Chaining on sloping ground

 Chaining on Sloping Ground (Simple Notes)

When measuring distances on a hill or slope, we always need to find the flat horizontal distance, not the actual sloped ground distance. There are two main ways to do this:

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1. Direct Method (Stepping Method)

In this method, you measure the flat horizontal distance directly on the field by creating small, flat steps.

• Best For: Short, bumpy, irregular, or gentle slopes.

How it works (Step-by-Step):

1. Start: The Follower holds the 0-end of the tape flat on the starting ground point A.
2. Stretch: The Leader pulls a short, comfortable length of the tape forward and lifts it up until it looks perfectly flat and straight by eye judgment.
3. Drop: Because the front end of the tape is hanging in the air, the Leader drops a plumb-bob (a weight on a string) down to find the exact vertical point on the ground.
4. Mark & Repeat: They stick an arrow into that ground point. The Follower moves to this new arrow, and they repeat the steps all the way up or down the hill.

Formula to Copy:

Total Horizontal Distance = d1 + d2 + d3 + ... + dn

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2. Indirect Method

In this method, you measure along the sloped ground first, and then use a quick math calculation to find the flat horizontal distance.

• Best For: Long, smooth, regular, and very steep hills.

Here are the three simple techniques used in this method:

Technique A: By Measuring the Slope Angle

• What you do: Measure the actual sloped distance (L) with a tape. Use a tool like a clinometer to find the angle of the hill (a).
• Formula to Copy:
  Horizontal Distance = L * cos(a)

Technique B: By Measuring the Height Difference

• What you do: Measure the sloped distance (L). Use a leveling tool to find the exact vertical height change (h) between the top and bottom of the hill.
• Formula to Copy:
  Horizontal Distance = L - ( (h * h) / (2 * L) )

Technique C: By Applying Hypotenusal Allowance

• What you do: When walking up a hill, 1 chain length on the slope is actually shorter than 1 chain length on flat ground. To fix this instantly on the field, you pull the chain a little bit extra forward along the slope.
• Formula to Copy:
  Extra Links to Pull = 100 * ( sec(a) - 1 )
• Benefit: You don't need to do any calculations later in the office; the markings on the ground are already correct.

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Direct Method vs Indirect Method Comparison

• Direct Method (Stepping):
  • Measures flat distance directly on the field.
  • Tools needed: Tape, Plumb-bob, Arrows.
  • Best for: Short, bumpy, or uneven slopes.
  • Math work: No formulas needed. Just add up the steps.
• Indirect Method:
• Measures sloped distance and calculates flat distance later.
• Tools needed: Tape, Clinometer, or Leveling tools.
• Best for: Long, smooth, and very steep hills.
• Math work: Requires formulas to get the final answer. 
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• Quick Comparison

Feature	Direct Method (Stepping)	Indirect Method
How it works	Measures flat distance directly on the field.	Measures sloped distance and calculates flat distance later.
Tools Needed	Tape, Plumb-bob, Arrows.	Tape, Clinometer, or Leveling tools.
Best For	Short, bumpy, or uneven slopes.	Long, smooth, and very steep hills.
Math Work	No formulas needed. Just add the steps.	Requires formulas or extra calculations.