What ordonnance for what situation?

[Cheetah]

This is what I do, I use demi-cannons two per each army. Canister helps a lot.

Deploy your main line facing the enemy. So far so good. Push one flank a bit forward (I do it with the right), this will be the gun flank. The idea is to position your cannons so that they can give a flanking fire to the enemy troops engaged in shooting with your main line. Of course you have to protect them. I use line infantry (ofc guards are fine too), basically I use my line infantry as a sliding door.

Before battle:

............................................................... -sk-
...........................................................-sk-
.........................................................-L-
.................................................-G-G-
*insert left flank here* -L-L-L-L-L- -L-L-

During battle:

..................................................-E-E-.....-sk-
...........................................................-sk-
...................................-E-E-E-E-..-L-L-L-
.................................................-G-G-
*insert left flank here* -L-L-L-L-L-

Left flank can be anything. L: infantry of line, G: guns, sk:skirmishers, E: enemy. Right flank is deployed oblique to the main line. When the enemy gets close I move up the line inf to close the door in front of the guns.
I have to add that the BAI is not completely dumb, in all battles it attacked my right flank more heavily then it did my left, so prepare to defend your guns. You might lose them to small arms fire even with infantry in front of them but given that these are just demi-cannons IMO it worth the trade. For example last night I got 116 kills with a cannon deployed in this manner (I had canister) and lost 12 men from the crew. Not bad IMO. Ofc after the battle I could refill the crew.

[Prussian to the Iron]

i prefer the 'V' formation.

the best way to use it is to have 3 units of line infantry per arty position. basically, you put 1/3 of your infantry facing perfect straight, then 2/3 loking slightly inward to help protect arty.

[Tillan]

Another disadvantage is the way it shortens the length of your overall battle line, which reduces the opportunities for envelopment. I like a nice envelopment when I can pull it off. Also the AI doesn't always cooperate and march right into the killing zone of the "V." Still, it's a neat idea when it works just right.

Thats the major dissadvantage as far as I can see, yes the guns in a V do have a tendency to shoot up your line, but I dont mind the micro manage involved in stopping that. However, if you are trying ensure there are no survivors that will pillage your lands after the battle, an envelopment is the best way to go. The V doesn't really allow that.
While it is true the AI doesnt always cooperate in running down the funnel, this tends not to matter *to* much, as I mainly use it as a way of protecting the guns, while ensuring they can fire as much as possible. So long as the AI doesnt outflank me, its all good.

[Slaists]

Thats the major dissadvantage as far as I can see, yes the guns in a V do have a tendency to shoot up your line, but I dont mind the micro manage involved in stopping that. However, if you are trying ensure there are no survivors that will pillage your lands after the battle, an envelopment is the best way to go. The V doesn't really allow that.
While it is true the AI doesnt always cooperate in running down the funnel, this tends not to matter *to* much, as I mainly use it as a way of protecting the guns, while ensuring they can fire as much as possible. So long as the AI doesnt outflank me, its all good.

Integrating the guns in a straight line (option # 5 in the formation list) seems to work well too, at least for me and especially in situations when I have more than 2 artillery crews (which is quite rare). It's easier to change the facing of such line than the one of the V formation too.

Speaking of the V formation, there is something about the offensive BAI that allows it to exploit its nag for flanking easily.

Put your army in a formation like this:

|\a_a/|

"a" is for arty, |'s are for line infantry.

For better counter-BAI efficiency, extend the vertical |'s to two units rather than one.

For some weird reason, if the AI faces this formation, it seems to forget about flanking and heads dead center... While it does that, the vertical I's can be "fanned out" for better envelopment.

[Prussian to the Iron]

??? so, you want 2/5 of line infantry facing sideways rather than keeping up fire on the line? ive almost never had a flanknig maneuver by the a.i. with anything but cavalry, and then some infantry if they succeed.

it seems much more practical to have those 2 side units facing on a shallow angle, so they can easily turn, but can also fire on the line.

[Peasant Phill]

I feel we're getting off topic towards artillary placement instead of ordonnance use.

Basicly I had something like this in mind:

Direct fire: use roundshot unles enemy close then grapeshot unles enemy in column in front of your gun.

Arching fire: use ... unles ... unles ....

[resonantblue]

Round shot - use it against bulidings and only when nothing else is in range (it has a longer range than any other type of shell). Round shot is also quite effective if the AI ever gets all its units into a smaller area/ball while moving... round shot will tear through them better than anything else. Also, if you are playing a mod that improves accuracy, round shot on the flank of an infantry regiment/line can be devastating... unlike shrapnel round will go right through as many men as you can put up in front of it. I had one round shot shell wipe out almost half of a full strength infantry regiment - take out most of 2 ranks in one go. On default/vanilla accuracy, I find it's usually better to use shrapnel shot.

Shrapnel shot - if you don't have a large mass of troops bunched together at long range, use shrapnel.

Cannister - should be the choice of shot whenever enemy units are in its short range. One salvo can tear a full strength infantry regiment to shreds.

As has been pointed out, if you're using foot or horse artillery, the best way to use them is to integrate them into your line or otherwise give them clear lines of side from the flanks - horse artillery is especially useful for this as they can change positions quickly. My main field army only uses horse artillery. In my current grand campaign my main field army only has 1 artillery battery (I limit the size of my stacks to increase the challenge) and it's a horse artillery battery - experience level 7 and I'm in the 1730s. You can probably imagine how many men it had to kill to get to that experience level in spite of the occasional casualties.

For howitzers/mortars, I'm not a huge fan. I basically only ever use them in my one specialized siege assault/defence stack. But:

Round - only use it against hardened targets like buildings or walls or if nothing else is in range. The bounce makes round shot kind of pointless to attack troops.

Quicklime / Percussive / Explosive etc - honestly I can't tell the difference in effectiveness, but given that I don't use the howitzer/mortar family that often I'd defer to the opinions of others. I just know that explosive seems to really suck.