From scratch measurement units

My presumption is the "radio" is like a real radio and translation is accurate and effectively instant: There is no significant delay. I presume the planet is normal, rotating (not tidally locked), and orbiting a star. Edit: We can deal with delay as long as it is reasonably consistent and/or not very long; we can measure the average round-trip time for a response (a ping in network terms), presuming the other side is constantly monitoring.

Position: For two groups effectively anywhere on a strange planet, even on opposite sides of it; positioning is going to have to be accomplished by solar and Constellation position. First we can establish (by radio) our relative Longitude; similar to a time zone on Earth; by measuring through the radio the timing of high noon, meaning zero shadow for an upright pole. (noon because sunrise and sunset can be confused by being on mountains or in valleys).

(upright): water can find a level on a plain; or show how to make level; and right angles are easily constructed to insure the pole is at right angles to a level field. Water in a long thin channel or tube will suffice. (We can also ensure a noon stick is plumb with danglers (free weights on long threads, thin ones (think like heavy needles) extending very slightly away from the pole in 8 compass directions, from close to the top of the pole; they must not touch the pole; and the pole should be perfectly centered in the vertical channel they create.)

We have two natural directions; the sunrise direction and sunset direction. If my sunrise is after yours, I am in the sunset direction relative to you; and vice versa. However long a day is (sunrise to sunrise from a given position is best) by any measurement of time, the difference in the time of high noon tells us how far around the planet the other group is. Facing the sunrise, at right angles, we can call North on the left and South on the right.

Latitude: this is the position between the two axis points of the rotation; our north and south pole. This will be less accurate and require sun angles and / or constellation angles. The Noon stick, for example, halfway to the North Pole, will never have a zero shadow if it is plumb: (Presuming the planet equator is in line with its sun, like on Earth; but the math is still deterministic of that is not true). The noon stick radiates from the center of the sphere; so if it isn't near the equator, it will always cast some shadow. The shape "cut out" by that shadow throughout a day can tell you how far you are from a pole, and the direction of the equator: At the equator, the shadow is a simple line. Well north or south; the sun cannot be directly overhead and the shadow will always have length; its shortest length is noon; and that must always fall on the same side, and opposite that side is the direction of the equator. To find each other, head for the equator.

Length: Slightly tougher; you need a very tall noon stick! on the order of ten to twenty feet. Different lengths for the two groups is fine; but you need enough so you can distinguish a fine difference in length for sticks that are a significant difference apart; as I will explain.

The length will be, for example, a few arcminutes (an arcminute is 1/60 of one degree, about 1.16 miles on Earth). The point is that we want two Noon sticks, separated by some number of miles (but not so far that people cannot signal each other from end to end). What we seek is the distance that causes a specific, small percentage of change in the length of the shadow. (Because that percentage is actually the tangent of an angle).

The line from the shadow tip to the top of the noon stick is the hypotenuse of a right triangle. Without measuring the sides (pole height and shadow length) we know their ratio, by any arbitrary measure (like the width of a piece of straw), is the tangent of an angle; and a specific tangent implies a specific angle. i.e. the tangent of 1 degree is 0.0175, or one part in 57.29. For one arcminute, we need one part in 3437.75; so we want our noon-stick to be measurable to that precision using any found object that is quite thin. That can include, for example, thread from clothing: Tightly wound, we can get over 100 threads per inch; so to get to 3437.75 threads would just mean 34.3775 inches which is less than a yard. To be accurate, I'd probably like my noon stick to be about 10,000 threads tall. (The 'inch' is just for your reference; the group measures both stick height and shadow length in threads, period; and takes the ratio: The measuring unit cancels out to reveal the tangent).

The point is we can, now, measure an arcminute (or any specific angle) worth of planet on the ground: We want noon-sticks (which can be different lengths) separated on the ground, far enough apart to be at least an arcminute apart. We can then measure that distance; say 1.16 miles, or 6143 feet. Again, it doesn't make a difference how the group measures this; they can have different units of measure. Measure it in threads. (If you wind up 1000 threads on a straight piece of stick; you can cut something like another stick to precisely that size (with a little sanding using a stone), and use that to measure things in 1000 thread units. Meaning you don't have to wind thread to get to 1.16 miles long).

The point is that 1 arcsecond of planet is the same distance for both Group A and Group B, there is only one planet! Subdividing that distance will give them an accurate common measurement of distance; say dividing it by 100,000: On Earth that would be what we call 0.73723 inches. Both sides can do that sub-division and call that their standard unit: Maybe 74 of the threads used by Group A and 86 of the threads used by Group B.

It does not depend on the threads used, or the size of the noon-sticks used.

Now you have a standard measurement, call it a "fleck", and volume is measured in cubic flecks. Weights are measured as the weight of water in a cubic fleck, and also call that density 1.0. Other densities are the weight of a cubic fleck of the substance, divided by the weight of a cubic fleck of water.

And so on; using the metric system as a guide to compute other types of measurement (heat, energy, etc).

posted over 7 years ago

Amadeus‭

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