# Calculating Line of Sight and Obstruction in Restaurant Redesign

• swopidopi
In summary, the floor in front of the observer obstructs a view of the horizon by about 1/1370th of the total length.
swopidopi
Member advised to use the homework template for posts in the homework sections of PF.
I'm working on re-designing a restaurant by the sea. I'm a interior decorator so I know very litle about physics. Here's my question:

let's say you're in the back of a room with 90 meters of floor in front of you. You are 7 meters above ground but your eyes are only 10 cm above the floor. I've calculated that 7.1 meter up with a clear view gives you a line of sight of 9.6 km. Will i be able to see the horizon with the floor infront of me and if yes; how much of my line of sight will be obstructed by the floor. I've drawn a picture so you can understand the question better.

Thank you.

Hi swopidopi, Welcome to Physics Forums.

Please remember to use the template provided to format your homework help requests.

Your problem is not so much a physics problem as an exercise in math/geometry. It boils down to determining where (or if?) a ray originating at the observer's eye and just grazing the outer edge of the platform intersects curved surface of the Earth. You should be able to write equations for both the circle represent the Earth's surface and the line which incorporates the ray.

swopidopi said:
I'm working on re-designing a restaurant by the sea. I'm a interior decorator so I know very litle about physics.
A restaurant whose customers lie on the floor at the back of the room? One hopes that this but a passing fad.

Based on the text, I shall assume this is not homework.
From the eye to the far edge of the floor, the line of sight drops .1m in 90m, or 1 in 900.
From there to the horizon, it drops 7m in 9600m, or 1 in 1370. So that settles whether the horizon will be visible.
As to how much of the view is lost, it depends how you measure it. Say it is in terms of optical angle. If you were to stand at the edge of the drop you would see 90 degrees, from vertically down to horizontal. From the given viewing height of 0.1m from the back edge, you will see less than one tenth of a degree. But I would think customers that drunk won't care.

haruspex said:
From there to the horizon, it drops 7m in 9600m, or 1 in 1370.
Does this take into account the curvature of the earth? I get that the line of sight to the horizon would drop more than this, about 1 in 670.

TSny said:
Does this take into account the curvature of the earth? I get that the line of sight to the horizon would drop more than this, about 1 in 670.
That's true, but I was not expecting it to make that much difference. Thanks for checking that.

## 1. What is an obstructed line of sight?

An obstructed line of sight refers to a situation where an object or obstacle blocks the direct path between an observer and a target object, making it difficult or impossible to see the target.

## 2. What are some common causes of obstructed line of sight?

Some common causes of obstructed line of sight include physical obstacles such as buildings, trees, or mountains, atmospheric conditions like fog or smoke, and technological factors like interference from other objects or signals.

## 3. How does obstructed line of sight affect scientific research?

In scientific research, obstructed line of sight can impact the accuracy and reliability of data collection. It can also limit the ability to observe and study certain objects or phenomena, hindering the progress of research and discovery.

## 4. What are some methods used to overcome obstructed line of sight?

Some methods used to overcome obstructed line of sight include using remote sensing techniques, such as satellite imagery or drones, to observe objects from different angles, and using computational methods to reconstruct or fill in missing data points.

## 5. How does the study of obstructed line of sight apply to real-world situations?

The study of obstructed line of sight has practical applications in various fields, including telecommunications, transportation, and military operations. It can also inform urban planning and design to optimize visibility and safety in built environments.

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