 Project Center of Gravity

Background

Any object rotates around and translates through its center of gravity.  For a flying machine, knowing the location of the center of gravity is crucial for determining size and placement of control surfaces.    Great care is taken to precisely control the center of gravity on passenger planes.  Fuel tanks are managed so that they are emptied in a symmetrical way.  Cargo is loaded precisely.  Passenger seating is designed taking note of center of gravity.

Complex calculations involving mass, density, and part placement relative to a reference line are used in locating the CG for full size aircraft.  For paper airplanes there are easier methods using the basic, defining characteristics of the center of gravity to plot it’s location.

Throwing the aircraft so that it spins and noting the rotational center of the spin can easily show the center of gravity.  Suspending the aircraft from a string is another method.  On some paper airplane shapes, like The Tube, the CG is not actually on the aircraft, so the string method is difficult.

Question: Do different paper airplane designs share a similar position of center of gravity?

Hypothesis:  By locating the center gravity on a variety of paper airplane designs, a pattern of CG placement will emerge.

Methods:

Make at least seven paper aircraft designs that are different in shape and flight characteristics.  Use the spin test and the suspension method to locate the center of gravity on all the designs.

Chart the CG location relative to the front of the aircraft.  Correlate CG location with wing shape (square, delta, multi-wing etc.).  Also correlate CG location with flight path (glider, dart, and stunt plane).

Results here may suggest further experiments involving moving the center of gravity to create a particular kind of flight.  Using math to locate the CG is done every day loading cargo onto every passenger plane.

Finding the CG of a uniform block of metal is relatively simple.  The geometric center of this regular shaped object, with uniform density, can be done with simple meaurements.

Since the block is 6 inches long, 3 inches in from the front edge will locate the CG.  If we assume the block is one inch thick, the precise CG is three inches in and a half inch below the surface.  If the block were to spin during free fall, that's where the center of rotation would be.

What if, like a full size airplane, all the parts and packages weigh different amounts? The center of gravity can be thought of as the point where the average weight of the object resides.  In computing an average, you have many pieces that get measured.  The first step in finding the CG in a more complex structure is to break the whole into parts.  Let's break our block into six parts.

Let's us use a formula related to levers to find the average weight of the object.  Establishing a reference line out in front of our object is the first step. Let's choose 2 inches as our reference line's distance to the front of the block.  Because we're dealing with levers, measuring the distance from the reference line to the center of each segment is required.

Now we know the weight of each segment, and the distance to the reference line.  Time for applying a formula. Here, we've chosen convenient weights and measurements, so you can see how the formula works.  Now it's time to try it on a paper airplane.

Hint: Use graph paper to fold the plane.  Determine the weight of each square by using 4.5 grams as the weight of the paper.  That's what a 20lb sheet of 8.5 x 11 inch paper weighs.

Hint 2: Use your knowledge of how to find the area of right triangles to help count the squares in each part of the plane.  Your results will be accurate to roughly half the width of one slice.  The better you measure and count, the more accurate your results.