The ⚀accelerel, or ⚀gravity
- John Kodegadulo
In the derivation of Primel units, the second “mundane reality” is the acceleration due to the gravity of the Earth. All of us experience this acceleration every day of our lives. It is the one acceleration that is most inescapable here on the surface of our planet. Consequently, Primel chooses this as its base unit of acceleration, the ⚀accelerel (abbreviation ⚀accℓ). It can also be referred to colloquially as the ⚀gravity (“Primel gravity”) or ⚀gee (abbreviation ⚀G).
We can define the ⚀accelerel in terms of other base units:
1 ⚀accelerel = 1 ⚀velocitel / ⚀timel = 1 ⚀lengthel / ⚀timel2
which means that one ⚀accelerel is a rate of change in velocity of one ⚀velocitel per ⚀timel, or one ⚀lengthel per ⚀timel per ⚀timel (one ⚀morsel⋅length per ⚀vibe per ⚀vibe).
Choosing Earth's gravity as the base unit of acceleration allows Primel to adhere to the principle of 1:1 coherence between units. In particular, as we will see when we get to units of force, this choice allows us to express the mass of an object, as well as its weight, using essentially the same numeric value, just with different units (⚀massels vs. ⚀forcels).
But what exactly is the value for Earth's gravity? Net acceleration at Earth's surface varies appreciably due to a number of factors. Chief among these is the effect of Earth's rotation about its axis. This induces a centrifugal force that party counteracts the gravitational force due to Earth's mass. This means net acceleration varies with latitude due to the difference in distance from Earth's spin axis. (See Earth's Gravity as a Function of Latitude.) It is lowest at the equator, about 9.780327d m/s2 or 32.08769d ft/s2; and highest at the poles, about 9.832186d m/s2 or 32.25783d ft/s2.
All things being equal, just about any value within this range could be a candidate for “the” unit of acceleration. However, it seems reasonable to choose a median value to be the standard unit. This would minimize the deviation from the standard that would occur across the globe.
The SI standard for gravity, 9.80665d m/s2 or 32.174d ft/s2, evidently was intended to be the value occurring at the median latitude, 45°d or 16z b↓⊙. However, at the time this was standardized, it was based on measurements made in the 19thd century (in the 10thz biqua⋅ennium) that were not as accurate as we are able to make today. Based on the World Geodetic System 1984 (WGS-84) Ellipsoidal Gravity Formula, the actual median-latitude gravity is about 9.8061992d m/s2 or 32.17257d ft/s2.
However, this median-latitude gravity is not actually the median gravity on Earth's surface. This is because not all latitudes are equal; parallels of latitude become progressively longer approaching the equator, and thus cover progressively more of Earth's surface. When integrated over surface area, the estimated median of Earth's gravity is actually about 9.79756684237487d m/s2. This corresponds to a gravity occurring at a latitude of about 35°16⚀10″d or 12.136475z b↓⊙.
Primel defines as its standard for gravitational acceleration, a slightly lower value with an exact definition:
Primel standard gravity = 1 ⚀accelerel = 9.79651584d m/s2 = 32.1408d ft/s2 ≈ 0.998966603274308d SI standard gravity
This acceleration corresponds to the net gravity that occurs at a latitude of about 34°01′34.56″d, or 11.73ᘔƐ566ᘔ23z b↓⊙. This standard is about 0.02284%z lower than the estimated average, while the SI standard is about 0.17283%z higher; so Primel's standard is nearly 9 times closer to the average than SI's.