When you upgrade a unit to another unit who's base cost is the same (upgrading Light Horse to any of Light Cavalry/Elite Light Cavalry/Hussar is a good example), the cost to upgrade is static--the price is twice the base cost of the unit (Military technologies slightly modify this, but the intrinsic value is still there).

If the unit and its upgrade have different prices (but cost the same materials, e.g. upgrading Cataphracts/Knights to Heavy Knights/Cuirassiers), the cost to upgrade the unit is
Upgrade_Cost = [2 * Base_Cost_of_Upgraded_Unit] + [Number_of_Existing_Units_to_be_Upgraded * Difference_in_cost_between_the_2_units]

(I typed it like that so you could see exactly what numbers are involved.)

In the case of Cataphracts --> Cuirassiers:
Cataphracts have a base cost of 50 Wealth/60 Metal
Cuirassiers have a base cost of 60 Wealth/70 Metal.

Let's say you have 10 Cataphracts (whether already created or in queue) to Upgrade; using the above formula, the values are
Base_Cost_of_Upgraded_Unit = 60 W/70 M
Number_of_Existing_Units_to_be_Upgraded = 10
Difference_in_cost_between_the_2_units = 10 W/10 M

So our formula is:

Upgrade_Cost = [2 * (60 W/70 M)] + [10 * (10 W/10 M)
= 220 W/240 M]

Go ahead and try this with your units (don't forget this works only for units that cost the same materials before and after). If you find this isn't ALWAYS true, let me know and I'll see what I can find out.

As for the case in which the 2 units (upgradee/upgrader) cost different resources, I have a good idea on how it works now, after a little bit of detective work. When you upgrade a unit to one which has at least one resource different than its predecessor, the Difference_in_Cost_between_the_2_units value is half of the resource that of the unit to be upgraded to (rounded down to the nearest 10, if necessary). I think some examples are in order.

Cuirassier --> Light Tank:
Cuirassier base cost: 60 Wealth/70 Metal
Light Tank base cost: 60 Oil/80 Metal
We have 10 Cuirassiers in existence/in queue.

Then:
Base_Cost_of_Upgraded_Unit = 60 Oil/80 Metal.
Number_of_Existing_Units = 10
Difference_in_Cost_Between_the_2_Units = 30 Oil/10 Metal

Everything is pretty much like the second case, (you should easily see where the 10 Metal cost difference comes from) with one exception, the cost difference of 30 Oil. This value stems from the fact that the upgraded unit costs Oil; while the upgradee does not. Thus, the cost difference (of 30 Oil) is added in due to this difference--its value is half that of the cost of the upgraded unit (1/2 of 60 Oil is 30 Oil).

The total cost to upgrade:
Upgrade_Cost = [2 * (60 Oil/80 Metal)] + [10 * (30 Oil/10 Metal)]
= 420 Oil/260 Metal

Another example: Hussar --> Armored Car:
Hussar base cost: 60 Food/40 Timber
Armored Car base cost: 90 Food/40 Oil
Suppose we have 10 Hussars in existence/in queue.

Base_Cost = 90 Food/40 Oil
Number_to_Upgrade = 10
Cost_Difference = 30 Food/20 Oil

The 30 Food cost difference comes from the actual difference in costs between the two units (90 - 60 = 30). The 20 Oil cost difference is half the cost of the upgraded unit (40 / 2 = 20), since the two units cost different second resources.

So,
Upgrade_Cost = [2 * (90 Food/40 Oil)] + [10 * (30 Food/20 Oil)]
= 480 Food/280 Oil

One final example: Carabineer --> Armored Car:
Carabineer base cost: 60 Timber/40 Wealth
Armored Car base cost: 90 Food/40 Oil
We have 10 Carabineers in existence/in queue.

Base_Cost = 90 Food/40 Oil
Number_to_Upgrade = 10
Price_Difference = 40 Food/20 Oil

Okay, I need to explain the price difference (again). Since none of the resources match (Carabineer: Timber/Wealth; Armored Car: Food/Oil), we must use the "half rule" for this one. You can easily see the 20 Oil difference now (40 / 2 = 20), but the 40 Food seems weird. This is due to the rounding I mentioned earlier (if the difference in cost is not a multiple of 10, you must round it down to the nearest 10); so, 90 / 2 =45, rounded down to 40--that is, 40 Food.
(Technical Aside: this is probably due to the way that the game calculates unit costs; the cost for a unit might say 6f/4t; the game then multiplies this by 10 (rules.xml) to get the final unit cost: 60F/40T; thus, I suspect that when it divides the 9f cost by 2; it rounds it down to 4f, then applies the x10 multiplier)

Back on track now, the final upgrade cost:
Upgrade_Cost = [2 * (90 Food/40 Oil)] + [10 * (40 Food/20 Oil)]
=580 Food/280 Oil

So, remember:
Upgrade_Cost = [2 * Base_Cost] + [Number_to_Upgrade * Price_Difference]

The formula is easy except for the final case (different resources).

Hope this sheds some light (at least for some of you) on unit upgrades.

IMPORTANT NOTE: if your values you get from upgrading the units are lowe than what I stated, it is because you have more Military techs than is required to upgrade to that particular unit. In that case, each additional Military tech reduces the upgrade cost by 10% (of the value found out with the formula).

EDIT: Updated the upgrading units that cost different resources section

[This message has been edited by Scot_free (edited 07-12-2003 @ 06:20 PM).]