# From scratch measurement units

An exploratory spaceship holding strangers from many cultures and races has a problem leading to escape pods being deployed to a nearby world that is conveniently survivable. The pods crash land in at least two separate points on the planet, no way of telling where or how far apart, and because it's convenient to the plot burn to the ground taking all tools and supplies with them.

Group A, due to luck and basic survival training, has within a few months gotten comfortable in the sense they are reasonably sure how to eat and not be eaten tomorrow and have a good place to sleep tonight when they find a radio. A simple bright yellow unmarked box with a solar panel on top. It permits talking to the ship who will translate and forward messages, nothing else. They find a hello from Group B and establish communications as quickly as possible.

Group B is or includes a master survivalist specifically trained to deal with situations like this one. He found his red, spherical radio right after the crash and has been hoping for a call. Based on his training in school he has learned how to:

1. Figure out his position
2. Teach Group A to find their position
3. Figure out units of length, mass/weight, and volume (these aren't arbitrary, they would be the same units another expert would arrive at if they were part of Group A)
4. Communicate those units to Group A (so he can ask them to gather the bits needed for the beacon that gets them rescued or whatever)

I want to know how he could do 1-4. For this question we are concentrating on:

Could he figure out units of length, mass/weight, and volume and if so how? If you can I'd like sub mm precision.

You can assume the master survivalist has at least neolithic tool making skills and a firm grasp of things like math at least in areas that would apply to the problem.

I should have put this in before: Groups A and B could not see each other's burning escape pods flame or smoke after landing and they burned long enough the clearer headed could climb to the closest high point and look.

• They traveleld on the same ship. They will all be educated and have common units. there is no need whatsoever to re-invent them. – Burki Jun 12 '17 at 10:26
• Either nothing survived and a beacon is impossible or parts survived and can be used as a standard of measurement. Of course the real question is, who cares, a standard of measurement is not going to be much help for them. – John Jun 12 '17 at 10:29
• You should define a precision for those units. If you want a meter with a tolerance of a millimeter, there is just no way. If you are ok with 5 cm tolerance, this might be doable but difficult from scratch, that means without any normed items that one might have - for example a sheet of paper. If you are ok with error margins above 10%, this becomes trivial and anyone can do it. Just out of interest: Why do you need those? They might be on different continents btw. This is an interesting idea certainly – Raditz_35 Jun 12 '17 at 13:17
• @M.Herzkamp on the ship they wouldn't be, everyone has to work with someone, if the astrogators all speak latin and the engineers all speak french the pilot will have a good grasp of both(at least within those subject matters, poetry he may fail at understanding) There may be gaps now based on who survived and someone may be taking a crash course :) The translator is there just in case. – Darkhorse Jun 12 '17 at 14:18
• ?? So, two groups on the ground and one ship in space. I don't understand why in the world the groups on the ground care about their position. I don't understand why B would need to teach A anything. And worse, if they're communicating by radio, then they've both ALREADY got a "beacon". Perhaps you should add a 5th requirement: that the cook in group A needs to teach group B how to prepare an ice cream sundae - I mean we are being arbitrary, right? – user39310 Jun 12 '17 at 15:57

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).

• Very good. The catch is the radio doesn't work like that. It's a, "check for messages," sort of system. I am allowing constant checking to give you within ten minutes, if the spacecraft can see both of you. – Darkhorse Jun 12 '17 at 15:44
• That only makes things slightly more difficult; the instructions above can apply to either group to find nearly everything except for an exact synchronization of longitude. Timing can still be established with delayed communications, by measuring round-trip times: "respond immediately; I am timing this message". A few seconds or minutes in time would make too much difference in timing high noon. Unless you just want to piss on the idea by making the ship have arbitrarily random lag times for no rational reason at all... If the lag time is consistent; it can be compensated for. Using a sundial. – Amadeus Jun 12 '17 at 16:09
• I meant, would NOT make too much difference in timing high noon. (duh). – Amadeus Jun 12 '17 at 16:37

# Everyone who has handled rope or cloth knows how long a metre is.

It's the length from your nose to your outstretched hand or some other similar distance. People who walk a lot know how many strides make 100 meters for much the same sort of reason. Your man is a survivalist, he knows how to measure a metre.

Metric is great. 1 litre of water is 1 kilogram. 1 litre is a 10cm cube. 1 cubic metre of water is 1 tonne. Make some sort of container on with a known volume, fill that with water to get a known mass. To be able to travel together, the various groups will have needed to use a standardised measurement system. Metric or not, it doesn't matter, there will be equivalent relationships, though perhaps not so simple.

# Figure out their position

3 points, triangulate for position. It's a standard navigation skill that every child is taught in the scouts, that's if they have maps. If they don't have maps, it has no meaning. Your location is defined as your position relative to a datum, another known position. With no datum they have no location.

All points on Earth are defined relative to 0,0. A spot in the middle of the ocean directly south of the naval college at Greenwich. It's ultimately arbitrary, but it gives meaning to a location.

# Teach group A how to find them

I suggest that unless group B has injured persons, group A has the better established position and group B should be trying to find group A. No matter which group does the searching, only one group should move, the other must remain in their declared location.

If they don't have maps then they're going to have to use some old fashioned navigation skills.

• Both groups need to make a sextant.

Using their radio communication as a time signal, this can be used to find their relative positions on the planet.

• One group sends a ping at their noon with the sun's angle above the horizontal, the other group measures solar position at their noon.

Since communication is by answerphone message there will be a little delay getting the ping but that's acceptable for the level of accuracy involved. There is a message on the system or not. Once there is a message on the system you know the appropriate time has passed, the time between your last check and your current check is your error margin. If it's less than a few minutes then that's as good as you need.

The relative angles above the horizontal at noon gives latitude, the time to noon gives longitude. Neither group needs to know where they actually are, only where they are relative to the other group. The distances to travel are arc sections of the planet, not necessarily fixed known distances, but given the initial conditions, a sextant, and a time signal they can navigate one group to the other. A compass would help but is not required.

The closer you are the less important the time signal becomes and the more important your accuracy with the sextant becomes. The trick is to be on the same latitude and know whether you should be moving East or West rather than needing to precisely place a location.

# Being found

The stationary group will need to spend the intervening time making themselves as big a target as they can. They can do this by building upwards or outwards depending on the local geography. Reasonable outward building includes marking or cutting trees, leaving cairns or beacons on hilltops, carving arrows in rocks etc. Find landmarks, follow the river to the sea, climb the highest hills around, leave marks in mountain passes. Make your presence felt in the surrounding area.

• Since OP tagged alien and wrote races, we should not assume even the meter and second are standard and well-known. You know, the human race is only one race. – dmcontador Jun 12 '17 at 9:50
• @dmcontador, it doesn't really matter, they'll have standard units to be able to travel together. – Separatrix Jun 12 '17 at 9:54
• @Separatrix You'd think edition.cnn.com/TECH/space/9909/30/mars.metric.02 . While that's a different problem, I would be wary of them having a working knowledge of equivalent length measures. Though having a convenient time synchronization measure I suppose they should be able to get length right? – DRF Jun 12 '17 at 10:46
• @DRF, yep, it's that sort of expensive mistake that should force their hand in future :) You're looking at navigation by arc sections not measured distances, the measurements are actually completely redundant for this purpose. I'm assuming the OP has different reasons for them. – Separatrix Jun 12 '17 at 10:54
• @Darkhorse, I send a message at noon, you check your messages every 10mins from dawn to dusk, when you get my message is no more than 10mins after I sent it, you know when noon is local time, that's the relative time zone. If you're not sure of 10mins, build a sand/water clock. If my message comes overnight, don't bother trying to unite the groups. – Separatrix Jun 12 '17 at 14:59

## 1 & 2 - Location

Use the sun

Get two equal length straight branches and stick one (upright) in the ground. At chosen intervals, exchange the relative length and direction (in relation to sunrise of the branch's shadow. The relative sunrise/sunset times will tell you the relative longitudinal difference. The direction and height will tell you the latitude. These will only put you vaguely in the right vicinity since we're doing it with sticks but a large fire should be able to draw the attention of your survival expert.

# 3 - Units

Everyone knowing their height, as already mentioned, is a good idea but if that isn't satisfactory here is another idea.

You have your day - noon to noon the next day - you can now split this up using a water clock (and, for those interested, a video of one being made/in action). These aren't so difficult to make and you can measure it in terms of whatever volume you're using. Now measure how many of these it takes for a day to pass (ideally test a few times but once will do if time is short), you can use a stone to mark your container to show when different times have passed and agree these with your team on the other end of the radio.

Now you have the basis for all sorts of experiments. A pendulum's period depends on the length (and some constants), work out the time it takes a pendulum to swing, vary lengths and you should be able to agree with each other on how long a particular length of pendulum takes to swing and so know you have the same length. This could be defined as the length it takes for one period to be a thousandth of a day...or some such measure, however you wish to split up your days.

Now you should probably just use standard measures, as Seperatrix says:

Metric is great. 1 litre of water is 1 kilogram. 1 litre is a 10cm cube. 1 cubic metre of water is 1 tonne. Make some sort of container on with a known volume, fill that with water to get a known mass. To be able to travel together, the various groups will have needed to use a standardised measurement system. Metric or not, it doesn't matter, there will be equivalent relationships, though perhaps not so simple.

But if you don't want to here are some more ideas:

For mass you need a rope hung over a tree. On one side will be the mass you want to measure and on the other the top of our water clock. Fill the water clock such that the weights balance and, from a measured height, let the water begin to drain. As the resistance against gravity slowly reduces your weight will begin to fall. Measure the time it takes to hit the ground and you have a precedent for mass. As long as you both agree on time and length you should be able to determine particular masses.

# 4 - You have been communicating the whole time so should both know the units you're using

• using water clock to establish length is a questionable approach because you can graduate the vessel, but unless you have the same size hole and same size cross-section (which is possible if they have the same survival things they can use to make the clock - straw, water glass) – MolbOrg Jun 12 '17 at 11:56
• My thinking was that if you first use a set time (noon to noon) to choose a time you can always convert. So you know it takes fourteen of your coconuts with one hole size to measure a day but it takes them twenty. Then you can also mark the inside of the nut for particular agreed divisions. I don't expect these are perfect methods, however, just a different approach to those already mentioned. – Lio Elbammalf Jun 12 '17 at 12:15
• Matching clocks should be easy, but it seems like your going to have to drill your holes to better precision than I know my height to. How do you know the sunrise and sunset times? Mass via rope over tree, I haven't tested but it seems like it would work but would require matching ropes and tree barks. – Darkhorse Jun 12 '17 at 13:52
• I've been searching the answers for "shadow" because I wanted to know if anyone caught up on the longitude / latitude thing yet. Well done, sir. ;-) – DevSolar Jun 12 '17 at 13:56
• very well done, but he still need angle measure, a planatary time standard and a clock of some precision to get longitude to closer than the nearest quarter globe. – Darkhorse Jun 12 '17 at 14:23

1. figure out his position:

Easiest step: Find 3 distinctive Landmarks in your surrounding. Interpolate your position between them, communicate that to group B.

2. teach Group A to find their position:

Tell them what you did. Hope they have some distinct Landmarks also. Or via position of landmarks relative of sun at a certain time. If you don't see the landmarks you can use relative height of the sun and apparent time of day to approximate position of the groups relative to each other.

3. figure out units of length, mass/weight, and volume:

Probably everybody knows his own height (From which you can make a meter) and roughly his weight. From that you can determine your volume (Water displacement for example).

4. Communicate those units to Group A:

This is harder since you want to have a conversion factor of 1 between the groups. Height is not much of a problem. You could for example measure how long a drop of water needs fall down your height and tell group A that so-and-so many seconds a drop needs to fall a meter. How do you get seconds? Have group A set an arbitrary time unit that roughly resembles a second and have them transmit the clicks to group B for the drop measurement Since you both now have a distance unit thats roughly the same, for weight you can tell them to measure a volume of water which is the same as yours to get a weight unit.

EDIT: Logic error

I think your question has a logical error tbh. There is no use for the two groups for point 3 and 4. For now, all they really need to know is where the others are to meet up with them. Once they have physical contact, exchanging the other measurement systems is easy.

• The ship is broken and only provides message store and forward. What if he gets heavier or lighter due to his new diet/exercise . – Darkhorse Jun 12 '17 at 7:18
• I have misread that. Doesn't change the system though. Have group A set an arbitrary time unit that roughly resembles a second and have them transmit the clicks to group B for the drop measurement – Fl.pf. Jun 12 '17 at 7:21
• assuming the planet is earth like the drops fall around 10 meters in the first second, to get cm or mm is going to be lots of precise clicks. – Darkhorse Jun 12 '17 at 7:29
• You only need clicks for the meter. cm and mm you get from fractions of the meter – Fl.pf. Jun 12 '17 at 7:33
• You can extrapolate. Build a tower 10 times the measuring height person. Let somebody who's a musician do the clicks (he probably has the most consistent clicking) – Fl.pf. Jun 12 '17 at 7:34

## Pendulum

The wiki article alone is exciting reading, considering how many different pendulum systems were over time, with different uses, different properties of those systems.

When using it as a plot device for determining length, you just limited by the wish how complex the system can be and how much work they should put to make the system and extract results.

According to the wiki article, it was proposed to use the pendulum to establish a unit of length based on pendulum properties, before it was become known that gravity varies slightly from place to place. And it took them some time to measure the variations, so you can imagine how small is the difference.

They may or may not know parameters of the planet and thus by measuring angles of stars and sun and synchronizing over the radio they can determine their latitudes and eliminate the uncertainty involved by rotation of the planet thus precision will be limited by local deviations which is relatively small.

Gulf gravimeter in the article reported being able to measure gravity with the accuracy of (0.3–0.5)×10−7, thus if we assume equal gravity and account things we can account, the accuracy can be length accuracy.

Pendulum was a part of clock design for a long time, and I definitely saw on the YouTube the instruction of a master survivalist how to make a pendulum clock, ClickSpring playlist, Making A Large Wheel Skeleton Clock

Pendulum system does not require precise intervals or time interval synchronization because you can measure not a single time interval, but many time intervals, basically as much as you would like to have, but at least you count oscillations of a minute or two and compare the number of oscillations in the period. Also, it allows fine tuning of the length with simple means - regulator

NB clock making does not require common measuring system, they can choose arbitrary unit at the initial stage.

## Atmospheric pressure

If you have pipes you can make atmospheric pressure gauge, for water you need about 10m, for mercury about 0.760m.

Mercury gauges are relatively simple if you have glass and have ores of mercury.

Mercury extraction is just heating the ore in enclosed vessel and condensing it.

Cinnabar is mercury ore (HgS) - has very distinctive brilliant red color. So if you would like them to do some digging.

Measuring pressure is also useful to forecast weather conditions, so they may wish it to have for those goals too.

By averaging pressure values they can establish precise enough units of length.

## Eratosthenes

They may or may not know the circumference of the planet, but they can measure it in initially arbitrary units by repeating the experiment.

You can use the way if you would like them to travel a lot(far enough)

## Precision, what is enough

Practically you do not need a super high precision of establishing those units, they should be about right.

If the master survivalist is willing to guide the group A to create their means of survival the units has to be about right but not necessary the same.

The reason for it is that methods of producing and manufacturing things do not depend on the unit of length most of the time. They begin to be more or less important in things where tensile strength is important and safety factor is low (stressed constructions used to maximum of their capabilities)

It might be important to have a master length in each location, and it might be important to have similar lengths to make fewer adjustments later when they synchronize their master length by exchanging physical object.

0.1% accuracy in establishing initial units means 0.1mm difference of a 10cm detail or piece of machinery - in a lot of cases, it's not a bad accuracy, especially for simple machines and devices. And realistically speaking if they start from zero, such accuracy is just great. It is definitely a good accuracy for up to 1900-1920 tech levels and in a lot of cases today.

And if you build engine, and if you have only one factory, it is important to have the master length in the factory, if you produce multiple copies of the engine or wish to have a repair kit for the engine. But that all is about having accurate repeatability, not about the absolute length of the unit. And those master length has started about that way, not exactly informative in terms of how to do things but interesting in terms of piece of history Don Bailey, at A.A. Jonson metrology quarters

Also, I recommend another master survivalist and his playlist for different techniques, prototyping/manufacturing techniques for lab applications from Dan Gelbart

## Precision

It is possible to make DIY lasers such as Carbon dioxide laser, Ruby laser

Synthetic Ruby interesting article about subj. Another master survivalist talks about methods used to make crystals, Lab-Grown Rubies and Sapphires: Flux Vs. Flame Fusion

So, starting from relatively imperfect measuring length they can develop means to establish length unit in wavelength units without exchanging physical implementation of the length. And this is another reason to not seek for exactly precise units from the start. Anyway, people need time to learn skills and knowledge before they can implement and learn technologies which require precise measurements, and when they master skills they can create equipment which allows them to establish length in wavelength units.

It will require optics, lasers, mirrors but not so much of electronics as an example(zero electronics). It might be not that precise as we might do today(or better to say convenient to measure and replicate the length and account for temperature and such), but precision will be more than enough for most of the shops and factories of today.

• Not ignoring you, waiting for time to give that volume of words the attention they deserve. – Darkhorse Jun 12 '17 at 15:48
• There are some brilliant ideas in there. And a clock which implies a machine shop which implies a precision measuring system. And there is a mercury barometer implying glass tubes. and a laser requiring artificial ruby. Those imply mining and refining copper, tin, mercury and iron. All solid goals but maybe for the 10 or 20 year plan not immediately. – Darkhorse Jun 13 '17 at 19:55
• @Darkhorse "And a clock which implies a machine shop which implies a precision measuring system." - not so much, clock making was available since at least 1300 AC. Glass since 3500 BCE, synthetic ruby since 1837, in industrial quantities since 1902, optics since about 1609. – MolbOrg Jun 13 '17 at 23:33

The trick to precision units is to start big and then subdivide to get small. If you start big, your inaccuracies with crude tools can be minimized.

It turns out that, for most purposes, the actual size of the units isn't important. The only reason you could ever need to know the actual mass of a kilogram is if you have some re-entry documentation which gives all of the survival-related masses in kilograms. For everything else, units are really just a way of taking physical measurements and turning them into numbers (that could be conveyed over a radio).

As everyone has noticed, the first thing you want is a clock. Why? Because its the easiest place to start with this system. Build a water clock, or a pendulum, or anything of the sorts. However, we're not going to try to build it to any specification. Instead, we're going to calibrate it. Build a pinhole camera that you can use to track the sun's position. Lock this pinhole camera down as best as you can, so it can't move. Using the radio, pick a time of day and mark the position of the sun at that moment (if you're too far apart, and there's no time where both of you have daylight, this synchronization process will have to be done later, and it will be harder). This is your epoch mark -- all time points are measured from that point on that day. Time durations will be measured in days. Now, let your clocks run for several days straight. Observe the time the clocks read N days later, when the sun crosses the epoch line again. With this, you can create a conversion ratio from clock readings to days.

You can now use this clock to subdivide time. For example, if you had a water clock that you had to refil 400 times in the 4 day period you tested, that lets you know that each refil is 1/100th of a day. Now you can use this information to try to build shorter timepieces. Calibrate each one to the master clock's time, which itself should be periodically checked to make sure it lines up with the true master clock - the sun.

The next step is to get a length standard. For this, we assume that the altitude variances in the planet have a marginal effect on gravity. If you can haul the radios around, this is easy. Grab a bunch of decent sized boulders and head up to a larger cliff. Orchestrate between the two sides until you can find a cliff on each side where if you release a rock at the same time, it impacts at the same time. Mark this point in space. The distance down from this point to the bottom of the cliff is your reference distance. Now you can use trigonometry to subdivide this length.

If you can't move the radios, you'll need those clocks. Agree to find a cliff that is some fraction of a day's worth of a fall. You can build a small clock and tune it while you're near the radio, and then take it out to find a cliff.

Now you have time, and length. Length quickly means you have volume. Most importantly, you have time, length, and volume defined on very large scales, where crude human errors have been minimized. You can now scale these down independently of eachother. Make faster clocks, make shorter length measurement rods (using right triangles). Whenever there's any question about lengths or times, you return to the original reference (the cliff or the master clock) and re calibrate.

Now the hard part's up to you. I conveyed time and length. Now you have to do, you know, the whole survival on a hostile alien planet thing. Seems far more difficult, if you ask me.

From the question, I thought they really had very few tools if any, in which case, why would you need mass and volume? Did I miss something?

Step 1. You walk until you get a good view and find a nearby landmark.

Step 2. You estimate how many days or partial days it will take to get there.

Step 3. You tell everyone that information.

Step 4. Even if you or they aren't quite there, you light a fire and keep it burning until everyone can make it to the source. The units of time are days or parts of days (very rough) and distance and mass aren't necessary. Once everyone it together, you can figure out units of mass/volume/time or whatever you need. Plus you can share the workload and be rescued all together.

Of course, I'm assume the escape pods land in the same region. Are they on different continents or something?

• No way of knowing if they are close or on opposite spots on the globe. – Darkhorse Jun 12 '17 at 13:18

## Figure out his position

Relative to what? That's the question. From the question it sounds like he has nothing but his radio and what he and his fellows can make with stone knives and bearskins.

Lattitude can be determined by measuring the elevation of the sun from the horizon, which is a relatively simple measurement to make. However, you have to account for the axial tilt of the planet. So he's either going to have to know that, or spend a year taking measurements and then do a bunch of trigonometry to figure it out. Relative lattitude compared to the other group though won't care about axial tilt as long as the measurements are taken within a couple of days of each other (assuming earth-like year length. The shorter the year, the more precise the timing of the measurements.)

Longitude has no purely naturalistic way to measure. Mastering that one required high-precision clocks on Earth. Also, he'd have to pick a reference point... Relative longitude however can be determined just by using their radio. First, determine how long the RTT (Round Trip Time) is on the messaging. (Group A sends a message, and measures how long it takes Group B to receive and respond when everybody's going as fast as they can.) That will let them know the offset, and any variations in the timing will give you what the tolerance is, then they compare the elevation of the sun to the horizon at as close to the same time as possible. By comparing that to the length of the day they can figure out what fraction of the planet lies between the two groups and in which direction. By tracking how far the moving group goes versus how much the measurement changes over a few days, they can calculate the rough diameter of the planet and figure out how far the trip will be.

If the RTT is too long, or too unstable for this to work (doubtful unless the technology itself is horribly unreliable) then they'll need to look for some event that is visible to both groups at the same time. Needless to say, this could take a while.

## Teach Group A to find their position

Send the above instructions over the radio. It's not that complicated a process.

## Figure out units of length, mass/weight, and volume

This is actually relatively easy if he's from a country where they still use the Avoirdupois system of measurement, and really quite difficult if he's from one where they only teach the metric standard.

Make no mistake, metric is nice for doing calculations in, but it's pretty well useless if you have to make your own measuring devices out of sticks and rocks. To illustrate: Grab a pen and paper (pretend your carving notches on a stick. (Unless you'd rather grab a stick and a knife, your call.)) Draw a line on the paper and pretend it's a meter. (Accuracy doesn't matter for this, just any reasonably wide length will do.) Now, divide that "meter" into evenly sized "decimeters" (tenths). Good luck. Using nothing but your pen and paper, it will take you hours to get it reasonably close. Then do it again to one of the decimeters for centimeters...

Now, the secret is that the human brain is remarkably good at dividing things in half. And it can do thirds with a small amount of practice. So, pretend your line is a "foot" and cut it in half. then cut the two halves in half. Then cut the quarters into thirds. Presto! You've got inches, and if you have any reasonable level of coordination and put a modicum of effort into it, they're probably as close to the same size as is humanly possible to draw without mechanical assistance. The Avoirdupois system is designed around fractions that the human brain can handle easily, instead of tenths. Which makes the math hard(er slightly), but the creation of measuring devices easy. And when you have to build your measuring devices with your bare hands, having the math be slightly more difficult to remember is a small price to pay.

So: Find the male in the group who is the closest to 5'8" tall and normally proportioned. You will be able to derive measurements as follows:

The length of his foot will be close to a standard foot. A foot can be easily divided into reasonably precise inches by hand. The distance from the first to second knuckles of his index fingers is likely to be reasonably close when in a hurry. The distance from the tip of his nose to the end of his laterally outstretched arm will be three feet (1 yard). The amount of material he can hold in his two cupped hands will be just about one cup. Two cups makes a pint. Two pints makes a quart. Four quarts makes a gallon. One pint of water weighs a pound. Using a stick and a string as a balance beam, and knowing the principle of force*leverarm, he can divide the pound into sixteenths to make ounces. 1000 walking paces will be just about a mile.

Sub millimetre precision will require crafting devices to allow more precise division of units. The process is not technically complicated, but it does require a fairly large time investment. You used to be able to get entire books on the techniques from Lindsay Publications, but they've closed down for retirement, and I have yet to find a replacement source. Many of the books about how to create such devices efficiently from scratch have not been printed in any significant volume in over a hundred years, so your survival expert may or may not be familiar with them. Discovering the most efficient methods for creating high-precision tools with simple hand tools from scratch will up the time requirement immensely.

You didn't specify time synchronization, but two pendulums of the same length, lifted to the same height, will swing at the same frequency. But that probably doesn't matter until later since they won't be moving fast on foot and won't be trying any complicated coordination of activities until the two groups get brought together.

## Communicate those units to Group A

Have them find the male in their group who is closest to 5'8" tall and normally proportioned. Send him the instructions for how to create the measurement devices. (Yes, the male thing is actually important since men and women have different average hand and foot sizes relative to their height. Of course, the size of man specified assumes they're trying to get close to the standard measurements. If they don't care, then just pick the two individuals who are the same sex and closest to the same height.) It won't be exact, but it will probably be close enough for rough navigation to bring the two groups together. It should at least let them make precise enough measurements of relative latitude and longitude that they can get close enough to each other to be able to see the same landmarks. Simple angles between multiple landmarks should let them meet up from there.

• Lindsay Publications closed? I may cry, I spent most of highschool/collage going through their catalog and plotting evil and wishing I had money to send them. – Darkhorse Jun 13 '17 at 20:14
• @Darkhorse 'Tis the end of an era for sure. I just hope somebody scoops up all the vintage titles and digitizes them onto the Internet before they're lost forever. – Perkins Jun 13 '17 at 20:56

It would be a great use for natural units https://en.wikipedia.org/wiki/Natural_units

They don't depend on anything arbitrary, so they could also come in handy for sending measurements to alien cultures.

• how does group A derive them? How do they become a yardstick? – Darkhorse Jun 13 '17 at 19:27