Units  (Page 3/4)

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$\frac{1\text{km}}{1\text{km}}=\frac{0\text{.}\text{621}\text{mile}}{1\text{km}}$

Clearly the left hand side of this equation is equal to 1. That is

$1=\frac{0\text{.}\text{621}\text{mile}}{1\text{km}}$

This will serve as our conversion factor to solve our problem at hand. It is important to remember that this conversion factor is nothing more than a carefully selected form of the number 1.

Let us return to the quantity 25.2 kilometers that we wish to convert to miles. We can apply the conversion factor as follows

$\text{25}\text{.}2\text{km}×\frac{0\text{.}\text{621}\text{mile}}{1\text{km}}=\frac{\text{25}\text{.}2\text{km}×0\text{.}\text{621}\text{mile}}{1\text{km}}$

We observe that the unit ( km) appears in both the numerator and denominator and can be removed from the from the fraction. So our result is

$\text{25}\text{.}2\text{km}×0\text{.}\text{621}\text{mile}=\text{15}\text{.}\text{65}\text{miles}$

Thus we establish the result that 25.2 km is equivalent to 15.65 miles .

In obtaining the result, we developed a fraction that was equal to the integer 1. We then multiplied our original quantity by that fraction to give rise to our result. This is the basic idea behind unit conversion.

A two-step procedure for producing correct unit conversion factors

Here we will present a simple two-step procedure that produces the conversion factor that can be used to convert between a given unit and a desired unit. For the purpose of illustration, let us use the conversion between the given unit ( pounds ) and the ( desired ) unit of kg .

Step 1: We begin by writing an equation that relates the given unit and the required unit.

$1\text{kg}=2\text{.}\text{205}\text{lb}$

Step 2: Convert the equation to fractional form with the desired units on top and the given units on the bottom.

$\frac{1\text{kg}}{2\text{.}\text{205}\text{lb}}=\frac{2\text{.}\text{205}\text{lb}}{2\text{.}\text{205}\text{lb}}$
$\frac{0\text{.}\text{454}\text{kg}}{\text{lb}}=1$

So to covert from pounds to kg we may use this as the proper conversion factor.

Another notable engineering failure: the “gimli glider”

Like the NASA Mars Climate Orbiter, the “Gimli Glider” incident is an engineering failure that can be attributed directly to the errors involving the mismatch of units. The “Gimli Glider” is the nickname of the Air Canada commercial aircraft that was involved in an incident that took place on July 23, 1983. In the incident, a Boeing 767 passenger jet ran out of fuel at an altitude of 26,000 feet, about midway through its flight from Montreal to Edmundton via Ottawa. The aircraft safely landed at a former Canadian Air Force base in Gimli, Manitoba, thus contributing to the nickname associated with the aircraft. (New York Times, 1983) We will trace some of the steps that led to the incident while making use of data drawn from the website (Wikipedia).

Air Canada Flight 143 originated in Montreal. It safely arrived in Ottawa on its first leg. At that time, the pilot properly determined that the second leg of the flight (from Ottawa to Edmundton) would require 22,300 kilograms of jet fuel. The ground crew at the Ottawa airport, performed a dipstick check on the fuel tanks. They measured that there were 7,682 liters of fuel onboard the aircraft upon its arrival to Ottawa.

Based on these data, the air and ground crew proceeded to calculate the amount of jet fuel that would need to be transferred to the fuel tanks in order to assure safe arrival in Edmundton. However, they used an incorrect conversion factor in their calculations. At the time of the incident Canada was converting from the Imperial system of measurement to the metric system. The new Boeing 767 aircraft were the first of the Air Canada fleet to calibrated to the new system, using kilograms and liters rather than pounds and Imperial gallons .

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