DEFY S. McQUAID! #76: Inning and Outings

The Question

Adam asks:

Who decided it was a good idea, in baseball, to denote portions of innings pitched as “.1″ and “.2″? Some broadcasts use the proper notation of 1/3 and 2/3 innings pitched, but some—sometimes both are used on the same game!—use the mixed up .1 and .2. What’s a tenth of an inning anyway? Clearly one out is one third of an inning pitched.

The Answer

This is an interesting question. Researching the answer was difficult – yet, an answer, there is. (says Yoda).

Here’s the deal. Basically, when you see something like “3.2” in the inning measurement system, it is in BASE 3 to the right of the decimal point, and BASE 10 to the left. Since the innings are measured in thirds (as you point out), the base for a percentage of an inning measurement is 3. Hence, “3.1” really means “3 1/3”.

Who thought of this? Someone constrained by their technology, someone who just could display fractions on their television set, someone like you and me, Adam. Technology advances, so this nomenclature is no longer “required” by the properties of the display, but, like a bad penny, it keeps turning up. When you see both types of measurement in the same game, that’s when you know that not all displays are running on the same software, or that you’ve got someone running one of the displays who subscribes to the “old school” measurement.

DEFY S. McQUAID! #75: Curves Again

The Question

Shaun McQuaid, who is never afraid, don’t be delayed or I’ll be dismayed. ..

How much money could one save in gas by always staying to the inside of a curve by shifting lanes while driving on the highway? I’m not looking for an exact value, just a relative comparison between always on the outside of a curve, the middle, and always on the inside. You can ignore traffic and assume that all lanes are equal speed.

Yer Pal,

The Answer

Let’s make a lovely little “perfect” world. In our perfect world, Boston is at the exact center of a half circle inscribed by Rte. 495 in Massachusetts. In real life, we’ll use I-495 from the intersection of I-93 in Andover, MA to the north, and I-495’s intersection with Rte. 24 in the south. This allows for an almost (meaning not really at all) perfect half-circle around Boston. Using I-90 as the diameter line, we discover that the radius of our circle is 27.5 miles, or 145200 feet.

The plan is simple – we will inscribe 2 circles, one on the “inner” lane of this simplified route, and one on the outer lane. According to my research, the most common lane width is 12 feet. Let’s assume a 3-lane highway – so, the “inner” lane has a radius of 145200 feet and the outer lane adds 24 feet to that total – 145224.

Calculating the perimeter of the circle will give us the distance traveled in each lane. Perimeter of a circle is calculated via 2 * (pi) * r, so a half circle is simple: (pi) * r. (For our estimation, pi is estimated at 3.14159).

Inner lane distance: 86.39 miles
Outer lane distance: 86.41 miles

Assuming 30 miles per gallon in your vehicle, this means:

Inner lane gas used: 2.879 gallons
Outer lane gas used: 2.880 gallons

So, in essence, by travelling only in the inner lane, you would save 0.001 gallons of gas. (Because of the tiny amount here, I ignored the “middle” lane and stuck with the right and left only).

Not quite as exciting as expected, is it?

DEFY S. McQUAID! #74: Rain and the speeding automobile

The Question

Dear Mr. McQuaid,

Long time reader, first time questioner (is that even a word). I was recently informed that if you are driving fast enough in a convertible with the top down while it’s raining then you, and the interior of the car itself, will not get wet. Is this true? And, if it is true, how fast must you be going in order to stay dry?

Curious in Worcester,

The Answer

It’s doable…but extremely unlikely in a convertible. The problem is that you are unlikely to achieve the required speeds in any car. Sprinkling and misting are another story….

In order for the steady rain to not fall in the car, you will need to provide some force that pushes it away (up or to the side). Generally speaking, the rain will fall downwards and into the car when it is moving at normal speeds – aerodynamic flow is not enough. There’s always going to be some rain ready to fall into the car no matter how fast you are going. If I could draw in MSPaint, I’d supply you a picture, but for our purposes, imagine raindrops falling across the screen, and your car under them.

If you wanted to go fast enough to repel the rain, you’d need to create a shock wave powerful enough to shift the rain away from the vehicle. This requires some major speed, and the only way to do it reliably is to approach and break the sound barrier. The compressed air from your vehicle traveling at above the speed of sound should be enough to shift the rain away from car and keep you dry. Of course, you are dealing with other risks, such as the air damaging your head…

Now, if it’s just sprinkling or misting, that’s another story. The aerodynamic flow of air over the roof of the car is probably enough to divert most of the rain in that case. The speed required is proportional to the size of the raindrops. But a hard rain won’t be shifted by anything less than a shock wave…

DEFY S. McQUAID! $73: Why charge a Mill?

The Question

Becky asks:

Why does every gas station charge an extra $.009 per gallon? I vaugly remember hearing something about taxes. However, why don’t the stations just round it up and keep the extra fraction of a cent? Personally, I’m happy they don’t round up, but it bothers me that they use a nonexistant monitary unit.

Also, is there anything else in the world that is sold like this?

The Answer

It’s an intriguing question, isn’t it? Why would anyone do this? And what else does this?

First, let’s answer the “why”.

It turns out, the reason that gas stations add tenths of a cent on to their price is purely marketing; nothing to do with taxes, nothing to do with esoteric gasoline laws – it’s simply a marketing ploy. Gas stations feel that customers are more likely to select them if they advertise their price as $2.899 than $2.90. And nothing prohibits them from doing so. Also, keep in mind that gas stations round UP the final price, so if your final pump price is $32.982, it’s really $32.99. (There may be exceptions to this rule, but I haven’t found them).

So, the “why” is pure marketing.

Interestingly enough, in 1786, a unit of currency was legislated into legality, equal to “1000th of a dollar” or “a tenth of a cent”, known as a “Mill”. However, this currency was never minted by the federal government. Some states and local townships did use the mill for some time to settle taxes on really cheap stuff, but the practice fell out of use fairly quickly.

The mill is still legal today, but you’d be hard-pressed to find it commonly used in sales anywhere other than gas stations. HOWEVER, many municipalities use the mill when calculating their property tax. Property tax can be expressed in terms of mills per dollar. For example, a millage rate for property taxes of 2.094 mills per dollar will cost the homeowner of a $200,000 dollar home 0.002094 * 200000 = $418.80. (The mill rate for my town is currently 9.93, assessed bi-annually).

So, there’s more than just gas that uses the mill, but not much more. Enjoy your mill knowledge!