Look at page 58, designers notes:
"combines attacks of its chaos warrior handlers and also the chaos steed that pulls it to battle". I find it to be uncertain at best though I must agree. However given the attacks profile of 5, 'handlerS and steed', I find it inferable that it has 3 constituent parts. If that is in fact not true, then I would definitely be swapping for the mark of tzeentch and just keeping my khornate modelled shrine.
Generally, what I do in 8th edition to stop the dragon being cannonball sniped is the following:
1. In 8th edition, if a monstrous target is not slain by a cannonball, the cannonball stops, in addition to that, fences and barricades now stop a cannonball but are destroyed.
2. Place the warshrine sideways infront of the target you want to protect, if you have a mark of tzeentch, this in effect gives your dragon a 3+ ward save versus cannonballs, unless they are really lucky their chances of bouncing it over the top are very very slim, generally 1/6. (it's cheesy, but so is losing a dragon in the first turn to a 100pt unit). I have found that most people won't fire a cannon with the 3+ ward in place.
3. Move the dragon into cover if possible, failing that move the warshrine up it's 8" with the dragon directly behind it. This will put you 16-18" away from enemy units, so in your second turn you can charge and reasonably reliably get the charge off, if it fails simply move the warshrine up again to protect the dragon.
4. Whilst that happens, the hellcannons will hopefully have sniped the enemy cannons, the bonus of this tactic is it seems to provoke paranoia in war machine users, tending to target everything towards the dragon/warshrine, generally without much effect.
5. Engaged versus a hoard unit you can reliably expect it to knock them out quite rapidly with two breathe weapons, thunderstomp, around 13 attacks at S5/6.
6. Knights move up to support, splitting their fire between yet another unit.
The knights, originally were put in a large unit, instead of my usual two smaller units to:
Maximise on blasted standard
Minimise on cost for marks and command.
Sethis is right, my main reason for the dragon is that I love it to bits (stupid logic in a tournament I know!) and have worked to find ways to make it work. Generally I have found its greatest impact is on my opponent psychologically, they tend to spend their entire game trying to counter/avoid it out of fear (being rarely seen even the experienced ones fall for this). With the new breathe weapons I've had it wipe entire units off of the field, I faced an 80 man empire unit and knocked out a good 30-40 of them with the two breath weapons.
In the new rules, dragons don't lose you VP or fortitude unless the Dragon AND the Lord are slain, so in win at all cost games, if it's mortally wounded, it hides behind a building in a corner

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I'm interested to get some comments on my army, which is essentially based around two main objectives: Points denial and target saturation.
With this edition requiring complete annihilation of the enemy unit to score victory points, larger units are harder to wipe off of the table, so by fielding knights in a unit of 9 it's easier for me to keep them alive, than if they were in two separate units (barring lore of metal naturally). One 'counter' I had to the knight issue, was to give a character in the unit the wrath of khorne (2+ ward versus magic). The hellcannons and dragon share the points sink aspects of the knights. This makes the army in general, very hard to score many/any points from, compared to the enemy army in which I can knock out marginal numbers of units and come away with a strong victory.
The second aspect is target saturation, in combat I have virtually nothing to fear, my biggest concern is ranged attacks, by having 4 big and nasty targets, the enemy war machines have a very large number of targets to pick from, making it more confusing and difficult for them to pick the correct target at the correct time.