It's a public university, but like you said above, we will likely comply with the rules to avoid anything like that. Is the COA the same thing as the 333 exemption? What would applying for several at once help? Also, which one is the one everyone gets? And which ones would give greater freedom for research? Are these different applications, or would they just be specifications I make on just one application. As for the rest of it, I believe I will be able to do that fine, so that shouldn't be a problem. I apologize for all of the questions, this is just a confusing process to me and I'm trying to figure out exactly what's going on. I looked through the website and the exemption details and it was difficult to understand some of it. Thanks for your help.
So much misinformation, so little time.
The FAA considers research by universities as commercial flight. There have been drone programs at some schools that had to curtail their flight operations. Nateweger's suggestion applies if the university is state owned and the state conducts civil aircraft operations under the statutory definition of "public aircraft," in Title 49 of the United States Code (49 U.S.C.) §§ 40102(a)(41) and 40125 (the statute), then you might be able to fly a small UAS without an airman's certificate.
Advisory Circular 00-1.1A - 'Public Aircraft Operations' may help you to determine if this could apply to your intended use. The odds are not in your favor because the flights have to be for state business purposes.
Anyone may apply for and receive an FAA Modernization and Reform Act of 2012 Section 333 exemption which exempts an operator from some FAA regulations which would prevent using a small UAS for commercial purposes. However, the person controlling the aircraft must have a current FAA-issued airman's certificate.
Flying under a Section 333 exemption also requires that a COA (Certificate of Authorization) be obtained for every flight. This can be as simple as an email letter of agreement or as formal as a permanent COA for a flying club. The COA is obtained from the local SDO (Flight Standards District Office) and must be requested no less than 24-hours and no more than 48-hours in advance of the flight and they generally, except for the permanent COA's, expire in 24-hours. Yes, this is dumb and nothing like it is required for manned aircraft. However, you may be able to obtain a permanent COA for your stated purpose. Fortunately, there is also a
blanket COA that all Section 333 holders have that is likely to cover your planned flights.
I would recommend that the school apply for a Section 333 as soon as possible. If you don't already have a specific drone then say in your petition that you are flying a "DJI Phantom". When you do receive your exemption, it's a relatively simple to petition for an amendment to add additional aircraft. Many petitioners have included a dozen or more sUAS models in their petition. Measure, LLC has the record with 324 sUAS aircraft models in their petition.
Hope this helps.