#Maths
I was looking over the main co-ordinating book, and suddenly realised I needed to add a large section on Maths, I did not like maths at school, I got through it, just, but it was not a subject I liked or understood. But that all changed when I started work, and suddenly it all fell into place, I saw the need, on a simple program which began to help me explore this subject, that, and a book called Construction Mathematics. The book in the format I like, did not come out till much later in my career, but it was, as the title says, specific to the construction industry, therefore relevant.
The program was VisiCalc one of the first spreadsheets, on an Apple II that a few engineers were using. they taught me how to use it and I was thrilled, Maths came alive.
So back to present day, I realised we needed a complete chapter on Maths, not a bland overview, but specific to the Construction industry, taking a look at some of the general science and maths needed for general day to day surveying, checking of dimensions, and simple beam calculation to gain a little understanding of the Civil and more the Structural Engineers role
So this short article is my initial copy for the book, it will change and it will get larger.
We tend to think the computer will solve all our maths problems, and mostly it will, but checking is part of everday life, making sure the imput is correct and the final calculation fits what you expected.
We also deal with any number of engineers for all sorts of calculation, its not our job to do the calculation, mostly our PI will not alllow it, but we should understand the basic principles and physics behined the calculation.
I want to start with something I keep going back to, its pencil and paper, like any other subject, practice makes,,, well mathers better, so if you see an angle that needs calculation, or a length try to solve it longhand, not jump to the CAD program and copy a line length.
YouTube has many excellent tutorial on this, take a few in and practice.
Triganometry
We deal in angles all the time, checking wall alignemnts, I have not seen a square house in a long time, the fall of a road or slope, the length of a beam, in construction its a constant, but we rely on computers and modern instroments to tell us the answers, often relying on the information to be passed to another formula, we rarley check just rely on the magic of computers.
But there are often times we need to fall back on good old fashioned Trig to check the calculation, or the power supply fails and we need to get an answer. Drag out the pencil and paper and do it long hand.
There are some simple formulas we need to remember to do this. Modern schools teach the phrase SOH-CAH-TOA I was taught a simple poem “ Some People Have Curley Brown Hair Till Partly Bald
Or
S P/h
C B/H
T P/B
There are many more !
But as SOH-CAH-TOA is the modern way, lets stick to it
This simple acronim describes the formulas to canculate any angle, most if not all calculater and certainly any spreadsheet has built in answers to these formulas, but long hand requires some tables I still have mine from school 1965 - 1969 and Technical college 1969 - 1978.
So what does the string of letters mean
SOH Sign= Opposite/Hypotinues
CAH Cosign=Adjacent/Hypotinues
TOA Tangent/Adjascent
The chart shows the relationship between the sides and this is for right angle Triangles only, for none right angle triangles circles, and odd shapes, there are other formulas, I can never remember them all, so have collected cheat sheet with them all on, including Circles and strange shapes, ir plots of land. I have many examples on my Pinterest page Pinterest page
There are three ways to do this”
* Phone Calculator
* Spreadsheet
* Pencil and paper
Phone Calculator
Most modern phones have a half decent calculator built in, if like me your on a an iPhone, then the Scientific mode is the one you need to calculate Trig values, its not difficult, but each phone, Ie Android, Samsung, and iPhone seem to have a slightly different imput method, YiuTube has a load of excellent tutorials.
Spreadsheet
Almost all construction projects have spreadsheets involved somewhere, for some reason, I have several for doing Angles and quickly working out SOH-CAH-TOA, ok I still use Curley brown hair, its what my dad taught me !, and I use Appple Numbers which again is different to any other populat spreadsheet.
It save so much time, but never loose sight of the pencil and paper, one day your calculator, or phone will not work. So always have a fall back. You will need some trig tables, I still have my dads books with a set at the back, but NASA have a page dedicated to Sine-Cosine-Tangent with a basic list of tables, good enought for NASA !
Pencil & Paper
For this to work, you need access to some old log tables, see above, I still have my fathers books and as a steel structural Engineer, he used log tables almost on a daily baisi
But they are still available
This last method is not on my list, but its quickly becoming a method a lot of CAD opperators are turning to:
Graphical Programing
In the next chapter on the Future, its clear, CAD is changing, and we will rely more on AI and programing the design given peramiters and specific formulas Graphical Programing
This style of Maths is made easier with formulas embedded into graphical blocks we drag into a programing area within the cad program drawing sheet, linking not one but many clocks with electronic string, so its directly related to the project, and can use perimeters from the drawing Room length, height, width, wall thickness, and best of all, if the perimeters or vslues change, then so does the calculation.
Global Compatibility:Metric Vs Imperial Measurements
With most of the world useing the metric system (SI units), ( 97%} ( Wiki ) with the United States, Myanmar, and Liberia being the primary exceptions that still use the Imperial (or US Customary system, working on international projects, and collaborating with teams in different countries, or sourcing parts globally, often brings a compatability issue. Understanding both is essential for seamless communication and avoiding costly errors. Having said this, many of the older English speaking countries still have a blend of both units, with even the UK still refering to imperial, in cars measuring miles / Gallon, and many maps still using miles to measure land area.
Add to this the difference in the repair of older property, with new doors and bricks converted to a metric size, that are not compatable with older doors frams and doors, with the classic difference in brick sizing and coursing being a classic, see my older notes on this.
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