Drawing of a Diagonal Scale

In this article, we will discuss the procedure for drawing a diagonal scale with problem-solving examples.

Concept, principal & Use of Diagonal Scale

1. Terminology:

The Greek word “diagōnios” where  “dia” means “through” and  “gonios” represents  “corners”. The Latin word “Diagonalis” has been coined from it.

2. Definition: 

A diagonal scale is a length measuring instrument which is composed of a set of parallel straight lines, obliquely crossed by another set of parallel straight lines followed by the principle of similar triangles.

3. Principle:

In a diagonal scale, the short length is divided into several parts in which sides are proportionally divided into the required number of equal parts.

4. Use: 

Diagonal scales are often used to measure small fractions of the unit of measurement in Geographic and engineering drawing to read lengths with higher accuracy. It represents a unit into three different multiples in meters, centimeters, and millimeters as well as other units accordingly. 

Principle of Diagonal Scale

Graphical Construction of Diagonal Scale:

Here are my videos on the Graphical Construction of Diagonal Scale. Feel free to check out for a better understanding and concept.

Graphical Construction of Diagonal Scale Part 1 Graphical Construction of Diagonal Scale Part 2
Videos of Diagonal Scale

Example of Diagonal Scale with Problems and Solution.

Q1. Draw a diagonal scale to read 3Km 7Hm and 75 M for the map where R.F 1: 32,000 What will be the minimum length of the scale?

Solution: Calcultaion Part

Calculation Part

Drawing Part

Drawing Part

Q2. Draw the diagonal scale to read 2yard 2feet 11 inches for the map where R.F 1: 32 & also calculate the minimum length of the scale?

Solution: Calculation Part

Calculation Part

Drawing Part

Drawing part

Q3. Draw a diagonal scale to read 45.65KM for the map where R.F 1: 2,81,000.

Soultion: Calculation Part

Calculation Part

Drawing Part

Drawing Part

Q4. Draw a diagonal scale to read 1/100th part of an inch as conventional scale and marked an arrow line to read 5.67 inches on it.

Solution: Calculation Part

Calculation Part

Drawing Part

Drawing Part

Q5. Draw a diagonal scale to read 54.39 KM for the map where R.F 1: 3,40,000.

Solution: Calculation Part

Calculation Part

Drawing Part

Drawing Part

Q6. Draw a diagonal scale to read 23.79 KM for the map where R.F 1: 1,60,000.

Solution: Calcultaion Part

Calculation part

Drawing Part

Drawing Part

9. Conclusion and Homework assignments:

Diagonal scale mostly uses in the cartographic drawing for the geographers and engineering departments for the precise measurement of length. All the above problems and answers will help the concerned fields. Here are some problems for your practice. Few short answer-type questions should be answered in the comment box.

Homework Assignments:

HQ1. Draw a diagonal scale to read 4.725 Km for the map where R.F 1: 33,000 What will be the minimum length of the scale?

HQ2. Draw a diagonal scale to read 51.57 Km for the map where R.F 1: 4,10,000. Also, calculate the minimum length of the scale?

HQ3. Draw a diagonal scale to read 54.39 KM for the map where R.F 1: 2,50,000. Also, calculate the minimum length of the scale?

HQ4. Draw a diagonal scale to read 20.19 KM for the map where R.F 1: 1,65,000

HQ5. Draw a diagonal scale to read 1/200th part of a cm. as a conventional scale and marked an arrow line on it to show the 6.925 km ground distance for the map with R.F 1:50,000

Advanced short answer questions (Answer expected on the comment box of this article) •

Q1. What will be the minimum total length of the scale in Q1?  if you have to read 4Km 7Hm and 75 M?

•Q2. What will be the minimum total length of the scale in  Q3. to read 35.65Km? •

•Q3. What will be the minimum total length of the scale in Q6. to read 20.79 KM?

For submitting the answers to the above questions you can email us at [email protected] or contact us

One thought on “Drawing of a Diagonal Scale

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