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CHAPTER 1

Selecting and Preparing Your Paper

First, a word about the basic origami folding essentials: having fun folding paper airplanes doesn’t require much. All you need is:

• A few sheets of suitable paper.

• A clean, hard, folding surface.

• Good lighting.

• Something to trim your paper to size.

• Something to help you make sharp, accurate creases.

The last two items are not essential. We can easily trim paper without tools by creasing and tearing, but the last item is worth a little discussion. Great planes have properly-placed, sharp creases. Generally, the back of your thumbnail works fine for installing creases, but some folders prefer to use their favorite “folding tool,” a handy device that comes in a variety of shapes and lengths, available in craft stores. They may be plastic, or fashioned of wood, stone or bone (bone folders), but there are plenty of no-cost substitutes: Young children with tiny fingers, and teens sporting fashionable fingernail artistry, can still make sharp creases using the bottom of a spoon. Beginners can define a crease line by folding the paper up against a straight edge, but soon you will easily use several fingers to roll the paper between two points before you press down on the curl to commit to the crease placement.

Paper airplanes demand precise placement of the creases, so don’t skip the introductory Symbols Key and folding tips presented in the next chapter, even if you have other paper folding experience. If the models you fold do not fly well, go back and master the simple, but critical folding techniques. In a short amount of time you will learn a lot about paper, develop fundamental folding skills, understand the symbols in an origami diagram, and learn what makes these paper airplane designs so neat.

Paper Selection

Paper selection for competition may be important, but for practice paper, just look in your recycle bin. You can find suitable paper for airplanes nearly everywhere. The designs presented in this book work well with the most widely available paper types: letter-size, 20-pound bond, and common sizes of square “origami paper.” Printer and copy paper is fine for any project in this book. If more types are available, use the heavier papers for simpler designs, and save the larger, lighter-weight papers for the more complex designs.

Paper is often supplied at a paper airplane competition (which simplifies the judging) but sometimes you will be given a choice. For competition, first select the best airplane design for the category (e.g., greatest distance, greatest time aloft, best aerobatic, best target accuracy, coolest design, etc.) and then select the paper for that design that works best for you. When you have a choice of papers, consider:

• Paper format

• Squareness

• Weight

• Thickness

• Foldability

• Rigidity

• Aesthetics (color, finish, graphics)

This photo shows an assortment of common paper rectangle types: square, 8 ½ by 11-inch US office paper and A4 letter paper.

Paper Formats

Most published origami paper airplanes have been designed to be folded from one of these three common, handy rectangles: square origami paper; 8½ by 11-inch office paper used in North America; or A4 letter paper used most everywhere else.

We have included designs for all three formats. We have also included instructions on how to produce these three rectangles from stock so that you may enjoy folding all of the designs, no matter what format of paper is handy. For practical purposes, rectangular papers can be expressed in terms of absolute measurements, aspect ratio and diagonal angle measurements. Understanding these expressions will allow you to scale rectangles into larger or smaller sizes as needed.

Avoid performance-affecting inconsistencies, such as the one shown in this illustration, by taking care to use only accurately, cut rectangles.

Rotate part of a stack of paper 180 degrees, square one end, and then check the other end for squareness.

You can also inspect squareness by folding a piece of paper in half to make sure that the loose corners line up on both sides.

Squareness

Many folders blame themselves if their folding seems off, without ever considering that the paper may not be cut properly. When you open a package of square origami paper, remove a few sheets from the center of the stack, rotate it 90 degrees, and align the ream with one edge of the stack on the table. If the sheets you turned stick out, either on top, or on a side, you know that paper was not square. Similarly, when you open a ream of office paper, turn a few sheets from the center around 180 degrees and align one end with a tap on the table. Look at the top edge to see if the rotated sheets are even along the top, or if they stick out at either side.

You can also try the following folding experiment. Take a sheet of letter paper and fold it in half, long edge to long edge. Are the edges and corners of the top layer matching those of the layer beneath?

Next, unfold the paper and form a simple “airplane point” at one end of the sheet by folding the two halves of a short edge to meet at the center crease. Do the two square corners meet?

Unfold the paper and try the same thing at the other end. It is not uncommon for a sheet to fail these tests for trueness. In most cases, trim discrepancies are slight and can be accommodated for folded paper airplanes. However, when the trim error is off by several millimeters you should consider re-trimming the paper to true it up. This will be especially important for performance-critical contest entries.

To learn if your store-bought origami paper is acceptably symmetrical simply fold the sheet in half diagonally, corner to corner. The edges and the free corner of the top layer should match those of the bottom layer.

Thickness

The planes in this book were designed to be folded from many common types and sizes of paper—either origami paper or 20-pound letter bond—but a general guide will be to use thinner papers on the complex models and thicker on the simplest ones.

There is also the issue of relative thickness, which can be expressed as a ratio of thickness to area. You can use a thicker paper if the area is increased, but thinner stock must be used if you decrease the area of the sheet.

If you were to graph the variables of the acceptable planes, you would determine the designs’ acceptable range of relative thickness. Each paper airplane design will have an optimum size for a given thickness. When designing new paper planes it is wise to keep the technical handling of the folds well within the doable limits of the paper with which you are experimenting. Some paper folding design plans may accumulate many layers in certain places, such as the nose or the leading edge of the wings. Choose paper thin enough to accommodate the folding in the thickest places of the model. If an airplane folded from thick paper does not perform well, perhaps that design should be folded from a larger sheet, in order to bring the design back into the “doable range” (or window of acceptability).

Weight

Most office and printing stocks fall into one of two types: “Bond,” and “Offset.” Each type has different weights, sold in packs, or reams, of 500 sheets. The ream is marked with a number indicating the weight, such as 20-pound (abbreviated 20 #, 20 lb, etc.). When you lift a 500-sheet ream of 20-pound bond, the first thing you notice is that it cannot possibly weigh 20 pounds. That is because all grades of bond are labeled with the weight, in pounds, of a much larger ream measuring 11 by 22 inches—which is called the basis size for bond papers.

It’s confusing, but reams of so-called “offset” paper stocks (including “book,” “text” and “coated” stock) used in professional printing presses are made by different machinery, so their weight is described by a different basic size sheet: 25 by 38 inches. You can’t compare the two types by only considering the area. The 50-pound offset stock is slightly lighter than 20-pound bond because the machinery that makes the offset paper uses a process that makes it thinner and denser.

The system is useful when comparing the weights of the same types of paper: 24-pound bond is 20% heavier than 20-pound bond (24-20=4; 4/20= 20%), and 60-pound offset is 20% heavier than 50-pound offset paper (60-50=10; 10/50=20%).

Metric units are more direct. When paper “weight” is described in grams per square meter, this removes confusion, but we are probably stuck with knowing and using at least a few different systems for a while.

Only simple, large models can be folded from heavy papers. When you fold the same design from different weights of papers with the same area, those from heavier papers will glide farther, but are less likely to look neat because of bunching caused by the increased thickness. When you lift an airplane and launch it, your arm is imparting a force on the mass of the plane. Those folded from heavier papers have greater mass, but essentially the same area and resistance to air molecules. Other variables being equal, increased mass translates to increased potential energy, and greater distance.

Foldability

How well does the paper take a crease? How many times can the paper be folded back and forth before it splits or cracks? How long does that crease stay crisp? Many papers today are coated with plastic, paint, clay, varnish, wax or even silicone. Some are fused to metal or plastic films. Heavily coated papers and foils are unforgiving of poor technique, so it is important to choose papers that fit your folding skills. At the very least, it is fun and instructive to test an origami airplane on many kinds of papers. This is when the paper is your best teacher.

Rigidity

Rigid paper planes are generally more efficient and fly better than floppy planes. The rigidity can come from the weight and size of the paper, but also the folding method. Compare a paper towel to a sheet of letter paper. Each was formulated and manufactured differently to best suit a particular need. A soft paper towel does not make a good paper airplane: it would be too floppy. However, a paper plane that is folded from a very large sheet of office paper, say four times its typical size, could be so heavy, that the shape of the flaps and wings would distort.

Moisture in the air changes from day to day and also affects paper’s rigidity. On very humid days, you may have noticed that fins flutter and wings droop—this change of shape affects motion. As a deformation propagates along the surface, it results in extra wind resistance and unwanted drag. Energy expended to flex the structure is energy drained from the momentum (forward path of force), shortening or even stalling a flight. Unequal distortions to wing or fin can also result in an erratic path. Using slightly smaller sheets of paper can improve rigidity, as can choosing models that have multi-layered wings with several folded edges.

Special planes intended for photography or display often benefit from the use of crisp tracing paper, which really shows off the intricate folds and precise workmanship.

Rigid wings of balsa or from composites of paper card will always perform better than pure origami planes. Nevertheless, origami airplanes can produce some impressive and very satisfying performances.

Aesthetics Impact Performance

Color pigments, printing inks, and toners on the paper may have a small, but measurable impact on a paper airplane’s mass (and therefore density), surface roughness and symmetry. Besides these technical aspects, the aesthetics of a paper airplane’s appearance may influence the crowd and psych-out the competition. Do drivers of bright red cars receive more speeding tickets? Does the car’s color somehow motivate the driver to hit the gas pedal harder? Do people who are more likely to speed select car colors of the more aggressive hues? Use plain white paper if you subscribe to the maxims “Beauty is only skin-deep,” or “Don’t judge a book by its cover.” This lets you appreciate the elegance of the plane’s lines and geometry. Aesthetics can also be a function of age and culture, so you must decide how to play this card.

Putting It All Together

Paper selection depends upon why you are folding the model. If you are just practicing, use anything available. If you have plenty of used copier paper handy in a recycle bin, begin by learning the models that work well from that format. If you are supplying the paper for an airplane competition, a ream of 20-pound office paper is readily available and inexpensive, so that is what most people use. If a local printing company will donate the paper, ask for 50-pound offset, but don’t be fussy. Thank them profusely, even if they give you misprints. (There are plenty of sponsorship opportunities here.)

When folding paper airplane models for display or photography, we sometimes prefer to fold thin, crisp, white tracing paper with a hard surface finish (this stock is translucent, which shows off the interesting lines of internal folds). These models may not fly as well because the paper is light. Although the creases look sharp, they are also weak. One final note: terms such as “bond,” “offset” or “letter” paper are generic. You should expect quality to vary between different brands, and even paper formulations of the same brand can be changed from time to time. Test, test, test!

Testing Papers

Trial and error is a good teacher, but using the scientific method will help you to organize your investigations and better evaluate your findings. The following is a simple experiment to test papers against airplane designs.

1. Choose one design.

2. Fold several versions with the same size, but different types of paper.

3. Fly each and make notes about their performance.

4. If performance correlates with a given characteristic (say, weight), fold more models with even heavier paper, to determine where the performance benefits trail off.

5. Note the weight that gives you the best performance.

6. You can run the tests again with the same design but with a different variable, say square area.

Eventually you will be able to match paper type, size and airplane design to get your best performance. Remember, you are a variable, too!

Now that you know more about paper types and choices, you will be rewarded by being able to make better choices and evaluations, whether at a paper airplane competition or for your own enjoyment.

Fold the same design at different sizes to discover which scale works best for a given plane.

Additional Paper Handling Tips

Here are some additional tips to optimize your folding experience:

• Make sure your hands are clean and dry. Sorry for nagging, but paper can easily absorb oils and moisture from your skin.

• Leave the paper in the packaging. Paper left out of its packaging is subject to damage from a variety of agents.

• Examine both sides of the paper carefully. Some papers have a finished side that is smoother than the other side. Know which side will show when you fold your model. We have color-coded our diagrams to help you: White is the inside of the model and the colored side is the predominant display side of the finished model.

• When using pages from discarded magazine or calendars, or other “trash” papers, make sure the sheet is completely flat and that the corners are square. Trim to remove any ugly wrinkles or bruised edges.

• If you are adding graphics to your paper, be sure to leave enough time for toner to cool, or inks to dry before folding. Incidentally, papers that pass through the heated rollers of toner-based printers and copy machines seem to become crisper and make better planes.

• Planes that sit around for a while will tend to lose the sharpness in their creases, making them sloppy, unbalanced and not airworthy. Always refresh your creases and check symmetry before flight.

Preparing Your Paper

In the following sections we provide several methods for trimming paper to the proportions used in this book. Use a straightedge or ruler, pencil, and scissors or paper cutter, to easily scale your papers, making larger or smaller sheets of each format. You can use any of the numbers, displayed with each of the rectangular icons in this section, as factors to scale or trim your paper.

Square Paper

Square paper is the simplest format to prepare, and you can even do it without any tools. This is perhaps why the square is the most common format for origami design. Vertical and horizontal sides are equal, so the ratio of a square’s adjacent sides is 1:1. To prepare the largest possible square from any rectangle simply fold one of the short edges to match an adjacent long edge. If you do not want to make a diagonal crease, use two sheets of the same size rectangle, overlapping them at one corner while aligning the second perpendicular to other. Trim the excess of each for two clean squares.

The technical specifications of a square.

To turn a long rectangle into a square, fold at a 45-degree angle, short edge to long edge. Unfold, and trim. Don’t toss those trimmed strips into the recycling bin just yet! See page 87 for a great use for these scraps.

A Word About A-Series Paper and the Silver Rectangle

A4 letter paper is a common format outside of North America. The A-Series format, prescribed by the International Organization for Standardization (ISO), is a Silver Rectangle, with adjacent sides having an aspect ratio of 1: √2. The larger side is as long as the length of the diagonal of the largest possible square. One particularly desirable characteristic of paper in this format is that when a Silver Rectangle is divided in half through its long edges, the resulting, smaller rectangles have adjacent sides in the same proportion as the parent rectangle.

If a diagonal crease is not desired, simply take another sheet of the same dimensions, turn it 90 degrees, and lay it atop the first sheet. Trim away the excess.

The technical specifications of A4 paper.

Turn US letter size paper into a Silver Rectangle by executing the steps depicted in the series below.

Scale Any Rectangle

It is useful to know how to cut smaller or larger rectangles of the same proportion to make paper planes that perform well and look better on display. No matter the kind of rectangle, the method is the same. Inscribe a diagonal line that spans two corners of the rectangle. Intersect this line at any desired point, and connect that point back to each edge with perpendicular cut lines leading to the vertical and horizontal edges.

Forming a US Letter Proportion from a Square

Letter paper commonly found in North America measures 8½ inches by 11 inches. You can measure and cut these rectangles from odd stock and you can use the above method (see “Scale Any Rectangle”) to make larger or smaller examples. However, there is a quick approximation you can use to make rectangles with proportions close enough for the projects in this book. Fold the square in half, edge to edge, but make only a pinch to mark the center. Open. Fold one edge to the pinch and trim off the resulting flap. The remaining rectangle will have an aspect ratio of 1: 0.75, which is acceptably close to the proportions of US letter paper (1: 0.77) to be used for the majority of the planes in this book.

Forming a US Letter Proportion from an A4 sheet

A4 paper is handy to paper plane enthusiasts in Europe and Asia. Though some of the models in this book can be easily adapted to the A4 sheet, most of the US letter models will look better and fly best if folded from rectangles with those proportions. It is an easy task to trim the A4 sheet to the correct proportions: simply cut a 1-inch (2½-centimeter) strip from a short edge of the sheet. Incidentally, these slightly smaller models fly extremely well!

It’s a simple matter to scale any rectangle up or down: just draw a diagonal line between two corners and intersect at any point.

The technical specifications of US letter paper.

You can quickly adapt any square to approximate US letter proportions using the steps shown here.

You can quickly convert any A4 size sheet to US letter size using the steps shown here.