What does a successful NecTAR application look like This is quite specific question, though, it specificness is largely related to the fact it can only be answered by someone with experience with computational research in Australia.

NeCTAR grants Cloud computing resources, in the form of VM's to Australian researchers.

To apply for resources there are several fields.

The allocation documentation is quite sparse on recommendations for what they are to contain.

The most significant of which is the "Research use case" which has the description: 


  Research use case [Form Box Here] Note: A short write up on how you intend to use your cloud instances will help us in our decision making. 


It's not much to go on.

The box is quite small though it is expandable.
I'm not sure how much to write. It doesn't support rich text or any kind of markup. I am wondering if I should reference my statements (seems awkward without rich text).

Or if I should be describing other avenues of getting compute power attempted etc.

The documentation does note:


  If there are any issues with your request, we will get in touch with you.
  You may be asked to provide more detail about your research or to clarify your technical requirements.


So perhaps what I write the first time does not even matter,
since they will just ask for clarification until I have appropriate amounts of information?

I am really looking for an example of an application that someone has done successfully in the past. Just to get an idea of what it would be like.
I don't have any personal experience with NeCTAR; maybe someone who does will chime in.

But if it's anything like the US and EU analogues I have worked with (e.g. PlanetLab, GENI, OneLab), this information is used mainly 


to collect information about how the system is being used (e.g. to report back to funding source), and
to filter requests that are clearly ineligible (e.g. "I want to host my personal website on your cloud"),


not because they reject some serious, eligible requests based on application details. 

If that's the case here, too, you really don't need to worry too much about what you write. Something of the form


  My research is on X. I will use the system in order to do Y.


should suffice. (If you happen to have a project website, adding a link to it is also nice.)