Should tank divisions avoid defending in dense/rough terrain?

[Beethoven1]

23.5.2 of the manual says:

In dense terrain, the CV of infantry type ground elements is doubled and the CV of AFV and combat vehicle type ground elements are halved

Dense terrain includes Rough, Heavy Woods, Swamp, Mountain, as well as Urban/Heavy Urban.

Also, in 23.8.3, it says:

Units defending in Heavy or Light Urban terrain receive
a doubling of their Combat Value when determining the
winner and loser of the battle. This doubling is in addition
to all other modifiers.
These effects can be summarised as:
§§ Infantry elements double their CV in Dense terrain.
§§ AFV elements halve their CV in Dense terrain.
§§ Infantry elements quadruple their CV in Double Dense
terrain.
§§ AFV elements quarter their CV in Double Dense terrain.

So, my question is, does these mean it is a bad idea to have tank divisions dig in to defend in dense terrain? As far as I understand the above, it is only AFV elements that take a penalty in Dense terrain. However, most of the elements of a typical tank division are not AFVs, but things like infantry squads, mortars, etc.

Does that mean that the penalties only apply for the AFV elements but not for the infantry squads etc within tank divisions?

If so, if you have a choice of digging a tank division in on Clear terrain or on Rough terrain (hills, for example), is it better to dig in on the Clear terrain or on the Rough terrain?

In other words, is the penalty that you take in rough terrain on the AFV elements larger than the bonus you get for non-AFV elements within a typical tank division?

Of course, often/normally you would not want tanks defending the front line in the first place, but there are some times when this may be necessary (e.g. first turns for the Soviets).

[devoncop]

As a real noob I would be interested in the answer too as it is very relevant in the Soviet Winter when advice appears to be to lodge the Panzer Divisions in cities in towns

[TheFerret]

If the manual's wording is accurate then the defender's CV would be better in rough terrain - AFVs have 1x CV (halved then doubled), non-AFVs have 2x CV, versus clear terrain where both have 1x CV. I wonder how significant the combat range effects mentioned in the last paragraph is for attacking infantry and defending AFVs, though?

[loki100]

its an element based rule, so the infantry are treated separately to the armour.

In the player's notes (& my beta AAR) you will see references to how poor the Soviet tank corps are defensively up to the 1944 TOE (with the advice of using a mech/mot brigade as a SU to compensate). That is partly this sort of rule at work where the elements can be treated very differently regardless to their notional formal unit

[devoncop]

Thank you . Good to know.

[tyronec]

If so, if you have a choice of digging a tank division in on Clear terrain or on Rough terrain (hills, for example), is it better to dig in on the Clear terrain or on the Rough terrain?

Taking this as a tactical question rather than a technical one (which Loki has answered):
With a line of tank units they are going to defend better on rough terrain than in open terrain. They will have a higher defensive CV (you can verify the difference in game). Also attacking tank units will have lower CVs.
They will dig in more slowly, so organising defensive forces to create a deep line of fortifications is different to how you might set up once the enemy has made contact and is attacking.
With a mixed line of tanks and infantry, and a mixture of terrain types, then it would usually be best to have the tanks in the open and infantry in the rough. However not always, maybe you want a strong defense on a particular hex or to put a weak unit where they are less likely to be attacked.

[The_Drill_SGT]

I have no idea about the game mechanics, but as a former tank guy, I'd rather be defending a woodline or the edge of city than line abreast on a steppe knowing the other guy has both Air and Arty superiority