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Doctoral Program

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The Doctor of Philosophy (PhD) degree is intended primarily for students who desire a career in research, advanced development, or teaching. Students in the PhD program obtain a broad education in the core areas of Aeronautics and Astronautics through coursework, while also engaging in intensive research in a specialized area, culminating in a doctoral thesis.

Minor in Aero/Astro

A student who wishes to obtain a PhD 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 PhD Reading Committee and University Oral Committee must each include at least one faculty member from Aero/Astro.

PhD Qualifying examination (Quals)

Before beginning dissertation research for the PhD degree, a student must pass the departmental qualifying examination. Admission to Stanford University for study beyond the master’s degree does not imply that you have been admitted to candidacy for the PhD — that special designation is reserved for students who have passed the department’s PhD Quals. After passing the exam, the student will then need to submit an approved program of PhD course work on an Application for Candidacy for Doctoral Degree (PDF) to the Student Services Office.

The purpose of the PhD Quals is to evaluate your capacity to perform outstanding research and that you are adequately prepared to undertake the research. The basis of this examination is a series of oral examinations given in the four fields of dynamics and controls; fluids; structures; and applied mathematics and computation. 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 decision on the qualification of each student for the PhD program is based on the student's:

  • Ability to assimilate knowledge.
  • Aptitude for independent thought.
  • Fundamental understanding of the basic principles.
  • Potential to conduct research.


All Ph.D. students must attempt the department qualifying procedures by the end of their second year of graduate study to remain in good standing in the Ph.D. program. The Aero/Astro Ph.D. Qualifying Examination is given once in the Autumn Quarter and once in the Spring Quarter, usually in the second week of November and May. Exact dates are announced several weeks before the exam. The Application for the Aero/Astro Ph.D. Qualifying Examination is made available early each examination quarter, with the application deadlines early in April and October. The application must have the signed approval of the student's proposed Ph.D. advisor.

General advice for Quals research:

  1. Be sure that the faculty member understands your timeline for taking the qualifying examination - the type of project and level of interaction may differ from a simple "let me try this field" AA 290.
  2. If the supervising faculty member is not in the Aero/Astro Department, you should consult with the Aero/Astro Student Services Office and your Aero/Astro advisor in advance to ensure that this research will meet the Quals requirement.


A student in the Aero/Astro MS program who wishes to pursue doctoral study must take the qualifying examination in autumn or spring of the second year. A PhD student who did not study in our MS 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 PhD program. All petitions to waive specific Quals conditions or to defer the exams must include advisor signature and appropriate documentation.


To be eligible for the Aero/Astro Qualifying Examination, a student must meet the following conditions by the appropriate deadline.

  • Current enrollment in a graduate program at Stanford University with at least 30 units of coursework completed.
  • The candidate should have the official commitment of one faculty to advise them. There is no explicit requirement regarding having taken one or more AA290 classes with the advisor.
  • The student must take two courses in each of three core areas. The three core areas must be chosen from the following list of four core areas: Controls/Dynamics, Fluids, Structures, and Applied Mathematics and Computation. The average GPA for these classes (considering, for any waived courses, the Stanford grade obtained during the course waiver exam, which is recorded by the AA Student Services Manager) should be higher than or equal to 3.8. Furthermore, the overall average GPA should be higher than or equal to 3.5.
    • Students can waive one or more of these classes by following a two-step process: (step 1) showing that they have taken a sufficiently related class at a prior institution (which needs to be certified by the AA Director of Graduate Studies) and (step 2) taking an exam for each of the classes the student desires to waive and achieving a grade of A or higher (the instructor can handle the exam in the form of their choosing, e.g., through an oral exam or a written exam).

Qualifying Examination core courses per area:

Controls and dynamics

  • ENGR 205: Introduction to Control Design Techniques
  • AA 242A: Classical Dynamics


  • AA 200: Applied Aerodynamics
  • AA 210A: Fundamentals of Compressible Flow


  • AA 151: Lightweight Structures
  • AA 240: Analysis of Structures

Applied Mathematics and Computation

  • AA 203: Optimal and Learning-based Control
  • AA 214: Numerical Methods for Compressible Flows
  • AA 222: Engineering Design Optimization (CS 361)
  • AA 228: Decision Making under Uncertainty (CS 238)


The Application for the Aero/Astro Qualifying Examination serves as the basis for exam scheduling. The application form is made available early each Quals quarter and is due approximately two weeks later. The application must have the signed approval of the student's Ph.D. advisor.

All petitions (to waive specific Quals conditions or to defer the exams) are due prior to the start of the Quals quarter (deadline announced); they must include advisor signature and appropriate documentation.

Examination procedures

  1. The candidate student will be examined by 3 faculty members (advisor not included; the advisor may attend the exam session as a “silent observer”). At least 2 of the faculty should be AA faculty (no courtesy). The student, in consultation with their advisor, will provide a list of suggested examiners (at least five, ranked in order of preference). The AA Student Services Manager will determine the final list of examiners, based on the provided list and faculty availability.

  2. The advisor submits a one-paragraph recommendation of the student to the examiners. The recommendation will inform the discussion and evaluation of the student at the end of their exam.

  3. The student is asked to prepare a 30-minute presentation based on their research work. The presentation should clearly address the following points:

    a. What is the research problem? Why is it hard? Who does it impact?
    b. What is the state of knowledge in the field today? What are the limits of current practice? c. What is the new technical idea? Why can we succeed now?
    d. Are there others dedicated to finding a solution to the problem?
    e. What is the impact if successful?

  4. The student supplies to each examiner a 1-page report summarizing the student’s research project and a plan for the Ph.D. The report is due to the examiners two weeks before the exam. The role of the report is to give some time to the examiners to familiarize themselves with the student’s research project.

  5. The exam is 1 hour long and is divided in two parts:

    • During the first half hour the student presents the research project. The second half hour comprises a 30-minute QA session related to the research project. During this session the examiners can ask questions related to the fundamental concepts covered during the presentation. This gives the opportunity to the examiners to assess general mastery of the area the student is working on, beyond the traditional confines of coursework. The examiners should make sure that there is enough diversity in the questions asked.

    Qualification decision

    Right after the exam, the examiners meet for approximately 30 minutes to discuss student’s performance, and make one of the following decisions:

    • Pass
    • Pass, with a list of classes the student should take to strengthen their background (at most three); the student should receive a grade of at least B in these classes in order to defend their thesis
    • Fail, with retake option (if first time) or removal of the student from the PhD program (if second time)

    After a decision has been made, the decision should be promptly communicated to the AA Student Services Manager. If there is no consensus on the exam outcome, the examiners will send a summary of the discussion to the Department Chair, who will make the final decision. Exam results will be sent to the student via email by the AA Student Services Manager.

    The student can take the quals at most twice. The first time should be either in the Fall or Spring of the second year; the second time, if applicable, should be the next available Qualifying Examination.

    After the Exams

    A student who passes the Qualifying Examination must file for candidacy before the end of the quarter. A student who fails to qualify may remain in the Ph.D. program only if he or she passes the next available Qualifying Examination. 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 PhD program by the Aero/Astro Faculty Committee. In this quarter, the department will not approve a leave of absence or reduced tuition requests.

    If a student elects 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 in Axess.


    There are two requirements for admission to Ph.D. candidacy in Aeronautics and Astronautics: students must first pass the departmental qualifying exam and must then submit an application for candidacy. The Application for Candidacy for Doctoral Degree (PDF) must be submitted to the Aero/Astro Student Services Office before the end of the quarter in which a student passes the Qualifying Examination. The candidacy form lists the courses the student will take to fulfill the requirements for the degree. The form must include the 90 non-MS units required for the Ph.D.; it should be signed by the advisor and submitted to the Aero/Astro Student Services Office for the Director of Graduate Studies’ approval signature. Aero/Astro uses a department-specific candidacy form, which may be obtained in the Aero/Astro Student Services Office. It is incumbent upon Ph.D. students to request letter grades in all courses listed on the Application for Candidacy form. Students must receive a passing grade, and maintain a minimum GPA of 3.0, on all courses listed on the Candidacy form. Changes can be filed at any time by submitting a revised Candidacy form with advisor's signature, and submitting the form to the Aero/Astro Student Services Office for the Director of Graduate Studies’ approval. In order to graduate or go TGR, you must have completed all units listed on your current Candidacy form.

    Once achieved, candidacy is granted through year seven of graduate study for students completing the M.S degree, or through year six of graduate study for students admitted with an M.S. degree in a related discipline, unless terminated by the department (e.g., for unsatisfactory progress). This term is not affected by leaves of absence. The candidacy end date is listed on the student’s record in AXESS. Students who are unable to graduate before their candidacy expires may submit an extension request for up to one additional year of candidacy.

    Candidacy extensions requests require review of a dissertation progress report, a dissertation draft, timetable for completion of the dissertation, and any other factors regarded as relevant by the department. Students must submit the candidacy extension request before the end of their program's time limit. Once candidacy has expired, registration privileges are terminated and the student will need to apply for reinstatement into the Ph.D. program. Extension requests should be submitted to the Aero/Astro Student Services Office. Note, the department is not obligated to grant an extension, and all requests are subject to final approval by the Aero/Astro Department Chair.

    Course requirements

    Each individual Ph.D. 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. Ph.D. candidates must complete a minimum of 135 units. Ph.D. candidates who received their MS from Stanford may count up to 45 units towards the 135-unit total. Students who received an MS degree at another institution may petition (through the university Registrar’s Office) to transfer up to 45 units toward the 135-unit requirement.

    Of the 90 units required beyond the M.S., a student must complete a minimum of 27 units (including 9 units of mathematics) of approved courses in advanced study in engineering, science, and mathematics (excluding research, directed study, and seminars) beyond the MS degree. These units must be taken for a letter grade, and all courses must be numbered 200 and above. Note: One math course may be taken at the 100 level if approved by the advisor. 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. An advisor approved Ph.D. course proposal must be submitted when applying for Ph.D. candidacy.

    Ph.D. students in Aeronautics and Astronautics must take 3 mathematics courses (a minimum of 9 units), with at least 6 units from courses numbered above 200. The Aero/Astro Department and the other engineering departments offer many courses that have sufficient mathematical content that they may be used to satisfy the mathematics requirement; a pre-approved list of mathematics requirements (PDF) is included in the department's handbook, but there are many others which may be acceptable. Please consult with your advisor and the Aero/Astro Student Services Office before assuming that a particular course will be accepted in your own program.

    Ph.D. Minor

    If choosing to take a Ph.D. minor in another department, a maximum of 9 units from the minor program may be included in the 27 units of formal coursework; the remaining minor units may be considered free electives, and included within the 90-unit total (beyond the MS) required for the Aero/Astro Ph.D.

    Grade Point Average

    A minimum grade point average (GPA) of 3.0 is required to fulfill the department’s Ph.D. It is incumbent upon Ph.D. students to request letter grades in all courses listed on the Application for Candidacy form.

    Dissertation reading committee

    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 Examination. Thereafter, the student should consult frequently with all members of the committee about the direction and progress of the dissertation research. The student’s principal advisor and dissertation reading committee have the responsibility of supervising the research work and insuring that high standards of performance are maintained. Conversely, it is the student’s responsibility to keep their reading committee members informed about their research progress. The signatures on your dissertation represent the final certification of its adequacy.

    A Dissertation Reading Committee consists of the principal dissertation advisor and at least two other readers. If the principal advisor is emeritus or the principal research advisor is not within the Aero/Astro Department, there should be a non-emeritus co-advisor. 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 in special circumstances that must be justifiable, one non-Academic Council reader if the person brings unusual and necessary expertise to the dissertation research, and has no conflict of interest (for example, this person should not be part of the research project or directly associated with the funding authority). Generally, this non-Academic Council reader will be a fourth reader, in addition to three Academic Council members. It is the student’s and the advisor’s responsibility to justify to the Chair why this non-Academic Council member is proposed as a fourth reader.

    The student must submit a Doctoral Dissertation Reading Committee form, signed by each of the readers, to the Aero/Astro Student Services Office for approval by the Department Chair. Approval of a non-Academic Council reader requires submission of a Petition for Non-Academic Council Doctoral Committee Members. Any changes to the committee must be submitted to the Aero/Astro 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.

    University oral examination

    Each Ph.D. candidate is required to take the University Oral Examination after the dissertation is substantially completed but before final approval of the dissertation. The dissertation draft must be in writing, with the expectation the final dissertation will be ready to submit within one quarter of the examination. The student should make available the draft copy of the dissertation to members of the examination committee prior to the exam. The examination itself is intended to verify that the research represents the student’s own contribution to knowledge and to test their understanding of the research. Candidacy must be valid and the student must be registered in the quarter in which the University Oral Examination is taken. The coordination of this exam is the responsibility of the department (primarily the student and advisor). The Registrar reviews but does not participate in the examination. The examination normally begins with a presentation by the PhD candidate during which clarifying questions may be asked. This part of the examination is typically open to the public. After a brief recess, the examination continues in private session, with only the candidate and members of the examining committee in attendance.

    This Committee is comprised of four faculty examiners plus a chairman. The examination should be conducted according to the major department’s stated practice, although it should not exceed three hours in length. A typical exam in Aero/Astro is expected to take three hours. At the conclusion of the examination the candidate should be asked to leave so that the committee can confer in private. A vote is taken and the chair tallies the votes of the members. The Orals Chair should submit the results of the examination to the Student Services Office immediately following the exam. The student’s advisor will notify the student of the outcome.

    The University Oral Examination Form can be found on the Registrar’s Office website. The form must be submitted with a thesis draft to the Aero/Astro Student Services Office at least three weeks prior to the date arranged for the oral examination. The department will provide a (red) folder which includes the exam schedule, ballots, and department and university guidelines for the exam. Note: Students must be enrolled during the quarter when they take their University Oral Examination. If the orals take place during the break time between quarters, the student must be enrolled in the prior quarter. Once the oral examination has been passed, the student finalizes the thesis for reading committee review and final approval.

    Doctoral dissertation

    Please refer to the Directions for Preparing Doctoral Dissertations, which outlines the university guidelines for preparing a PhD dissertation. When the final draft of your dissertation has been completed, make an appointment to consult with the Graduate Degree Progress (GDP) officer in the Registrar’s Office to go over a review of the completion of your PhD program and the strict formatting requirements for the dissertation. Submit the final version of your dissertation to the GDP no later than the dissertation deadline of your submission quarter. 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 "Statement of Completion" in Axess after degree conferral. Prior to requesting a Statement of Completion, the submission must first be approved by both the Final Reader and Registrar's Office. Note: students will receive email confirmation once the submission is approved by the Registrar's Office. This email confirmation will provide instructions for obtaining the letter by essentially logging on to AXESS, and going to the eDissertation/eThesis Center, where it should be ready and available as a link to the student.

    Note: Students may be eligible to petition for a Graduation Quarter during the quarter they plan to submit the dissertation. For details, contact the Aero/Astro Student Services Office. International students should consult carefully with the International Center before selecting specialized registration status because their visas may prohibit it.