Coal Bag: Number Crunching Time

There's no denying that the coal bag is a very useful piece of equipment.  It holds 27 additional coal- which is a lot if you happen to be training Smithing, like me.  The cost is pretty low- just four thousand Dungeoneering tokens.  That's only about forty dungeons (assuming one gets about 1000 xp per dungeon).  It's a good deal.
But what I'm going to do here is calculate a bunch of numbers.  Don't worry, they'll be useful.

Mining
50 xp per coal
27 coal slots in coal bag
For bag only: 50*27= 1350 xp
28 inventory slots
For inventory only: 50*28=1400 xp
Coal Bag + Inventory: 50*27*2=2700 xp per filled inventory

Smithing (Smelting part)
Comparing Iron to Steel (Is it worth it to get 2 coal to make steel?)

Iron Bar
Smithing Level+35= percentage change that your iron will smelt into a bar.  Cannot be greater than 80% (level 45 Smithing).  I'll take my Smithing level as an example (50).
50+35=85
85>80 so my percentage change of getting a bar is 80% (which is still relatively low).
But assuming that one smelts an inventory of iron ores (28 ores-28 bars)
28*12.5=350 xp, assuming that there is no loss of ores (highly unlikely, as 20% is still a sizable chance)

Steel Bar
So someone smelts an inventory's worth of steel bars (from ores, 18 coal and 9 iron)
ONLY steel bars: 9 (total number of steel bars produced with inventory full of resources)*17.5=157.5 xp, which is a lot lower than 350 xp (and we're just on the smelting part!)
But for Iron, there is a risk.  For steel, there is not.
Now let's bring in the Coal Bag.
Inventory's worth of resources: (27 coal from bag+9 coal in inventory+18 iron ores)
That equals 18 bars (twice that of the above result), which is 315 xp, which is unfortunately still less than 350.  But compared to the first scenario, this is twice the xp.

Now for the actual smithing of gear.

Smithing (Smithing part)

Iron 
25 xp per bar used in Smithing
Assuming that you lose no iron in smelting: 25*28=700 xp
Add that to the first figure, and you get 700+350=1050 xp per 28 iron ore

Steel
37.5 xp per bar used in Smithing
18*37.5= 675 xp
Add that, 675+315= 990 xp per full coal bag, 9 coal, and 18 iron ore.

Iron would be easier to do for training, but there is a risk factor involved.

Now for the higher tier bars.

Mithril bar

1 mithril ore
4 coal
30 xp
Without Coal Bag: 20 coal, 5 mithril ore is the highest you can get.  Sorry.
So...5 bars*30 xp per bar=150 xp.  That is actually pitiful.
But 50 xp per bar used in Smithing, so 50*5=250.
250+150=400 xp for 20 coal and 5 mithril ore.  Sad.

Enter the Coal Bag.
Full coal bag (27)+10 Mithril ore+13 coal
So that would be 10 Mithril bars.
10*30=300 xp.
10*50=500.
300+500=800.
Now I know to what to train with.

Adamantite Bar (aka Adamant)

1 adamant ore
6 coal
37.5 xp
Without Coal Bag: 24 coal, 4 adamantite ore
4*37.5=150
62.5 xp for each bar used.
62.5*4=250
150+250=400.
Wow.  Just wow.

Add the Coal Bag.
Full Coal Bag+15 coal+7 adamantite ore
7*37.5=262.5.
7*62.5=437.5.
262.5+437.5= 700 xp exactly.

Do you realize yet that the higher tier we go, the less xp one gets with an inventory full of resources?

Runite Bar (aka Rune)

1 runite ore
8 coal
50 xp
Without coal bag: 24 coal, 3 runite ore
3 bars possible, 3*50=150 xp.  Hey, it's the same as the one for Adamant.
75 xp per bar used.
75*3=225.
225+150=375 xp.

Add the Coal Bag...
Full Coal Bag+21 coal ore+6 runite ore
6*50=300.
6*75=450.
300+450=750 xp.

So without the coal bag, making Runite bars is worse than Adamantite, but with the Coal Bag, it gets better.  Strange.

Anyhow, if I were training (as a matter of fact, I am), I would stick to steel, because:
-Higher tier bar-->more coal needed
-Iron ore is easy to get (heck, I can mine it myself)
-Does not pose the risks that iron does.

But for those who happily disagree with what I said (and support Iron):
-Potential to harvest more xp per inventory load (note the word potential)
-Harvesting just iron ore is easier (especially if you're mining it)

Oh, and if you ever need iron, go to a populated world and then go to the Al Kharid Mine (the one with scorpions).  There's bound to be some Mining pure dropping iron ore at some time.

~ReconnaisX