# Measuring SI Units on a Desert Island

1. Aug 9, 2012

### Fine Man

A few years ago, I was reading about a contest open to everyone. The question was something like : if you were on a desert island, with unlimited natural resources, and access to a book with the most accurate values of properties for various natural things (i.e. gravitational acceleration on Earth, density of sea water), how would you measure the SI units of meter, kilogram and second. The prize was to the person(s) who could measure the units with the greatest accuracy. I wonder if anyone remembers this since I can't recall where I saw it.

In either case, how would you go at it? For that matter, what about the other units (kelvin, ampere, candela)?

I was thinking meter would be the easiest to guess at right away. Then using that, you could try to purify water and use a volume of water to define the kilogram, then use that and the meter to build a pendulum and define the second. But I'm sure my way could be improved upon.

Yes, given enough time I suppose you could just build modern measuring device, but that's not really in the spirit of things. Maybe have a limit of 50 years or something.

2. Aug 9, 2012

### bigerst

to measure the second u could build a super laser and shine it on the moon, the time gap betweeen turning on the laser and geetting a reflection could be calculated in turns of seconds

3. Aug 9, 2012

### Nabeshin

This is probably the worst way of measuring the second I could have imagined.

4. Aug 10, 2012

### CWatters

For Length... Make a sundial (using the shadow of the tree?). Then make big long and heavy pendulum. Count the number of swings in 24 hours (or some shorter time?).

5. Aug 10, 2012

### voko

The kelvin is easiest, being equal to a degree on the Celsius scale, so you just need the temperature of the freezing and boiling water as a reference.

For time, build a clock, then calibrate it from astronomical observations. A water clock is very easy to make, a pendulum-based clock would be more difficult to build, and just a pendulum decays too rapidly to be useful.

Once you have a time measure, you could use gravity to obtain the length unit. Simply drop objects from some height and measure how long it takes to reach the ground. Or use a pendulum, as suggested. That will not be too accurate, though. For more accuracy, you could build a Fizeau or Foucault apparatus and use the known speed of light to measure the distance.

Then you define the mass unit from a known volume of distilled water.

6. Aug 10, 2012

### Staff: Mentor

With the unlimited natural resources, build a boat, take a ton of gold, sail to the mainland, and donate the gold to the NIST in exchange for measuring the SI units.

7. Aug 10, 2012

### ZapperZ

Staff Emeritus
Hum... with unlimited resources, why can't you duplicate the exact experimental measurements that define those SI quantities? Even the "kilogram" now no longer require a "standard length" anymore since it can now be tied to Planck constant.

Zz.

8. Aug 10, 2012

### Staff: Mentor

Well, you could reproduce it as good as the current knowledge of the Planck constant, the official definition is still "that thing in Paris".
I do not think "unlimited resources" includes atomic clocks, frequency combs and so on. And if you have to build that by hand (with just raw materials available), good luck.

Astronomy -> time (clock + day length)
Gravity + time -> length (pendulum)
length + gravity -> mass
Would be my approach, too.

A quick&dirty-approach would be to use the own body height (~1cm uncertainty corresponds to ~0.5%). Cannot be improved, but it is not easy to get a better precision with the "proper" methods.

9. Aug 10, 2012

### GarageDweller

Well if you know your height, then you can just estimate it I guess.
with the meter measured you can then define a second for an object to drop by some height, and then mark that height on a tree

10. Aug 10, 2012

### bigerst

for using astronomy to determine day length dont u have to know exactly when a day has passed? how are u gonna do that, by determining the position of stars?

11. Aug 10, 2012

### jbriggs444

Noon to noon with a sun-dial is the obvious technique to measure the solar day. That would be my choice.

Watching for a particular constellation to rotate around and back to some fixed sight line is the obvious way to measure the sidereal day.

12. Aug 10, 2012

### voko

The Sun is rather big, so by watching it directly you would have a noticeable error. By watching a shadow, such as in a sun dial, you would suffer from very small changes of the shadow's length around the noon, again getting an error. Plus the Sun itself moves noticeably along the ecliptic during a day.

You would be far better off observing some "fixed" stars.

13. Aug 10, 2012

### Staff: Mentor

Use some fixed vertical object, find a position and time when two arbitrary stars appear to be right next to the object, wait until it happens again.
Sunrise/set behind some nearby object should work, too.

Based on an experiment, I can confirm that you can indeed use the shadow of an object to determine noon with a precision of less than 5 min (I used pebble stones to track the shadow and a sheet of paper to get a right angle), but this is very unprecise compared to other methods.

14. Aug 10, 2012