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Antarctic Math-pedition – 3 – Ponies and Ice

pancake ice

This may seem like a bit of unusual question for an Antarctic Expedition, but are there horses in Antarctica?  (Thank you, for your question).  As far as I can tell, no, there are none there right now, but there have been in the past.  Ernest Shackleton, who made a series of famous expeditions to Antarctica in 1901-1922, took a dozen Manchuran Ponies on an early expedition with him to help pull sleds of supplies.  Unfortunately, this did not work out so well.  One of the officers was injured when a pony kicked him in the knee, one of the ponies fell in a crevasse (a large crack in the ice) and had to be rescued, and eventually the ponies may have saved the lives of the starving expedition, when they provided food for the men.

A crevasse in the Antarctic ice.

To find out more about Ernest Shackleton and his expeditions to Antarctica, check out these links, at coolantarctica.com and wikipedia.org

And for some more fun pictures of Antarctica (like the one at left), go to  http://www.coolantarctica.com/gallery/Antarctica_gallery_home.htm

When I was a kid, we went ice fishing a lot.  My Dad always decided when the ice was thick enough for us to walk or ice skate on.  Here is some information about how thick the ice should be to hold a person (6” thick at least, preferably more) or a car (8” at least, and most people prefer 12”).

I would like it a lot thicker than that!  Fortunately, in Antarctica it is.  (Take a look at that crevasse again.)

Now let’s do a little pony math.  How thick does the ice need to be to hold one of Shackleton’s ponies?

First, what makes ice break?  You might say having too much weight will make the ice break, but if we spread that weight out over a large area, the ice would be able to support it.  What makes ice break is having too much weight on too small a space (too many pounds per square inch).

Let’s figure out how many pounds per square inch the ice is holding when a man stands on 6” thick ice.  To figure this out, we are going to have to make some approximations (educated guesses).   Let’s estimate the area a typical man stands on.   

Find a man, and measure the length and width of an imaginary box drawn around his feet.  My husband’s feet are 10.5“ long and about 12” wide (the two of them together).  Find the area by multiplying these two numbers (10.5 x 12 = 126 square inches).

Now let’s assume the average man weighs 150 pounds.

 To find out how many pounds per square inch he puts on the ice, take his weight and divide by the square area.   This would be 150 pounds / 126 square inches = 1.2 pounds per square inch.  So let’s assume that 6” ice can hold that many pounds per square inch. 

Now let’s do the pony math.  How many pounds per square inch would one of Shackleton’s ponies put on the ice?  Ponies like this probably weigh about 1000 pounds.  Each of their feet is about 5” x 5” (25 square inches).  With four feet, this will be 4 x 25 square inches = 100 square inches. They will put 1000 pounds / 100 square inches = 10 pounds per square inch.  So will the 6” ice hold the pony?  No way!  The 10 pounds per square inch pony is a lot more than 1.2 pounds per square inch man.

How about the car on the  8” ice?  A car weighs about 4000 pounds according to answers.com.  Measure how much of the tire is on the ground. Mine is about 12” long and 6” wide (12”x6” = 72 square inches).  There are four tires, so this is a total of 4 x 72 = 288 square inches.  The car puts about 4000 pounds / 288 square inches = 13.8 pounds per square inch on the ice.  So, if the ice (8-12” thick) can hold a car, it should also be able to hold a pony. 

Now let’s go find out how thick the ice in Antarctica is.  According to answers.com, the ice in Antarctica is typically over a mile thick!  It might even be up to 4 miles thick!  

I don’t think the ice will be that thick on the coast where we will be, but I don’t really know how thick it will be.  I will be excited to tell you when we get back! 

Sea ice forming.

Now, for a little more advanced analysis, let’s talk about what could go wrong with the approximations and calculations we just did above.  First, ice is not uniform. There are all kinds of imperfections, cracks, breaks, etc. in most ice sheets.  Just because ice held up a car in one place on a lake does not mean it will hold it up in all places on the lake.  For the Engineers amongst you, here are the details on how strong ice really is.  For the students who are learning about the periodic table at St. Xavier School in Kansas, check out Figure 1 in that link, which shows how four water molecules bond to form an ice crystal.  And here is a cool applet that shows you more about how the water molecules bond to make ice, which is why ice floats!

One of the things I really love about Engineering, is that you are ALWAYS learning something new and fascinating!

  • JGATCH

    My Pre-Algebra (Orange Book) math students are learning about using properties of equality to solve equations. We are making equations equal and performing the same operation on both sides of the equal sign.

    We are also learning about how to find the areas of combined polygons. We find the area of the polygons by splitting them into smaller polygons that have easier areas to calculate. Then we add the areas.

    How can you use math like this in the Antarctic?

    Mrs. Gatch’s Orange Math Group

  • JGATCH

    This is from Mrs. Gatch’s 7/8th grade Green Math Class.

    Last week we learned about areas of rectangles. Our teacher made us write a formula which is A=LxW. (Our teacher is big on having us write our formulas before we calculate.) You also multiply the length and the width to get the area. The units are called square units. (Our teacher is big on units too.)

    How do you use this math in Antarctica?

    Mrs. Gatch’s 7/8th Green Math class

  • JGATCH

    Mrs. Gatch’s 7/8th Red Math Class

    Last week we learned about the coordinate plane. The coordinate plane is a grid o which any point can be identified by an ordered pair of numbers. The two axis divide the plane into for regions called quadrants. The two axis are y-axis which is vertical and the x-axis which is horizontal.

    How do you use the coordinate plane in Antarctica?

    Mrs. Gatch’s 7/8th Red Math Class

  • JGATCH

    This is the 5/6th grade Red Math Group. We learned about coordinate planes. It is like latitude and longitude. You can make pictures out of it. You make certain coordinates and make certain shapes.

    How do you use this in Anartica?

    -Mrs. Gatch 5/6 Red Math Book

  • Bina

    Interesting math equations and calculations. Can a chopper land on ice. Is it lighter than a car from a square inch pressure perspective?

    • http://www.ece.utah.edu/~cfurse Cindy Furse

      The choppers certainly do land on ice. And the large haggalunds, etc. also drive all over the ice there. When the ice is 2meters thick … even a large plane can land on ice! (See our photos at http://cfurse.wordpress.com/ , linked on the right hand side).