Ph.D. in Aero/Astro

In order to be admitted to study for the degree of Doctor of Philosophy in Aeronautics and Astronautics, students must have fulfilled the requirements for the Department's Master of Science degree or its substantial equivalent.

Applicants who have received their M.S. from other institutions may apply directly to the Ph.D. program. Students who are currently pursuing the M.S. in our department and wish to continue for the Ph.D. should submit a Graduate Program Authorization petition form online through Axess at the beginning of their last quarter in the Master's program. Current Stanford students in other degree programs who wish to be considered for admission to the Aero/Astro Ph.D. program will also follow the procedures described above, but will need to submit additional supporting materials; check with the Aero/Astro Student Services Office for details. (See Admissions and Financial Aid: Current Stanford Students.)


The doctoral study program is essentially a specialized continuation of the program for the Master's degree. Each individual program, designed by the student in consultation with the advisor, should represent a strong and cohesive program reflecting the student's major field of interest. A total of 90 units of credit is required beyond the M.S. Of these 90 units, a minimum of 36 must be formal coursework (excluding research, directed study, and seminars), consisting primarily of graduate courses in engineering and the pertinent sciences. The remainder of the 90 units may be in the form of either Ph.D. dissertation units or free electives. Units which were applied toward the M.S. degree cannot be used again. For students who elect a minor in another department, a maximum of 12 units from the minor program may be included in the 36 units of formal coursework; the remaining minor units may be considered free electives and are included within the 90 unit total required for the Aero/Astro Ph.D.

Mathematics: Students who are working towards the doctoral degree in Aeronautics and Astronautics must take 12 units of mathematics courses, with at least 6 of these units taken from courses with numbers over 200. There are many courses offered by the Aero/Astro department and the other engineering departments that have sufficient mathematical content that they may be used to satisfy the Mathematics requirement; a partial list is included in this Guide, but there are many others that may be acceptable. Please consult with your advisor and the A/A Student Services Office before assuming that a particular course will be accepted in your own program.


At Stanford, Ph.D. students must complete the candidacy process and be admitted to candidacy by their second year of doctoral study. There are two requirements for admission to Ph.D. candidacy in Aero/Astro: students must first pass the departmental qualifying exam (for detailed deadlines, see the section on Ph.D. Qualification, following), and must then submit an official Application for Candidacy. This "candidacy form" lists the courses the student will take to fulfill the requirements for the degree. The form must include the full 90 non-MS units required for the Ph.D.; it should be signed by the advisor and submitted to the A/A Student Services Office for the candidacy chairman's signature. Aero/Astro has a department-specific candidacy form, which may be obtained in the A/A Student Services Office.

The Application for Candidacy is due in the A/A Student Services Office before the end of the quarter in which you pass the Qualifying Examination. Changes can be filed at any time by submitting a revised Candidacy form; obtain your advisor's signature and submit it to the A/A Student Services office for the candidacy chairman's approval. In order to graduate or go TGR (Terminal Graduate Registration), you must have completed all the units listed on your current candidacy form.

Candidacy is valid for five years; this term is not affected by leaves of absence.


Before beginning dissertation research for the Ph.D. degree, a student must pass the departmental Qualifying Examination. (Students may be admitted to the Ph.D. program and begin doctoral coursework before taking the Qualifying Exam.) The basis of this examination is a series of oral exams in the general areas of control theory and dynamics; fluids; structures; and applied math and information technology.


The Aero/Astro Ph.D. Qualifying Exam is given once in the Fall quarter and once in the Spring, usually in the second week of November and May. The exact dates will be announced several weeks before the exam.


A student in the Aero/Astro M.S. program who wishes to pursue doctoral study must take the Qualifying Examination in Autumn Quarter of the second year. A Ph.D. student who did not study in our M.S. program must take the first available Qualifying Examination after two quarters of study here. Honors Cooperative students who have enrolled at less-than-fulltime for most of their study should take the Qualifying Examination within two years after entering the Ph.D. program.


Eligibility - A student must meet the following conditions by the appropriate deadline to be able to take the Qualifying Examination:

  1. Current enrollment in the Ph.D. program in Aeronautics and Astronautics with at least 30 units of Master's coursework completed in our department. A student who has completed fewer than 30 units may petition to take Quals.
  2. Stanford graduate GPA of 3.5 or higher.
  3. Investigation of a research problem, under the direction of a faculty member who will evaluate this work as evidence of the potential for doctoral research. The minimum requirement for taking Quals is to complete 3 units of AA 290 before the Quals quarter.


Examinations are given in the four fields of Dynamics and Controls, Fluids, Structures, and Applied Math/IT. Every student is examined in three of these fields: one field for a Major Field Exam and two other fields for Minor Field Exams.

  • The Major Field Exam will be a sixty-minute test of knowledge and understanding on topics selected by the committee, based on the student's chosen area, including fifteen minutes devoted to pertinent mathematics. It will be conducted by a committee of four examiners, chaired by either the academic or research advisor. Committee members should be from Aero/Astro faculty participating in the exams, from the field closest to the student’s specialty. If the student has done significant research in this area with another faculty member however, the student may petition to have that professor on the Major Field Exam committee. Also, for Applied Math/IT, committee members may be faculty from other departments at Stanford who are specialists in these areas.

  • There will be two examinations in each Minor field. Each Minor examiner will conduct a separate 15-minute oral exam. Questions are usually from materials in courses (ENGR 105, AA242A, AA200, AA210A, AA240A, AA240B, courses listed under Applied Mathematics and IT), or their equivalent at other universities, but may cover fundamentals from earlier (undergraduate) courses as well. Examinations are not intended to evaluate course work, but focus on general understanding, aptitude, and assimilation of knowledge. Minor examiners are to be chosen from the faculty participating in the exams in each field.


    • Controls and Dynamics
      • Engr 105: Feedback Control Design
      • AA 242A: Classical Dynamics
    • Fluids
      • AA 200: Applied Aerodynamics
      • AA 210A: Fundamentals of Compressible Flow
    • Structures
      • AA 240A: Analysis of Structures
      • AA 240B: Analysis of Structures
    • Applied Math and Information Technology (IT). Students can choose one sub-area in this field as a choice for a Major or Minor Field Exam.  The exam will be based on two non-overlapping courses selected from a sub-area below.  Additional courses in any sub-area may be proposed with advisor consent, and will be reviewed for approval by the Candidacy Chair.
    • Mathematics of Continuous Systems
      • CME 204: PDEs in Engineering (ME 300B)
      • CME 303 = MATH 220: PDEs of Applied Mathematics (MATH 220)
      • EE 261: Fourier Theory
      • MS&E 313: Vector Space Optimization
    • Linear Algebra and Numerical Methods
      • EE 263: Intro to Linear Dynamical Systems
      • CME 200 = ME 300a: Linear Algebra with Application to Engineering Computations
      • CME 302: Numerical Linear Algebra
      • CME 306: Numerical Solution of PDEs
    • AI / Machine Learning
      • CS 221: Artificial Intelligence: Principles and Techniques
      • CS 229: Machine Learning
    • Stochastic Processes & Control
      • MS&E 221: Stochastic Modeling
      • CME 308 = MATH 228: Stochastic Methods in Engineering
      • EE 278: Intro to Statistical Signal Processing
      • ENGR 207b: Linear Control Systems II
      • MS&E 251: Stochastic Decision Models
    • Optimization
      • CME 304: Numerical Optimization
      • AA 222: Intro to Multidisciplinary Optimization
      • EE 364a: Convex Optimization



    The Qualifying Exam includes a thirty-minute research presentation consisting of a twenty-minute presentation and ten minutes of questions and answers. The research presentation committee will be selected from your major exam area, and will include at least three Aero/Astro faculty members, counting the advisor. We will sometimes also reach out to other Stanford departments for additional examiners. The content of the presentation should be based on AA290, focus on what the student has done, and show an understanding of the research process.
    General advice for Quals research:

    Be sure that the faculty member understands you are doing Quals research - the type of project and level of interaction may differ from a simple: "Let-me-try-this-field" AA290. If the supervising faculty member is not in the Aero/Astro department, you should consult in advance with the Aero/Astro Student Services Office and your Aero/Astro advisor to ensure that this research will meet the Quals requirement.


    All petitions to waive specific Quals conditions or to defer the exams are due the first week of the Quals quarter; they must include advisor signature and appropriate documentation.

    Application forms (including the dates and participating faculty for this exam) are made available early each Quals quarter and are due approximately two weeks later; the application serves as the basis for exam scheduling. The application must have the signed approval of the student's advisor and research supervisor.


    Following the Qualifying Examination, the results will be discussed by the department faculty in a closed meeting. In addition to performance on the examination, the student's research potential and academic performance are considered. FINAL DECISIONS WILL BE RELAYED TO THE STUDENT BY THE ADVISOR. The actual decision on the qualification of each student for the Ph.D. program is based on the student's:

    1. Ability to assimilate knowledge.
    2. Aptitude for independent thought.
    3. Fundamental understanding of the basic principles.
    4. Potential to conduct research.


    A student who passes the Qualifying Examination must file for candidacy before the end of the quarter; doctoral candidacy is valid for five calendar years.
    A student who fails to qualify may remain in (or be admitted to) the Ph.D. program only if he or she passes the next available Qualifying Examination. The Qualifying Examination may not be taken more than twice. A student who fails to qualify after two attempts may remain in the AA-Ph.D. program for one additional quarter. After this additional quarter, a student will be formally dismissed from the Ph.D. program by the Aero/Astro Faculty Committee. In this quarter, the department will not approve a leave of absence or any form of reduced tuition.

    If students elect to formally enter the Engineer degree, they must discontinue the Ph.D. at the same time they add the Engineer degree via the Graduate Program Authorization Petition.


    Each Ph.D. candidate is required to establish a reading committee for the doctoral dissertation within six months after passing the department's Ph.D. Qualifying Exam. Thereafter, the student should consult frequently with all members of the committee about the direction and progress of the dissertation research.

    A dissertation reading committee consists of the principal dissertation advisor and at least two other readers. (If the principal advisor is emeritus, there should be a non-emeritus co-advisor.) If the principal research advisor is not within the Aero/Astro department, then the student's Aero/Astro academic advisor should also be a member of the reading committee. It is expected that at least two members of the Aero/Astro faculty will be on the reading committee.

    Although all readers are usually members of the Stanford Academic Council, the department Chair may approve one non-Academic Council reader if the person brings unusual and necessary expertise to the dissertation research. Generally, this non-Academic Council reader will be a fourth reader, in addition to three Academic Council members.

    The student must submit a Doctoral Dissertation Reading Committee form, signed by each of the readers, to the A/A Student Services Office for approval by the department chair. Approval of a non-Academic Council reader requires submission of an additional petition. The initial committee should be officially approved within six months of passing Quals. Any subsequent changes to the reading committee must be submitted to the A/A Student Services Office for approval by the department chair prior to submission of the dissertation. [The “Change of Advisor or Reading Committee” form requires the signature of anyone who is added to the committee; advisors/readers who signed the original form do not need to sign again.]


    Each Ph.D. candidate is required to take the University oral examination after the dissertation is substantially completed (with dissertation draft in writing) but before final approval of the dissertation. The examination consists of a public presentation of dissertation research, often during a seminar, followed by substantive private questioning on the dissertation and related fields by the University Orals Committee. This Committee is comprised of four faculty examiners plus a chairman. The examiners usually include the three members of the student's Ph.D. Reading Committe. The chairman must not be in the same department as the student or the advisor. (For students who elect a Ph.D. minor, the minor department may require representation on the Orals Committee.) Once the oral examination has been passed, the student finalizes the thesis for Reading Committee review and final approval.

    Forms for the University Orals Scheduling are available in the A/A Student Services Office. These forms must be submitted with a thesis abstract to the A/A Student Services office at least three weeks prior to the date arranged for the oral. (Please refer to "Student Procedures for Scheduling University Oral Examinations.") Note: Students must be enrolled during the quarter when they take their University Orals. If the Orals take place during the vacation time between quarters, the student must be enrolled in the prior quarter.


    For specific information regarding the format and deadlines for submission of doctoral dissertations, please refer to the handbook Directions for Preparing Doctoral Dissertations, available on the Web or in the Graduate Degree Progress Office, which is the office to whom you will submit the completed dissertation. Note: All members of the Reading Committee must sign the dissertation before the filing deadline.

    Mid-year degrees are not officially conferred until the first week of the quarter after degree completion, and actual diplomas are printed only once a year for distribution at the University's Commencement in June. However, students who have submitted the dissertation and have no outstanding Stanford obligations (financial or academic) may obtain an official University "certificate of completion" from the Graduate Degree Progress Office.

    Note: Students who have passed their University Oral Exams in a prior quarter may not need to be registered in the quarter they submit the dissertation, if they were registered in the immediately preceding quarter. For details, contact the Aero/Astro Student Services Office regarding the Petition to Graduation Quarter. Note: international students should consult carefully with the International Center before planning to use a grace quarter because their visas may prohibit it.


    The following is a typical timeline for an Aero/Astro Ph.D. Student.

    • Update AXESS with your address, email, etc. To establish full-time student status, enroll in 8 units (typically: AA210a, 240a, and 242a) – you can add/change later.

    First quarter

    Registration day(s):

    • Come to Durand 250. Receive department information packet, advisor assignment. Meet the central office staff. Attend A/A Orientation events.
    • Meet with advisor to discuss plan of study. Map out tentative plan for entire year, then a more definite schedule for the first quarter. (This quarter's schedule should include a few alternatives.) Discuss Qualifying Examinations, including which courses may be necessary or advisable as preparation, when to do research, etc.
    • Talk with continuing students about courses, realistic workloads, etc.
    • First two weeks: Go to classes; decide which to take; enroll/add/drop via Axess.
    • Between midterms and finals: meet with advisor to review progress, revise plan for entire year, map out next quarter's options.
    • Before finals: Fill out Master's Program Proposal, obtain advisor's signature, and submit to A/A Student Services Office.

    Second quarter
    (also: third quarter of M.S. study, for students thinking about a Ph.D.)

    • Meet with advisor – discuss overall plan, quals preparation, and this quarter. Repeat enrollment process from first quarter.
    • Do at least one quarter of directed research as the basis of quals research evaluation.
    • Talk with several factuly – about the quals, courses, research. Learn to communicate effectively – especially to listen well and to express yourself orally.
    • Join or create a study group to prepare for the qualifying exams.

    Qualifying exam quarter

    1. Repeat class selection/enrollment process. You must be a fulltime student when taking quals.
    2. Petitions are due during the first week of the quarter (to delay exams or to waive a pre-requisite.)
    3. Quals applications are usually available the third week of quarter (the deadline will be announced).
    4. Qualifying Exams usually take place in the second week of November and May.
    5. After passing: submit Ph.D. candidacy form, signed by the advisor. Candidacy is valid for 5 years.


    1. Submit Dissertation Reading Committee form within 6 months of quals
    2. Each quarter: repeat class selection/enrollment process. Enroll in research as well as classes.
    3. Confer regularly with advisor and reading committee about thesis progress.
    4. When the course/unit requirements have been met, file for TGR status.
    5. Schedule University Oral Exams, in defense of the (draft) dissertation. Submit Orals form to A/A Student Services for approval three weeks before the exam.

    Final year:

    1. Plan for commencement. In January, apply to graduate, using Axess. Order cap and gown, etc.
    2. Spring quarter: if dissertation will not be completed before Spring deadline, obtain advisor’s approval on walkthrough petition and submit to A/A Student Services. (See “Annual Events”)

    Final quarter

    1. Apply to graduate using Axess. (If you applied for a previous quarter, you need to re-apply!)
    2. Complete dissertation; obtain signature of all readers; submit to University.

    Annual Events

    • Autumn quarter, registration days: new students attend the Aero/Astro administrative orientation, to find out how things work around here.
    • Autumn, first week: Aero/Astro department orientation. New students meet the faculty; then there’s a party for the entire department.
    • October: AIAA (the Stanford chapter of the American Institute of Aeronautics and Astroautics) fall barbeque - food, sport, fun. Annual quals information session.
    • November: Ph.D. Qualifying Exams.
    • December: Holiday Gala
    • January: of the year you intend to graduate, apply to graduate on Axess.
    • April-May: Commencement information is available for everyone who has applied to graduate during the year. Walk-thru petitions are available for those who wish to participate in commencement a quarter before graduating. Order Cap & Gown.
    • May: Ph.D. Qualifying exams.
    • Early June: pick up cap and gown for Commencement. Course assistant applications available
    • Commencement weekend: Ceremonies, diplomas are distributed, proud friends and family celebrate. Both University and departmental events.
    • August: Course assistant assignments made.


    A student who wishes to obtain a Ph.D. minor  in Aero/Astro should consult with the Aero/Astro Student Services Office for designation of a minor advisor. The minor may be obtained by completing 20 units of graduate-level courses in the Aero/Astro Department, following a program (and performance) approved by the Department's candidacy chair. The student's Ph.D. reading committee and University oral committee must each include at least one faculty member from Aero/Astro.