# What is Ruling Span?

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If all spans in a section of line are of the same length then the tension on individual span will be equal.Keeping the span lengths the same is possible on lines constructed on open terrains. However, for construction along highways and residential areas, the span lengths can never be equal. The owner of the property wants the poles be installed on the boundary of his/her lot. This causes a diverse length of spans that will affect the sag and conductor tension of the individual spans.

## What is a ruling span?

A ruling span, also known as equivalent span or mean effective span (MES), is an assumed uniform design span which approximately portray the mechanical performance of a section of line between its dead-end supports. The ruling span is used in the design and construction of a line to provide a uniform span length which is a function of the various lengths of spans between dead-ends. This uniform span length allows sags and clearance to be readily calculated for structure spotting and conductor stringing.

## How to use Ruling Span?

A value for the ruling span should be assumed before spotting structures because the actual ruling span can only be calculated after the structure locations are determined. In most cases, the actual ruling span should be greater than or equal to the assumed ruling span to ensure design clearances.

One or more assumed ruling spans, based on experience, has to be used for the field design of new line because the theoretical ruling span of a line section cannot be determined until after the line is staked. If the land is reasonably flat, it is appropriate to use a ruling span that approximates the level ground span. The required ground clearance may be subtracted from the attachment height of the lowest conductor to determine the sag limited by ground clearance. This sag value can then be used to determine a ruling span length whose sag is approximately equal to the sag allowed by the basic structure height. For rugged terrain, a ruling span that is longer than the level ground span is usually more effective.

After staking, the theoretical ruling span should be calculated and computed with the design ruling span. Using a design ruling span appreciably different from the theoretical ruling span of the section will produce unpredictable sags and tensions. Slack sags may cause clearance problems while tightly drawn spans may cause uplifts problems. Higher than predicted tensions may exceed the permitted load on support assemblies or may cause aeolian vibration problems.

## The Ruling Span Theory

During stringing and sagging, the conductors are placed on the travelers (or rollers) and are dead-ended at the ends of the stringing section of the line. While the conductor is on travelers and free to move between spans, the conductor tensions, and length in any span is a function of the combined averaged tension of all the spans and the total conductor length of the dead-ended stringing section.

When the spans are of unequal length and the supports are of varying elevations, the mathematics become too complicated to be easily calculated.

The assumptions of Ruling Span Theory:

1. The supports are at equal elevations
2. The horizontal tension is constant throughout the stringing section
3. The uneven spans are replaced by a series of equal spans

### THE THEORETICAL RULING SPAN EQUATION:

$\fn_phv&space;S_{R}&space;=&space;\sqrt{\frac{\sum&space;S^{3}}{\sum&space;S}}&space;=&space;\sqrt{\frac{S_{1}^{3}+S_{2}^{3}+...&space;S_{n}^{3}}{S_{1}+S_{2}+...&space;S_{n}}}$

where:
SR =  the theoretical ruling span
S1,S2, … Sn = are the 1st, 2nd, … nth span length respectively

Although this equation is not exact because of the assumption made but its accuracy is sufficient for most line designs, it is the equation most often to calculate the ruling span for new overhead distribution lines.

After being tied in, each span virtually becomes a dead-end span with approximately the same tension as the theoretical ruling span. When the tied spans in the section are of different lengths, changes in temperature, loading and elongation due to creep will cause a difference in tension between spans. These differences in tension will cause a flexing or bending of poles and arms.

This ruling span rules the behavior of the sagged section of the line. The sag characteristics of the ruling span set the sag characteristics of every span in the section. If conductors are installed using a sag-tension table with the wrong ruling span, actual final sags and tension will not be the same as predicted. The greater the difference, the greater the error!

## Estimated Ruling Span

Knowledge gained from a reconnaissance of the proposed line route may make it possible to estimate a ruling span. A traditional “rule of thumb” equation that may be helpful in the estimation of a ruling span is:

$\fn_phv&space;\fn_phv&space;S_{E}&space;=&space;Average\;&space;Span&space;\;&space;+&space;2/3&space;\;(Maximum\:&space;Span&space;-&space;Average&space;\;Span)$

Use this rule for estimating the ruling span with caution! This “rule of thumb”, used indiscriminately, has significantly different sags and tensions that the true ruling span equation. Even one span much longer than the average span may cause estimated ruling span to be much greater than the actual theoretical ruling span. This formula should only be used for estimating the ruling span when the actual spans are not yet known. When the spans are known, the theoretical equation should be used.

The estimated ruling span equation is easily solved and convenient for field used. When engineering calculator is available, used of the following equation provides greater accuracy:

$\fn_phv&space;S_{E}&space;=&space;\sqrt{\frac{\left&space;[&space;\frac{(\sum&space;{S&space;-&space;S_{m}})^{3}+S_{m}^{3}}{(N-1)^{2}}&space;\right&space;]}{\sum{S}}}$

where:
SE = Estimate Ruling Span
ΣS = Estimate total length of all spans in the stringing section
N = Estimated number of spans in stringing section
SM = Length of the estimated longest span in the stringing section

Another form of the estimated ruling span equation is:

$\fn_phv&space;S_{E}&space;=&space;\sqrt{\frac{N_{E}&space;S_{a}^{3}+S_{M}^{3}}{N_{E}S_{a}+S_{M}}}$

where:
S= estimated average span of stringing section, exclusive of the longest span

## Effect of Wrong Ruling Span

The greater the difference between the theoretical ruling span and the design ruling span, the greater the variation will be between the actual and predicted sag and tension values. The magnitude by which actual sag and tensions will differ from the predicted values is a function of conductor temperature and loading.

1. if the design sag is greater than the theoretical sag, then the actual sag of the installed conductors will be less than the predicted sag. This condition will lead to increased conductor tensions, which may exceed the permitted loads of support structures and guying assemblies.
2. If the design sag is less than the theoretical sag, then the actual sag of the installed conductors will be greater than the predicted sag. This condition may result in the inadequate ground clearances.

## EXAMPLE

In this example, we will calculate the ruling span base on the four equations above and see their differences.

## Span Lengths Summary

SpanSectionSpan Length (m)
1Pole 1 - Pole 266
2Pole 2 - Pole 360
3Pole 3 - Pole 475
4Pole 4 - Pole 565

Using Equation 1:

SRULING = √(663 + 603 + 753 + 653)/(66 +60 +75 +65) = 67.17 meters

Using Equation 2:

Average Span = (66 +60 +75 +65)/4 = 66.5

SMAXIMUM = 75

SESTIMATED RULING  =  66.5 + 2/3 (75 – 66.5) = 72.17 meters

Using Equation 3:

∑S = (66 +60 +75 +65) = 266 , N = 4

SESTIMATED RULING = √[((266 – 75)+753)/(4-1)2]/266 = 55.56 meters

Using Equation 4:

Saverage (exclusive max span) = (66 +60 +65)/3 = 63.7

SESTIMATED RULING = √ (4 * 63.73 + 753)/(4 * 63.7 +75) = 66.42 meters

Using Excel Spreadsheet, here is the summary:

In the next post we will calculate the sag and tension of the individual spans based on the calculated ruling span.

References:

1. RUS Bulletin 1724E-200
2. RUS Bulletion 1724-152
3. IEAI  MAGAZINE: The Effects of Ruling Span on Sag and Tension