(under construction)

The Primel Base Unit of Acceleration: The ′AccelerelEdit

The acceleration due to the gravity of the Earth is the second fundamental reality of the Primel system (as it is for TGM). All of us experience this acceleration every day of our lives, 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 ′Acℓ). 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:

′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 ′jiff per ′jiff).

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. 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 16%⊙z. However, at the time this was standardized, it was based on measurements made in the 19thd century (in the 10thz biquennium) 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 12.136475%⊙z.

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 (exact) = 32.1408d ft/s2 (exact) = 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 11.73ӾƐ566Ӿ23%⊙z. 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.

Earth's Gravity as a Function of LatitudeEdit

The following table shows the relationship between latitude and the net acceleration due to Earth's gravity, local to each turnlet (biciaturn) of latitude. Note that the deviation from 1 ′accelerel is always less than half a "pergross" or half a bicia (0.6%z). So local acceleration always rounds to 1.00z ′accelerel (when rounded to the nearest bicia). Hence, assuming a local gravity of 1 ′accelerel is a fairly accurate approximation for most purposes.

Latitude Net Gravitational Acceleration
Turnlets Degrees SI Units USC Units Primel Units
00%⊙z 00°d 9.780327d m/s2 32.087686d ft/s2 0.ƐƐ918Ӿz ′Acℓ
01%⊙z 02°30′d 9.780425d m/s2 32.088009d ft/s2 0.ƐƐ91Ɛ4z ′Acℓ
02%⊙z 05°d 9.780719d m/s2 32.088973d ft/s2 0.ƐƐ9269z ′Acℓ
03%⊙z 07°30′d 9.781206d m/s2 32.090572d ft/s2 0.ƐƐ9372z ′Acℓ
04%⊙z 10°d 9.781884d m/s2 32.092795d ft/s2 0.ƐƐ9504z ′Acℓ
05%⊙z 12°30′d 9.782746d m/s2 32.095623d ft/s2 0.ƐƐ96Ӿ3z ′Acℓ
06%⊙z 15°d 9.783786d m/s2 32.099037d ft/s2 0.ƐƐ9908z ′Acℓ
07%⊙z 17°30′d 9.784997d m/s2 32.103009d ft/s2 0.ƐƐ9Ɛ75z ′Acℓ
08%⊙z 20°d 9.786370d m/s2 32.107512d ft/s2 0.ƐƐӾ263z ′Acℓ
09%⊙z 22°30′d 9.787893d m/s2 32.112509d ft/s2 0.ƐƐӾ590z ′Acℓ
%⊙z 25°d 9.789556d m/s2 32.117965d ft/s2 0.ƐƐӾ933z ′Acℓ
%⊙z 27°30′d 9.791345d m/s2 32.123837d ft/s2 0.ƐƐƐ108z ′Acℓ
10%⊙z 30°d 9.793249d m/s2 32.130081d ft/s2 0.ƐƐƐ510z ′Acℓ
11%⊙z 32°30′d 9.795251d m/s2 32.136651d ft/s2 0.ƐƐƐ93Ɛz ′Acℓ
11.74%⊙z 34°02′d 9.796516d m/s2 32.140800d ft/s2 1.000000z ′Acℓ
12%⊙z 35°d 9.797337d m/s2 32.143496d ft/s2 1.00018Ӿz ′Acℓ
13%⊙z 37°30′d 9.799492d m/s2 32.150564d ft/s2 1.000637z ′Acℓ
14%⊙z 40°d 9.801698d m/s2 32.157803d ft/s2 1.000ӾƐ8z ′Acℓ
15%⊙z 42°30′d 9.803940d m/s2 32.165157d ft/s2 1.001387z ′Acℓ
16%⊙z 45°d 9.806199d m/s2 32.172570d ft/s2 1.00185Ɛz ′Acℓ
17%⊙z 47°30′d 9.808460d m/s2 32.179985d ft/s2 1.002134z ′Acℓ
18%⊙z 50°d 9.810704d m/s2 32.187348d ft/s2 1.002604z ′Acℓ
19%⊙z 52°30′d 9.812914d m/s2 32.194600d ft/s2 1.002Ӿ86z ′Acℓ
%⊙z 55°d 9.815074d m/s2 32.201688d ft/s2 1.003335z ′Acℓ
%⊙z 57°30′d 9.817168d m/s2 32.208556d ft/s2 1.003787z ′Acℓ
20%⊙z 60°d 9.819178d m/s2 32.215152d ft/s2 1.003ƐƐ8z ′Acℓ
21%⊙z 62°30′d 9.821091d m/s2 32.221426d ft/s2 1.004402z ′Acℓ
22%⊙z 65°d 9.822890d m/s2 32.227330d ft/s2 1.00479Ɛz ′Acℓ
23%⊙z 67°30′d 9.824563d m/s2 32.232818d ft/s2 1.004Ɛ45z ′Acℓ
24%⊙z 70°d 9.826096d m/s2 32.237848d ft/s2 1.005274z ′Acℓ
25%⊙z 72°30′d 9.827478d m/s2 32.242382d ft/s2 1.005565z ′Acℓ
26%⊙z 75°d 9.828698d m/s2 32.246385d ft/s2 1.005815z ′Acℓ
27%⊙z 77°30′d 9.829747d m/s2 32.249825d ft/s2 1.005Ӿ41z ′Acℓ
28%⊙z 80°d 9.830616d m/s2 32.252677d ft/s2 1.006022z ′Acℓ
29%⊙z 82°30′d 9.831299d m/s2 32.254918d ft/s2 1.006176z ′Acℓ
%⊙z 85°d 9.831791d m/s2 32.256531d ft/s2 1.006280z ′Acℓ
%⊙z 87°30′d 9.832087d m/s2 32.257504d ft/s2 1.006336z ′Acℓ
30%⊙z 90°d 9.832186d m/s2 32.257829d ft/s2 1.006360z ′Acℓ

Comparative Gravity in Various Cities Around the WorldEdit

City Gravitational Acceleration
SI Units USC Units Primel Units
Kuala Lumpur 9.776d m/s2 32.0735d ft/s2 0.ƐƐ85z ′Acℓ
Mexico City 9.776d m/s2 32.0735d ft/s2 0.ƐƐ85z ′Acℓ
Singapore 9.776d m/s2 32.0735d ft/s2 0.ƐƐ85z ′Acℓ
Jakarta 9.777d m/s2 32.0768d ft/s2 0.ƐƐ87z ′Acℓ
Bangkok 9.780d m/s2 32.0866d ft/s2 0.ƐƐ91z ′Acℓ
Manila 9.780d m/s2 32.0866d ft/s2 0.ƐƐ91z ′Acℓ
Calcutta 9.785d m/s2 32.1030d ft/s2 0.ƐƐӾ0z ′Acℓ
Hong Kong 9.785d m/s2 32.1030d ft/s2 0.ƐƐӾ0z ′Acℓ
Havana 9.786d m/s2 32.1063d ft/s2 0.ƐƐӾ2z ′Acℓ
Rio de Janeiro 9.788d m/s2 32.1129d ft/s2 0.ƐƐӾ6z ′Acℓ
Taipei 9.790d m/s2 32.1194d ft/s2 0.ƐƐӾӾz ′Acℓ
Kuwait 9.792d m/s2 32.1260d ft/s2 0.ƐƐƐ2z ′Acℓ
Cape Town 9.796d m/s2 32.1391d ft/s2 0.ƐƐƐƐz ′Acℓ
Los Angeles 9.796d m/s2 32.1404d ft/s2 1.0000z ′Acℓ
Buenos Aires 9.797d m/s2 32.1424d ft/s2 1.0001z ′Acℓ
Nicosia 9.797d m/s2 32.1424d ft/s2 1.0001z ′Acℓ
Sydney 9.797d m/s2 32.1424d ft/s2 1.0001z ′Acℓ
Denver 9.798d m/s2 32.1457d ft/s2 1.0003z ′Acℓ
Tokyo 9.798d m/s2 32.1457d ft/s2 1.0003z ′Acℓ
Auckland 9.799d m/s2 32.1490d ft/s2 1.0005z ′Acℓ
Athens 9.800d m/s2 32.1522d ft/s2 1.0007z ′Acℓ
Madrid 9.800d m/s2 32.1522d ft/s2 1.0007z ′Acℓ
Lisbon 9.801d m/s2 32.1555d ft/s2 1.0009z ′Acℓ
Washington, D.C. 9.801d m/s2 32.1555d ft/s2 1.0009z ′Acℓ
New York City 9.802d m/s2 32.1588d ft/s2 1.0010z ′Acℓ
Rome 9.803d m/s2 32.1621d ft/s2 1.0012z ′Acℓ
Wellington 9.803d m/s2 32.1621d ft/s2 1.0012z ′Acℓ
Chicago 9.804d m/s2 32.1654d ft/s2 1.0014z ′Acℓ
Skopje 9.804d m/s2 32.1654d ft/s2 1.0014z ′Acℓ
Ottawa 9.806d m/s2 32.1719d ft/s2 1.0018z ′Acℓ
Zurich 9.807d m/s2 32.1752d ft/s2 1.001Ӿz ′Acℓ
Istanbul 9.808d m/s2 32.1785d ft/s2 1.0020z ′Acℓ
Montréal 9.809d m/s2 32.1818d ft/s2 1.0022z ′Acℓ
Paris 9.809d m/s2 32.1818d ft/s2 1.0022z ′Acℓ
Vancouver 9.809d m/s2 32.1818d ft/s2 1.0022z ′Acℓ
Seattle 9.811d m/s2 32.1883d ft/s2 1.0027z ′Acℓ
Frankfurt 9.814d m/s2 32.1982d ft/s2 1.0031z ′Acℓ
Brussels 9.815d m/s2 32.2014d ft/s2 1.0033z ′Acℓ
London 9.816d m/s2 32.2047d ft/s2 1.0035z ′Acℓ
Amsterdam 9.817d m/s2 32.2080d ft/s2 1.0037z ′Acℓ
Stockholm 9.818d m/s2 32.2113d ft/s2 1.0039z ′Acℓ
Copenhagen 9.821d m/s2 32.2211d ft/s2 1.0044z ′Acℓ
Helsinki 9.825d m/s2 32.2343d ft/s2 1.0050z ′Acℓ
Oslo 9.825d m/s2 32.2343d ft/s2 1.0050z ′Acℓ
Anchorage 9.826d m/s2 32.2375d ft/s2 1.0052z ′Acℓ

Comparative Gravity on Various Solar System Objects Edit

Body Gravitational
Time to Fall 1 ′Stadial Speed after Falling 1 ′Stadial (1 ′q↑Lgℓ)

274.10d m/s2
899.28d ft/s2
23.Ɛ903z ′Acℓ

1.1d s
33z ′Tmℓ

305d m/s
1100d km/h
1002d ft/s
683d mph
759z ′Veℓ


25.93d m/s2
85.07d ft/s2
2.7919z ′Acℓ

3.6d s
Ӿ5z ′Tmℓ

94d m/s
338d km/h
308d ft/s
210d mph
237z ′Veℓ


11.28d m/s2
37.01d ft/s2
1.1998z ′Acℓ

5.5d s
13Ӿz ′Tmℓ

62d m/s
223d km/h
203d ft/s
139d mph
163z ′Veℓ


11.19d m/s2
36.71d ft/s2 1.185Ӿz ′Acℓ

5.5d s 13Ɛz ′Tmℓ

62d m/s 222d km/h
203d ft/s
138d mph
162z ′Veℓ


9.81d m/s2
32.17d ft/s2 1.0000z ′Acℓ

5.9d s
150z ′Tmℓ

58d m/s
208d km/h
190d ft/s
129d mph
150z ′Veℓ


9.01d m/s2
29.56d ft/s2
0.Ɛ053z ′Acℓ

6.1d s
158z ′Tmℓ

55d m/s
199d km/h
182d ft/s
124d mph
143z ′Veℓ


8.87d m/s2
29.11d ft/s2
0.ӾӾ4Ɛz ′Acℓ

6.2d s
15Ӿz ′Tmℓ

55d m/s
198d km/h
180d ft/s
123d mph
142z ′Veℓ


3.73d m/s2
12.23d ft/s2
0.468Ɛz ′Acℓ

9.6d s
236z ′Tmℓ

36d m/s
128d km/h
117d ft/s
80d mph
Ӿ6z ′Veℓ


3.70d m/s2
12.15d ft/s2
0.4697z ′Acℓ

9.6d s
237z ′Tmℓ

36d m/s
128d km/h
116d ft/s
79d mph
Ӿ5z ′Veℓ


1.79d m/s2
5.87d ft/s2
0.2237z ′Acℓ

13.8d s
339z ′Tmℓ

25d m/s
89d km/h
81d ft/s
55d mph
73z ′Veℓ


1.63d m/s2
5.33d ft/s2
0.1ƐӾ8z ′Acℓ

14.5d s
358z ′Tmℓ

24d m/s
85d km/h
77d ft/s
53d mph
z ′Veℓ


1.43d m/s2
4.68d ft/s2
0.18Ɛ6z ′Acℓ

15.5d s
386z ′Tmℓ

22d m/s
79d km/h
72d ft/s
49d mph
66z ′Veℓ


1.35d m/s2
4.41d ft/s2
0.1794z ′Acℓ

15.9d s
39Ӿz ′Tmℓ

21d m/s
77d km/h
70d ft/s
48d mph
63z ′Veℓ


1.31d m/s2
4.31d ft/s2
0.1739z ′Acℓ

16.1d s
3Ӿ4z ′Tmℓ

21d m/s
76d km/h
69d ft/s
47d mph
63z ′Veℓ


1.24d m/s2
4.07d ft/s2
0.1629z ′Acℓ

16.6d s
3Ɛ9z ′Tmℓ

21d m/s
74d km/h
67d ft/s
46d mph
60z ′Veℓ


0.80d m/s2
2.62d ft/s2
0.0Ɛ91z ′Acℓ

20.6d s
4Ɛ5z ′Tmℓ

17d m/s
59d km/h
54d ft/s
37d mph
z ′Veℓ


0.78d m/s2
2.56d ft/s2
0.0Ɛ55z ′Acℓ

20.9d s
503z ′Tmℓ

16d m/s
59d km/h
53d ft/s
36d mph
49z ′Veℓ


0.61d m/s2
2.00d ft/s2
0.08Ɛ7z ′Acℓ

23.6d s
581z ′Tmℓ

14d m/s
52d km/h
47d ft/s
32d mph
43z ′Veℓ


0.38d m/s2
1.24d ft/s2
0.056Ӿz ′Acℓ

30.0d s
724z ′Tmℓ

11d m/s
41d km/h
37d ft/s
25d mph
34z ′Veℓ


0.38d m/s2
1.24d ft/s2
0.056Ӿz ′Acℓ

30.0d s
724z ′Tmℓ

11d m/s
41d km/h
37d ft/s
25d mph
34z ′Veℓ

Dozenal Orders of Magnitude: AccelerationEdit