PhD Engineering Statement of Purpose Example: Really Top-10 Approved!

Last year, my friend Beth was rejected by every mechanical and aerospace engineering program she applied to. This is astonishing, because Beth was (and is) an absolute rock star. This year, however, she armed herself with a new SOP and was admitted…practically everywhere! As of this week, she’s a PhD candidate at her #1 choice university, a top-5 program in the U.S., and her story is amazing. Let’s take a look at her engineering statement of purpose example, see what changes Beth made, discover what a GOOD statement of purpose should include, and hopefully, save you a year of heartache as you submit your own (truly brilliant) applications.

The Transformation: From 0 to 5 Admissions in 1 Year

It always breaks my heart reading stories of blanket PhD rejections. You give so much to this brutal admissions process — one that oh-so-tricky universities love to keep vague. And that’s not even mentioning the fortune you spend on application fees!

The crazy thing is, these stories don’t always involve students who have low GPAs, or who need more research experience. Often, truly excellent students get the same results. That was the case with Beth, who was no underdog. She’s absolutely brilliant. A true rock star in fluid dynamics.

So, what happened over the last year to transform Beth into the success of all successes? Let’s hear it from the applicant herself:

Key Takeaways

1. Her research didn’t change — Beth’s experience is no better this year than it was last year.
2. She was more proactive contacting PIs — If you’re not aware, this is 100% required. Luckily, this step-by-step guide to contacting PIs will make things easy. Otherwise, you’re just throwing your time and money away.
3. She got a scholarship — This is definitely a big plus. Departments love it when they don’t have to spend money. Yet, a scholarship alone isn’t enough to earn admission.
4. She overhauled her SOP — Using our free PhD SOP Starter Kit, Beth completely revamped her statement of purpose to make it more focused on her research questions. What was the effect? Well, as Beth said after getting an offer from arguably the best program in her field:

What Should a Statement of Purpose Include?

Truthfully, this depends on whether you’re applying to Master’s or PhD programs. Master’s applicants should read our Master’s SOP Starter Kit and check out this blazingly awesome Electrical Engineering sample statement of purpose.

For PhD applications, however, every good statement of purpose MUST answer the following four questions:

• What are my research questions? (What problems do you want to solve, in an ideal academic world?)
• Why am I interested in pursuing these questions? (What recent events prompted this new intellectual journey?)
• How will this PhD program help me explore these questions? (What’s your “study plan”? How do you “fit” with the program’s professors?)
• What proof do I have that I’m intellectually qualified to pursue these questions as a PhD candidate? (What are your big academic highlights, your “greatest hits list”?)

I don’t recommend you structure your statement of purpose in exactly that order. But even so, as you’ll learn in the PhD SOP Starter Kit, if your essay did nothing more than answer those four questions in bullet points…hey, that’d be pretty good! You’ll be way ahead of the vast majority of applicants who only answer 1-2 of these questions in their SOPs. (Honestly, most applicants only answer the fourth one.)

Don’t believe me? When asked what a statement of purpose should include, here’s what one admissions committee chair said:

Now, let’s read Beth’s engineering statement of purpose and see if it answers those four, all-important questions.

PhD Engineering Statement of Purpose Example

Turbulence is visually fascinating and common in many natural fluid flows and engineering applications. But, as the renowned Peter Bradshaw succinctly encapsulates, this “invention of the Devil on the seventh day of Creation” is notoriously difficult to predict. I learned this myself while struggling with large-eddy simulations (LES) on a laptop during a remote internship with Gotham National Laboratory. Alongside five years of research experience in experimental and computational fluid dynamics (CFD), the internship showed me that CFD simulations involving turbulence still require immense computational power. Yet, CFD represents a realm of tremendous possibility for engineers, as these virtual wind tunnels enable rapid design and prototyping of vehicles and engines.

By studying turbulent flow physics, and harnessing the plethora of available data to improve both machine-learning (ML) models and other computational tools, I hope to make turbulent CFD simulations more efficient. Leveraging existing data to model complex flows (using simple canonical flows as “building blocks”) reduces the need for costly simulations. At the same time, complementing data-driven models with higher-quality data and physical interpretations will make high-fidelity CFD simulations more accessible and comprehensible to engineers. My career goal is thus to mesh fluid dynamics with ML to make better simulation tools for industry partners, and I hope to do this as a principal investigator at Wayne Aerospace. As such, I am applying to Gotham’s Mechanical & Aerospace Engineering PhD program with funding and support from the Wayne Foundation Scholarship, as I am strongly attracted to Gotham MAE’s expertise in CFD.

At Gotham, I am most interested in working with Dr. Lucius Fox, whose development of generalized turbulence models for combustion specifically aligns with my interests. I strongly believe that ML can quicken simulations by using the large volume of existing data as a base to predict results for new complex setups. To this end, data-driven models have great potential in reactive flows, because of the multitude of scales and species present in such flows. They are extremely nonlinear, multidimensional, and not inherently stable, which means they are expensive to simulate. Meanwhile, the world’s shift towards more sustainable aviation fuels will likely require combustion CFD codes to adapt: more chemical species mean more equations to solve, and better models will be needed to spatially and temporally resolve more complex flows.

However, models must be able to extrapolate themselves to unseen scenarios. This requires careful imposition of physical constraints: turbulent flows are still subject to the laws of nature, despite being stochastic and easy to describe statistically. Therefore, physics-blind models risk being overfitted to the data on which they are trained. I am thus also interested to work with Dr. Viktor Fries on LES and direct numerical simulations (DNS) of non-linear fluid dynamics systems, as such work will provide insights into simulation bottlenecks for data-driven methods, to better target them. My desire to build more efficient models also leads to my interest in Dr. Selina Kyle’s research on reduced-order modeling and optimization for turbulent flows. I think these techniques, including resolvent analysis, will be essential to the future aerodynamicist as they capture underlying modes of fluid structures without needing DNS, which reduces development cost.

I believe my unique blend of experimental and CFD experience accords me the requisite skills and fluid-dynamics intuition to engage in the proposed research. As a freshman supervised by Dr. Talia al Ghul at Arkham University, I visualized [redacted] using laser-induced fluorescence and particle-image velocimetry. Our visualizations, published in an International Fluid Mechanics Journal article (for which I was the first author), looked like those from [redacted]. However, the mechanism underpinning [redacted] was entirely different. When I presented these results at the International Conference on Fluid Mechanics, the multitude of colorful CFD talks sparked my interest in the subject. But our results also revealed some asymmetries in the flow cross-section which were not seen in previous CFD simulations. This showed me that even though experiments are costly and time-consuming, CFD must still be validated. In this manner, my experimental experience remains useful in interpreting error sources and fluid behavior: similar-looking flows may not actually have the same underlying physics, which might not be discernible to a model.

My Master of Engineering candidacy at Empire State University, under Drs. Dick Grayson and Alfred Pennyworth, has also provided me with insight into some intricacies of CFD. We aimed to challenge the [redacted] assumption underpinning wind tunnels and CFD simulations, but faced significant challenges ourselves: high computational costs. We used overset meshing to overcome this, avoiding costly dynamic remeshing and unstructured meshes. Comparing [redacted] and the same [redacted] in a large domain of quiescent fluid, we found some differences in the drag. This affirmed our hypothesis that the two scenarios may not necessarily be [redacted], and an article summarizing the results has just been submitted to the Journal of Fluid Dynamics Research. This showed me that even if a model [redacted] is robust, specific scenarios [redacted] may cause a violation of the constraints [redacted]. We also noticed that convection was highly sensitive to the timestep used – small timesteps were most desirable, which increases our already intractable computation time from simulating a sizeable volume of ambient fluid. Yet, modeling scenarios like the spread of coronavirus particles in a theater may indeed require these large domains and small timesteps. How can we make these turbulent CFD simulations faster and cheaper?

Gotham’s collaborative culture and wide scope for multidisciplinary research make it the ideal place for me to attain the advanced fluid dynamics knowledge and computing skills I need to address that question. I am also drawn to Gotham’s small Ivy League community, as I will benefit greatly from forging closer relationships with bright minds from around the world. Gotham’s MAE PhD will thus propel me towards my goals, and in doing so, further the fluid dynamics community’s common interests in addressing turbulence, the chief outstanding difficulty of our subject.

What Makes This Statement of Purpose So Amazing?

Obviously, Beth’s essay is an intellectual tour de force. She’s a rock star in aerospace engineering and fluid dynamics. She has a clear direction for her research. And, she understands her place in academia. But let’s see how she answers the 4 questions:

What are her research questions? What problems does she want to solve?

Beth’s goals are apparent in every single word of her essay, but two quotations perfectly encapsulate them — her Sentence of Purpose and final conclusion:

“By studying turbulent flow physics, and harnessing the plethora of available data to improve both machine-learning (ML) models and other computational tools, I hope to make turbulent CFD simulations more efficient.”

“Gotham’s MAE PhD will thus propel me towards my goals, and in doing so, further the fluid dynamics community’s common interests in addressing turbulence, the chief outstanding difficulty of our subject.”

She wants to address “the chief outstanding difficulty of our subject.” Man…it doesn’t get more ambitious than that.

Why is she interested in researching these problems?

Beth’s introduction is a perfect example of the “frame narrative” model we teach for structuring powerful statements of purpose. It summarizes her intellectual inspirations via a meaningful “catalyst moment” when her curiosity swelled to a peak:

“I learned this myself while struggling with large-eddy simulations (LES) on a laptop during a remote internship with Gotham National Laboratory. Alongside five years of research experience in experimental and computational fluid dynamics (CFD), the internship showed me that CFD simulations involving turbulence still require immense computational power.”

You might compare Beth’s intro to this equally profound statement of purpose sample, written by a Mechanical Engineering/Robotics student at the top program in the world.

How will this PhD program help her explore these questions?

Beth’s “Why This Program” section is virtuosic. Obviously, it answers Question #3 from the start:

“At Gotham, I am most interested in working with Dr. Lucius Fox, whose development of generalized turbulence models for combustion specifically aligns with my interests.”

Yet, there’s something unique about Beth’s argument. When describing “fit” with certain PIs, most applicants write a paragraph that revolves around a professor’s past research and how it intrigues them. Beth, however, revolves her entire argument around how those PIs are relevant to THE PROBLEMS she wants to solve.

Does this mean it’s a mistake to structure your “Why This Program” section like the outline on the left? Not at all! Many applicants have done so and earned great success. It’s easier, and that’s a great thing when you’re writing 10 different SOPs.

Yet…it’s worth noting that Beth isn’t alone in staying ruthlessly focused on her research questions/problems. Our rock star Mech Eng/Robotics essay above did the same (7 PhD admissions), as well this amazing Biomedical Engineering statement of purpose example (6 PhD admissions).

Success leaves clues, folks. However you organize your answer to Question #3…make sure you stay focused on how this program will help you solve your oh-so-unique and fascinating research questions.

What proof does she have that she’s qualified to chase these problems?

Most of us will read Beth’s “Why I’m Qualified” section (paragraphs 5-6) and shed a small tear at her incredible research experience. But don’t be fooled. This is the exact same profile that got Beth rejected everywhere last year. The simple fact that she HAS big experience isn’t what matters. What matters is how she weaves her credentials into an argument — how she proves she’s qualified to make turbulent CFD simulations more efficient.

Once again, Beth proved this by staying focused on her research questions. The topic sentences of each paragraph make this plain:

“I believe my unique blend of experimental and CFD experience accords me the requisite skills and fluid-dynamics intuition to engage in the proposed research.”

“My Master of Engineering candidacy at Empire State University, under Drs. Dick Grayson and Alfred Pennyworth, has also provided me with insight into some intricacies of CFD.”

Throughout these paragraphs, Beth doesn’t just say: “Hey! Look at me! I’m smart!” In fact, she doesn’t mention anything — not one single thing — that isn’t related to her goal of making turbulent CFD simulations more efficient. If something from her past isn’t related to CFD (I still don’t understand what this voodoo is), she doesn’t mention it. Everything is 100% laser-focused on her ability to solve the “chief outstanding difficulty” of her subject.

Want to be as successful as Beth?

Forget about your long list of credentials, friend. No one cares. Everyone in academia has great credentials. All that matters is whether you’re capable of:

1. Expressing lucid research questions, and…
2. Proving you know how to find answers to them in the next 5 years.

Conclusion on this Awesome Engineering Statement of Purpose Example

I’m incredibly grateful to Beth for allowing me to share her work. It’s a perfect example of all that a statement of purpose should include, and how we should strive to answer those four all-important questions:

1. What are my research problems/questions?
2. Why am I interested in pursuing these questions?
3. How will this PhD program help me explore these questions?
4. What proof do I have that I’m intellectually qualified to pursue these questions as a PhD candidate?

What’s more, Beth’s story should give you hope. Even the best students in the world get rejected. It’s part of the game. Yet, that doesn’t reflect who you are as a person in any way. The best scholars know that grad admissions is a zero-sum game, and that it’s up to you to make yourself as competitive as possible. Beth did that by proactively communicating with more PIs, and transforming her SOP. Now, we want you to do the same.

Want to read more engineering statement of purpose examples? Find them here!

Want to learn the exact steps for writing an SOP as blindingly brilliant as Beth’s?