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!