Townships, Sections, and Land Descriptions

Chapter: Townships, Sections, and Land Descriptions

I. Introduction

The Rectangular Survey System (also known as the Public Land Survey System or PLSS) provides a systematic approach to dividing and describing land, primarily in the United States. This system, based on principal meridians, baselines, townships, and sections, offers a structured method for land identification. Understanding its principles is fundamental for surveyors, real estate professionals, and anyone involved in land management. This chapter will delve into the intricacies of the Rectangular Survey System, covering its scientific foundation, practical applications, and related calculations.

II. Scientific Principles Underlying the Rectangular Survey System

A. Geodetic Framework:

1. Earth’s Shape and Datum: The Earth is approximated as a geoid, which represents the mean sea level surface❓❓ and serves as a reference for elevations. Mathematical models, such as the World Geodetic System 1984 (WGS84) ellipsoid, are used to approximate the geoid for geodetic calculations.
2. Coordinate Systems: The Rectangular Survey System relies on a grid system based on latitude and longitude. These geographic coordinates are then projected onto a plane using map projections, introducing distortions that must be accounted for in surveying.
3. Meridians and Parallels: Meridians are lines of longitude that run from pole to pole, while parallels are lines of latitude that run east-west. The convergence of meridians as they approach the poles is a critical factor that necessitates adjustments within the Rectangular Survey System.
   • Convergence Angle (α) approximation: α = Δλ * sin(φ), where Δλ is the difference in longitude and φ is the average latitude. This formula demonstrates how the convergence angle increases with latitude.

B. Surveying Principles:

1. Measurements and Errors: Surveying involves making precise measurements of angles and distances. Errors are inherent in any measurement process and can be classified as systematic or random. Systematic errors have a predictable pattern and can be corrected, while random errors are unpredictable and require statistical analysis.
2. Traversing: Traversing is a surveying method used to establish a series of connected lines with known lengths and directions. The accuracy of a traverse is assessed by calculating the closure error, which is the difference between the calculated and known coordinates of the starting point.
   • Closure Error (E): E = sqrt(Ex^2 + Ey^2) , where Ex and Ey are the errors in the x and y coordinates, respectively. This formula helps quantify the overall accuracy of the traverse.
3. Leveling: Leveling is the process of determining elevations of points relative to a datum. Differential leveling involves using a level instrument and a leveling rod to measure vertical distances.
4. Angular Measurements: Accurate angular measurements are critical for establishing the direction of survey lines. The precision of angular measurements is affected by factors such as instrument calibration, atmospheric refraction, and observer skill.

III. Townships and Ranges

A. Establishment of Principal Meridians and Baselines:

1. Principal Meridian: A principal meridian is a north-south line used as the reference for a particular survey area. Each principal meridian has a unique name (e.g., San Bernardino Meridian).
2. Baseline: A baseline is an east-west line that intersects the principal meridian and serves as the reference for townships.

B. Tiers and Ranges:

1. Tier Lines: East-west lines running parallel to the baseline at intervals of six miles are called tier lines.
2. Range Lines: North-south lines running parallel to the principal meridian at intervals of six miles are called range lines.
3. Tiers: East-west strips of land located between tier lines.
4. Ranges: North-south strips of land located between range lines.

C. Townships:

1. Definition: A township is a square parcel of land that is nominally six miles by six miles, formed by the intersection of a tier and a range. Therefore, each township contains 36 square miles.
   • Area of Township (A): A = 6 miles * 6 miles = 36 square miles. Since 1 square mile = 640 acres, A = 36 * 640 = 23,040 acres.
2. Designation: Townships are identified by their location relative to the principal meridian and baseline (e.g., Township 1 North, Range 3 East, or T1N, R3E). The “North” indicates the number of tiers north of the baseline, and “East” indicates the number of ranges east of the principal meridian.

D. Example Application:

To locate T2S, R4W, begin at the intersection of the principal meridian and baseline. Move two tiers south of the baseline and then four ranges west of the principal meridian. The resulting square is Township 2 South, Range 4 West.

IV. Sections and Aliquot Parts

A. Sections:

1. Division of Townships: Each township is divided into 36 sections, each approximately one mile by one mile.
   • Area of a Section: A = 1 mile * 1 mile = 1 square mile = 640 acres.
2. Section Numbering: Sections are numbered in a serpentine pattern, starting with Section 1 in the northeast corner of the township, progressing west to Section 6, then south to Section 7, and east to Section 12, and so on, ending with Section 36 in the southeast corner.
3. Importance of accurate numbering: It is important that the numbering proceeds in a systematic and accurate way so that accurate referencing can be done.

B. Partial Sections (Aliquot Parts):

1. Subdivision: Sections can be further divided into halves, quarters, quarter-quarters, and so on, creating smaller parcels.
2. Description: Partial sections are described by successively listing the divisions, starting with the smallest division❓ and ending with the largest. For example, the “Southwest quarter of the Northeast quarter (SW 1/4 of NE 1/4)” describes a 40-acre parcel (640 acres / 4 / 4 = 40 acres).

C. Area Calculations of Aliquot Parts:

Example: Calculate the area of the parcel described as “NW 1/4 of SE 1/4 of Section 10.”
* Step 1: Determine the area of the SE 1/4: 640 acres / 4 = 160 acres.
* Step 2: Determine the area of the NW 1/4 of the SE 1/4: 160 acres / 4 = 40 acres.
Therefore, the area of the parcel is 40 acres.

V. Adjustments and Irregularities

A. Convergence of Meridians:

1. Issue: Due to the Earth’s curvature, meridians converge as they approach the poles. This means that townships and sections cannot be perfect squares.
2. Correction Lines (Standard Parallels): To account for convergence, range lines are adjusted at intervals of 24 miles (every fourth township line) north and south of the baseline. These adjustment lines are called correction lines or standard parallels.
3. Guide Meridians: Similarly, range lines are corrected every 24 miles East and West of the principal meridian. These are called Guide Meridians.

B. Irregular Sections and Government Lots:

1. Location of Irregularities: Irregularities caused by convergence and other factors (e.g., bodies of water) are usually accounted for along the north and west boundaries of a township.
2. Government Lots: Irregular parcels that do not constitute a full section or quarter section are known as government lots. They are identified by a special government lot number.

C. Importance of Field Surveys:

Accurate determination of boundaries, particularly in areas with irregular sections and government lots, requires precise field surveys to establish the exact location of property lines.

VI. Rectangular Survey System Descriptions

A. Standard Procedure:

Land descriptions using the Rectangular Survey System start with the smallest division (e.g., quarter-quarter section) and list each larger division in sequence, culminating in the township, range, and principal meridian.

B. Example:

“The Northwest quarter of the Southwest quarter of Section 33, Township 6 South, Range 13 West, San Bernardino Base and Meridian.” This can be abbreviated as “NW 1/4 of the SW 1/4 of Sec. 33, T6S, R13W, S.B.B. & M.”

C. Additional Information:

Land descriptions should also include the county and state to avoid confusion.

VII. Geodetic Survey System and Quadrangles

A. U.S. Geological Survey (USGS):

The USGS maintains a geodetic survey system and publishes detailed topographic maps called quadrangles.

B. Quadrangle Maps:

These maps typically show:

1. Baselines and Principal Meridians
2. Section Lines
3. Topographic Features (towns, roads, bodies of water, contour lines, elevations)

C. Usefulness of Quadrangles:

Quadrangles provide valuable information for land surveying, planning, and environmental studies.

VIII. Practical Applications and Exercises

A. Boundary Disputes:

The Rectangular Survey System is essential for resolving boundary disputes. Surveyors use the system to retrace original survey lines and determine the correct location of property boundaries.

B. Land Development:

Developers rely on the Rectangular Survey System to divide land into lots and create subdivisions. Accurate land descriptions are crucial for ensuring clear title and facilitating property transactions.

C. Geographic Information Systems (GIS):

The Rectangular Survey System is integrated into GIS software, allowing users to create digital maps and analyze land-related data.

D. Example Experiment/Exercise:

1. Objective: Determine the area of a parcel described using the Rectangular Survey System.
2. Materials: USGS quadrangle map, calculator, ruler.
3. Procedure:
   • Identify the parcel on the quadrangle map.
   • Determine the aliquot parts that make up the parcel.
   • Calculate the area of each aliquot part.
   • Sum the areas to find the total area of the parcel.

IX. Conclusion

The Rectangular Survey System provides a structured framework for dividing and describing land. Understanding its principles, including the role of principal meridians, baselines, townships, sections, and aliquot parts, is crucial for professionals in various fields. Accurate application of the system ensures clear land titles, facilitates property transactions, and supports effective land management. The adjustments for the Earth’s curvature and the handling of irregular sections demonstrate the system’s adaptability to real-world conditions. Continued study and application of these concepts are essential for mastering the Rectangular Survey System.