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The Math of Maple SugaringPowerPoint Presentation

The Math of Maple Sugaring

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The Math of Maple Sugaring. By Mary Carter GED 613 11/30/09. It’s a Vermont Thing.

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It’s a Vermont Thing

Every spring, plenty of Vermonters get ready for the sweetest time of year… Sugaring season! It’s a very complicated process, and although we love to use phrases like, “pert near” and “thay-at thair”, there are actually rather specific math concepts incorporated into the making of this delicious maple syrup.

Into the Sugarbush

People who sugar have an area filled with maples that is known as a sugarbush. Mine is about 13 acres and is equipped with over 500 taps. That means there are over 38 taps on every acre of land.

When everything is just right…

- The sap used for maple syrup comes from sugar maple or red maple trees.
- When a tree reaches 40 degrees F, starches that were stored in its roots convert to sugars which then enter the tree sap.
- At 45 degrees F, the tree stops producing sugars.
- As it gets warmer in the spring, pressure within the tree causes the sap to be pushed out. These are called periods of flow.
- The times at which a tree is producing sap can be shown on a number line:

39°F

40ºF

41ºF

42ºF

43ºF

44ºF

45ºF

46ºF

47ºF

It begins with a tree…

The size of the tree is important. A tree must be at least 10in. in diameter to be tapped.

Diameter refers to the length of a straight line passing through the center of a circle and ending at the edge.

10 in.

Other ways to measure…

You can also measure the circumference of the tree.

The circumference refers to the length of the boundary line of the circle.

A tree must have a circumference of 31 inches in order to be tapped.

31 in.

Ratios of Taps to Tree Size

As trees get larger, they can accommodate more taps. This is shown in the table on the right. No tree, no matter how big, should have more than 3 taps.

Drilling the Tap

A tap should be drilled into the southern-facing side of a tree about 3 feet off the ground for the greatest flow. Using a 3/8 drill bit (depending on the size of your taps), drill a hole with an upward slope to help the sap flow freely downward with gravity. The hole should be drilled 1 ½ - 2 inches deep to pierce the veins of the tree.

Rate of Sap Drips

The rate that sap drips into a bucket or tubing depends on the temperature and the pressure being exerted on the tree. The greater the pressure, the faster drip per second ratio.

Liquid Measures

Sap is measured throughout the sugaring process in the containers used. A standard sap bucket holds 3 gallons of liquid, but should be emptied at 2 ½ gallons. Sap is also stored in large tanks. They can range from holding 35 gallons to over 1500 gallons of sap! It would take 600 gallons to fill a tank that size! Instead, tanks this large are usually filled using tubing instead of tap buckets. The tubing runs from tree to tree, collecting sap from taps that flow directly into the tube.

How much sap can one tap make?

In an average year, each tap can be expected to produce enough sap to make a quart of syrup. That doesn’t seem like a lot, but wait until you find out how much sap it takes to make syrup!

A lot of sap goes in but just a little syrup comes out…

Earlier in the season, it takes less sap to produce a gallon of syrup because the sugar content in the trees is high. Later in the season as the sugars decrease, more sap is required to make maple syrup. These changes average out to a ratio of 40 gallons of sap per one gallon of syrup. If one tap makes a quart of syrup a year, how many gallons of sap will it produce?

Boiling points of evaporators

Finally we get to the fun part… boiling! Sap is poured into the pans of an evaporator to be boiled. As the temperatures heat up, the water in the sap evaporates and leaves behind sweet sugars that make maple syrup! The syrup will be the right consistency when the sap reaches a boiling point of about 219 degrees F, or 7 degrees F above the boiling point of water, which can vary depending on elevation and barometric pressure. If the sap starts out at a cool 40 degrees F, that means it must heat 179 degrees F before it’s ready! That can take a long time.

Additives Cut the Froth, Add the Flavor

When syrup boils, it gets very frothy. To prevent the froth from spilling over, sugarers need to add something to bring it down. We add butter, and it gives it an excellent flavor. Vermonter’s might say to add “a bit” but really we add about a tablespoon per tray. A tablespoon is the equivalent of 3 teaspoons, or 1/16 of a cup!

Bottling it Up

When the syrup is ready, it can be bottled. It must be bottled hot at 180 degrees F with very little air to create a tight seal. Syrup is typically bottled in half-pints, pints, quarts, ½ gallons, and gallons.

Syrup for Sale!

Syrup prices differ depending on where you buy it, but we sell ours for relatively cheap. A half-pint is $5, a pint is $8, a quart is $12, a ½ gallon is $20, and a gallon is $35. If we make an average of 40 gallons of syrup per year, and sell it all off in quarts, how much money will we make? How would we have to sell it to make the most money? What other possible sale/profit combinations might we have?

Clean Up Time

It’s the end of the season, and time to clean up! The equipment must be sterile, so a specific solution of one part bleach to 20 parts water must be used to clean it all out! That is a ratio of 1:20, or 5% bleach. Now we are ready for a new season!

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