Grip refers to the unthreaded portion of the shank. This is the portion of the bolt that should bear against the inside of the hole. The threaded portion is not as strong as the shank in shear and does not present a good bearing surface for the parts being bolted together. Under vibration or movement, the threads can damage the hole.

Thread Length is constant for each bolt diameter. It is calculated to be enough for one AN960 flat washer under the head, a full-height AN365 or AN310 nut, and one AN960 flat washer under the nut. Grip lengths are in 1/8' increments. AN960 washers are 1/16' thick (1/32' thick for the L version). If your application falls between two grip lengths, you can add one or two more washers to a bolt with the next longer grip.

AN bolt nomenclature follows this format:

12 x 24 x 1″ 12 x 30 x 1″ 14 x 14 x 1″. Simply measure the length and width of your filter with a tape measure and choose the closest size (to 1/8”) in the drop down menu. 1/8” tolerance is standard and should not cause a problem in any standard filter application. 1 Maccabees 8:1. Now Judas heard about the Romans’ reputation for being strong and loyal to all who made an alliance with them. They pledged friendship to those who came to them.

ANd(H) - g(A)

d is the bolt diameter (in sixteenths of an inch)

H indicates that the head is drilled for safety wire (no H indicates undrilled head)

g refers to the grip length*

A indicates that the shank is NOT drilled for a cotter pin (no A indicates drilled shank)

Examples:

AN4-15A: 1/4-28 bolt, 1 3/16' grip, undrilled head, undrilled shank

AN6-20: 3/8-24 bolt, 1 7/16' grip, undrilled head, drilled shank

AN5H-27A: 5/16-24 bolt, 2 7/16' grip, drilled head, undrilled shank

* Note: A popular misconception is that the dash number gives the shank length in full inches plus eighths of an inch (-15 would mean 1 5/8' shank length). The numbering sequence seems to back this up -- the dash numbers skip right from -7 to -10 (i.e., -8, -9, -18, -19, etc. are not used). This would be convenient, but in reality it is not the case. Each dash number specifies a different length for different bolt diameters. You must refer to a size chart or AN bolt gauge to find the correct dash number.

The bolt grip length charts linked below are especially handy when replacing non-AN bolts. Measure the total thickness of the parts being bolted together (not including washers, nut, or female threads). Locate the bolt diameter and grip length (total thickness) in the table to find the required dash size.

AN Bolt Grip Length Chart (Decimal)

AN Bolt Grip Length Chart (Fractional)

AN Bolts

8.1l

AN Bolt Identification Gauge

Maccleanse 8 1 24 Hour

Printable AN Bolt Grip Length Chart (Decimal), PDF Format

Printable AN Bolt Grip Length Chart (Fractional), PDF Format

In mathematics, the infinite series1/2 + 1/4 + 1/8 + 1/16 + ··· is an elementary example of a geometric series that converges absolutely. The sum of the series is 1.In summation notation, this may be expressed as

${\displaystyle \frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\cdots =\sum _{n=1}^{\mathrm{\infty }}{\left(\frac{1}{2}\right)}^n=1.}$

The series is related to philosophical questions considered in antiquity, particularly to Zeno's paradoxes.

Proof[edit]

As with any infinite series, the sum

${\displaystyle \frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\cdots }$

is defined to mean the limit of the partial sum of the first n terms

${\displaystyle s_n=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\cdots +\frac{1}{2^{n-1}}+\frac{1}{2^n}}$

as n approaches infinity.By various arguments,^[a] one can show that this finite sum is equal to

${\displaystyle s_n=1-\frac{1}{2^n}.}$

As n approaches infinity, the term ${\displaystyle \frac{1}{2^n}}$ approaches 0 and so s_n tends to 1.

History[edit]

Zeno's paradox[edit]

This series was used as a representation of many of Zeno's paradoxes.^[1] For example, in the paradox of Achilles and the Tortoise, the warrior Achilles was to race against a tortoise. The track is 100 meters long. Achilles could run at 10 m/s, while the tortoise only 5. The tortoise, with a 10-meter advantage, Zeno argued, would win. Achilles would have to move 10 meters to catch up to the tortoise, but by then, the tortoise would already have moved another five meters. Achilles would then have to move 5 meters, where the tortoise would move 2.5 meters, and so on. Zeno argued that the tortoise would always remain ahead of Achilles.

The Eye of Horus[edit]

The parts of the Eye of Horus were once thought to represent the first six summands of the series.^[2]

In a myriad ages it will not be exhausted[edit]

A version of the series appears in the ancient Taoist book Zhuangzi. The miscellaneous chapters 'All Under Heaven' include the following sentence: 'Take a chi long stick and remove half every day, in a myriad ages it will not be exhausted.'^{[citation needed]}

See also[edit]

References[edit]

1. ^Wachsmuth, Bet G. 'Description of Zeno's paradoxes'. Archived from the original on 2014-12-31. Retrieved 2014-12-29.
2. ^Stewart, Ian (2009). Professor Stewart's Hoard of Mathematical Treasures. Profile Books. pp. 76–80. ISBN978 1 84668 292 6.

1. ^For example: multiplying s_n by 2 yields ${\displaystyle 2s_n=\frac{2}{2}+\frac{2}{4}+\frac{2}{8}+\frac{2}{16}+\cdots +\frac{2}{2^n}=1+\left[\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\cdots +\frac{1}{2^{n-1}}\right]=1+\left[s_n-\frac{1}{2^n}\right].}$ Subtracting s_n from both sides, one concludes ${\displaystyle s_n=1-\frac{1}{2^n}.}$ Other arguments might proceed by mathematical induction, or by adding ${\displaystyle \frac{1}{2^n}}$ to both sides of ${\displaystyle s_n=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\cdots +\frac{1}{2^{n-1}}+\frac{1}{2^n}}$ and manipulating to show that the right side of the result is equal to 1.^{[citation needed]}