Estimating Speed

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Section 1.1 Estimating Speed

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In this section, we will learn how to estimate speed on the waʻa.

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The core concept covered in this section is unit conversions.

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What was the speed limit on the road coming to school today?

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Suppose it is

25 mph = 25 miles per hour.

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This means that if you keep moving at this speed for one hour, you will have traveled 25 miles.

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When you ride your bike, what might be a good speed? Let’s say you bike at 5 mph. How far will you go in one hour? Answer: 5 miles. To visualize how far 5 miles is, use landmarks such as stores or parks that are located 5 miles from your school.

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Subsection 1.1.1 How do we measure speed

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We don’t typically discuss speed in terms of feet per second. Is 5 feet per second fast or slow? To make this more relatable, let’s convert feet to miles and seconds to hours. Remember, there are 5,280 feet in one mile, 60 seconds in one minute, and 60 minutes in one hour. Here’s how it works:

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Step 1: Convert seconds to minutes:

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\frac{5 ft}{1 s} \cdot \frac{60 s}{1 min} = \frac{300 ft}{1 min}

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Step 2: Convert minutes to hours:

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\frac{300 ft}{60 min} \cdot \frac{1 hour}{60 min} = \frac{18, 000 ft}{1 hr}

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Step 3: Convert feet to miles:

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\frac{18, 000 ft}{1 hr} \cdot \frac{1 mi}{5280 ft} \approx \frac{3.4 mi}{1 hr} = 3.4 mi/hr

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Now, we’re using a unit of measurement that’s more familiar to us - miles per hour.

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Subsection 1.1.2 Measuring the speed of a waʻa

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If we’re driving in a car, we can estimate our speed by dividing the distance by time. For instance, if we know the distance between utility poles is 125 feet and it takes 2 seconds to travel between them, our speed would be:

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speed = \frac{125 ft}{2 sec}

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We can convert this to a more familiar measurement of speed, miles per hour, using the steps above. In this case, we combine all three steps at once:

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\frac{125 ft}{2 sec} \cdot \frac{60 seconds}{1 minute} \cdot \frac{60 minutes}{1 hour} \cdot \frac{1 mile}{5, 280 feet} \approx 42.6 mph

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Out on the water, we don’t have familiar landmarks to measure speed. Instead, we use the canoe itself as a reference. We know how long it is.

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To find out how fast the canoe is moving, we time how long it takes to go from the front to the back. It’s not always easy to tell how far we’ve gone, so we use things like bubbles or even things like orange peels to help. When these things pass the front, we start counting seconds until they pass the back, and we write down that time.

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Now that we know how long the canoe is and how long it took to cover that distance, we can figure out the speed. Speed is just how far we traveled divided by the time it took. This helps us measure the canoe’s speed accurately, even without usual markers in the vast ocean.

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Example 1.1.1. Estimating Speed on Hōkūleʻa.

As Hōkūleʻa sails, the crew spots bubbles in the water and prepares to time the passage. The distance from the front ʻiako (crossbeam) to the back ʻiako is 42 feet, and it took 5 seconds to cover. What is Hōkūleʻa’s speed? In the ocean, speed is commonly measured in knots. One knot is defined as one nautical mile per hour. One nautical mile is approximately 6,076 feet.

Solution.

We calculate the speed of Hōkūleʻa:

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speed = \frac{42 ft}{5 sec} = \frac{8.4 ft}{sec}

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To express our answer in knots, we’ll first convert seconds to minutes:

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speed = \frac{8.4 ft}{sec} \cdot \frac{60 sec}{min} = \frac{504 ft}{min}

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Next, we convert minutes to hours:

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speed = \frac{504 ft}{min} \cdot \frac{60 min}{hour} = \frac{30, 240 ft}{hour}

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Finally, we convert feet to nautical miles using the fact that one nautical mile is 6,076 feet:

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speed = \frac{30, 240 ft}{hour} \cdot \frac{1 nautical mile}{6, 076 ft} \approx 4.98 \frac{nautical miles}{hour} \approx 5 knots

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Thus, if it takes Hōkūleʻa 5 seconds to sail past an object, then Hōkūleʻa is sailing at a speed of 5 knots.

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Subsection 1.1.3 Magic Speed Number

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Now that you know how to find Hōkūleʻa’s speed, you might wonder if it’s a lot of work every time. But here’s the trick: the canoe’s length and the conversions we use for distance and time stay the same. So, if we figure out everything except the time (which can vary), we’ll get a special number we’ll call the magic speed number. When we divide this number by the time in seconds, we’ll get Hōkūleʻa’s speed in knots for any time.

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Combining the steps from the example into one line and omitting the specific time (5 seconds), we get the following expression for our magic speed number:

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\begin{aligned} magic speed number & = 42 ft \cdot \frac{60 sec}{min} \cdot \frac{60 min}{hour} \cdot \frac{1 nautical mile}{6, 076 ft} \\ \approx 24.88 \frac{nautical mile}{hour} \cdot sec \\ \approx 25 knots \cdot sec \end{aligned}

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Thus, we have

magic speed number = 25,

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which has units of knots times seconds. Dividing the magic speed number by our time in seconds, we obtain units of knots, which is our desired speed:

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Speed = \frac{magic speed number}{Time (sec)} \approx \frac{25 (knots) \cdot (sec)}{Time (sec)} \approx \frac{25 knots}{Time}

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We can confirm this formula with the example, where we calculated that if it took Hōkūleʻa 5 seconds to sail past an object:

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Speed = \frac{25 knots}{5} \approx 5 knots

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This formula of

speed = \frac{25}{time} knots

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only works if the distance between ʻiako is 42 ft. If you are on a canoe with a different length, you will need to calculate a new number. You can obtain that number by replacing 42 feet in the previous example with the length of your canoe.

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Example 1.1.2. Estimating Speed on the Makaliʻi.

On the Makaliʻi, the distance between the first and last ʻiako is 25 ft.

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Determine the magic speed number for Makaliʻi, rounded to the nearest integer.
If it takes Makaliʻi 3 seconds to pass an object in the ocean, use the magic speed number to calculate its speed.

Solution.

We’ll use the same method as we did for Hōkūleʻa, but since Makaliʻi is shorter, we’ll replace 42 ft with 25 ft.

$\begin{aligned} magic speed number & = 25 ft \cdot \frac{60 sec}{min} \cdot \frac{60 min}{hour} \cdot \frac{1 nautical mile}{6, 076 ft} \\ \approx 14.81 \frac{nautical mile}{hour} \cdot sec \\ \approx 15 (knots) \cdot sec \end{aligned}$

So, the magic speed number for Makaliʻi is 15. For any given time, we can calculate her speed with this equation:

$Speed = \frac{magic speed number}{Time (sec)} = \frac{15 (knots) \cdot (sec)}{Time (sec)} = \frac{15 knots}{Time}$
If it takes Makaliʻi 3 seconds to pass an object, her speed can be calculated as:

$Speed = \frac{15 (knots) \cdot (sec)}{Time (sec)} \approx \frac{15 (knots) \cdot (sec)}{3 sec} \approx 5 knots$

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Subsection 1.1.4 Classroom Activity

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Activity 1.1.1. Measuring Canoe Speed Activity.

Here’s how to measure and calculate the speed of your canoe:

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Get into groups. It’s okay if some groups have more people than others.
Choose one person to be the front of the canoe and stand at the front. Everyone else stands behind, keeping a one arm’s length distance between each other. Make sure to keep this distance the same throughout.
We’ll measure the distance from the front to the back to find out how long your canoe is.
Now, figure out your canoe’s special speed number.
Next, walk in a line with your group. Leave a one arm’s length distance between each person.
Pick something like a person, a desk, or if you are outside, maybe a pole or a tree, to be your marker.
When the front of your "canoe" passes the marker, someone shouts "Begin!"
Start counting "one thousand, two thousand, three thousand..." until the back of your "canoe" passes the marker. Then someone shouts "Stop!"
Write down how many seconds it took for your "canoe" to pass the marker.
Do this again for each group.
Now, calculate your canoe’s speed. Divide the special speed number by the seconds you counted.
Talk about your results. Did longer canoes go faster? Did the fastest-looking group really have the fastest speed? Compare the times to find out!

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Estimate the speed of Kanehunamoku

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Estimate the speed of Paikea, now use 1 nautical mile is equal to 1,852 meters

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