EN3: Introduction to Engineering and Statics

 

Division of Engineering
Brown University

 

 

2. Measurement and Estimation

One of the most valuable skills that an engineering training will give you is the ability to think quantitatively. This is a very powerful tool in problem solving and in developing and presenting an argument. As Foghorn Leghorn (a big loud-mouthed chicken) so eloquently puts it `That’s Mathematics, son! You can argue with me, but you can’t argue with figures!’

So, we start this course with the big picture. What can we measure, how do we quantify our measurements; how accurately can we measure things; and what can we do with the measurements?

2.1 The role of measurement and modeling in engineering

Engineering at its best is a precise science. According to Lord Kelvin (the guy temperature is named after): `If you can measure that of which you speak, and can express it by a number, you know something of your subject; but if you cannot measure it, your knowledge is meager and unsatisfactory.’ It is not enough to be 60% certain that your bridge design will support its service load; or that your new airplane will remain controllable at approach speed, you have to be sure .

Over the years, we have learned to measure, and predict, things with quite extraordinary precision. To take a humble but easily understood example, consider the civil engineering discipline of surveying.

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When civil engineers build a bridge, or bore a tunnel, they usually start construction at the two ends of the tunnel or bridge and arrange to meet in the middle. A good example is the Chunnel, which required tunnels to be bored from opposite sides of the English Channel between Britain and France (a total distance of 30 miles) and meet up in the middle with a precision of a few millimeters. This is a routine exercise for surveyors.

 

The table below will give you an idea of the precision and accuracy expected in surveying. To locate our position on the earth’s surface, we currently use the High-Accuracy Reference Network (HARN). This consists of a set of points on the surface of the earth that have been located very carefully. The procedure is to choose a few points (primary control points) that are located super-accurately. We then use these to establish lots more secondary control points, which are located slightly less accurately. Local surveys are referenced to these secondary control points.

Survey category	Order	Accuracy standard
Global-regional geodynamics	AA	1:100,000,000
National geodetic reference system - primary	A	1: 10,000,000
National geodetic reference system - secondary	B	1: 1,000,000
National geodetic reference system (terrestrial	1 2-I 2-II 3	1: 100,000 1: 50,000 1: 20,000 1: 10,000

When we conduct local surveys, we normally work to order 3 accuracy (the lowest). This still requires us to measure distances, angles, etc. to within 1 part in 10,000. So even a simple exercise like using a tape measure becomes a challenge. When surveyors use a tape measure, they don’t just slap a tape on the ground and read the distance – they carefully pre-tension the tape with a known load so they can compensate for its sag; they measure the temperature of the tape so that thermal expansion can be accounted for, and so on.

As a second example, consider a routine mechanical engineering component – bearings. Ball bearings are cheap – you can get a precision bearing for around $10 or so.

 

But they are amazing products. The balls have to be spherical to within 1/10000 of an inch; raceways are manufactured to similar tolerances; the surface finish is better than 10 microns. Devising a method to even measure whether something is round to within 1/10000 of an inch is challenging, never mind manufacturing parts cheaply to this tolerance. But again, this is routine.

As a final example, consider manufacturing microelectronic circuits. The picture shows a cross section of a typical integrated circuit – the picture is about 0.8 microns high. The different colors are different materials in the device. The orange are copper wires making electrical connections between devices; the white parts are little tungsten connectors; the green, orange and blue are oxides and semiconductors making up the gate, source and drain of a typical CMOS transistor.

A typical integrated circuit contains millions of these. They have to be manufactured cheaply and reliably. Moreover, because of competition, the dimensions have to be halved every two years or so, and costs have to fall at a similar rate.

 

Dealing with uncertainty: And yet, engineers often need to make decisions based on incomplete or potentially inaccurate data. You can’t always predict how people will use your product; you can’t control or foresee the price and availability of materials and supplies; often you need to make decisions quickly and don’t have time to do the research or testing required to generate data with the accuracy you might need.

 

Modeling Engineers also rely on models to understand how the world works. A model is a mathematical idealization of a system or design – anything from a spacecraft to a transistor in an integrated circuit. All models are approximate, and attempt to describe only the most significant variables in a system. To take a trivial example, if you were designing a clock, you might find the formula for the period of oscillation, T, of a pendulum helpful

where g is the acceleration due to gravity. But this formula is approximate. It assumes that the angle of swing is small, it neglects air resistance and friction in the hinge, it neglects rotational inertia of the pendulum bob and mass of the shaft; it neglects deformation in the shaft due to forces or temperature changes; it does not account for relativistic effects… the list goes on. Does this matter? Well, that depends. If you are designing a clock that will sit in your room and drive your roommate crazy by chiming every hour, it doesn’t. But if you are designing a clock for celestial navigation purposes, it needs to be accurate to within a second or so in a year (and much more accurate still for modern navigation systems such as GPS). This needs an accuracy of one part in 32 million. Then, yes, it does matter. So engineers also need to appreciate potential sources of uncertainty in their calculations and need to know how to deal with them.

Nevertheless, engineers try, if possible, to develop theoretical models of everything. If you can model something, you understand it; if you understand it, you can control it. A few examples of engineering models are illustrated in the pictures below.

 

Aerodynamics                                                       Structural Analysis

Materials Processing                                     Chemical reactions

 

 

 

So, an engineer’s goal is quantify the universe, and to use that understanding to solve problems. The objective of an engineering training is to develop your quantitative problem solving skills.

Here are some suggestions to get you started:

 Learn how to make estimates. Engineer’s ability to make accurate, fast estimates is perhaps their most valuable asset. Learn how to combine quantities you may be familiar with to make estimates.

 Try to develop a good feel for characteristic magnitudes of quantities of interest. Try to remember typical values for material properties, typical magnitudes of forces, characteristic dimensions of devices in integrated circuits, typical frequencies of electromagnetic waves…

 Learn, and remember, sources of data and information. Keep a little black book of information that you think might come in useful later. If you use a handbook or database in a course that looks helpful, make a note of its title and publisher and something that will remind you what was in it. Keep your textbooks! Maintain a bookmark file of useful web sites. Keep in touch with classmates; record contact info for professors, visiting lecturers and anyone else who might be a resource to you later.

 Get comfortable with systems of units. We tend to favor the SI system of units in solving class problems. But in reality (particularly in the US) you need to use other systems of units.

 Develop a habit of converting numbers into forms that make sense to you. If someone tells you that the thickness of a semiconductor film in a microelectronic circuit is 10 nm, you could think of that as a thickness of about 30 atoms.

 Be skeptical. When you read a news report, or listen to a sales pitch, examine numbers for credibility. Is a 3.5 hour trip from JFK to London HR on a Boeing 777 feasible? Is a reading of 30lb/square inch a reasonable stress in a human tibia? Is a 150% risk-free return on an investment probable?

 

In the remainder of this section of the course we look at measurement and quantitative problem solving at the most basic level. We review the SI system of units and the consequences of adopting a system of measurement (Dimensional Analysis). We discuss briefly how to make good estimates.

Go to 2.2 Measurement: The SI system of units