Proposing a research project when contacting potential supervisors before master’s admission?
Your assessment of the situation is accurate: Faculty members usually have very little time to spend on your e-mail and likely do not like to wade through a project proposal just to assess your introductory email. However, your proposed project could be a decisive asset – be it only by showing your commitment.

With that in mind, you can write a short email declaring your interest and mentioning your project in one sentence, like you suggested. However, add something along the lines of:


  If you wish to know more, please find a sketch of the project appended.


(… and append your project). This way, the addressee can read what is essential in a minute, and if they decide that they wish to know more about your proposal, the information is already at hand.