DIY · Card 74 · Engineering · Energy
Setting up dominoes one by one is slow, and one wobble knocks them all down. Build a little cart that lays them for you, perfectly spaced, then find out why a domino can topple one half as big again.
01The brief
Let the wheels measure, and the dominoes do the rest.
πD ⁄ N
the spacing: wheel circumference shared between the cam bumps
1.5×
the biggest domino one domino can knock over
29
dominoes from 5 mm to taller than the Empire State Building
Every domino builder knows the moment: the row is nearly done, a sleeve brushes one domino, and the whole thing goes. Machines that lay dominoes for you solve that, and the clever part is very simple. A wheel turns once for every circumference it rolls, so anything tied to the wheel happens at perfectly even distances.
Fix a gate that opens once per bump on the wheel and the cart leaves dominoes behind like a seed drill sowing seeds. Then comes the fun part: knocking them down, and understanding why a chain of falling dominoes is one of the best demonstrations of energy there is. Try it alongside the marble run and the thread-spool tank.
02Kit
A board, four wheels, some craft sticks and a box of dominoes.
Tick off what you have
0 of 5 ready
03Method
A chassis, a magazine, a gate and a cam on the wheel.
Step 1 of 8 · Minute 0
You need a thin board or stiff card about 20 × 10 cm, four wheels of the same size (wooden toy wheels or bottle caps), two wooden skewers or dowels, two straws, craft sticks, a rubber band, a glue gun and a set of dominoes.
Dominoes fall over as they’re laid.
Why
The cart is moving too fast, or the opening is too high above the floor.
Fix
Roll it slowly and lower the end of the channel until each domino barely drops before it touches down.
Two dominoes come out at once.
Why
The gate stays open too long.
Fix
Make the cam bumps smaller or the lever shorter, so the gate only flicks open for a moment.
The row stops toppling half-way.
Why
The spacing is too wide, or a domino stood crooked.
Fix
Add another bump to the cam to shorten the spacing, and lay the row on a smooth, flat floor.
04Chain reactions
The wheel and the cam decide the spacing; the spacing decides whether the row falls. Each domino must tip far enough to hit the next one squarely, but not so far that it reaches the floor first.
Choose a wheel and a cam and test the row:
Spacing
3.1 cm
Gap ÷ height
50 %
Row length
6.3 m
Wheel turns
50
Each turn of the wheel rolls the machine forward by its circumference, π × 4.0 = 12.6 cm, and its 4 cam bumps release 4 dominoes on the way, so they land 3.1 cm apart. For 48 mm dominoes, a gap of a third to a half of their height works best: close enough to reach, far enough apart to tip with some speed.
A falling domino can even knock over one that is bigger than itself. Chain enough of them together and the sizes explode:
First domino
5 mm
Domino 13
64.9 cm
Energy released
2.8 × 10⁸ ×
Every domino is 1.50 times taller, wider and thicker than the last, so it weighs 3.4 times as much and its middle falls 1.50 times as far: 5.1 times the energy. Multiply that 12 times and a nudge on a 5 mm domino releases 2.8 × 10⁸ times as much energy at the end.
05The big idea
A nudge
can grow.
Standing up a domino is like winding a spring: the energy goes in slowly, when you set it up, and comes out all at once when it falls. The push that starts a chain is tiny compared with what the chain releases.
Make each domino bigger than the last and every step multiplies the energy by about five. Thirteen steps turn the tap of a fingertip into something hundreds of millions of times bigger. That is the power of exponential growth.
06The math
1 · Spacing
s = π D ⁄ N
D the wheel diameter, N the bumps on the cam.
2 · Tip before contact
sin θ = d ⁄ h
d the gap between dominoes, h their height.
3 · Growing chain
hₙ = h₁ · rⁿ⁻¹
Height of domino n, each r times the last.
A 4 cm wheel with 4 bumps lays a domino every π × 4 ⁄ 4 ≈ 3.14 cm. Minus the domino’s 7.5 mm thickness, that leaves a gap of 2.4 cm, half the height of a 48 mm domino, so each one tips sin⁻¹(0.5) = 30° before it strikes the next. A box of 200 makes a row over 6 m long.
In a chain growing by 1.5 from 5 mm, domino 13 is 5 × 1.5¹² ≈ 650 mm tall, and domino 29 is 5 mm × 1.5²⁸ ≈ 426 m, taller than the Empire State Building. Each step multiplies the energy by 1.5⁴ ≈ 5.1, so across 13 dominoes it grows about 5.1¹² ≈ 300 million times.
07Real life
From television records and reactors to the nerves in your arm.
Domino Day
For years, teams in the Netherlands built enormous domino displays for television. In 2009 they toppled 4,491,863 dominoes in one go, a world record at the time.
Nuclear chain reactions
In a reactor, one splitting uranium nucleus releases neutrons that split more nuclei. Kept to exactly one new split per split, it runs steadily. In 1942, Chicago Pile-1 ran the first such controlled chain reaction.
Nerve signals
A nerve impulse is a domino wave along a cell. Each patch of membrane, triggered by the one before, opens tiny channels and triggers the next, so the signal arrives as strong as it set out.
Seed drills
Around 1701 Jethro Tull built a horse-drawn seed drill whose turning parts dropped seeds into rows at even spacing. Your domino machine works the same way: the wheels measure distance, a mechanism lets one go.
Rube Goldberg machines
The cartoonist Rube Goldberg drew absurdly complicated machines for simple jobs. Builders today make real ones, chains of falling dominoes, rolling balls and swinging levers, each part triggering the next.
Avalanches of sand
Drip sand onto a pile and it builds up until one grain sets off a slide. Physicists study these sandpiles because tiny triggers can unleash events of every size, just like a carefully stacked chain.
1983
In 1983 the Canadian physicist Lorne Whitehead published a short paper in the American Journal of Physics with a playful title: a domino chain reaction. He had found that a falling domino can topple another about one and a half times its size.
To show it, he made a set of 13 dominoes, each 1.5 times larger than the one before. The first was tiny; the last was big and heavy enough that it took far more energy to knock over than any fingertip could supply. A gentle nudge at one end did it anyway, a lesson in amplification that physics teachers have repeated ever since.
08Is and isn’t
The first push knocks down the whole line.
It only tips the first one. Every domino supplies its own energy, stored when you stood it up, so a long line runs on its own.
The closer the dominoes, the better.
Packed very tight, each one barely tips before it hits the next, and the machine knocks them while laying. A gap of a third to a half of their height is safer.
A domino can knock over any size of domino.
Only up to about 1.5 times its own size. Any bigger and it bounces off.
Doubling the size doubles the energy.
A domino twice the size weighs eight times as much and its middle falls twice as far: sixteen times the energy.
09Go further
A
Time the wave
Lay 100 dominoes in a straight line and time the toppling. Does a wider spacing make the wave faster or slower?
B
The growing chain
Cut dominoes from card, each 1.5 times bigger than the last. How far can you get before one fails to fall?
C
Curves and splits
Steer the machine round a curve, then build a split so one wave becomes two. What spacing works on the bends?
D
Uphill
Can the wave climb a ramp of books? Try steeper and steeper slopes until it stops.
E
A cam with words
Space the cam bumps unevenly. What pattern of gaps does the machine lay, and can you make it repeat?
10Questions
Build a small cart with a channel on top that holds dominoes standing in a row, pulled towards a rear opening by a rubber-band pusher. A gate blocks the opening, and bumps on a back wheel flick it open once per bump, so the cart leaves one domino behind at a fixed spacing as it rolls.
For ordinary 48 mm dominoes, a gap of about a third to a half of their height works well. Too close and each one barely tips before it hits the next; further apart than its own height and it can’t reach the next one at all.
One about 1.5 times its own size. The physicist Lorne Whitehead described this in 1983, with a chain of 13 dominoes in which each was 1.5 times larger than the one before.
Starting from a 5 mm domino and making each one 1.5 times larger, the 29th domino would be taller than the Empire State Building’s 381-metre roof. Exponential growth gets very big, very fast.
Standing a domino on end stores a little energy, by lifting its middle. A push releases it, and as it falls it releases the next, and so on. The push only starts the chain; each domino supplies its own energy.
Safety · A grown-up should handle the glue gun, which gets hot. Skewers have sharp points: snip them off after fitting the wheels. Keep dominoes and small parts away from children under three.
All DIY cards →Keep wandering
A few more pieces in the same spirit — math, design, and slow attention.
How to Build a Marble Run From Cardboard Tubes
Split tubes, a wall and some tape: a zigzag run that keeps a marble busy for half a minute on a one-metre drop it could fall in less than half a second. Height is the fuel; the trick is spending it slowly.
Open
How to Build a Cotton Reel Tank (Thread Spool Tank)
An empty cotton reel, a rubber band, a pencil and a slice of candle. Wind it up and it crawls across the floor and over books, slowly giving back every turn you put in.
Open
Balloon Car Race: How to Make a Balloon-Powered Car
Half a cup, four bottle tops, two skewers and one balloon. Blow it up, let it go, and a jet of your own breath sends the car racing across the floor.
Open
How to Make Square Wheels That Roll Smoothly on a Bumpy Road
Two cardboard squares, a skewer and a necklace. Trace a hanging chain, turn it upside down for a road, and square wheels roll as smoothly as round ones.
Open
How to Make a Galton Board That Draws a Bell Curve
A board, forty pins and a handful of beads. Every bead zigzags at random, yet together they pile into the same graceful hump every time: the bell curve.
Open
How to Do the Egg Drop Inertia Trick: Newton’s First Law
Knock a tray out from under an egg and the egg drops straight down into a glass of water. The trick is speed, not strength, and the egg’s weight turns out not to matter at all.
Open