Can You Build a Box That Keeps Ice Frozen All Day?

You have already done research like a scientist in Grade 8: a question, a hypothesis, a method, data and a conclusion Grade 8: Research work. Engineering uses the same care with measurements, but it starts somewhere else. It starts with a problem: something people need that doesn’t exist yet, or doesn’t work well enough.

	Science	Engineering
starts with	a question about the world	a problem people have
example	Does a black box get hotter in the sun than a white one?	Make a box that keeps ice from melting until 6 pm.
ends with	an answer, an explanation	a thing that works, and the tests that show it
how many right answers?	one (the way the world really is)	many: several designs may work, each with its own strengths

If you have read Can You Make a Hand Warmer?, you have been round the engineers’ loop once: set the goal, build, test, improve. Here you will go round it more carefully, with each step done the way professionals do it.

“A box that keeps ice cold” sounds clear, but it isn’t. How much ice? For how long? How cold is the day? Can it be as big as a cupboard? Can it cost Rs 5,000? Two teams given that sentence would build completely different boxes and both claim they had succeeded. So engineers start by writing the problem down precisely.

The things a design must do, to count as a success, are its criteria. The limits it must be made within (money, size, weight, materials, time, safety) are its constraints. Both must be things you can check: with a scale, a clock, a ruler, a price list. “Keeps ice well” can’t be checked. “At least 250 g of a 1,000 g block left at 6 pm” can.

Here is our problem, written the way an engineer would write it.

The problem. On a hot, sunny day (about 32 °C in the shade), keep ice for drinks from 8 am until 6 pm, outdoors, with no electricity.

Criteria

• a.It holds 1,000 g of ice, put in at 8 am.
• b.At 6 pm, at least 250 g of ice is left (a quarter), out in the sun all day.
• c.It can be opened to take ice out, and closed again.

Constraints

• a.It costs no more than Rs 300 to make.
• b.It is no bigger than 25 cm along any side, and someone can carry it with one hand.
• c.It is made from materials a student can get; nothing that is dangerous to handle.
• d.Its materials do as little harm as possible to people and the environment when it is thrown away.

Some of these are musts: a design that fails one is out, however good it is otherwise (criterion b, and every constraint). Others are wants: of two designs that both pass, the one that is cheaper, lighter or kinder to the environment is better. Sorting “must” from “want” before you start saves many arguments later.

Thinking about people and the planet

Notice the last constraint. A good engineer asks not only “does it work?” but “who does it affect, and how?” Thermocol, the white foam of packing boxes, is one of the best insulators you can buy. It is also a plastic that never rots: thrown away, it breaks into little beads that blow into rivers and fields and stay there, and when it is burned with rubbish it gives off harmful smoke. Rice husk, a waste from every rice mill in the Terai, insulates not far behind it, costs almost nothing, and can go back onto a field afterwards. Thinking about this at the start, while the problem is being written, can change which designs are even allowed.

Ice in a box melts because heat gets in. The ice and the box’s inside stay at 0 °C while there is any ice left: every joule that leaks in goes into melting, 334 J for each gram (you can see why in Where Does the Heat Go When Ice Melts?). So the slower heat gets in, the longer the ice lasts. A good ice box is a heat-stopping box, and you know the three ways heat travels from Grade 8.

1. Conduction, through the walls, lid and floor Grade 8: Conduction. Stop it with a thick layer of a material with a low thermal conductivity. The best are mostly trapped, still air: thermocol, crumpled newspaper, rice husk, sawdust, wool.
2. Radiation, from the sun Grade 8: Which box gets hottest?. A dark box absorbs most of the sunlight that falls on it and warms up; a white or shiny one reflects most of it. Shiny foil on the outside, or simply keeping the box in the shade, cuts this.
3. Convection, through gaps. Air inside the box is cooled by the ice and sinks; if there is a gap low down, it pours out, and warm air is pulled in through any gap at the top. A lid that fits tightly, with no cracks, stops it.

A thermos flask stops all three as well as anything can, with a vacuum and silvered walls Grade 8: Thermos flask. But a vacuum box big enough for a kilogram of ice costs far more than Rs 300. Our box must do the same job with ordinary materials: that is what the constraints are for.

Thickness ÷ conductivity: the R-value

How well a layer stops heat depends on two things: what it is made of, and how thick it is. Twice as thick lets heat through half as fast; a material that conducts twice as well lets it through twice as fast. Builders put both into one number, the layer’s R-value (R for resistance):

$$R = \frac{\text{thickness (m)}}{\text{thermal conductivity (W per m per °C)}}$$

The bigger the R-value, the better the layer insulates. In many countries, insulation for houses is sold by its R-value, so that a buyer can compare a thin, expensive sheet with a thick, cheap one.

Filling	Thermal conductivity, roughly (W per m per °C)
thermocol (expanded polystyrene)	0.035
crumpled newspaper	0.05
rice husk, loose	0.05
sawdust	0.07
still air	0.025

(These are typical values; a real sample depends on how tightly it is packed and how dry it is. Damp rice husk or sawdust insulates much worse.)

With the problem written and the science in hand, a team first comes up with many ideas, without judging them yet: a thermocol box from a shop; a carton inside a bigger carton, with rice husk between; ice wrapped in old sweaters; a steel tiffin in a towel; a box covered in foil; ice buried in sawdust, the way ice was kept a hundred years ago. Then they choose the most promising few to try.

But building and testing each idea takes a whole day of sun. Engineers save time with a model: a simpler version of the design that can be tested quickly and cheaply, to find out which ideas are worth building. A model can be a small copy, a drawing, or, as here, a set of rules worked out on a computer from the science. The model below uses the R-value idea to work out how fast heat leaks into a box, and so how fast the ice melts.

A model is only as good as the science in it, and every model leaves things out. This one assumes the lid fits perfectly (no air gets in), the ice starts at exactly 0 °C, and the filling is dry and evenly packed. A real box will do a little worse than the model says. That is why a model guides testing but never replaces it: the model tells you which designs to build, and the real test tells you whether the model was right.

Better and better: optimizing

Play with the model, and you will notice something. Going from 0 to 2 cm of thermocol makes a huge difference: the heat leaking in drops from about 16 W to 6 W. Going from 2 to 4 cm helps much less: 6 W to 4.5 W. And every extra centimeter makes the box bigger and heavier. Somewhere there is a best thickness: thick enough to pass with some ice to spare, no thicker than it needs to be. Finding it, by testing a design, changing it a little and testing again, is called optimizing, and it is how almost every product you own was finished.

Now build the best few designs, and test them all at the same time, in the same place, in the same way, so that the only difference between them is the design. That is a fair test, the same rule you used in science: change one thing, keep everything else the same.

Here are the results of one class’s test of four designs. (Made up for this book, but typical of what you would get.) Each box had 1,000 g of ice at 8 am, and stood in the sun; the ice was weighed every two hours.

Design	What it was	Ice left at 6 pm	Cost	Weight (empty)
A	a thermocol box from a shop, 2 cm walls	395 g	Rs 250	0.3 kg
B	a carton inside a bigger carton, 4 cm of rice husk between	335 g	Rs 40	1.2 kg
C	a carton lined with 3 cm of crumpled newspaper, covered in foil, a folded-flap lid	310 g	Rs 60	0.6 kg
D	a steel tiffin wrapped in a thick towel	100 g	Rs 0	0.9 kg

Design D fails a must, so it is out, whatever else is good about it (it cost nothing). A, B and C all pass. Which is best?

It depends on what matters most, and different people would answer differently. Engineers make the choice fair and open with a decision matrix. Each design is given a score for each “want”, from 1 (poor) to 5 (excellent), using rules fixed in advance. Each want is given a weight: how much it matters, agreed by the team before the results are in, so that nobody can pick weights to make their favorite design win. A design’s total is each score times its weight, added up.

Want	How it is scored	A	B	C
keeps the most ice	380 g or more 5; 350–379 g 4; 320–349 g 3; 290–319 g 2; 250–289 g 1	5	3	2
cheap	up to Rs 50 5; Rs 51–100 4; Rs 101–150 3; Rs 151–200 2; more 1	1	5	4
light to carry	0.5 kg or less 5; up to 0.8 kg 4; up to 1.1 kg 3; up to 1.4 kg 2; more 1	5	2	4
kind to the environment	what happens to it afterwards (see below)	1	5	3

For the environment: A is thermocol, used a few times and then thrown away, where it never rots (1). B’s rice husk goes back onto a field and its cartons can be recycled (5). C’s newspaper can be recycled, but crumpled, used foil usually can’t (3).

The matrix doesn’t decide for you: people still choose the weights. What it does is make the choice visible. Anyone can see why B won, and if a shopkeeper who carries the box all day says “weight matters more than you thought”, everyone can see exactly how the answer changes.

Choosing a winner is not the end. Look at the data again, and ask what each design did well, and why. Often the best design is none of them, but a new one that takes the best feature of each.

Design	Did well	Why (the science)	Did badly
A	kept the most ice; light	thermocol has the lowest conductivity; its molded lid fits tightly, so no air gets in	costly; bad for the environment
B	cheap; kind to the environment	rice husk insulates nearly as well as thermocol	heavy; brown outside absorbed sunlight
C	cheap; light	newspaper is light; the foil reflected sunlight	its folded-flap lid let air in, so it did worse than its walls should have

Look closely at C. Its walls had about the same R-value as A’s (0.60 against 0.57), and the foil should have helped it more. So why did it keep less ice? The model said a box like C should keep about 400 g; the test gave 310 g. The difference points at the one thing the model left out: air through the gaps in its folded-flap lid. That is how a test teaches you something a model can’t.

So the class combined the best features into design E: 4 cm of crumpled newspaper (light, cheap and recyclable, like C), foil outside (C’s idea, to reflect the sun), and a lid that fits tightly with an overlapping rim, sealed with a strip of cloth (A’s best feature, made from cardboard). Then they tested it, the same way, on another sunny day.

E keeps more ice than A, costs less than a third as much, and can go into the recycling. It is heavier than A (0.7 kg against 0.3 kg): no design is best at everything, and an engineer always gives up a little of one thing for more of another. This is called a trade-off.

And the loop goes on. Could a thinner layer of newspaper still pass, and make the box lighter? Would rice husk instead of newspaper work as well if the box stays in one place, so its weight doesn’t matter? Each question is another trip round the loop: model, build, test, compare, combine. Engineers call this iterating, and it stops only when the design is good enough for its users, or the time or money runs out.

• Where does the heat go when ice melts? Why the ice in your box stays at 0 °C until it has all melted, and why melting it takes so much heat.
• Can you make a hand warmer? The opposite problem: a pack that makes heat, and keeps it, designed round the same loop.
• Why can you hear through a wall but not see through it? Why foil reflects sunlight and a black box soaks it up: what waves do when they reach a surface.