--- title: "Diagonal scale: hydropower dam-powerhouse" subject: "Surveying I" chapter: 1 key: "semester_3/surveying_i:diagonal-scale-hydropower-1m" source: https://www.bctengineer.com/q/semester_3/surveying_i/diagonal-scale-hydropower-1m site: BCT Engineering --- # Diagonal scale: hydropower dam-powerhouse Surveying I · Chapter 1: Introduction - Asked in: 2079 Bhadra, 4 marks - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_3/surveying_i/diagonal-scale-hydropower-1m - Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-1 ## Question In a preliminary study plan of a hydropower project, the horizontal distance between the dam and the powerhouse, which is 1 km on the field, is represented by a line 25 cm. Calculate the representative factor used in the map. Draw a diagonal scale to read upto 1 m and long enough to measure 500 m. Also indicate the following distances: (i) 123 m (ii) 256 m. ## Short answer RF is 1/4000 and scale length is 12.5 cm, with one extra 2.5 cm subdivision to the left. Main divisions are 100 m each; diagonals give 1 m steps. Mark 123 m as 100+20+3 and 256 m as 200+50+6. ## Answer #### RF 1 km $= 1000$ m $= 10^5$ cm on the ground is represented by 25 cm. $$ \text{RF} = \frac{25}{10^{5}} = \frac{1}{4000} $$ #### Scale length $$ \text{Length for 500 m} = \frac{500 \times 100}{4000} = 12.5\ \text{cm} $$ Therefore 100 m $= 2.5$ cm, 10 m $= 0.25$ cm, 1 m $= 0.025$ cm. #### Construction 1. Draw a line 12.5 cm long and divide it into 5 equal main divisions of 2.5 cm (100 m each). Add one more division of 2.5 cm to the left of the zero, so the total drawn is 15 cm. Number 0, 100, ... 500. 2. Divide the left extra division into 10 equal parts of 0.25 cm (10 m each). 3. Draw a rectangle of any convenient height (say 2.5 cm), divide the height into 10 parts and draw 10 horizontal lines. 4. Join the top of the first sub-division (10 m) with the bottom 0 of the main scale; draw parallel diagonals through the other sub-divisions. Each step along a diagonal equals 1 m. ```text 10| / / / / / / / / / /| 5| / / | 0+---+----+----+----+----+----+--+ 90..0 100 200 300 400 500 (m) ``` #### Distances - **123 m** $= 100 + 20 + 3$: vertical at 100, the diagonal from the 20 m sub-division, 3rd horizontal line. - **256 m** $= 200 + 50 + 6$: vertical at 200, diagonal from 50 m, 6th horizontal line. **Answer: RF = 1/4000; length of scale = 12.5 cm (plus the left sub-divided part).** ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. 1 km on ground is 25 cm on the map. The RF is A. 1/400 B. 1/40,000 C. 1/4000 D. 1/2500 Answer: C. 25/10^5 = 1/4000. (Key point: RF) 2. Length for 500 m is A. 12.5 cm B. 5 cm C. 25 cm D. 1.25 cm Answer: A. 500 x 100 / 4000 = 12.5 cm. (Key point: Length) 3. One metre on the scale is A. 0.25 cm B. 0.025 cm C. 2.5 cm D. 0.0025 cm Answer: B. 100 m = 2.5 cm, so 1 m = 0.025 cm. (Key point: 1 m) 4. 256 m is located using A. vertical at 200, diagonal from 5 m, 56th line B. vertical at 250, diagonal from 6, 2nd line C. vertical at 300, diagonal from 44, 6th line D. vertical at 200, diagonal from 50 m, 6th horizontal line Answer: D. 256 = 200 + 50 + 6. 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