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.

**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:

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.

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.

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