Maths in Science - Don Kinard

Dr Don Kinard is a Senior Technical Fellow with Lockheed-Martin, involved in the development and production of the F-35 fighter jet. His early studies were in chemistry and his doctorate looked at physical (polymer) chemistry. Much of his later work has involved him in engineering, production and manufacturing of aircraft for Lockheed-Martin, one of the world's leading Aerospace companies. 

I was very interested to hear from a scientist who works in one of the most advanced technical industries in the world, to hear how his understanding of mathematics relates to his work as a scientist.

Dr Kinard was kind enough to answer my 10 questions about maths in science.

Here is what he had to say.
 

The Questions:

1. Describe what maths lessons were like for you at school.

I was always pretty good at math but it was generally pretty boring at least until Graduate school.  The lessons taught the mathematical basics but were devoid of substance and application.  I believe that we need to change the way we teach mathematics in schools to illustrate that mathematic formulas and patterns were invented to solve problems or define relationships in the physical world.  Calculus in college is a good example, we learned the formulas and solutions for three years but it would have been much more enlightening and stimulating if we had also learned why Newton had to invent it in order to solve his motion equations.  The first math class that really made sense to me was Differential Equations (here in the US this is taken after 3 years of calculus) where it was taught with an Engineering approach and we solved real problems.  I also really liked Statistical Thermodynamics where I learned how what the equations really meant and how they were derived.

2. Was the maths that you learnt at school useful to you later in life?

Absolutely, although I didn’t really appreciate it until I applied it to my research in Graduate school.   In Grad School I was studying the motion of water molecules in tight cavities such as collagen and elastin along with synthetic polymers.  Water in these tight spaces doesn’t freeze, it turns behaves like a polymer.   I described the behavior using viscoelastic equations and Laplace Transform equations.   Polymer mechanical and solution behavior is also typically modeled using statistical mechanics.  In general I have found that a good knowledge of mathematics is one of the key turning points for young people.  Those that understand it have the entire world of opportunities, those that don’t tend to back away from any subject that utilizes math to any great degree.  I believe that we need to rethink how we teach math and not use it to separate students.  For the past 30 years I have been involved in the design and manufacture of advanced fighter aircraft like the F-22 and F-35.  Much of the work utilizes mathematics in some form or another and although I may not be an expert in any particular mathematical field I find that a solid knowledge of math can provide a great deal of confidence and background when tackling difficult topics and working with the true mathematical experts.

3. How good do you need to be at mental arithmetic to do calculations in your head?

I’ve never been very good at mental arithmetic so it’s hard for me to judge.  What I do well is apply mathematical relationships (a particular variable varies as the inverse square of another for example) to understand behavior of complex systems and to find solutions to engineering problems.  At some point you have to get down and do the math but the relationships are the key to being a scientist and understanding what’s physically going on with your data and observations.  Being a scientist or engineer is sometimes like being a detective, you have a problem and you need to find a solution, you investigate the facts and try to deduce the culprit.

4. Mathematics teaches us that you can put two things together to make a new thing. Is this important in what you do?

Yes, Aircraft are very complex systems where problems or solutions are rarely black and white, everything is an optimization problem.  Often a problem is a combination of issues involving temperature, pressures, chemical reactions, mechanics, vibration, etc.  Again, it’s about relationships.  Systems such as flight controls and hydraulics for example are integrated with the vehicle system software.

5. Mathematics is about finding patterns. Do you need to look for patterns, or exceptions to patterns, in your research?

Yes, patterns are the relationships between system behaviors.  When I was researching composite materials we were looking for relationships between the elasticity of the resins compared with the stiffness of the fibers and the adhesion of these resins to the fibers.  Turns out the resin modulus is key to toughness and damage tolerance but is detrimental to the compression strength.  If you look at some sophisticated avionics like radar the key is to recognize patterns in the data and suppress all of the electronic noise in order to find targets and separate real threats from background noise.  Mathematics is especially important in electronics and electrical engineering where you are concerned not only about the performance of the system but the analysis of the data from your sensors while also understanding the heat generated from the avionics and issues like vibration and stability.

6. Mathematics also teaches us about balance and equality. Is this idea useful in your research?

Mechanics of materials is a good example of balance and equality.  How much load a particular structure will take is a relationship between the basic material properties and the geometry of the structure.  We apply loads to the structure either manually or using finite element analysis and determine if the structure will deform or break.  Another example is applying fluid mechanics to the heat transfer and flow of fluids such as fuel or hydraulic fluid in an aircraft.

7. Mathematics helps us to represent quantities and measurements numerically. Do you do this in your work?

Whether you are calculating and resolving loads on a structure, determining how much fuel you need to get to the engine per second, or understanding the heat that will be generated by avionics it’s all about quantities and measurements.  You measure variables in order to understand the system behavior and many times variables from one system impact variables from another system thus requiring for example a design of experiments approach in order to understand the interactions.

8. Is estimation good enough or do you need to measure things accurately?

Estimation is best when you are trying to understand complex interactions and are trying to determine the most important variables that may be affecting the system.   This could be when you are engaged in advanced design activities trying to come up with new aircraft shapes and you need to use your experience and estimation to help define the solutions space.  When you get down to the actual designs/drawings you need to measure and calculate as accurately as possible.

9. How do you use statistics to analyse your results?

Yes, Most complex systems cannot be resolved directly using basic principles and formulas.  Systems behave statistically whether it’s a strength of materials problem or the span time for building a particular air craft of component.  We determine and calculate the probability of failures of systems in order to determine maintenance frequencies.  We test various batches of materials and do statistically valid numbers of specimens in order to calculate the design-to properties.  We do monte carlo statistics on our schedule positon for example to try and get insight into the variability of accomplishing our tasks on time.

10. Do you have any other insights to offer into how you use maths in your work?

Scientists use mathematics to understand the behaviors of systems and by determining the relationships mathematically determine how the systems will vary as the parameters vary.  Engineers utilize mathematics to take scientific principles and turn them into useful products and services.  My basic philosophy is that mathematics is the language of the Universe (the language of God so to speak) and that understanding math is the key to understanding the universe.  Math is a fundamental tool to scientific advancement and will be more and more important to societies that want to be technological leaders in the world.  In addition there is a basic confidence that comes from really getting the math, confident students will be better able to take on challenges and become productive in their careers.  The US (don’t know about Australia) cannot afford to abrogate scientific discovery and technology to countries like China where much greater percentages of their college students are majoring in STEM (science, technology, engineering, and math) than here in the US.  Without math there is no understanding, without understanding there is no science, without science and engineering there is no future.  Take Global Warming as an example.  Although a vast majority of the science makes it clear that human’s use of fossil fuels contributes to planetary warming (regardless of any planetary cycles), the general public is not sufficiently understand the science to understand the concepts.   Many people simply tune this out and just assume someone else is taking care of it.  This leads to the ability of those that want to diminish the importance of the human impact and support current industries to delay us from taking any real action thus, perhaps, putting everyone at risk.  Science and politics are intertwined, the better we understand science the better we can make informed decisions and insure that our government is taking appropriate action on important issues.

 In his e-mail to me, Dr Kinard had some other interesting comments to make:

Interesting questions Mr. Ferrington; they made me think and allowed me to philosophize a bit.  I am pleased that you are taking the time to collect information on how math is used in the real world to better impress upon your students that math is fundamental to all science and engineering advancement and is literally the key to the future for your students as well as for society as a whole. 


A huge thank you to Dr Kinard for his time and interest in participating in the Maths in Science project. I hope you have enjoyed this interview as much as I have.