With a nod towards @mrrgl's answer, I have a question.
As a person not intending to spend real-world money on Spiral Knights (nor do I typically carry enough crowns to buy crystal energy), I find myself often running short on energy to experience dungeons past Moorcraft Manor.
Is it possible to somehow make it deeper than 10 dungeons on the free energy? The only answer I can come up with is to leave SK running and let the energy replace itself over time while idling in game…but that would involve me having to leave my computer on quite a bit.
Best Answer
While, generally speaking, you are limited to ten floors of a dungeon per day, each dungeon is split into 3 separate Tiers. Each of these tiers starts at a different depth - 0, 8, and 18, So if you have Tier 2 Clearance, you can start at floor 8, and go all the way to floor 20 (no energy costs to access floors 13 and 18).
Likewise, if you start at floor 18 (tier 3 clearance), you can make it all the way to the core, Level 29, and still have 10 energy left over.
The one downside of this is that starting at Tier 2 or 3 costs Crowns (the in-game currency) -- 200 or 500 respectively. However, if you work your way through one gate sequentially - getting to floor 8 the first day, getting to floor 18 on the next, etc. you will avoid having to pay the cost in crowns.
Since gates have an 8-day cycle, this means you will be able to delve all the way to the Core 6 out of 8 days, avoiding the 'tax' for jumping directly into the deeper tiers. Alternatively, just jump directly into Tier 2 and Tier 3 without clearance; the Crown tax isn't that bad, and you will generally recoup your entry fee within the first floor or two.