While it is important for an engineer to utilise all sensory options to fully understand any challenge, the ability to visualise remains the most vital skill.
So in this article, I am going to talk about a way you can improve this.
It might seem a bit hippy, but it works.
Pretty much everything you do can be improved with dedicated training. From something physical like running to something incorporeal like having compassion for all others. So it would be the same for your ability to visualise.
There is a practice that requires, probably more than anything, excellent visualisation skills.
And that’s meditation.
In some parts of the world, this is considered a daily activity. In others it is thought to be similar to prayer. In much of the West, it is associated with hippies and alternative life styles.
Regardless of how you view it, I am, in this article, going to view it as a cognitive process – and then take from it aspects that are useful for visualisation, and thus engineering.
Because I was raised in an area that had a community with a significant element of people pursuing an alternative lifestyle, I was introduced to meditation and its various tools in my teens.
Later in life, I found that the visualisation skill this developed in me, was perfect for many engineering tasks.
And what follows is the primary technique used to develop this skill. Try it daily if you feel your ability to visualise could be improved.

1. Find a quiet place you can sit or lie down for a period without being disturbed.
2. Relax. If you have a technique you use for this, then use that. Otherwise, Try this:
   1. Close your eyes.
   2. Now focus on the peripheral sounds around you. Slowly work out to the sounds farthest away (not the quietest – the farthest away).
   3. As you do this, think about the greater world and your physical place within it. This will help distract you from other worries so you can relax.
   4. Now focus on your breathing so your breaths become deeper and slower.
   5. You might not be totally relaxed, but you will be in a better position to try the next step
3. Imagine you are sitting in a movie theatre – visualise the colour of the furniture, all the seating, the screen in front, the speakers on the wall, the aisles for people to enter and leave, the exit signs. All the different details – try to see them in your mind’s eye at the one time. It might not be easy, but this is training so you can always come back to it to see it get better.
4. Now imagine the lights going dark so you can see what will be presented on the screen.
5. An image is now projected onto the screen. It is nothing more than a bolt. But you can visualise every aspect of the bolt. The thread, any flash from forging, the shape of the head, the colour. Focus on creating every detail in your mind’s eye. Again, it might not be easy, but this is training so you can always come back to it to see it get better.
6. Keep this image in your mind’s eye for about a minute. You will likely lose the image at times, and you will need to bring it back – this is all part of the training and improving your skill.
7. Open your eyes and remember to do this again tomorrow – until you feel you are better at visualising.

There are many other things you could use meditation for (including engineering) so don’t think the above was meant to be a thorough coverage of meditation. It is simply a training exercise to help you improve your visualisation skill.

Ever since I came across it, I have been amazed by the utility and power of dimensional analysis. While many engineers vaguely recall if from their degrees as “some fluid mechanics thing”, I have used it to assess noise generated by spa pumps; optimise machine elements; augment the Design Of Experiments (DOE); review the potential to change a pressure sensor design; recall a formula in an exam that did not have a formula sheet, but did list key constants and their units; and assess the potential of a universe with different fundamental laws.
Because it can do so much more for engineers than would “some fluid mechanics thing”, it is a tool that any global engineer should master so that they can quickly adapt to new challenges. And that’s why dimensional analysis is the topic of this article.
The Universe Does Not Know What a Kilogram Is
The first thing to understand is that dimensional analysis is not really about units.
That might sound wrong because it is often taught as though it is about units. You check that metres are on both sides of an equation. You make sure seconds cancel out. You confirm that you haven’t added a force to a velocity and hoped nobody would notice.
That’s useful. But it is not the main power of the technique.
The real power is that dimensional analysis gets underneath the units.
The universe does not know what a metre is. It does not know what a mile is. It does not know what a second is or what a kilogram is. These are human inventions. They are labels we use so we can communicate consistently with one another.
But the universe does understand relationships.
It understands ratios.
If a pendulum behaves a certain way, it does not behave that way because we measured its length in metres instead of feet. If a structure vibrates at a certain frequency, it does not care if the mass was recorded in kilograms or pounds. If a fluid produces drag, it does not care if the engineer prefers SI units or imperial units.
The phenomenon is the phenomenon.
Our units are just our way of describing it.
Dimensional analysis works because it forces us to describe physical systems in a way that is independent of our arbitrary measuring sticks. It asks: what are the fundamental types of things involved here? Length. Time. Mass. Temperature. Charge. Maybe a few others depending on the problem.
Then it asks: what combinations of these things can actually matter?
That question is far more powerful than it first appears.
It is so powerful that even if the universe were to reform with different laws, dimensional analysis would still work. The laws might be different, but once there are quantities that interact, those quantities would still need to relate to each other in dimensionally consistent ways.
This is why it feels like cheating.
You can sometimes know something must be true before you know why it is true.
Rayleigh Knew This
This is not a new trick.
Lord Rayleigh used dimensional reasoning in the development of what is now often called Rayleigh’s method of dimensional analysis. He used it to explain why the sky is blue. His method is one of the classic approaches taught alongside the Buckingham Pi theorem, and Rayleigh’s method is commonly described as an early method of dimensional analysis.
In simple terms, Rayleigh’s method assumes that the dependent variable in a physical problem can be expressed as a product of the relevant independent variables, each raised to some power. You then solve for those powers by requiring the dimensions on both sides to match.
That sounds like a mathematical trick.
And in one sense it is.
But it is also more than that. It is a way of letting the structure of reality constrain your thinking before you do any testing. It tells you what forms of relationships are possible and what forms are impossible.
That is the part many engineers miss.
They think dimensional analysis is just something you use when you cannot remember the formula.
But it is really something you use when no formula exists.
Why People Think It Is Only a Fluid Mechanics Thing
The reason many engineers think of dimensional analysis as “some fluid mechanics thing” is understandable.
It is used heavily in fluid mechanics because fluid mechanics is hard. In fact, turbulence is so difficult that even with modern mathematics and computing power, we still cannot simply solve many turbulent flow problems from first principles in the nice clean way we might like to.
So fluid mechanics needed dimensional analysis.
Engineers needed Reynolds number, Mach number, Froude number, Nusselt number, Prandtl number and many others because we needed a way to understand and compare systems that were too complex to solve directly.
This is where dimensional analysis became famous.
But this also created a problem.
Because people saw the technique being used in fluid mechanics, they assumed the technique belonged to fluid mechanics.
That is like seeing a spanner used on a car and deciding spanners are only for cars.
The tool was useful there because the problems were hard there. That does not mean the tool is limited to that domain.
Dimensional analysis can apply anywhere physical variables interact.
Machines. Structures. Heat transfer. Acoustics. Electromagnetics. Manufacturing systems. Biological systems. Economic systems even, if you are careful with what you mean by dimensions.
And that should get your attention.
Because global engineers are constantly being thrown into systems they have not seen before.
Why Scientists Often Do Not Seem to Use It
There is something else interesting about dimensional analysis.
It gives insight without always explaining the mechanism.
That makes it extremely useful for engineers, but perhaps less satisfying for scientists.
A scientist often wants to know why.
Why does the system behave this way? What is the underlying mechanism? What is the causal structure? What is the theory beneath it?
And that is appropriate. That is science.
But engineers often need something slightly different.
An engineer needs to know what to do next.
Can I scale this? Can I reduce this? Can I make this quieter? Can I make this cheaper? Can I make this more reliable? Can I change this variable and get enough benefit to justify the cost?
Of course, the engineer would also like to know why. But if the bridge needs to stand up, the pump needs to be quieter, or the machine element needs to survive another duty cycle, then insight that supports a decision is already valuable.
This might be why dimensional analysis seems underused in scientific research.
I have only seen one paper where dimensional analysis was used in a way that really stood out to me, and I have only heard one physicist talk directly about using it as a research tool. That does not mean scientists do not use it. Clearly some do. But it does mean it does not seem to be emphasised as much as its power would suggest.
Engineers should not make the same mistake.
We do not need to wait until we can fully explain the phenomenon before using the insight.
How Engineers Can Use It
So how should an engineer actually use dimensional analysis?
The first use is to partially solve the relationship between variables.
Suppose you think a result depends on five or six variables. Without dimensional analysis, you might feel you need to test all combinations. That quickly becomes impossible. If each variable has several levels, your experiment count explodes.
But dimensional analysis can reduce the number of variables by combining them into dimensionless groups.
This does not usually solve the whole problem.
You may still need experiments. You may still need simulation. You may still need judgement.
But you need far fewer experiments than you would have needed otherwise.
This is where it works beautifully with Design of Experiments. Instead of designing experiments around raw variables, you can design experiments around dimensionless groups. You are then testing the structure of the phenomenon more directly.
It also works well with simulation.
If physical testing is expensive, slow, or difficult, then simulations can be used to explore the reduced relationship. You can use dimensional analysis to define the form of the problem and then use simulation to fill in the missing functional relationship.
That gives you something very close to a formula for optimisation.
Not a perfect formula necessarily.
But a useful one.
And useful is often what engineering needs.
Finding the Levers That Matter
Dimensional analysis can also tell you which dimensions you can change to get the effect you want.
This is one of the most valuable engineering uses.
Some variables give you much more bang for the buck than others.
If a quantity depends on one variable squared, another variable to the half power, and another variable inversely, then you now know something important. You know where the leverage is likely to be.
This helps prevent wasted effort.
Engineers can spend a lot of time changing things that are easy to change, rather than changing the things that matter. Dimensional analysis helps you see the structure of the problem before you fall into that trap.
It can tell you:

• This variable probably matters a lot.
• This variable probably matters, but weakly.
• This variable might not matter at all.
• This combination of variables is what you should really be thinking about.

That is powerful.
Especially when you are looking at a system you have never seen before.
The Global Engineer Advantage
This is why dimensional analysis belongs in the toolkit of the global engineer.
A global engineer cannot rely only on familiar systems.
You might find yourself working on a manufacturing problem in one country, a maintenance problem in another, a product issue somewhere else, and then a forensic investigation in a completely different industry.
You will not always have the right formula.
You will not always have the right standard.
You will not always have someone nearby who has seen the problem before.
So what do you do?
You start from first principles.
But first principles can be slow if you try to derive everything from scratch. Dimensional analysis gives you a shortcut. It lets you frame the problem quickly. It helps you identify the variables. It helps you reduce the complexity. It helps you see where  experimentation or simulation should be focused.
Dimensional analysis does not make you clever by itself. But it gives a clever engineer a way to move faster through unfamiliar territory.
And that is exactly what global engineering demands.
How to Master It
I cannot explain dimensional analysis fully here.
If I tried, this article would become a textbook chapter, and probably not a very good one.
But I do hope I have motivated you to take it seriously.
Not as something you vaguely remember from fluid mechanics.
Not as a unit-checking exercise.
Not as an academic trick.
But as one of the most powerful first-principles tools available to engineers.
If you do want to master it, then I strongly recommend having Applied Dimensional Analysis and Modeling by Thomas Szirtes in your book collection. The book provides mathematical background, procedures, and a wide range of engineering and applied science applications for dimensional analysis and dimensional modelling.
Dimensional analysis is one of those tools that can change how you see engineering problems. Once you get used to thinking dimensionally, you start seeing hidden structure everywhere.
And it might be one of the easiest ways to start using first principles properly.

There are some things in engineering that are very counterintuitive that, if not fully understood, prevent engineers from doing their best work. These perceived paradoxes can limit or misdirect your thinking such that you are not the engineer you can be. In this article, I am going to share two examples of this and then introduce a maxim that can help you with this.

Example 1 – quality is cheap
The above statement seems very counterintuitive; indeed, it is the case that you can often cut back costs at the expense of quality.
However, when a system is easy to implement, making it cheaper to realise, there is also less chance of a mistake being made, meaning quality is higher.
This was one of the reasons Toyota was so successful in the automotive industry – by focusing on making things easier to produce for higher quality, they also became cheaper. The opposite was true as well. By cutting out waste (wasted time, wasted parts, wasted steps) to reduce cost, there was less that could go wrong so quality increased.
This is not to dismiss the importance of more expensive items when needed, but often they will be cheaper in the long run anyway. It’s just that engineers can sometimes give themselves false assurity by choosing the more expensive option.

Example 2 – simple code can do more than A.I.
One would think that with more lines of code and a complex algorithm there would be more going on so it can do more.
But code that has been written explicitly can be tuned so that it achieves the exact goal desired. If a trained ML system does something wrong, then you likely have no idea what’s causing the issue. All you can do is make a few adjustments to the training system, retrain, and hope for the best.
If, on the other hand, you have explicit code, then you can understand what’s happening (or not happening), and make changes to improve performance.
This is not to be dismissive of things A.I. Comparing ELIZA to what’s on offer today shows how powerful A.I. systems have become. It is more that we can think A.I., because of its complexity, will be the better option regardless.
But still, when one considers the success in the early 1970s of much simpler systems – such as the one documented by F. T. de Dombal et al. in Computer‑Aided Diagnosis of Acute Abdominal Pain where a relatively simple program outperformed senior specialists (91% success vs 80%) – there is the potential for simpler code to do more.

What is missing in engineering thought for this to happen?

It can be found in the 1920s.

For some time, it could not be determined if light was a wave or a particle. It had properties of each – depending upon the test. However, by the 1920s, it was accepted that light was both a wave and a particle.

The “OR” was replaced with the “AND”.

And that’s the key thinking difference you need to adopt.

Stop thinking things like:

• We can have low cost or quality.
• We can have efficient code or accuracy.

Instead start thinking things like:

• What can I do to have both lower cost and high quality?
• How can I approach this so I can use simple code and increase accuracy?

​In short, stop asking the “OR” questions and start asking the “AND” questions. Make this a habit, and you will start producing better engineering outcomes – because you will not full into traps of intuition.
Everyone wants to have their cake and eat it too.
And engineers should be trying to make that happen!

If you want to become a great engineer (particularly a great global engineer), then there is one capability that matters more than most people realise.
It is not domain knowledge. It is not even intelligence. Most people think of those.
It is your relationship with time.
This idea is explored in The Time Paradox, by Philip Zimbardo and John Boyd. I also noted this in my book. The Time Paradox examines how people orient themselves toward the past, present, and future; and how those orientations shape behaviour, achievement, and satisfaction.
The important orientation I am talking about here is the future focus – because of its link to successful people.
The key to the future focus is the attitude that what you do now will pay off in the future.
You don’t try to frame problems, or apply first principles, or think systemically, see no immediate change in outcome, and then think: well, that didn’t work; what a waste of time!
You work on these skills now, and tomorrow and the day after that. Knowing that each time you do, you get a bit better at it.
If you go to the gym each day and lift weights, then you’re going to get muscles. If you keep on working deliberately on developing core engineering skills, then you’re going to become an excellent engineer – and keep getting better.
You probably already have a strong future focus – but there is likely room for improvement.
Because you are an engineer, you had to get through your degree. You gave up a significant number of years to invest in your engineering knowledge for a better outcome.
Still, you might have just taken it one step at a time or simply responded to each task put in front of you during your studies – viewing this time as a student as simply what you do and making the most of the present.
Think now about how you viewed this when you studied. Were you thinking about how each action was going to make for a better future or were you just doing what you did and making the most out of your situation at the time? This will help you work out your future focus tendency.
Does it work?
Have you ever noticed some people who are not that bright, but have still been successful?
You have likely come across people where you have thought “How did they get to that level?”
They simply do not seem to have that much going on upstairs and yet they have a senior role.
They might have been lucky, but the likely had a strong future focus. So they were able to keep on working on mastering key skills that were needed to get the role they wanted – and they are probably still working on getting the next role.
That can be you!
But what could be stopping you from having this perspective.
Have you ever met someone who just seems to react to everything? They don’t plan, they never seem organised, and they never seem to just pull it together.
These are people who have no future perspective. The things that rob people of a future perspective are:

• Culture – some cultures are more hedonistic, and they focus more on enjoying the present.
• Stability – if you come from a place or time that was economically or politically unstable, then you learn that there is no benefit in long-term plans. You simply focus on surviving each threat and stay ready for the next.
• Bad luck – some people have just had plan after plan invalidated by circumstance. Probability says it will happen to someone – even in a stable place and time. So that someone has misfortune, and then they lose their future focus.

Ask yourself now if your background discourages a future focus. If it does, then you know you need to start thinking more about how your actions now will pay off in the future. Especially when it comes to improving your engineering skills.
If your background does encourage a future focus, then you can probably still improve it further.
You have likely heard about the idea that you need ten thousand hours (or ten years) of practice to become skilled at something. So you likely know, logically, that time is needed. But is it having a strong future focus that allows you actually to put that time in – and keep at it after that.
So think now about maintaining a future focus so you can stay on the journey to engineering excellence and all that will come from it – be it material or personal gratification.