendicular as possible to reduce the chance of glancing off.

I have seen rules where a line is drawn from the further rear corner and through the nearer front one and extending towards the attacker. Depending which side of the imaginary line the attacker finds itself decides if front or side armour is targeted.
The problem with this is that the proportions of length and width determine the frontal arc: long, thin AFVs like the SdKfz 232 or Churchill to some extent, are penalised by having a smaller frontal armour arc but more square AFVs benefit from a wider frontal arc. This is in spite of most tanks having front & side armour at an angle of about 90° to each other but this method is not often used.

More satisfactory is the common 45° rule applied to the nearest corner of the target AFV. Again, a line is projected forward, this time at 45° to the front & sides and attacker placement in relation to the line determines which face of the target AFV is more 'flat on'.

Both methods treat the target AFV as metal boxes, with no rounded corners such as on the Sherman or Somua S35. By rights, if a rounded corner is hit, the face of the armour may well be perpendicular to the direction of the shell travel but where armoured faces meet may however be effectively thicker and stronger.

In any case, until recently there was a penalty in my rules if aiming at armour presented at shallow angles. This was to penalise attackers aiming at weaker side (and rear!) armour which may be at a far from ideal angle for penetration, thus simulating the 'glancing off' effect. At the same time, although I do not plot the fall of shells as such (or even take sloped armour very much into effect), I did not want to disallow targeting weaker parts of AFVs on some arbitrary principle of angles, if such shots might have been attempted in real engagements.

So in bed the other night, I got to wondering if there was a geometric formula or mechanism to decide the issue once and for all, obviously taking into account the target position/angle and also the relative thickness of front & side or side & rear armour but not the sloping of glacis plates and so on which would be another matter.

As expected, it is a very complex subject.

High velocity rounds (I suppose this could include the 2pdr and 37mm L45  as well as the 88mm Flak, during the France 1940 period) generate a good deal of heat on impact and can penetrate due to the softening of armour and grooving caused by the shell.

If we look at a Panzer III, which had a nominal 30mm of armour front & sides, one of the two faces is going to be presented at somewhere near to 90° to the LOS from attacker, so it doesn't make a lot of difference whether front or side is targeted, using this model. A Panzer IVD with 30mm of armour on the front and 20mm on the side is a different prospect. You would think that having 30% thinner armour on the sides means that shots would be able to strike at slightly more oblique angles and still be somewhat effective. Although there are exceptions, many tanks seem to fall like the Panzer IV into the 1.25 to 1.3 front to side armour ratios (at least in France 1940) but is that enough to justify taking shots at armour which is going to be angled at 45-60°?

I would say for game balance, it is not:

• I haven't done the maths for obvious reasons but my gut feeling is that thinner side armour would only allow 5-10° of extra shooting angle
• There would be yet another stat to look up on the charts, or a ruling could be applied across all AT weapon muzzle velocities and variations of front, side & rear AFV armour
• The game would be slowed down with more fiddling about with odd-angled triangles, t-squares and other obscure implements

Perhaps it would be possible in some 28mm or 54mm 1:1 wargame but on reflection, it's not something I would want to simulate!

Activation Test Skirmish

I've been activating units by drawing counters up until now, which was nice and random and helps the solo player keep track of what hasn't done anything yet in the turn.

However, after a test run of some of Robert's rules at the 2D6 Wargaming HQ, I wanted to have a go rolling for activation for a couple of reasons:

• although I am not sure what, if anything it is replicating in the real world, player selection of unit activation priority gives the gamer a feeling of some control over activation
• it is easier to tweak activation rolls with simple adjustments for unit type & quality and other tactical considerations than it is with card or token based draws, where you can only add extra tokens to increase probabilities

The skirmish itself consisted of PzII, PzIII & PzIV troops plus Schützen platoon vs AMR33, Panhard 178 & S35 troops plus motorised infantry platoon and 25mm AT section. Entry points were diced for and I used the 2D6 Wargaming objective cards (now available in three colours) to generate the German objective of the road junction and elimination of an infantry platoon for the French.

The Panzers swung left immediately to take the dominating high ground as a base to give support to the assault on the hamlet with the road junction. The rest of the German column and the French column (spearheaded by their armour) met head-on at the outskirts of the town, the Panhard armoured cars plugging the gap for most of the game but sacrificing themselves in the process.

The Somuas started a flanking move and found the Panzers. 25mm ATs were sent to the farm to secure the right flank for the Allies, forcing the Panzers into the path of the S35s.

Eventually, the PzIIs made a dash along their right flank distracting a screen of French infantry away, while the Schützen attempted a left hook around the battlefield to drive off the anti-tank guns and to secure the objective. Two thirds of the Allied infantry fell back to the cottages at the road junction.

Morale now starting to crumble, the Panzers were unable to support the Schützen who, although outnumbering the poorly-shooting defenders, could not get a foothold in the hamlet.

Final positions

I will probably now stick to dice activation as it provides more scope for adjustments, is no more time consuming than drawing tokens and makes the game just that little bit more involving for the player(s).

Randomization

Firstly, a big welcome and congratulations to Dale who is the first official follower of my humble blog!

Over on his Solo Battles blog, he has some philosophical musings and a goodly exchange of views in the comments section. One concern is that the turn sequence and other mechanics "changes the way [gamers] think and how they approach tactics, or...how to win the game", suggesting that you might end up exploiting the idiosyncrasies of the rules resulting in an unrealistically played-out scenario.

Some of Dale's ideas and followers' comments made me realize that the simple alternate turn sequence really ought to be improved upon, away from the clunky swinging of a grandfather clock's pendulum to something organic, with more flow, less 'whole army activation', by design giving the feel of engagement action instead of chess moves. Perhaps a bit more like initiative in Crossfire with a frequent shifting of activity from one side to the other to replicate the speed of action in a firefight with seconds (fractions of most game turns) between events and irregular & variable windows of opportunity. You could also try to replicate another player with a programmed opponent with the decisions of one (or both) sides of the game determined by rules.

However, if the player wishes to operate both sides, there are a few game features (some inspired by discussion at Yahoo Solowargames) which could be altered or included to add interest to the solo game:

• Unit activation: With a regular turn sequence, all units activate and complete their actions, then the opposing forces react. Sometimes this entails units moving back in time to where they became, for example, pinned down or destroyed. Having to enact on the gaming table the equivalent of  "actually, because of my dice rolls, that didn't happen" is a little unsatisfactory so I would use single unit activation but allow a reaction and for groups to be activated as opposed to units in the case of a number of units acting together or as one (advancing in line or waiting in ambush for example)
• Specifics of terrain features are unknown until scouted: The penetrability of woods, locations of river fording points and bridge strengths, fields that may or may not give cover due to crops, areas of soft ground or hard going and steeper slopes which may prevent vehicular access, are not known in advance. Also units would only discover if hedgerows were of the twiggy variety (offering cover only) or overgrown dry stone wall type (soft and/or hard cover, including possible AFV hull-down position) until encountered
• Surprise reinforcements: Unless scenario specific, the composition of units is diced for upon arrival on table
• 52 'randomly' triggered wildcard events: Reaching for the regular deck of playing cards instead of dice reinforces to the player that something off the wall is about to happen! It could be an orders glitch, command failing, ammunition, fuel or vehicle breakdown or reinforcements snag, or the event might be a stroke of luck like surprise reinforcements, radio message interception or other intelligence coup, a 'free change of plans' or dice roll bonus. Effects could be immediate or the card could be retained for play later in the game. Possibilities are limited only by imagination (partisans or 5th Column units!) but game balance should not be upset. I mostly use percentage dice in my rules so it is easy to set the triggering probability (any "0,0" or "9,9" occurring, for example)
• Battle-testing of conscripts: If the rules allow for variations in troop quality, the morale of second line or raw recruit units could be determined randomly at first contact
• Random battlegroup composition: The player draws up a few sets of forces for each side to tackle the scenario at hand, then dices to determine which army each uses

Up to now I have only introduced a random element through the use of wildcards but will do a bit of rule writing before the next game.

Rules Tweak: Return to 'Alternate'

After much agonizing I have decided to admit defeat and go back to an alternate turn sequence.

As a solo wargamer, using a simultaneous turn sequence created a lot of work trying to keep track of which elements had fired, or indeed, moved. This in addition to any other complications I decided to build into the rules!

Some rule sets restrict movement to half speed if firing; others apply a large penalty if moving at greater than half speed. (I guess the half-speed rule of thumb is an easy one to remember, not entirely unreasonable and simple to calculate). I tried to amalgamate all ideas into one by allowing most elements to do two actions each turn: fire twice, move twice (a 'doublemove' in other words) or 'fire and move', 'move and fire' or 'fire on the move'. That way, stationary elements get more rounds down towards the target whilst those opting not to fire at all can concentrate on going as fast as possible. So it is possible to 'fire and move off' or 'come to a halt and fire', all within the structure of the turn sequence. Communicating may also preclude firing and single-man turrets (eg French R35, H39 etc) would only get one shot per turn, irrespectively. Unfortunately, to do all this, one must remember (or record it somewhere) which elements might still have a shot left if it is all to happen in the correct order according to the turn sequence. For example, a hidden ambushing element which has watched its prey approach, should have first shooting priority whereas an ambushed tank may well fire last in an encounter after taking evasive action and traversing the gun onto target.

Using an "I fire then move, you fire then move" system, defenders will get reactive fire against any targets which have moved into view and attackers will be prevented from charging towards a target and opening fire at close range without first receiving fire.

In spite of the attractiveness of turn sequence innovations ('initiative through success', it has been described) used in games like Crossfire, I am returning to a more structured method (I was going to say 'simpler' but there isn't anything easier than...not having a turn sequence at all!). By doing only the absolutely necessary number-crunching (which has to be done by me for both sides), I will hopefully be more able to be impartial in my decisions and rulings and have a fuller enjoyment of the game itself.

Rules Tweak: FreeMove Turn Sequence

Had a rare moment of clarity on the way to work the other week and decided to have a go at developing a turn sequence with no subphases. In other words, no "Fire-Move-Fire-Move-Morale-Comms" etc.

I was always attracted to the simplicity and uniqueness of Arty Conliffe's tape-measure-free Crossfire game mechanic. If I have understood this correctly, initiative switches to the other player when or if an element fails in an attempted activity. For example, a player attempts a risky shot, fails and so play switches to his opponent. In this way, a player can keep control of the initiative as long as possible by executing the less dangerous tasks first. Also, elements can move from cover to cover, ad infinitum, should they escape detection and an effective countermeasure.

It is a beautifully revolutionary idea and although I haven't played a Crossfire game I can't work out how certain anomalies would work out. For instance, it would appear to me that an FT17 could be sent way out on the flanks and make it all they way round in one subphase, so long as it was not detected or successfully defended against. So an FT17 can effectively move just as fast as a Panhard 178.

I had been subdividing my Turn Sequence into small, specific subphases and arranging the firing order and certain activities into a strict and exacting order. This worked pretty well but I couldn't stop thinking about some kind of freer system with fewer restrictions where player choice might determine the sequence of play instead of a dice roll, card-based unit activation or rigid firing order.

My initial idea was to allow a player to execute any one (but only one) of the smallest of actions but then there has to be some sort of 'group move' otherwise an advancing line of units would get scattered all over the place. In Crossfire, initiative switches when one fails in an activity (shooting, rallying, etc) but if there is a close-range firefight there is a distinct possibility that all the elements of one side might successfully hit their targets to the detriment of game balance. By reversing the initiative switching to when an action is successful, a player can loose off all his risky shots and only loses the initiative when something goes right.

Holding up the advance

So I had an even smaller game than normal using this method and the section command rules mentioned in another post. It did work but next game I will use an initiative determination tweak I have just thought up.

Rules Tweak: Small Arms Group Fire Rule

With an ever increasing number of foot units (although it is unlikely I will ever have enough compared to my total AFV strength) I decided to devise a method of resolving infantry combat en masse.

I had come across this sort of thing many years ago at the wargaming club in Cornwall when I had a go with a 15mm English Civil War game. I have no idea what rules they were using & I am sure it is a fairly common game mechanic where one has a block of troops attacking another block of troops at essentially the same range throughout.

HMGs are excluded from the method (which I originally called 'Volley Fire') because of their difference in effectiveness both in terms of range & hitting power. Rifle Groups & LMGs (Bren, Hotchkiss, MG34) differ only very slightly in my rules against unarmoured targets so these were all made identical at very little cost to any unique characteristics of the weapons, besides, rifles & LMGs are the standard weapons common to all infantrymen. (AP capability of weapons involved was preserved for use using individual Direct Fire.)

Average probabilities of destroying and suppressing targets for small arms at each range bracket were calculated in an Excel table for ease of calculating the multiples of firing elements and a table of adjustments to these figures was devised for use with the usual percentile dice roll.

Integration with the main rules was complete when I realised that my existing rather unsatisfactory 'Suppressing Fire' rules (which used different mental arithmetic compared to other types of fire) could be replaced with very little adaption by the 'Volley Fire' method.

'Volley Fire' was renamed 'Suppressing Fire' and the whole concept tidied up quite nicely.

Breaking All The Rules

Retrospective: April to July 2009
Sadly, nothing to do with the fantastic Ozzy Osborne song but a metaphor for dissassembling rule sets and brain racking new game mechanics.

My customizing of rules began by simply extracting the data relevant to the period of WW2 I had nowWRG Rules but had separate charts drawn up which only referred to guns used in the Invasion of France and AFV armour data only listed those AFVs in use at the time. Much more Zen, I thought.

become obsessed with, after all I would never need to look up the armour class of a Tiger again! Hurrah! I still used the main text of the

Another aspect of the rules which was not very satisfactory was the probability ranges that threw up statistical anomalies, for example, Gun A penetrates Armour Class X on a roll of 4 on a D6 at ranges of 0-250m, but what if the range was 25m or 249m? Having the same chance of penetration right across the range bracket was too simple, so I began to draw up new charts based on the WRG probability data which had around ten probability brackets from point blank to extreme ranges. Admittedly, within each bracket the probabilities were still flat & linear but the brackets themselves were now a lot smaller, allowing for more detail in my opinion.

Having realised that the fall-off of hit probabilities is similar for, say, high velocity AT guns and similar across a selection of howitzers I then began designing a graphical representation of the 'to hit' chart which simply showed how the chance of hitting the target 'tended towards zero as the range got closer to the maximum range for that firing weapon. All you needed to know was which range bracket the target fell into for the particular firing weapon because at 'extreme range' the chance to hit is the same for a 2 pounder as it is for a 75mm L24. The only difference is that the extreme range bracket for the 2 pounder is, let's say, 1250-1500m but for the 75mm it may be 1500-1800m.
Attempting to come up with user-friendly graphics in 2D did my brain in for a few months until I realised that the problem lay in that you still had to refer to other charts or graphs when it came to armour penetration or destruction of unarmoured targets, unless you had some kind of curvaceous Henry Moore 3D probability model after factoring in the extra variable of target destruction.

The dice-rolling method for recreating probablilities of taking out a target did work, it just seemed a bit pedantic to me. Roll to hit; roll to destroy. You hit the truck but you didn't destroy it. Roll dice; roll some more dice.
Was there a way of using how good a hit you got to determine target destruction? I thought there was, after looking at my childrens' Cuisinaire Maths Rods.
If there was a 60% chance of hitting & a 30% chance of destroying the target, aside from neutralisation, pinning or immobilisation effects, we are really only interested in the overall 20% chance of total destruction.

So that was the major Game Mechanic I finally invented, now all that was left was to somehow convert the WRG data into my single dice-roll system...