#### How many time windows did the bridge builders have?

The construction of the Golden Gate Bridge, the winding universe of shoe sizes and a tricky technological puzzle. Here are three technology problems by physics professor Göran Grimvall.

**1. Teknikrebus **

The solution (two words) to this technical puzzle is a special building. As in crossword puzzles, you may have to let your mind run free and not interpret the details too literally. No distinction is made between uppercase and lowercase letters. (See the puzzle also in the large illustration)

U 1 000 000 2.718 0.1 nm Fe E 4 (1/3600) h STA exp (ln 10) J / m

**2. Golden Gate **

In suspension bridges, the carriageway hangs on ropes or cables that are stretched between towers or pylons at both ends of the bronze. The construction was known in China as early as the eighth century. During the end of the 20th century, many suspension bridges were built where the main span is more than 1 kilometer long, including the Great Belt Bridge (in 1998, main span 1,624 meters) and the High Coast Bridge (in 1997, 1,210 meters).

The Älvsborg Bridge over the harbor entrance in Gothenburg, inaugurated in 1966, has a span of 418 meters. Slanted cable bridges can be seen as a special form of suspension bridges. The bridge deck is anchored in cables at different heights on the pylons and at different parts of the bridge.

The Öresund Bridge, the Tjörn Bridge and the Uddevalla Bridge are examples of oblique cable bridges. Tjörnbron was inaugurated on November 9, 1981, in record time less than two years after the previous arch bridge collapsed when it was sealed one night. Sweden’s longest wooden suspension bridge for car traffic is Floda Kyrkälvbro over the Västerdalälven river (158 meters). It was destroyed by fire in 1980 but rebuilt and inaugurated in 1983.

The really big challenge would be to build the Messina Bridge between the Italian mainland and Sicily. It could have a bridge span of more than 3 kilometers. Not only does the length cause major engineering problems but also the risk of earthquakes.

The world’s most famous suspension bridge crosses the Golden Gate in California. It was inaugurated in 1937 and until 1964 was the world’s longest suspension bridge with a bridge span of 1,280 meters.

The construction of the bridge began with the erection of the two pylons. The northern one was easiest because there you could essentially build on solid rock. The southern pylon, where the water depth is 33 meters, caused great technical difficulties. The strong tidal currents in the Golden Gate Strait meant that you could only work during short time windows, 90 minutes long.

In the mini-problem, we ask the question: How many such time windows were there in a normal day? Think carefully because it is easy to think wrong.

**3. How long is a Paris point? **

The meter system, and later the SI system, has found out the units for many quantities. For example, we do not measure volumes in bushes (cereals), barrels (both wet and dry goods), jugs and stops (beer and other wet goods), parm (hay; cf. Parmmätargatan in Stockholm and Parmmätaregatan in Gothenburg), Russian (charcoal) or embrace (firewood).

The matter is complicated by the fact that at that time there could be large regional differences between how large a volume was actually intended. In a case that we all encounter in everyday life, however, there is a long way to go before a generally accepted international standard – the size of shoes and clothes.

In Sweden, shoe size is stated with a number that is typically between 36 and 44 for adults. Then the length of the shoe is expressed in the unit Paris point. A Paris point is exactly x / y centimeters, where x and y are small integers. What are the numbers?

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## Solutions

**1. Teknikrebus**

The answer is “Umeå railway station”. The letter U must be read as it is. M (mega) is the designation for 1 million. The basis for natural logarithms, e, is about 2,718. 1 angstrom is denoted Å and is exactly 0.1 nm (nanometer). Fairy stands for “iron”. E 4 is a “road”. The time unit s (second) is 1/3600 of an hour (h).

The letters STA should be read exactly like that. The exp function stands for the exponential function, “e raised to”. The base e for natural logarithms, raised to ln10 where ln denotes “natural logarithm”, gives the number 10. It should be read as the word “ten”.

Finally, the energy is 1 J (joules) equal to 1 Nm (newton meters); force times road. It gives J / m = Nm / m = N.

**2. Golden Gate**

The answer is four. The tide has two maxima per day (or rather in 25 hours). At these times, the tidal current reverses, that is, its velocity is close to zero. Between the two occasions there will be ebb, as the tide also turns. In total, the tidal current is low four times a day.

It is often said that it is the gravitational pull from the moon that gives rise to the tidal phenomenon. The sea meanders in the direction of the moon. But how do you explain that there is a river twice a day, and not just once? This is because the sea curves out even on the side that is furthest from the moon. A simplified explanation can go like this.

The moon does not rotate around the earth, but the two celestial bodies rotate together around their center of mass (which is inside the earth’s surface). Compare that to a couple holding each other’s outstretched arms and dancing around. Let the lady represent the moon.

She is drawn to her partner (corresponding to high tide on the side of the earth facing the moon), but at the same time a centrifugal effect causes her skirt to bulge out behind her (corresponding to high tide also on the side of the earth facing away from the moon) . The parable gives a greatly simplified picture of tides but captures the essential principle.

**3. How long is a Paris point? **

The ratio x / y = 2/3. It may be close at hand to compare with the unit of length 1 foot (ft, foot) = 30.48 cm. The only reasonable alternatives are x / y = 2/3 or 3/4. Then the length 1 ft corresponds to the shoe size 45.7 and 40.6 respectively. But we must also take into account that the last is about 2 cm longer than the bare foot. Then x / y = 2/3 and 3/4 would correspond to the Swedish shoe sizes 49 and 43, which is far too much.

So something must be wrong with this reasoning. Not even an adult male’s foot is usually 1 ft long. A survey showed that only 0.4 percent of all British men have feet that are longer than 12 inches (inch), where 1 ft = 12 in exactly.

It is unclear why 1 ft is so much longer than the actual length of the normal foot. One hypothesis is that the unit of length was based on the feet of the local ruler, and he may have wanted to exaggerate the size of the sim. Another idea is that the device referred to the size of the shoes on the feet. In any case, few Swedes have feet that are at least 1 foot long. The reader can try for themselves.

In addition to Paris point, there are several different ways to specify chimney sizes. In the UK, as expected, you connect the units foot and inch, but use the old unit barleycom, which is 1/3 inch. One starts from size 12 (corresponding to 1 ft = 12 in) and then counts backwards with one unit for each reduction by 1 barleycom. To further complicate the system, the calculation is somewhat different in the USA and distinguishes between men’s and women’s shoes.

The size of children’s shoes is a chapter in itself. The former Soviet Union, Japan and China, among others, use the internationally standardized Mondopoint system, which is based on the SI unit millimeters. And now we have just touched on all the details when it comes to shoe sizes.

Finally, we can return to the unit of length inches (inches, in) where 12 in = 1 ft. Since 1933 (USA) and 1950 (Commonwealth countries) there is officially an exact connection between American and British inches and the SI system; 1 in = 25.4 mm.

Many people think that 1 inch is the distance from the outer part of the inch to the first knuckle, but it is generally too far. Measure your own thumb! Instead, 1 inch is the width of the thumb when pressed against a solid surface. In this way, the carpenter could, for example, easily measure 2 inches by placing two inches next to each other. It would be much more difficult if the measurement was between the tip of the thumb and the knuckle.