Why does newspaper tear straight along its length but jagged across it?
― Inside paper, plant fibres lie side by side in one direction
Paper looks the same in every direction. But look inside and you find thin plant fibres lined up one way, like the grain of wood. A tear likes to travel through the gaps between those fibres.
You are packing for a move and tearing newspaper into long strips to wrap fragile things. Pull from top to bottom, and the paper splits in a clean straight line, as if you had used a ruler.
Turn the sheet and try to tear it sideways, and things change. It feels heavy, and the tear wanders left and right into a jagged line.
It is the same sheet of paper. Why does it tear so differently depending on direction?
Two things work together
Paper is made by scooping plant fibres, scattered in water, onto a screen. In a factory the screen moves fast, so the fibres settle lined up with the flow. This direction is called the paper's "grain".
Each fibre is strong, but the joins between fibres are much weaker. Tear along the grain and you only have to undo those joins. Tear across it and you have to snap many fibres.
So paper may look uniform, but inside it has a direction. It is much like a wooden board, which splits easily along its grain.
Why do paper fibres line up?
Paper starts as thin fibres teased out of wood. They are a few millimetres long and a fraction of a hair's width across. Spread them thinly in water, pour that onto a fine screen, and drain the water. What is left is a thin mat of tangled fibres. That is paper.
In a paper mill, the screen runs round like a belt. In fast machines it is said to move at over 100 km/h. Fibre-laden water is sprayed onto it with force. A long thin stick in a current turns to point along the flow. A twig floating on a river ends up pointing the same way as the water, for the same reason.
The paper then arrives at the newspaper company as a huge roll. The paper is printed along the roll's length and cut into lengths equal to one page's height. So in newspaper, the fibres lie along the vertical direction of the page.
Why does a tear choose the gaps between fibres?
Paper fibres are not held together by glue. As the paper dries, the surfaces of neighbouring fibres cling together, as if holding hands in tiny grips. That bond is far weaker than a fibre itself.
Look at Figure 1. The square on the left is the newspaper, and each short vertical line is one fibre. The thick slanted line is the tear. Move the slider to change the tear direction, and the bar on the right changes height. It is a rough count of the fibres crossed while tearing 1 cm.
When you tear lengthwise, the tear runs alongside the fibres. It snaps almost none and only undoes the joins between them. So it tears lightly and straight.
When you tear crosswise, many fibres stand in the tear's way. The tear keeps bending left and right, searching for any weaker spot. That is the source of the jagged edge. Look closely at a crosswise tear and you can see fibre ends sticking out and fluffed up.
In real newspaper, not every fibre points neatly up and down. Even so, the paper is said to be two to three times stronger when pulled one way than the other.
When making a book, the paper is cut so that its grain runs parallel to the spine. In the trade this is called "long grain". With the grain the wrong way, pages are harder to turn, and the paper tends to ripple in humid air. For a professional, the direction of the paper is part of its quality.
Traditional Japanese paper, such as the kind used in sliding screens, is made from the bark fibres of the kozo tree. These fibres are said to be about 1 cm long, several times longer than in ordinary paper. Long fibres tangle with many neighbours, so a tear has a harder time slipping through the gaps. Tear Japanese paper by hand and long hair-like fibres are left along the edge.
Summary
Paper is made by scooping plant fibres out of flowing water. The fibres lie in the direction of the flow, so the paper gets a wood-like "grain". A tear prefers the weak gaps between fibres, so it runs lightly and straight along the grain and goes jagged across it. In newspaper, that grain runs vertically.
Hidden inside paper is a grain, like that of wood.
A tear picks the path that lets it avoid snapping fibres.
For why paper weakens when wet, see Why does paper tear more easily when it gets wet?. For how wood's grain decides which way a board warps, see Why does a wooden board always warp the same way?. Stone has easy-split directions too (How can a stonemason split a huge rock with only wedges?).
- Tear it: Tear a newspaper or flyer 5 cm in each direction, lengthwise and crosswise. The direction that tears straight and easily is the way the fibres lie.
- Let it droop: From the same sheet, cut one narrow strip along its length and one across. Hold each by one end, sticking out flat. The strip that droops less runs along the grain.
- Wet it: Cut a square of paper and gently float it on water, one side only. The paper curls into a tube, and the tube's direction is the grain.
If all three methods agree, you can be sure. Try it on notebook and copier paper too. You will find that the grain direction differs from paper to paper.
For those who want more ― terms, formulas and links to textbooksEach part is labelled by level, from lower-secondary science to university courses
- Middle schoolCovered in lower-secondary science
- High schoolCovered in upper-secondary maths I and chemistry
- High school+Advanced upper-secondary content, or textbook sidebars
- UniversityUniversity specialist courses (mechanics of materials, geometric probability, pulp and paper engineering), not taught in high school
- ResearchNot yet settled even at university level; researchers are still studying it
Middle schoolTerms: this phenomenon has names
- Paper grain (machine direction): The direction in which the fibres lie side by side in the paper. It matches the flow direction in the paper machine.
- Long grain and short grain: Paper whose grain runs along the long edge is called long grain. Paper whose grain runs along the short edge is called short grain.
- Cellulose: The substance that plant fibres are made of. It is glucose joined into long chains.
Middle schoolHigh schoolChecking with a formula: how many fibres snap in 1 cm of tear?
When thin fibres are scattered through paper, you can estimate how many a tear line crosses using geometric probability. To keep it simple, assume all the fibres lie in the same direction.
| In symbols | N ＝ ρ × ℓ × L × sinθ |
| In words | Fibres crossed ＝ fibres per unit area × fibre length × tear length × (sine of the angle between tear and fibre) |
| Where it comes from | A fibre is crossed by the tear if its centre lies within a strip of width "ℓ × sinθ" on either side of the tear line. Multiply the area of that strip by the number of fibres per unit area (the idea of Buffon's needle). |
| Symbol | Meaning and unit |
| N | Number of fibres the tear crosses (snaps) |
| ρ | Number of fibres per square centimetre (fibres/cm²) |
| ℓ | Length of one fibre (cm) |
| L | Length of the tear (cm) |
| θ | Angle between the tear and the fibre direction. 0 degrees is the same direction, 90 degrees is a right angle |
| Fibres per square centimetre of newspaper (rough figure) | about 10,000 |
| Length of one fibre (rough figure) | about 2 mm ＝ 0.2 cm |
| Tear length | 1 cm |
| Sine of θ at 30 and 90 degrees | 0.5, 1 |
| Average sine for paper with random fibre directions (2/π) | about 0.64 |
| Number × length (ρ × ℓ) | 10000 × 0.2 ＝ 2000 |
| Multiply by tear length (ρ × ℓ × L) | 2000 × 1 ＝ 2000 |
| Tear crosswise (θ ＝ 90 degrees) | 2000 × 1 ＝ 2000 fibres |
| Tear at 30 degrees | 2000 × 0.5 ＝ 1000 fibres |
| Tear paper with random fibre directions | 2000 × 0.64 ＝ 1280 fibres |
| Tear lengthwise (θ ＝ 0 degrees, sine is 0) | 2000 × 0 ＝ 0 fibres |
Tearing just 1 cm crosswise snaps (or pulls out) about 2000 fibres. Tearing lengthwise, ideally, snaps none. In real paper the fibre directions vary, so the difference is not this extreme, and the strength ratio is said to be about 2 to 3. Even so, this formula explains the difference in heaviness you feel in your hand and the reason for the jagged edge.
High schoolHigh school+What holds the fibres together?
High schoolCellulose molecules carry many hydroxyl groups (a hydrogen and oxygen pair). As paper dries, the surfaces of neighbouring fibres join through hydrogen bonds. Each hydrogen bond is far weaker than the bonds inside a molecule.
High school+When paper is wetted, water molecules take the place of the partners in these hydrogen bonds. The fibres swell a lot across their width, but are said to change hardly at all in length. That is why paper wetted on one side only curls around the grain direction as its axis.
UniversityPaper is an "anisotropic material", and tearing can be read with geometric probability
A material whose properties differ by direction is called an anisotropic material. In papermaking, the flow direction of the machine is called the machine direction, and the direction at a right angle to it is the cross direction. Tensile strength and bending stiffness are greater in the machine direction, and in tear tests (the Elmendorf tear test) values are measured for each direction. The formula above uses the same idea as a geometric-probability problem known as Buffon's needle. By changing the ratio of the screen speed to the speed of the water jet (the jet-to-wire speed ratio), the machine can adjust how well the fibres line up.
📖 Derivation of the formula and further reading: Buffon's needle (Wikipedia, in Japanese) ／ Paper machine (Wikipedia, in Japanese)
ResearchWhat is still not well understood
- The strength of each fibre-to-fibre join. How much the bonds between fibres depend on hydrogen bonds, and how much on the tangling of surface fuzz, is still debated, starting with how to measure it.
- Predicting where a tear will bend. The fibre layout has random unevenness, and it is said to be hard to predict the exact shape of a jagged tear fibre by fibre.
- How fibres change in recycled paper. With each round of recycling, fibres become shorter and stiffer. How that affects paper strength is still being studied.
So the content of this article, too, is "an explanation within what is known today". Even the way a single sheet of newspaper tears still holds questions we cannot fully answer.
Links to textbooks (by level)
| Level | Subject / unit | Where in this article |
|---|---|---|
| Middle school | Science: "Structure of plants", "Materials around us" | Paper is made of plant fibres |
| High school | Maths I "Trigonometric ratios", Chemistry "Hydrogen bonds" | The sine changes the count; bonds between fibres |
| High school+ | Chemistry "Natural polymers (cellulose)" | Only the width swells when wet |
| University | Mechanics of materials, geometric probability, pulp and paper engineering | Anisotropy, Buffon's needle, fibre orientation in the paper machine |
| Research | Paper physics and fibre-network research | Bond strength, predicting tear shape |
| ― | Link to daily life | Tearing newspaper and flyers, bookmaking, sliding-screen paper |
- Wikipedia, "Paper" (ウィキペディア「紙」)
- Wikipedia, "Paper machine" (ウィキペディア「抄紙機」)
- Wikipedia, "Buffon's needle" (ウィキペディア「ビュフォンの針」)
- Japan TAPPI (紙パルプ技術協会), ed., Handbook of Pulp and Paper Technology (『紙パルプ技術便覧』)
- Niskanen, K. (ed.) "Paper Physics", Paperi ja Puu
* This article is a popular-science explanation for general readers. The numbers given are rough guides to help you grasp how things work. Fibre counts and lengths vary greatly with the type of paper.