Scientific
Method for Engineers
Debi Prasad Choudhary
Los Angeles
10/20/2016
As a religious youth, I used to meditate in
front of a picture of Sri Ram every evening while in high school. One day, I
noticed a speck of bright light right in the forehead of Sri Ram in the picture
and was delighted. I told my parents, who were happy and advised me to continue
quietly. I continued the practice of mediation, “as I understood”, for few more
days. But, I used to have doubt about my achievement, because I knew from my
father that getting God is not an easy affair. Many sages were meditating in
forest for “thousands of years” before they could get anything close. My doubt
intensified as time passed by and I started sealing the door and windows. The
light disappeared. I was disappointed but did not tell other about the results.
My doubt and the action to satisfy it was scientific method, but not telling
other fall short of it. Scientific method is essentially investigating the
observed phenomena and describe them with reasonable explanations. When a God
man produces an object by hand waving, the reasonable explanation is simple
magic trick, rather than complex method of producing the stuff from vacuum that
cannot be repeated by any other individual.
Scientific Method in Fundamental Science: Profound scientific discoveries are made by
following this simple method. One of the examples is to describe motion of
heavenly bodies such as planets and objects on earth with the same set of
physical laws. About 400 years ago, understanding the motion of “wondering
stars” in the sky was a mystery. These are untwinkling bright start like
objects in the sky, the planets, which appear to change position relative to
background stars over the years. They appear progressively westward and
suddenly reverse direction. It was clear in early days that these are unlike
the stars and might go around the earth just like the sun. But, such a model was
complex and was not able to predict their path easily. Using precise
measurements of their position in the sky by Tycho Brahe, Johannes Kepler
formulated three empirical laws that explain planetary motion around the sun
that include the earth. Kepler was a religious person and thought God created
the universe following musical rhythm. His devised following three laws to
describe the observations of planetary motion in the sky.
Kepler’s
laws:
Keplers Law 1 (Law of Ellipses): All planets
move around the sun in elliptical orbits with sun in one of it’s foci.
 |
| Figure 1a: Ellipses of different eccentricity e. Ellipse with zero eccentricity is a circle. |
Keplers Law 2 (Law of equal area): The orbital
motion of planets around the sun is such that in equal time interval they swipe
same area of the eclipse. As a result, when the planet is near the sun they
move faster.
 |
| Figure 1b: The planet swipes equal blue shaded area in equal interval of time. As can be seen it moves faster near the sun. |
Keplers Law 3 (Law of Harmonics): Square of
planetary period is directly proportional to the cube of planetary distance.
 |
| Figure 1c: The plot of T2 (planetary orbital period in Astronomical unit) versus R3 (planetary period in years) is a straight line. One astronomical unit is the average distance between earth and the sun (1.496 x 108 km). |
So, even though his laws worked and could
explain the motion of the planets in the sky precisely, it had no universal use
until they were understood with physical mechanism given by Sir Isac
Newton.
Newton showed that two bodies with mass M1 and
M2, separated by a distance R move around a common point in elliptical orbits.
The mutual gravitational force between them is given by:
Fgrav = G (M1 x M2)/R2
Or in case of sun-planet system,
Fgrav = G (Msun x Mplanet)/R2 (1)
Where G is the universal gravitational constant. As the planet goes around the sun (in
nearly circular orbit) with speed v, it
experiences net centripetal force, which can be written as:
Fcentripital = G (Mplanet x v2)/R2 (2)
The orbital velocity v can be expressed as:
v =(2pi
x R)/T (3)
Using these three equations, it is easy
to show that:
T3/R3
= 4 pi2 / (G x Msun) (4)
The right hand side of equation (4) is constant,
same value for each planet regardless of planetary mass. This law is now
universal and can be applied to any two objects orbiting around a central
point. When Galileo discovered the moons of Jupiter, their motion around the
planets could be described by the same equation (4) by replacing the mass of
sun by Jupiter. We can use this formula to determine the speed of artificial
satellites around the earth. We can show that the height of the geostationary
satellites is 35800 km. By studying the movement of remote astronomical
objects, the same law is used to discover dead stars as black holes and white
dwarfs, supermassive black hole at the center of our galaxy, dark matter around
the galaxies and planets around other stars.
Even though the equation (4) can be used to
explain the orbital period of the most planets satisfactorily, precise
measurements of the Mercury, the planet nearest to the sun showed anomalies. It
arrived at the perihelion position (nearest distance to the sun) shifted by 43
arc seconds per century as seen from the earth. Now, we have observed similar
phenomena when two massive compact objects, known as pulsars, move around each other. In
a binary pulsar system PSR 1913+16, the periastron (shortest distance between
two astronomical objects, here pulsars) advance by 4.2 degrees per years. Pulsars
are compressed stars that are produced at the end of the life of massive stars.
The compression is equivalent to keeping the entire sun in a volume of a sphere
of earth. This anomaly of shifting the perihelion or periastron position cannot
be explained by Newtonian formalism. Albert Einstein showed that massive
objects shape or distort the space-time geometry around them, in which they
move. This is the foundation of Einstein’s theory of General Relativity, the
consequence of which is used in modern GPS system to get accurate positions. Apart
from its utility value, the General Theory of Relativity is one of the most aesthetic
discoveries of mankind about the material world.
 |
| Figure 2: Shifting the perihelion positions P1, P2 and P3 of planet Mercury (represented by red blob) on its successive orbit around the sun (represented by yellow blob) |
Motion of massive objects studied by giants,
from Kepler to Einstein, is a perfect example to illustrate scientific method.
The “scientific method” in pure science is essentially searching the underlying
systematics in observations and generalizing them to discover unknown effects.
This is achieved by constantly revising the underlying principles based on new
observations. For example, in case of Kepler’s law, the plot given in Figure
1c, was not same for solar system objects and the moons of Jupiter. This phenomenon
can be explained using the Newtonian version of Kepler’s Law. Einstein’s
discovery of the properties of space-time using the tiny departure of
observations from Newtonian theory is an example of perpetual quest of
scientists for universal principles through intuitive imaginations guided by mathematical
foundations of prior work.
Application
of Science:
Apart from the intellectual satisfaction for individuals, science become relevant
to society when it is applied to improve living conditions. For example, the
Kepler’s Laws are important that opens up our view of solar system but, when
applied to launch satellites, it became relevant for society and government funding
is justified. The story of nuclear fusion is a perfect example of how a simple
quest for understanding a glaring phenomenon can lead to vast engineering enterprise.
In 19th century, astronomers were convinced that gravity is the
dominant force in the universe, so they conjectured that sun is shining by
releasing energy by “gravitational collapse” that last for few tens of millions
of years. By last 19th century, geologists were confident that earth
is much older, as we know today at least 4.5 billion years. There was a need to
explain the source of energy in the sun. In 1920, Sir Arthur Edington, a brilliant
British astrophysicist, presented to the British Association for the
Advancement of Science by using the measurement of mass difference of hydrogen
and helium that sun could shine for 100 billion years by converting 0.7% of
mass equivalent energy in accordance with Einstein’s mass-energy relationship.
In 1939 two astrophysicists, Subrahmanyan
Chandrasekhar and Hans Bethe, working independently, quantitatively showed the
processes of gravitational collapse and nuclear fusion as the source of energy
in the sun and stars. After this great achievement of intellectual
gratification, the question was if we can use this physical process in earth.
When so much energy is released in a tiny volume, that can be used as weapon
and source of useful energy. Following the second world war and success of atom
bomb, Edward Taylor of Manhattan Project worked on the problem and designed
hydrogen bomb that is several times more destructive than atom bomb. This
design required achieving the fusion reaction by bringing the deuterium nuclei
very close to each other in a small volume unlike in the sun and stars, where this
happens due to gravitational force. The conventional atom bomb is used to
implode a container with deuterium to achieve this condition where energy is
released in a uncontrolled fashion. The next step is to achieve controlled
thermonuclear fusion that would be the source of useful energy for our daily
application. This is not straight forward and needs several engineering
research along with understanding the behavior of high temperature hydrogen
plasma in a container. This is one of the hot research topics of contemporary
physics and engineering at several leading centers around the world.
Use of electromagnetic signal has been the predominant
single most important contribution of fundamental science facilitated by
engineering research. In 1865, with the publication of Dynamical Theory of Electromagnetic
Field James Clark Maxwell demonstrated that electric and magnetic field travel
through the space at the speed of light in the form of waves, where these two
fields vibrate in orthogonal planes that lie in plane perpendicular to the
direction of propagation. Starting in the beginning of 20th century,
major effort is spent in using these waves for communication and other variety
of application. This story illustrates the scientific method in engineering research,
which is close to use in our daily life is the development of electronics from
Vacuum Valves to IC circuits leading to the design of Apple by Steve Jobs, that
incorporated both science and art. Vacuum tubes, invented by John Fleming in
1904, were used for half a century to receive, amplify and transmit by manipulating
them for variety of purposes. Thery were replaced by solid state semiconductor transistors, invented by John Bardeen
and Walter Brattain in 1947 for which they received Noble Prize.
Since than technological research made it possible to produce devices that are densely
packed with components exponentially as shown in Figure 3.
 |
| Figure 3: Density of components in electronic device as a function of time. |
These two
examples illustrate the similarity and difference between methods in the field
of fundamental science and engineering. The similarity is in both fields the
approach is to work towards finding solution to a problem and build models that
explain the observations. The difference is in selecting the problems. In case
of fundamental science the problems are related to investigate natural process
irrespective of their utility value. In
engineering research, on the other hand, the utility factor is prime.
Regional
and Economic for Engineering Research: While the fundamental science is universal and
driven by pure curiosity, engineering research is primarily driven by
application. The applications are always derived from experience and hence
regional. So, engineering research would mostly benefit if they are driven by
regional needs. Global needs definitely drive engineering research, but such
work may not be suitable to all organization. It is possible to invent products
that has global market value. While Dr. C. V. Raman was giving a tour of Raman
Research Institute to Mahatma Gandhi, one of his associates asked if the
institute can engage in improving Charakha (that span threads for making
cloths). This might sound funny, but that is what should be inspiration for
engineering institutes to work on the local social needs. Princeton University
campus proudly display a bridge that was designed by the undergraduate student.
Let us discuss some possible ideas that are especially relevant to developing
countries.
Water Management: There is a water
shortage in rural and urban habitats in developing countries. In many places in
developing countries, for example in Odissa, there is draught followed by flood. The
ground water level has been receding. In smaller towns, where there are
locations of public distribution of water, the water flows from public taps
uncontrolled. These are some of the problems a casual onlooker could gather
without much effort. The scientific method for engineering research is rooted
in these observation.
The problem is glaring, but the solution would
be complex. The first step is to isolate a problem that can be solved with reasonable
effort. This step can be called as the Project
Design. Let us say, we want to find the solution for ground water level
depletion in a specific location. This step is very important; it defines the problem. Once the problem
is well defined, we need to gather all relevant information related to this
problem. We need to know the amount of rain fall over past couple of decade in
the area and adjacent locations. We need to know how much water level has been
depleted in past decade. Associated with this, we need to know the water usage
pattern of the habitants, water discharge through the rivers and cannels, the
depth of the rivers and cannels, number of open wells and ponds that store
water and charge the ground aquafer, water usage in agriculture, forest
coverage etc. This phase can be considered as background research, since all these factors contribute to the
water management of the area. The next step is to specify the requirements for the solution. Let us say, the goal of
the project is to solve a part of water crises by supplying enough water for
50% of needs from natural resources and charge ground water. The last step to
complete the project design is to outline a solution after weighing various
options. At this stage, the best practices for such problems should be studied
carefully. In our example, the goal can be filling the existing ponds or
creating new one. Identifying aquafers and direction water streams to recharge
ground water. Once the outline is prepared, the next step is to create an implementable mini project
and examine if it works. May be one or two villages can be taken for such a
study. Learn the problems that must be
improved. Finally, the project must be continuously revised and improved on
existing infrastructure. While this is an example, most such engineering
projects are based such steps. The key to success for engineering projects is
to divide the problem to smaller units and solve them in an integrated fashion.
The difference between the approaches in
basic science and engineering is that of objective of explaining the
unknown phenomena and using known explanations in an efficient manner to solve
a problem. On completion of the project, writing a report is the final step
that helps others in the field and verify what is achieved.
While the problem described here is a common problem
that can be found in most regions, engineering research generally adopt two key
steps design and implement. When an engineer is equipped with frontiers of
basic science, they can do great discoveries. The story of discovery of cosmic
microwave radiation by Penzias and Wilson in 1964 is an excellent example, for
which they received Noble Prize in 1978. On the other hand, the discovery of
blue Light-Emitting Diode by Isamu Akasaki, Hiroshi Amano and Shuji Nakamura received
Noble Prize in 2014, which is an excellent illustration of technological
invention based on the urge to know basic physical laws that govern
material properties. There are several technological innovations such as CCD
detector, fiber optics communication and Liquid Crystal received Noble prize. These
achievements require engineering skill and knowledge of basic physical
principles.
Finally, in engineering research the projects
are essentially application oriented and require team work. While the leader
must have the vision of the goal and a clear path to achieve the same, the
project should be divided in to smaller units that can be handled by subgroups
of individuals in a timely fashion. That would be the key to success and an
vital part of engineering research.
Home work:
1. Write an essay on the evolution of electronic
devices from vacuum tube era to the modern time.
2. Design an ideal village that could be self-sufficient
and sustainable.
3. House building is a problem in many
developing societies. Use of bricks and cements and agriculture land and
destroy the environment that is unsustainable in long term. Write a project for
a possible solution.
