How to Make and Use a Mariners Quadrant with Pattern
Fun Math Activities for Kids
I know it sounds like a contradiction in terms for most people, but fun math activities really do exist. This activity teaches measurement, geometry, astronomy, and even some history by allowing children to build and use a mariner's quadrant.
While activity can be used in a classroom, it is perfect for at home learning and fun because kids can measure the heights of objects using a quadrant or, with a little more math, figure latitude the same way Christopher Columbus did. A few minutes of preparation are likely to lead to an afternoon of rushing around the yard measuring trees, signs, rooftops, and more.
If the capitalization in this article seems strange, it follows the conventions. These are different from English or History standards, but they are what you will see if you read a scientific article or NASA press release. If your kid(s) read this hub, you can use the capitalization as part of the science lesson. Council of Science Editors
How to use a Quadrant
What is a Quadrant?
The mariner's quadrant is a simple navigational tool and has seen use since, at least, the 1400s. Other types of quadrants, such as an astronomer's quadrant, have existed since Ancient times. The quadrant takes its name from its shape - a quarter of a circle. The wedge of wood has a scale from 0-90 degrees along the curved edge. A sighting vein runs along the top and a line with a weight, called a plumb line and plumb bob, respectively, hang from the corner. To use a quadrant, the navigator looks through the sight vein, allows the plumb line to hang freely, and takes note of the line's position along the degree scale.
In terms of celestial navigation, a quadrant is "better" than an astrolabe, but "worse" than a cross staff, back staff, or sextant. These later instruments have finer scales and make it easier to sight the Sun without staring directly at it. However, a skilled navigator with an almanac can calculate latitude fairly accurately by using a quadrant.
Steps for a DIY QuadrantClick thumbnail to view full-size
More Fun Math
How to Make a Quadrant
Making a quadrant is easy. You need a quadrant pattern (provided below), a drinking straw, some string or yarn, a bead, tape, and scissors.
- Print the quadrant on cardstock.
- Cut the quadrant, staying as close to the outer line as possible.
- Use a pin, pen, needle, or even a hole punch to make a small hole in the corner where marked on the template.
- Measure a straight side of the quadrant. Then, measure and cut 1.5x this length of string. This is a great way to have children do simple division and addition.
- Cut a drinking straw to the same length as the quadrant's side.
- Carefully tape the straw, which is your sight vein, along the 'top,' as shown on the pattern
- Tie one end of the string through the hole.
- Tie the bead to the opposite end on the string. It needs to hang below the scale edge of the quadrant, but whether it hangs half an inch or several inches below does not matter. I used a dark, thick cord to make the pictures more visible, you may want to use something smaller and easier to tie.
If you do not have card stock, trace the quadrant on to cardboard or poster board, cut this stiffening piece out, and glue or tape it to the back of the quadrant. The quadrant must be somewhat rigid in order to use it. If this is also not an option, tape a second straw, popsicle stick, or something else stiff along the quadrant's other edge to add rigidity.
For older, or more enthusiastic children, you can draw the quadrant pattern at home using a compass and protractor to make the markings.
Need Help with Triangles?
- More Hands-On Math--Using the Pythagorean theorem
This Hub is about teaching Middle School Math through the use of a hands-on activity.
How to use a Quadrant to Measure Height
The first way to use a quadrant is to measure the height of tall objects. As long as the object stands straight, you can measure anything's height, as long as you can get far enough away and measure the distance between you and it. All you have to do is set up what is called a 45-45-90 triangle. In this type of triangle, the two legs opposite the 45 degree angles must be equal in length. If this sounds confusing, look at the diagram to the right.
The angle between the ground and the object is your 90 degree angle, so to find the height of the object, use the quadrant to find the location of your 45 degree angle. First, pick a starting location. Then, allow the plumb line to hang freely and look through the straw to find the top of the object. You should look through the straw with the curved end towards your body.
After sighting, hold the string in place with your thumb and check the angle. If the angle is more than 45 degrees, walk further away from the object. If it is less than 45 degrees, walk closer.
Continue sighting through the straw and checking the angle until you find the 45 degree angle's location. If you want a truly accurate measurement, get down on your stomach and sight from ground level. Once you find the 45 degree angle, measure the distance between your location and the base of the object. You can do this by taking steps, bringing out a measuring tape, or any other method you like. The distance between where you measured the 45 degree angle and the object's base is the same as the height of the object! So, if you sight to the top of the tree and find your 45 degree angle location is 25 feet away from the tree's base, the tree is 25 feet tall.
You can even measure the height of very tall objects if you have an accurate GPS or GPS capable smart phone, iPad, etc. Pinpoint your location and the object's location - the distance between you and it is the object's height! You can measure bridges, skyscrapers, or even mountains with the assistance of modern technology.
The sextant is still used by celestial navigators today.
How to use a Mariner's Quadrant to Measure Latitude
Historically, mariner's quadrants were used to determine latitude, or one's distance north or south of the Equator. During the day, ship's navigators would have to look into the Sun to determine latitude. This caused many navigators to go blind. Do not look directly at the sun! Instead, use the following simple, eye-saving technique. Without looking through the sight vein, try to line up the straw's mouth with the Sun. Then, place your other hand below the straw. Move the quadrant, changing its position and elevation, as necessary, until you get the Sun to shine directly through the straw. You will know when this happens because you will see a point of light surrounded by a shadow ring appear on your palm. This takes some fiddling, but persistence pays off! Then, read the quadrant by taking note of where the plumb line falls along the scale. This reading is the Sun's altitude.
If you use the quadrant at noon, when the Sun is at its zenith, or highest point in the sky, on the spring or autumn equinox, the Sun's altitude is your latitude. If it is not one of these two days, you must do additional math to determine your latitude. Navigators used almanacs to look up the date and their approximate position to find out how much to add or subtract. Without an almanac, you have to do some math. This discrepancy occurs because, when compared to the ecliptic, the Earth's axis is not straight up and down. The ecliptic is simply an imaginary ellipses created by the Earth's annual movement around the Sun. If the ecliptic is a straight line, the Earth's axis tilts, currently, 23.4 degrees.
Determining latitude with a quadrant also uses a 90 degree triangle. You sight the Sun at noon, which allows you to assume a 90 degree angle between the Equator and the Sun. Even though the Earth is curved, this curvature does not interfere with the reading because the curvature is so slight when compared to the literally astronomical measurements used.The quadrant measures the Sun's altitude and you have a 90 degree angle at the Equator, so simple math tells you your position. In theory, you simply have to find your corner of the triangle's measurement by subtracting the Sun's altitude from 90 degrees.
In actuality, you have to compensate for the Earth's 'tilt.' To make matters more complicated, this tilt changes from day to day. This means you must find how much the Earth is 'tilted' on the day you take your sightings. The solar year is divided in four with two equinoxes and two solstices. At the summer solstice, the Earth is tilted its furthest 'in' toward the Sun and at the winter solstice is is furthest 'away.' The are roughly 91 days between each of these dates. Divide 23.4 by 91 to determine the number of degrees the axis changes by each day. It is about .26. Then, calculate how many days you are away from the nearest equinox or solstice. At the time of writing, it is three days after the summer solstice, so I multiplied .26 by 89, the number of days until the next solar event. This is about 22 degrees. My noon Sun reading was 78 degrees. Subtract the reading from 90 degrees and add the modifying number. My math was 90-78+22 which is 34. I am in Charleston, SC and my latitude is actually 32.79, so I am a little more than a degree off, but that's not too bad, especially since I rounded a lot. The more decimal places you carry, the more accurate your calculation will be.
To accurately determine your latitude with the quadrant using the stars, go outdoors on a clear night and sight Polaris, the North Star, instead of the Sun. When you sight Polaris, its declination is your latitude, no matter the time of year. If your plumb line hangs at 33 degrees, then you are at (approximately) 33 degrees latitude. This is very easy on shore, but difficult on the rolling deck of a ship!
Celestial Navigation with a Sextant
Have Fun with Math
While most children do not get excited about math, cutting, taping, beads, and finding out the heights of very tall objects are fun. I have helped many children make quadrants during presentations about historic navigation techniques and know kids love making quadrants and the powerful feeling that comes from measuring enormous objects. If you really want to excite children, tell them this is what pirates used. A few years later you can let them know the quadrant was actually the record player of technology by the time pirates came around - for today, let them have fun doing geometry.