Does the stronger team always win a tug of war?
― The rope pulls both teams equally. The contest is decided at your feet
Tug of war is the star event of the autumn sports day. It's easy to assume "the stronger team wins" — but actually, the force the rope exerts on each team is exactly the same throughout the match. So what decides the outcome? Not the rope. The ground beneath your feet.
White lines are chalked on the schoolyard, and children line up on either side of a thick rope. At the crack of the starting pistol, everyone goes red-faced pulling as hard as they can.
For a while, the red marker at the rope's centre just drifts back and forth. Then, at some moment, one team suddenly gets dragged forward, and the match is over in a flash.
Did the losing team suddenly lose their strength at that moment? Actually, no. What gave way wasn't their arm strength — it was their footing.
Two things decide who wins
The rope pulls on both teams with the same force. The difference lies in the upper limit of the force the ground can push back with. Whichever team's feet slip first, loses.
Being pulled by the rope makes your body want to topple forward. Leaning your body back uses your weight to resist this, and holding the rope low makes you harder to topple.
Let's start with the most surprising part — that the rope's pull is always the same.
The rope always pulls both teams with equal force
Say you're holding one end of the rope and you pull hard. The rope pulls back on you just as hard. Push something, and it pushes back — that's a basic property of force.
The rope itself is very light, so the force passes straight through it unchanged. That means the force the left team exerts on the rope, and the force the right team exerts on the rope, are the same size at every single moment. It never happens that one side pulls harder than the other.
Look at Figure 1. The two arrows at the top are the forces the rope exerts on each team, pulling them toward each other. They're the same length. What holds each team in place against this pull is the arrow at their feet — the force of the ground pushing back (friction). This force has an upper limit. Whichever team has the smaller limit has their feet slip first, and they get dragged forward, rope and all.
The upper limit of how hard the ground can push back on your feet mainly comes down to two things. One is how heavily your feet press onto the ground — the heavier the team, the higher the limit. The other is how slip-resistant the sole of your shoe is against the ground. Even at the same weight, slippery shoes or wet grass lower that limit.
So tug of war is less a contest of arm strength than a contest of footing. In official competitions, teams are grouped into weight classes by combined body weight — because weight translates directly into strength here.
Why lean back? To avoid being toppled
Even if your feet don't slip, there's still another way to lose: being pulled forward and toppling over entirely.
The rope pulls your body forward at hand height. Your body tends to rotate forward, pivoting around your feet. The only thing that can resist this is your own weight. Shift your centre of gravity behind your feet, and your weight tries to rotate your body backward. When these two rotating forces balance, your body doesn't tip.
Look at Figure 2. The lower you hold the rope, the smaller the forward-rotating force becomes — so you need to lean back less to compensate. That's why experienced teams crouch low, hug the rope close under their arms, and end up almost lying down.
Why does the losing team collapse all at once?
Recall the opening scene: the marker drifts back and forth, then suddenly the match is decided. This, too, comes down to what happens at your feet.
Between a foot at rest and the ground, a large force can be resisted right up until the point of slipping. But once slipping starts, the push-back force drops to a noticeably smaller value. It's the same reason a heavy piece of furniture suddenly feels lighter to push the instant it starts moving.
In other words, once a foot slips, it becomes weaker than it was before slipping. Since the rope's force doesn't change, the slide doesn't stop — the whole team gets dragged along. That's why the match isn't decided "gradually" but "in an instant."
When an entire team's strength concentrates on a single rope, the force involved is comparable to hanging an object weighing several hundred kilograms (worked out in the expandable section below). Wrapping the rope around your wrist or arm means you can't get free if it's suddenly yanked or if it snaps — cases of serious injury from this have been reported. Hold the rope only in your palms.
Tug of war was an official Olympic event from 1900 to 1920. International competitions still exist today, contested in weight classes based on combined team body weight.
Summary
The force the rope exerts on both teams is always the same. What decides the winner is the upper limit of force your feet can get from the ground, and how well your body leans to avoid tipping forward. A heavier team, less-slippery footing, and holding the rope low all help. And because a foot that's started slipping becomes weaker, the match gets decided in an instant.
Tug of war isn't a contest of arms pulling against each other.
It's a contest of feet gripping the ground.
The idea of balancing "force × distance" around a pivot point shows up in the same form in why holding a load away from your body strains your lower back.
- Have two people hold either end of a towel and pull gently against each other on the floor. One person wears socks, the other goes barefoot.
- Pulling with about the same force, see whose feet slip first. Then have the one who slipped crouch low and hold the towel low, and try again.
- Finally, try it with the lighter person barefoot and the heavier person in socks. Compare which matters more — body weight or footing.
Don't pull too hard, and do this slowly in a wide open space where a fall won't cause injury. Never wrap the towel around your hand.
Want to know more? ― Terms, formulas, and textbook connectionsWe mark which level each part belongs to, from junior-high science to university specialist courses
- Jr. Highcovered in junior-high school science
- High Schoolcovered in high-school "Basic Physics" / "Physics"
- High School+advanced high-school content, or textbook sidebar material
- Universitynot covered in high school — university-level specialist courses (mechanics, tribology)
- Researchnot even settled "textbook fact" at university — something researchers are still actively investigating
Jr. HighTerms: this phenomenon has names
- Action and reaction: whenever you push or pull something, it always pushes or pulls back on you with equal force in the opposite direction. This is why the rope's force is the same for both teams.
- Friction force: the force between two touching surfaces that resists sliding. This is the force holding each team in place during a tug of war.
- Tension: the force a taut rope or string exerts, pulling on whatever is at each end. For a light rope, this is the same size everywhere along its length.
Jr. HighHigh SchoolChecking with formulas: the upper limit of force a team can withstand
Let's estimate the upper limit of rope force a 10-person team can withstand without slipping. Then we'll work out how far back one person needs to shift their centre of gravity to avoid tipping forward.
| In symbols | F ＝ μ × M × g (condition for not tipping: T × h ＝ m × g × d) |
| In words | the upper limit of force withstandable without slipping ＝ slip resistance (coefficient of static friction) × combined team weight × gravitational acceleration. The condition for not tipping: rope force × rope height ＝ one person's weight × backward shift of centre of gravity |
| Where the formula comes from | The top formula comes from the "law of static friction": the maximum friction force is proportional to the force pressing the surfaces together. The bottom formula is the balance of two rotational effects (moments of force) trying to rotate the body around the feet. The rope force being equal for both teams follows from the law of action and reaction. |
| F | the upper limit of force a team can withstand without slipping (in newtons) |
| μ | coefficient of static friction between shoe sole and ground (no unit) |
| M | combined weight of the whole team (in kilograms) |
| g | gravitational acceleration (about 9.8, in metres per second squared) |
| T, h | the rope force one person receives (newtons), and the height at which they hold the rope (metres) |
| m, d | one person's weight (kilograms), and the distance their centre of gravity shifts backward of their feet (metres) |
| Team size and combined weight | 10 people, 500kg total (50kg each) |
| Gravitational acceleration | 9.8 metres per second squared |
| Coefficient of static friction, sneakers on dry soil | taken as roughly 0.6 (varies a lot by ground and shoe) |
| Coefficient of static friction, slippery conditions (wet grass, etc.) | assumed roughly 0.4 |
| Height of holding the rope | about 1.0m, roughly hip height |
| Team's weight (newtons) | 500 × 9.8 ＝ 4900 |
| Upper limit F on dry soil | 4900 × 0.6 ＝ 2940 |
| Equivalent to hanging how many kilograms? | 2940 ÷ 9.8 ＝ 300 |
| Upper limit F in slippery conditions | 4900 × 0.4 ＝ 1960 |
| Rope force T received per person | 2940 ÷ 10 ＝ 294 |
| One person's weight (newtons) | 50 × 9.8 ＝ 490 |
| Forward-rotating effect of the rope (height 1.0m) | 294 × 1.0 ＝ 294 |
| Required backward shift of centre of gravity d (metres) | 294 ÷ 490 ＝ 0.6 |
| Holding the rope at 0.5m height | 294 × 0.5 ＝ 147 |
| d in that case (metres) | 147 ÷ 490 ＝ 0.3 |
On dry soil, a 10-person team can withstand a force equivalent to hanging about 300kg. On slippery footing, the limit drops to roughly two-thirds even at the same body weight. And halving the rope height also halves the needed backward shift, to just 30cm. That's the numerical proof that crouching low is an advantage.
High SchoolHigh School+What's really behind "weaker once it starts slipping"
High SchoolBasic Physics teaches that the upper limit of static friction (maximum friction force) is "coefficient of static friction × normal force," while kinetic friction while sliding is "coefficient of kinetic friction × normal force." For most material pairings, the coefficient of kinetic friction is smaller than the coefficient of static friction. That gap is why the losing team collapses all at once.
High School+In the tug-of-war stance, the body is stable when it's leaned so that the total ground force on the feet (normal force plus friction combined) passes close to the body's centre of gravity. That lean angle is related to the coefficient of static friction — at a coefficient of 0.6, it works out to roughly 31 degrees from vertical. The less slippery the ground, the more deeply you can lean.
UniversityThe friction coefficient isn't really a "constant"
The high-school relationship — "friction is proportional to the pressing force and doesn't depend on contact area" — is an empirical rule called Amontons–Coulomb friction. Real shoe soles are made of rubber, and rubber friction arises from both repeated viscoelastic deformation (hysteresis friction) and surface adhesion. Because of this, the friction coefficient varies with sliding speed, temperature, and the fine texture of the ground. The study of friction is called tribology. The body-lean condition is exactly the balance of moments of force treated in rigid-body statics.
📖 For the derivation and further reading: Friction (Japanese Wikipedia) ／ Moment of force (Japanese Wikipedia)
ResearchWhat's still not fully understood
- Does per-person force drop as team size grows? In the 1910s, France's Ringelmann is said to have measured that per-person force drops as more people pull together on a rope. How much of this comes from timing mismatches versus reduced motivation ("social loafing") is still debated.
- Can rubber friction be predicted from first principles? There's still no theory that accurately calculates the friction coefficient of shoe-sole or tyre rubber purely from material properties. In practice, direct measurement remains the standard.
- Does synchronising rhythm really make a team stronger? The effect of chants synchronising the timing of everyone's pull is known empirically, but there aren't many detailed measurements of exactly how much it affects whether feet slip, during an actual match.
In other words, even the contents of this article are "the best explanation given what's currently known." Treat the friction-coefficient values in particular as rough guides that vary a great deal by ground and footwear.
Textbook connections (by level)
| Level | Subject/unit | Where in this article |
|---|---|---|
| Jr. High | Science Field 1, "Effects of forces," "Action and reaction" | Why the rope's force is equal for both teams |
| High School | Basic Physics, "Friction force," "Balance of forces" | The upper limit before feet slip; why kinetic friction causes a sudden collapse |
| High School+ | Physics, "Equilibrium of rigid bodies (moments of force)" | The relationship between backward lean and rope height |
| University | Mechanics / tribology (rubber friction) | Why the friction coefficient isn't constant |
| Research | Group force output, theory of rubber friction | Team size vs. per-person force, predicting friction |
| ― | Everyday connections | Sports-day strategy; posture for pulling heavy objects on slippery floors |
- High school "Basic Physics" textbook (units on balance of forces, friction force)
- Wikipedia "摩擦" (Friction) (coefficient of static/kinetic friction, Amontons–Coulomb law)
- Wikipedia "力のモーメント" (Moment of force)
- Kravitz, D. A. & Martin, B. (1986) Ringelmann rediscovered: The original article. Journal of Personality and Social Psychology 50(5)
- Persson, B. N. J. 『Sliding Friction: Physical Principles and Applications』 Springer
- Tug of War International Federation (TWIF) and Japan Tug of War Federation, competition rules (weight classes)
※This article is a general-audience science explainer. The figures given are approximations meant to help illustrate the underlying mechanism. The friction coefficient varies considerably with ground, footwear, and weather. Follow your instructor's guidance during tug of war, and never wrap the rope around your body.