Isoptic: The Key to Achieving Good Visibility in Your Auditorium

What is Isoptic and Why is it Important for Auditorium Design?

Isoptic is a condition of equal visibility for the audience, allowing spectators to fully view a specific area. For example, a theater stage, a movie screen, or a conference podium.

Isoptic is important for auditorium design because it ensures that all attendees can enjoy the show without visual obstructions or distortions of the image. In addition, good isoptic improves the comfort and safety of the spectators, as it prevents them from having to strain their eyes or adopt uncomfortable postures to see better.

To achieve good isoptic, several factors influencing visibility must be considered, such as anthropometry, furniture, viewing angle, and point of interest. Anthropometry refers to human body measurements, like height, width, and depth.

Furniture refers to the elements placed in the auditorium to accommodate the spectators, like chairs, tables, or seats. The viewing angle refers to the angle formed by the spectator’s eye with the point of interest and the boundaries of the auditorium. The point of interest refers to the place where the main show or activity takes place.

The aim of this article is to explain how to calculate the isoptic and show you some examples of auditoriums with good isoptic. For this, we will distinguish between two types of isoptic: vertical and horizontal.

Vertical isoptic deals with the height or difference in elevation between rows of seats, while horizontal isoptic deals with the width or radius of the auditorium. Both are necessary to achieve optimal visibility from any point in the auditorium.

How is Vertical Isoptic Calculated?

The objective of vertical isoptic is to find convenient heights or elevation differences for the design of the stands or rows of seats. Its calculation defines the ascending curve generating the stepping of the floor between rows of observers that will allow achieving good visibility. Through mathematical methods, the isoptic line can be obtained with the following formula:

h’= (d’ (h+k) ) / d

Where h’ represents the eye height of the spectator, d’ is the distance of the spectator to the base point for plotting, h is the eye height of the spectator preceding the one being calculated, k is a constant indicating the level difference between the eye and the top of the head, and d is the distance from the base point for plotting to the spectators located in the row prior to the one being calculated.

To better understand this formula, you can view the following diagram that shows the variables involved:

Variables involved in isoptic calculation. Image taken from: Isoptic Calculations.

As you can see, the base point for the tracing is the lowest point of the stage or area of interest. From this point, a straight line is drawn to the eye of the first viewer (row 1). Another straight line is then drawn from the same point to the eye of the second viewer (row 2). The difference between both lines determines the height or level difference needed between the rows to achieve good visibility.

The recommended values for the variables depend on the type of auditorium and the kind of event being held. For example, for a theater-style auditorium, where the stage is elevated and the point of interest is the actors’ heads, it’s recommended that the height of the viewer’s eye be 3.61 feet, the constant k be 0.39 feet, and the viewer’s distance to the base point be 49.21 feet. For a cinema-style auditorium, where the screen is at floor level and the point of interest is the center of the screen, it’s recommended that the height of the viewer’s eye be 3.44 feet, the constant k be 0.33 feet, and the viewer’s distance to the base point be 32.81 feet.

To exemplify the vertical isoptic calculation, let’s take the case of an auditorium with 10 rows of seats and a stage 49.21 feet away. We’ll assume it’s a theater-type auditorium, so we’ll use the recommended values for that type. Applying the formula, we get the following results:

• For row 1, h´ = 3.61 ft, d´ = 49.21 ft, h = 0, k = 0.39 ft and d = 0. Therefore, h´= (49.21 (0+0.39) ) / 0 = undefined. This means there’s no level difference between the floor and the first seat.
• For row 2, h´ = 3.61 ft, d´ = 52.49 ft, h = 3.61 ft, k = 0.39 ft and d = 49.21 ft. Therefore, h´= (52.49 (3.61+0.39) ) / 49.21 = 4.36 ft. This means there is a level difference of 0.75 ft between the first and second seat.
• For row 3, h´ = 3.61 ft, d´ = 55.77 ft, h = 4.36 ft, k = 0.39 ft and d = 52.49 ft. Therefore, h´= (55.77 (4.36+0.39) ) / 52.49 = 5.12 ft. This means there is a level difference of 0.75 ft between the second and third seat.
• And so on, until reaching row 10.

To better understand this formula, you can see the following diagram that shows the variables involved:

Variables involved in the isoptic calculation. Image taken from: Isoptic Calculations.

As you can see, the base point for the line is the lowest point of the stage or area of interest. From this point, a straight line is drawn to the eye of the first viewer (row 1). Then another straight line is drawn from the same point to the eye of the second viewer (row 2). The difference between both lines is what determines the height or level difference between the rows to achieve good visibility.

The recommended values for the variables depend on the type of auditorium and the kind of event that is going to take place. For example, for a theater-type auditorium, where the stage is elevated and the point of interest is the head of the actors, it is recommended that the eye height of the viewer be 3.6 feet, the constant k be 0.39 feet, and the viewer’s distance to the base point be 49.2 feet. For a cinema-type auditorium, where the screen is at ground level and the point of interest is the center of the screen, it is recommended that the eye height of the viewer be 3.4 feet, the constant k be 0.32 feet, and the viewer’s distance to the base point be 32.8 feet.

To illustrate the vertical isoptic calculation, let’s take the case of an auditorium with 10 rows of seats and a stage 49.2 feet away. We will assume that it is a theater-type auditorium, so we will use the recommended values for that type. Applying the formula, we get the following results:

• For row 1, h’ = 3.6 feet, d’ = 49.2 feet, h = 0, k = 0.39 feet, and d = 0. Therefore, h’ = (49.2 (0+0.39)) / 0 = undefined. This means there is no level difference between the floor and the first seat.
• For row 2, h’ = 3.6 feet, d’ = 52.5 feet, h = 3.6 feet, k = 0.39 feet, and d = 49.2 feet. Therefore, h’ = (52.5 (3.6+0.39)) / 49.2 = 4.4 feet. This means there is a level difference of 0.75 feet between the first and second seat.
• For row 3, h’ = 3.6 feet, d’ = 55.8 feet, h = 4.4 feet, k = 0.39 feet, and d = 52.5 feet. Therefore, h’ = (55.8 (4.4+0.39)) / 52.5 = 5.1 feet. This means there is a level difference of 0.75 feet between the second and third seat.
• And so on until we reach row 10.

In this way, we can obtain the upward curve that defines the vertical isoptic for the auditorium.

How is the horizontal isoptic calculated?

The horizontal isoptic aims to find the appropriate width or radius for the auditorium design. Its calculation defines the minimum viewing angle that each viewer must have to see the entire stage or area of interest without missing any details. Through geometric methods, the minimum viewing angle can be calculated with the following formula:

α = arctan (b / (2r))

Where α is the minimum viewing angle, b is the width of the stage or area of interest, and r is the radius of the auditorium or the distance from the center of the stage to the last row.

To better understand this formula, you can see the following diagram that shows the variables involved:

Variables for calculating the horizontal isoptic. Taken from ArchDaily.

As you can see, the minimum viewing angle is the angle formed by the viewer’s eye with the ends of the stage or area of interest. This angle should be wide enough so that the viewer can see everything happening on the stage without having to turn their head or miss any details.

The recommended values for the angle depend on the type of auditorium and the kind of event that is going to take place. For example, for a theater-type auditorium, where the stage is elevated and has considerable depth, it is recommended that the minimum viewing angle be 45°. For a cinema-type auditorium, where the screen is at ground level and has considerable height, it is recommended that the minimum viewing angle be 30°.

To illustrate the horizontal isoptic calculation, let’s take the case of a circular auditorium with 20 rows of seats and a stage 32.8 feet wide. We will assume that it is a cinema-type auditorium, so we will use the recommended values for that type. Applying the formula, we get the following results:

• For row 1, α = 30°, b = 32.8 ft and r = 16.4 ft. Therefore, α = arctan (32.8 / (2*16.4)) = arctan (1) = 45°. This means that the first viewer has a viewing angle greater than the recommended, which is favorable.
• For row 10, α = 30°, b = 32.8 ft and r = 32.8 ft. Therefore, α = arctan (32.8 / (2*32.8)) = arctan (0.5) = 26.57°. This means that the tenth viewer has a viewing angle less than the recommended, which is unfavorable.
• For row 20, α = 30°, b = 32.8 ft and r = 49.2 ft. Therefore, α = arctan (32.8 / (2*49.2)) = arctan (0.33) = 18.43°. This means that the twentieth viewer has a viewing angle much less than the recommended, which is very unfavorable.

In this way, we can see that as the distance to the stage increases, the viewing angle decreases, and therefore the image quality deteriorates. Because of this, it’s important to design the auditorium with an adequate radius that allows maintaining a minimum viewing angle for all spectators.

Consulting for Auditorium and Theater Projects

In this article, I have explained what isoptics are, how they are calculated, and what benefits they offer for auditorium design. Isoptics ensure equal visibility for the audience, allowing spectators to fully view a specific area.

Isoptics are divided into vertical and horizontal, and are calculated using a mathematical formula and a minimum viewing angle, respectively. Good isoptics improve the comfort and safety of spectators, as they prevent people from straining their eyes or adopting uncomfortable postures to see better.

If you are interested in carrying out your own auditorium project with the best audiovisual, lighting, and acoustics technology, I invite you to contact Schallertech, a leading company in the industry that has a professional and experienced team who will advise you and offer the best solutions for your case.

You can visit our website or fill out the contact form to request more information or a no-obligation quote.

I hope this article has been useful and interesting for you. If you have any questions or comments about isoptics or auditorium design, feel free to write to us. We would be delighted to chat with you and address your concerns. See you soon!

Frequently Asked Questions and Answers

Below are some frequently asked questions and their answers about isoptics and its application to auditorium design.

• What are isoptics?

Isoptics are a condition of equal visibility for the audience, allowing spectators to fully view a specific area.

• How is vertical isoptics calculated?

Vertical isoptics are calculated using a mathematical formula that determines the convenient heights or level differences for the design of the stands or rows of seats.

• How is horizontal isoptics calculated?

Horizontal isoptics are calculated using a minimum viewing angle that aims to find the appropriate width or radius for the design of the auditorium.

• What values are recommended for vertical and horizontal isoptics?

The recommended values for vertical and horizontal isoptics depend on the type of auditorium and the type of event to be held. For example, for a theater-type auditorium, it is recommended that the eye height of the spectator be 3.6 feet, the constant k be 0.39 feet, the distance from the spectator to the base point be 49.2 feet, and the minimum viewing angle be 45°. For a cinema-type auditorium, it is recommended that the eye height of the spectator be 3.4 feet, the constant k be 0.33 feet, the distance from the spectator to the base point be 32.8 feet, and the minimum viewing angle be 30°.