Second Mundane Reality: Acceleration due to Earth's Gravity
Table of Candidate Gravities
| Candidate Gravity | SI & USC Equivalent | Corresponding Latitude | Primel Equivalent |
|---|---|---|---|
| Equatorial gravity | ≈ 9.78032677d m/s2 ≈ 32.0876863d ft/s2 | = 00°00′00.00″d = 00.00000000z b↓⊙ | ≈ 0.ƐƐ918969z ⚀accelerel |
| Primel ⚀gravity | = 9.79651584d m/s2 = 32.1408000d ft/s2 | ≈ 34°01′34.56″d ≈ 11.73ᘔƐ566ᘔz b↓⊙ | = 1.00000000z ⚀accelerel |
| Surface average gravity | ≈ 9.79758272d m/s2 ≈ 32.1443003d ft/s2 | ≈ 35°17′17.82″d ≈ 12.14731821z b↓⊙ | ≈ 1.00023123z ⚀accelerel |
| Median latitude gravity | ≈ 9.80619920d m/s2 ≈ 32.1725696d ft/s2 | = 45°00′00.00″d = 16.00000000z b↓⊙ | ≈ 1.00185Ɛ5Ɛz ⚀accelerel |
| SI standard gravity | ≈ 9.80665000d m/s2 ≈ 32.1740486d ft/s2 | ≈ 45°29′52.80″d ≈ 16.24827402z b↓⊙ | ≈ 1.001954ᘔ9z ⚀accelerel |
| TGM Gee | ≈ 9.81004940d m/s2 ≈ 32.1852014d ft/s2 | ≈ 49°16′05.51″d ≈ 17.70727872z b↓⊙ | ≈ 1.00247905z ⚀accelerel |
| Polar gravity | ≈ 9.83218637d m/s2 ≈ 32.2578293d ft/s2 | = 90°00′00.00″d = 30.00000000z b↓⊙ | ≈ 1.00636049z ⚀accelerel |
In the derivation of Primel units, the second “mundane reality” is the acceleration due to the gravity of the Earth, the one acceleration that is most inescapable here on the surface of our planet. With the exception of astronauts in orbit, or those who have visited the Moon, all human beings experience this acceleration every day of their lives. Consequently, Primel uses a value for net surface gravity as its coherent unit of acceleration, the ⚀accelerel (abbreviation ⚀accℓ). The advantage of this choice is that the ⚀forcel (the coherent unit of force) is then equivalent to the weight of one ⚀massel (the coherent unit of mass) under Earth's gravity (in other words, 1 ⚀forcel = 1 ⚀weightel).
The gravity experienced at the Earth's surface varies over an appreciable range. This is based on a number of factors, but chief among these is latitude, due to the counteracting effect of centrifugal force produced by Earth's rotation about its axis. Gravity is greatest at the poles, where centrifugal force is least: ≈ 9.83218637d meter/second2. Gravity is least at the equator, where centrifugal force is greatest: ≈ 9.78032677d meter/second2. Any value within this range is a candidate for a “standard” gravity.
The value Primel chooses as its standard ⚀gravity is exactly 9.79651584d meter/second2, or exactly 32.1408d foot/second2. This corresponds to Earth's gravity at latitude ≈ 34°01′34.56″d (11.73ᘔƐ567z bicia·turns). By the principle of 1-to-1 coherence, this choice leads to values for the ⚀velocitel and the ⚀lengthel with exact conversions to both SI and USC units. (This is due, in part, to the exact conversion of 1 inch = 127/5d|25.4d millimeters.) Hence, the ⚀velocitel comes out to exactly 0.93d feet per second, or 0.283464d meters per second, or a remarkable 1.0204704d kilometers per hour exactly. And the ⚀lengthel comes out to exactly 31/96d inches, or 3937/480d|8.202083d millimeters. Such relatively simple conversions are desirable if Primel is ever adopted widely, because they would simplify the design of machine tools that could manufacture industrial parts in Primel sizes, along with SI and USC sizes.
The Primel ⚀gravity is somewhat lower than the SI standard gravity of 9.80665d meter/second2. This is often described as an “average” gravity, but this is erroneous. In actuality, the SI standard appears to be a 19dth-Century estimate of gravity at median latitude, i.e. 45d° or 16z bicia·turns (an eighth of a turn, or 1 octant, of latitude). Even as such, it turns out this estimate was inaccurate, and the actual figure at that latitude is ≈ 9.80622789d meter/second2.
However, even this is not very good as an an “average”, because it weights all latitudes equally, and does not account for the distribution of surface area over a sphere. Latitudes cover progressively more surface area toward the equator. Consequently, the actual average gravity integrated over Earth's surface area is somewhat lower: ≈ 9.79758272 m/s², corresponding to a latitude of ≈ 35°17′17.82″d (12.11531347z bicia·turns).
The Primel standard ⚀gravity, at ≈ 0.02311ᘔ%z|0.010889%d below the average, is a closer approximation than SI·gravity, which is ≈ 0.17234Ɛ%z|0.092546%d above the average. Given that human population is also denser closer to the equator, such a lower latitude gravity value is also likely to be closer to the “demographic” average (i.e., the average of gravity actually experienced by human beings).
The Gee, the accelerel from Tom Pendlebury's TGM metrology, is ≈ 9.81004940d meter/second2 ≈ 32.1852014d foot/second2. This corresponds to latitude ≈ 49°16′05.51″d (17.70727872z bicia·turns), and diverges even further from the surface average than the SI·gravity does. Pendlebury chose this value for his accelerel because of the coincidence that it leads to a TGM lengthel (the Grafut, or the “gravity foot”) that is a simple fraction of the polar diameter of the Earth. This was something which scientists could measure with extreme accuracy in Pendlebury's day. But such an expedient is hardly necessary in order to achieve such fine precision today. With extremely accurate atomic clocks, and extremely accurate measurements of the speed of light, we can set up a precise equivalence with any prospective lengthel.