Practical Civil Engineer

To find the height of the 40th rod, we apply a linear progression where each step increases by **0.0275 meters** (27.5mm).
# # # Mathematical Calculation
The formula for the n-th rod height is:

For the 40th rod:

# # # Rod Height Schedule (1 to 40)
| Rod Number | Height (Meters) | | Rod Number | Height (Meters) |
|---|---|---|---|---|
| **1** | 2.6250 | | **21** | 3.1750 |
| **2** | 2.6525 | | **22** | 3.2025 |
| **3** | 2.6800 | | **23** | 3.2300 |
| **4** | 2.7075 | | **24** | 3.2575 |
| **5** | 2.7350 | | **25** | 3.2850 |
| **6** | 2.7625 | | **26** | 3.3125 |
| **7** | 2.7900 | | **27** | 3.3400 |
| **8** | 2.8175 | | **28** | 3.3675 |
| **9** | 2.8450 | | **29** | 3.3950 |
| **10** | 2.8725 | | **30** | 3.4225 |
| **11** | 2.9000 | | **31** | 3.4500 |
| **12** | 2.9275 | | **32** | 3.4775 |
| **13** | 2.9550 | | **33** | 3.5050 |
| **14** | 2.9825 | | **34** | 3.5325 |
| **15** | 3.0100 | | **35** | 3.5600 |
| **16** | 3.0375 | | **36** | 3.5875 |
| **17** | 3.0650 | | **37** | 3.6150 |
| **18** | 3.0925 | | **38** | 3.6425 |
| **19** | 3.1200 | | **39** | 3.6700 |
| **20** | 3.1475 | | **40** | **3.6975** |

To find the rod number for a height of **3725 mm** (3.725 meters), we use the inverse of the linear progression formula.
# # # The Calculation
We can rearrange the height formula to solve for the rod number (n):
Plugging in the values:
* **Target Height (H_n):** 3.725 m
* **Starting Height (H_{start}):** 2.625 m
* **Increment:** 0.0275 m
A height of 3725 mm corresponds exactly to **Rod Number 41**.

To find the number of rods between a known starting height and a known ending height, you can use a simple formula derived from the linear progression of the rods.
# # # The Formula
If you have the **Start Height**, the **End Height**, and the **Increment** (the height added to each rod), the number of rods is:
# # # Step-by-Step Example
If we use your previous parameters:
* **Start Height:** 2.625\text{ m}
* **End Height:** 3.6975\text{ m}
* **Increment:** 0.0275\text{ m} (27.5\text{ mm})
1. **Find the total height difference:** 3.6975 - 2.625 = 1.0725\text{ m}
2. **Divide by the increment:** 1.0725 / 0.0275 = 39
3. **Add 1 (to include the first rod):** 39 + 1 = 40
**Total Rods = 40**
# # # Important Notes for On-Site Use:
* **Units:** Always ensure your heights and increments are in the same unit (all in meters or all in millimeters) before dividing.
* **Rounding:** If your result isn't a whole number, it usually means the end height doesn't perfectly align with the standard increment, or there might be a small measurement error on-site.
Are you working with a specific set of start and end heights right now?