Tork – Return of Caveman Engineer

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Tork, caveman engineer, the first engineer in history, make that pre-history, returns for this week on

Tork noticed that he could run fast. Not as fast the non-engineer cavemen, but that is a different story. He also noticed that he could run much faster than a snake, but much slower than saber-toothed tiger.

Tork got to figuring, trying make sense of the world, as any engineer would do. Tork thought, “Hmg, no legs go slow, two legs go fast, four legs go faster.”

Tork even created a table, a spreadsheet of sorts, which he posted (scrawled) on his cave wall. While making it difficult to impress cavewomen with his interior decorating skills, Tork nevertheless tried to figure out this relationship between number of legs and speed.

Then one day, Tork saw a centipede. It didn’t fit into his algorithm well – actually not at all. Tork crushed it with a rock.

In the end, Tork abandoned his attempt at this heavily biological endeavor, leaving it to the caveman a few caves down who wanted to be a caveman doctor. Tork went back to his work of providing clean water for caves, finding great uses for that new invention, the wheel, and understanding the benefits of treating waste properly – or at least locating a waste site properly.

Pythagorean – Applied

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x2 + y2 = z2  et. al.

Engineers use the Pythagorean Theorem and the associated trigonometric functions, particularly cosine and sine, to a very great extent. You may think, “Hey, the Pythagorean Theorem is for mathematicians. Why are you claiming it for engineers?”

First, engineers use this equation to break down vectors into component vectors in an x-y coordinate plane. This is extremely powerful since vectors can represent forces or distance or velocity or a myriad of other phenomenon. I know. Wild, isn’t it? Engineers use Pythagorean’s old equation for great uses.

And here we see the second reason why this should be principally an engineering concept. I have a brother. He just had a birthday yesterday. But, that is irrelevant. What is relevant is that he is a math professor and as a mathematician the one thing he hates is to do anything “applied” with his math. He likes to keep it “theoretical. What? No real world solutions? – No. No solving a practical dilemma? – No. No serving the general public and supplying clean water, electricity, motors, highways, etc.? – No. My brother sees math as an end to itself. He hardly even deals with numbers anymore.

So, here the engineer is found to be far more noble and distinguished than the math professor. Sit and think about math, or use equations such as the Pythagorean Theorem to solve problems and help humankind? I think the answer is quite clear.

Thank you.


Spreadsheets R Us

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Once again, it does not surprise me.

My wife has a friend who is married to an engineer. This friend has been wanting a new car for a long time and her husband, an engineer, has been seen as dragging his feet on the issue. This is not the case. Now, I don’t ever want to get into the middle of a marital disagreement, but the fact that her husband is an engineer means a few things.

1. He understands that any present car they have, though over 10 years old, is paid for. It is not costing them monthly payments or a huge chunk of a savings account.

2. Only when the repair rate of the older car reaches that of the rate of all the costs of a new car is it worth buying a new car.

3. New cars cost more in insurance.

4. New cars cost more in registration taxes (if the state has it, ours does).

5. It will take a while to develop the spreadsheet of features, dealers, makes and models, car reviews, mpg rates, repair records, cargo space, safety ratings – to name just a few.
It is this spreadsheet that will take the real time. The old car will rust out faster than it takes to create, test, and tweak this spreadsheet. The old car may break down numerous times before the spreadsheet is complete. But, here is the important thing to remember. Once this spreadsheet is done, the decision will be a well-reasoned one and, geologically speaking, a quick one.

They should have a new car by this time next year. Or the year after.

METRIC WEEK – A Simple Bar Chart

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This week on, we will pull together in one week some of the posts that were written to inform and to promote the metric system, an incredibly obviously superior system of measurement to the one we here in the United States use.

Hoping you all are not like my coworker, “Wade”, who understands that the metric system is a decimal system, but doesn’t get the point of decimals…


Here is a simple bar chart that says it all from the perspective of most engineers.

The Number of Countries that Use the Metric System vs. the Number of Countries that Do Not Use the Metric System

If you didn’t know, the USA is represented on the right, one of the three countries that does not use the metric system. There are approximately 193 countries (depending on how one counts countries) that do use the metric system.

It’s us, and our friends in Liberia and Myanmar.

Nuff said.

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


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


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.

Torkitus – Roman Engineer

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A number of weeks ago, we introduced Tork, Caveman Engineer. He was the first engineer in history – make that pre-history. Later, we introduced Torkus, Medieval Engineer, who lived in the difficult time of the Dark Ages and tried as he could to make the world a better place to live, as engineers are made to do. This week, we will introduce yet another engineer from the past: Torkitus, Roman Engineer. Torkitus lived in the first century BC, when the Roman Empire was forming out of the Roman Republic.
Torkitus grew up calculating his odds of getting a beautiful women, or any woman, to be his wife. Roman culture highly prized two things: strength, in order to be a good soldier for the empire; and oratory skills, in order to be able to debate points of culture, history, arts, etc. before a group of people. At this time, brains (which Torkitus had) and braun (which he did not) frequently were not found in the same person. As for oratory skills, Torkitus was an engineer. ‘Nuff said.

Torkitus, viewing a beautiful woman in his city, figured out his chances of gaining her attention as:

P = (0.5*S + 0.5*PS) * 100


P = the percent chance that he will gain this woman’s attention and approval

S = Strength factor, from 0 to 1, how he compared to his male contemporaries

PS = Public Speaking, or oratory, skills, from 0 to 1

Needless to say, Torkitus’ odds, as he calculated, were not good. His equation told him he had between a 1.6 and 1.7% chance of marrying that woman. The interesting things is that engineers have been using equations like this, and far more complicated, often coded into computer programs, to this day in calculating the same thing – what are the odds of this girl I know to desire to date him (the engineer), with more a complicated equation for the odds of getting married.

And, as it is today, it was with Torkitus. Many engineers get married, as Torkitus did. They do not take into account in their equation the desire of the woman to have a stable, intelligent, consistent – albeit unromantic – man to marry.

Similar equation. Same wrong assumptions. Torkitus was definitely an engineer.


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A calculation near and dear to any engineer is b/c.

b/c is not short for because to an engineer. It represents the ultimate in engineering decision-making. The “b” represents the benefit an item or service has to the person buying it, and the “c” represents the cost. b/c is the benefit compared to the cost or, as engineers like to say, the benefit-cost ratio. The word “ratio” just adds an engineer-ish feel to it.

Engineers use the b/c ratio to determine if it makes sense to build a large factory, or set up a distribution center, or construct a highway, or dam up a river.

An engineer will also use the b/c ratio in his own life, to determine if it is wise to buy a certain car, or house, or make any other large purchase.

But, what an engineer will do even beyond this is to calculate b/c ratios for pretty much any area of life. Should one buy this pen? Calculate the b/c ratio. Should one get the air conditioner fixed in the car? Calculate the b/c ratio. Should one get married. Sure, why not calculate the b/c ratio.

b/c ratios are powerful tools and in the right hands, the hands of an engineer, they become the essence to an efficient existence.

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


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.

s = d/t

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This is a simple equation:

s = d/t


s = speed

d = distance

t = time

Watching the Olympics, an engineer can “enjoy” them better by running calculations on average speed in various races.

Take swimming for example. Looking at the four strokes for the men’s world record at 100 m:

butterfly s = 100m/49.82s = 2.007 m/s

freestyle s = 100m/46.91s = 2.132 m/s

breast s = 100m/58.46s = 1.711 m/s

back s = 100m/51.94s = 1.925 m/s

Therefore, when it seems like the breaststroke swimmers are going slow, the engineer will be able to tell you that compared to the freestyle swimmers, the breaststroke athletes are going 80.25% as fast as the faster freestylers. If you want to talk about efficiency, go with the freestyle. It will get you there at over 6% faster by speed than the next fastest stroke, the butterfly, which in itself is 4.26% faster than the backstroke.

Believe me, there are many more comparisons, all based on simple speed calculations, as one considers different speeds of the different strokes at different distances. And this is just swimming.

More on the Olympics, and fun one can have watching them, the rest of the week.

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