1 + 1 =

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This equation, and the answer to it, is of terrific value to the engineer. When deciding whether to ask a girl to marry him, the engineer will do an analysis. 1 + 1 = ________. The answer typically is 1.39664 or 1.43428. If it is less than 2, then it would make sense to get married. Marriage, as all things for the engineer, must be about efficiency. Whether the equation is for finances, which is a great asset in the engineer’s mind (living at lower cost), or for time savings (less time traveling around if not married and less coordination of schedules – he surmises), then if the number is less than 2, and it really makes sense to get married.

Sure, there is that vague concept of love, but how do you quantify that?

Stick with the calculations and a content life will be with that efficient couple.

Guess I should have written this one on Valentine’s Day.

dy/dx

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This concept is used in many equations engineers love – it is the rate of change. The rate of change, the change in a value y per change in a value x. That almost makes me giddy just writing that.

dy/dx is used so frequently and is so powerful in engineering applications, from falling objects, to increasing pressure with depth in a liquid, to electrical applications, flow, strength of materials, and the list goes on.

To make things even more fantabulous, engineers will frequently evaluate rate of change of rate of change. Woah! What-what?

Think about measuring an object moving – falling or rolling – in one direction. We can measure that rate of change of position in terms of dy/dx, or change in distance over change in time. This is velocity, speed if it is in one direction. But what if the velocity changes? Then we measure the change in velocity over time, or in other words, the change in distance over time over time, or something like that. It makes more sense in an equation. This is acceleration. What happens if we measure the change in acceleration? Well, we may just be going back in time. No. I am kidding.

But rate of change is powerful, and engineers use it frequently. An engineer could even use it to measure non-engineering things, like the rate of change in time for, say, his wife to get ready to leave for the evening, with change in the years of marriage. We may save that one for another day. But it can be done.

a = dv/dt

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Engineers love equations. Whether for understanding women or understanding laws of motion, equations are incredibly useful for making sense of the world. Another fabulous equation (this more from the laws of motions rather than understanding women) is:

a = dv/dt

where,

a = acceleration

dv = change in velocity

dt = change in time

Acceleration should be broken down into its vector components for a typical x-y-z coordinate system. This means that each direction of the coordinate space has its own acceleration, as well as its own velocity and distance.

Here is where teaching children is fun. Drive down the road and keep the car going at a constant speed of say, 40 mph. Keep the speedometer saying 40 while you take a curve and then ask your child if you are accelerating. Most children will fall for the trap and will say no. They think that since the speed is 40 mph and that stays constant, then the car is not accelerating. But acceleration is a measure, not of a change in speed, but of a change in velocity in a direction. So, if the car stays at a a speed of 40 mph, on a curve it is actually increasing its velocity in the direction perpendicular to the original direction. The original velocity in that direction was zero. Now it is something. Acceleration has occurred. At the same time the velocity in the same original direction has actually gone down, so we have negative acceleration, commonly called deceleration, happening in that direction.

Trust me, I could go on. But, as a parent, I wish not to embarrass my kids any more than I have to. They should know how the world really works, but not be humiliated – completely.

The Cost of Dry Hair

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My wife was riding with me in the car. She had just washed her hair and didn’t have time to dry it, so she opened a window and started to wind-dry her hair. She made the comment that this was saving all that money using the hair dryer. (It was a nice day.) She then stopped and wondered how much it did save.

So, to run the numbers, as an engineer will always want to do:

C = kW x t x r

where,

C = cost of electricity of using the hair dryer for one hair drying event, calculated in cents

kW = kilowatts used by the hair dryer

t = time of hair dyer use, in hours

r = rate of electricity cost, in cents per kilowatt-hour

For us, r, in the range of our confusing electric company’s tiered charges is around 5.5 cents per kilowatt-hour. The time, according to my wife (although I could have disputed this, from personal observation) would have been 5 minutes, or 0.0833 hours. The electric use rating of the hair dryer is 1875 watts, or 1.875 kilowatts.

So, we have:

C = 1.875 x 0.0833 x 5.5 = 0.86 cents

What I thought was that she obviously was not doing a full cost comparison between the cost of using a hair dryer. My calculation is only for the use of the hair dryer. But what about the extra cost of gas to propel the car with the added wind drag? On the other hand, there should be calculations made for the increase in air conditioning to cool down the home with all the heat added by the hair dryer. Then, there are the possibilities and the risk being taken that my wife will not hit her head on while we pass a branch, or a bird, or that she will not get chilled and get sick from drying her hair in the chilled air. This would involve probability and risk calculations.

When it comes down to it, it is just easier to dry her hair at home with the hair dryer.

d = (1/2) * 2πr

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Watching the Olympics over the weekend gave me the wonderful opportunity of not only being a spectator, but, as an engineer, thinking about how to improve the races for the athletes.

I watched parts of the 10,000 meter race for both the women and the men. That  distance equates to 6.2 miles, so this is no sprint. The athletes run around the 400-meter track 25 times. That’s a lot of running, and almost made me want to exercise.

So, I am watching these races and the lead runner often has a shadow, the runner in second place, running right off his or her shoulder, for many of the laps. It made me think, which is a good thing for an engineer to do. I wondered how much longer that second-place runner had to run every time around the track. The lead runner is running about a half meter off the inside line of the track and the second-place runner about a half meter outside of that. This means that the second place runner must be running further as he or she runs half the circumference of the curve of the track.

I looked it up. The track dimensions are laid out with a curve of radius 36.500 meters. Therefore, the distance around the curved end of the track is explained by the equation:

d = (1/2) * 2πr

where,

d = the distance along the curve

r = the radius of the circle

It is 1/2 of the full circumference of 2πr because the curve is 1/2 of a circle. Simple enough.

Considering we know the radius, and note that the first runner is 0.5 meters outside of the inside track line, and second runner, in same lane (the lanes being 1.17 meters wide), right off the first runner’s shoulder, is 0.5 meters outside of the first runner, we end up with a table like this:

Line                                 Radius (m)             Distance around curve (m)

inside lane line          36.500                              114.668

first runner                 37.000                             116.239

second runner          37.500                              117.810

We have found out that the second runner runs 117.810-116.239 = 1.571 meters further as he or she runs just off the first runner’s shoulder, and this happens every time around one curve of the track. For a full lap, this is doubled to 3.142 meters. When I was watching, a second place runner would easily hang out there for up to 10 laps, meaning that runner would run 31.42 meters longer! 10,000 meters is a long race, but the difference between first and second is often under 30 meters. I don’t know if it was over the weekend. I was busy doing calculations. But I was able to run the numbers and, if I had their cell numbers, would have texted the coaches of the second runners and tell them to  back off and run right behind or go ahead and run in front of the other runner. Save the distance. It could mean the distance between silver and gold.

The engineer helps improve the Olympics once again.

Another Basic Equation

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For engineers, the breakdown of life can be seen in equations. While some may be very complicated, like how a wife’s mind works, many are simple and constitute the basic building blocks of our world.

For example:

F = ma

where,

F = force

m = mass

a = acceleration

It really is as simple as V = IR. For this equation, F = ma, motion, forces, and the mass of the object are described in a beautifully simple equation that everyone, not just engineers, can appreciate.

How much speed can you get a car going by pushing it? F = ma

Would it help if the car was lighter (less mass)? F = ma

Would more people pushing make it easier? F = ma

For non-engineers, next time you are in a group of friends and, say, someone suggests that you figure out a way to move the trajectory of an asteroid heading straight toward earth, simply bring up this equation, F = ma, and you will be the person who saves earth. Finding a way to apply the force to the asteroid and all the little details that go along with the rest of the problem, those can be solved by others. You are the one who got it going, kick-starting the whole saving-the-world initiative by your understanding of force, mass, and acceleration, and their relationship to one another. You will be a hero.

The Basics

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When a sports team starts to lose, the coach typically makes a statement that the team is going back to the basics, that they will emphasize the fundamentals.

Engineers are way ahead of them, because engineers are all about the basics. As a service provided by engineeringdaze.com, we want to provide for all the non-engineers out there some of the basics, so that you can talk to the engineer in your life. First up, the basic, most fundamental equation for electricity:

V = IR

where,

V = Voltage

I = Amperage

R = Resistance

What simplicity. Three variables, one equation. No fractions (unless one want to solve for I or R), and no exponents. And it is as solid a foundation as they come. I actually had an electrical engineering professor say that if we had no idea how to solve a problem on a test, at least put down this equation, and he would give you partial credit.

V = IR is also useful. On a recent trip, my family and I were driving along a very long, relatively straight interstate and were paralleled by some high voltage lines. My daughter who just got through 8th grade started explaining how the electricity in our homes had to go through transformers to step down the voltage and (as my friend Tom would hear the next part) “Blah, blah, blah”. I would prefer it to say, “Yada, yada, yada.”

She, who wants to enter some strange, artsy profession like choreography, could actually relate to an engineer by almost referencing this basic equation.

So, you see, V = IR is a wonderful equation to use when communicating with engineers.

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