Diagonal Depth

J

judybgs

New member
Joined
Jun 3, 2022
Messages
8
Hello, I am a designer that is looking for a math formula to calculate the diagonal depth of a sofa. Usually this is measured physically in the store, but there must be a formula I can plug numbers into, without physically having the sofa. The diagonal depth is the measurement between F and B. Usually, the manufacturer will give the Height (A to B), the Depth (B to C) and the Arm Height (C to D). There must be a way to calculate F to B! Please share the secret formula. It's a magic number that ensures the sofa fits through doors and turns tight corners. Thank you!


1654268846549.png
 
judybgs said:
Hello, I am a designer that is looking for a math formula to calculate the diagonal depth of a sofa. Usually this is measured physically in the store, but there must be a formula I can plug numbers into, without physically having the sofa. The diagonal depth is the measurement between F and B. Usually, the manufacturer will give the Height (A to B), the Depth (B to C) and the Arm Height (C to D). There must be a way to calculate F to B! Please share the secret formula. It's a magic number that ensures the sofa fits through doors and turns tight corners. Thank you!


View attachment 32921
Click to expand...
There is no secret formula - just logical thinking.

use tan(Θ) = (97)/(36) and sin(Θ) = BF/(95) ........ and continue...... carefully .......

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:


Please share your work/thoughts about this problem
 
Last edited by a moderator:
judybgs said:
Hello, I am a designer that is looking for a math formula to calculate the diagonal depth of a sofa. Usually this is measured physically in the store, but there must be a formula I can plug numbers into, without physically having the sofa. The diagonal depth is the measurement between F and B. Usually, the manufacturer will give the Height (A to B), the Depth (B to C) and the Arm Height (C to D). There must be a way to calculate F to B! Please share the secret formula. It's a magic number that ensures the sofa fits through doors and turns tight corners. Thank you!


View attachment 32921
Click to expand...
Use similar triangles: △AFB∼△AED\triangle AFB\sim\triangle AED. You'll also use the Pythagorean Theorem.
 
Well you are all smarter than I am, as I haven't been in school for 20 plus years. If the diagonal FB dissected AD in the middle, I would get this. But as it is 90degrees to AD, I am stuck. This is math that I can't remember. I remember how to find the hypothenuse, but I thought this is different. I appreciate your help. I will have to google TAN and COS to understand that. Baby steps forward.
 
judybgs said:
Well you are all smarter than I am, as I haven't been in school for 20 plus years. If the diagonal FB dissected AD in the middle, I would get this. But as it is 90degrees to AD, I am stuck. This is math that I can't remember. I remember how to find the hypothenuse, but I thought this is different. I appreciate your help. I will have to google TAN and COS to understand that. Baby steps forward.
Click to expand...
Please understand that this site normally deals with students, so we try to get people to do as much of the work as possible themselves (even if the question doesn't look like an assignment). In this case, trusting that you aren't a student in disguise, I can go ahead and show the details.

1654290238781.png​

As I said,
Dr.Peterson said:
Use similar triangles: △AFB∼△AED\triangle AFB\sim\triangle AED. You'll also use the Pythagorean Theorem.
Click to expand...
These two triangles are proportional, so FBAB=EDAD\frac{FB}{AB}=\frac{ED}{AD}Solving this for the unknown FB, FB=AB⋅EDADFB=\frac{AB\cdot ED}{AD}
The Pythagorean theorem tells us that AD=AE2+ED2AD=\sqrt{AE^2+ED^2}. Putting this into the formula, FB=AB⋅EDAE2+ED2FB=\frac{AB\cdot ED}{\sqrt{AE^2+ED^2}}
Using the specific numbers AB=95,ED=97,AE=36AB=95,ED=97,AE=36, we get FB=95⋅97362+972=89.06FB=\frac{95\cdot 97}{\sqrt{36^2+97^2}}=89.06
Does that help? You don't need tan and cos, which are from trigonometry.

Here is a scale drawing confirming the answer:

1654291470373.png​
 
Last edited:
YES! Thank you! Thank you for spelling it out for me so concisely. This just proves you really need math in everyday jobs. I also really appreciate you answering even though I am no longer a student, but a student in life : )
Great site you have here. I will show it to my 15 year old. All the best.
 
judybgs said:
Hello, I am a designer that is looking for a math formula to calculate the diagonal depth of a sofa. Usually this is measured physically in the store, but there must be a formula I can plug numbers into, without physically having the sofa. The diagonal depth is the measurement between F and B. Usually, the manufacturer will give the Height (A to B), the Depth (B to C) and the Arm Height (C to D). There must be a way to calculate F to B! Please share the secret formula. It's a magic number that ensures the sofa fits through doors and turns tight corners. Thank you!


View attachment 32921
Click to expand...
tan(Θ) = 95/35 →

Θ = 1.215419 radian

sin(1.215419 ) = 0.937515374

BF = 95 * sin(Θ) = 89.06 cm

Since we are moving an object, for safety, I would make sure of clearance of at least 100 cm.
 
Sorry to bother you again. There is confusion of what Diagonal Depth is even among designers and forums. Some say the diagonal depth has to dissect AD in the center. If this is the case, and point f is actually in the center of AD, then how to I get to FB? Does this make sense? So now if point E is 90degrees, I should be able to figure out the angle at point A? Then what?
 
Last edited:
judybgs said:
Sorry to bother you again. There is confusion of what Diagonal Depth is even among designers and forums. Some say the diagonal depth has to dissect AD in the center. So that means no angle is a Right angle. If this is the case, and point f is actually in the center of AD, then how to I get to FB? Does this make sense?
Click to expand...
1654300543618.png

If I understand the New problem correctly, we have a point F' on AB such that AF' = DF' = 51.73 cm then

AF = 95 * cos(Θ) = 32.84200909

FF' = AF' - AF = 51.73 - 32.84200909 = 18.88799091

BF' = √(BF^2 + FF'^2) = 91.04086885 = 91 cm ....... again I would consider 100 cm for clearances.


​
 
Yes. You understood correctly. Now this math is complicated. I will try to understand this. I really appreciate your help.
 
judybgs said:
Sorry to bother you again. There is confusion of what Diagonal Depth is even among designers and forums. Some say the diagonal depth has to dissect AD in the center. If this is the case, and point f is actually in the center of AD, then how to I get to FB? Does this make sense? So now if point E is 90degrees, I should be able to figure out the angle at point A? Then what?
Click to expand...
Before I would consider doing that calculation, I'd want to see a justification for such a definition.

Your own picture nicely shows why your perpendicular measurement makes sense: it gives the narrowest hallway it could be carried down (as shown by the parallel lines).

The alternative has no meaning in similar terms. Here is what you would get:

1654303216419.png​

This does not give the width of anything meaningful. Do they say what it does mean? Can you provide a link to a discussion about it? (My best guess is that someone decided this would be easier to measure on actual furniture, and would be (typically) a reasonable approximation.)

I need to add that, since the back of the sofa is not a narrow line (nor, sometimes, vertical), the advice to add extra clearance is important.

EDIT: It looks like there are a variety of definitions, suggesting no one really knows what it's meant for. This site, for example, says "The next step is to measure the diagonal depth of the sofa. You do this by placing a straight tape measure from the top back of the frame to the bottom front." That may be the longest distance across the sofa; but they don't say what you use it for! On the other hand, the picture here is ambiguous, but they clearly state the purpose.

I also found where your picture comes from, and the explanation given with it: https://en.wikipedia.org/wiki/Wikip...matics/2020_October_10#Diagonal_depth_of_sofa
 
Last edited:
Dr.Peterson said:
Before I would consider doing that calculation, I'd want to see a justification for such a definition.

Your own picture nicely shows why your perpendicular measurement makes sense: it gives the narrowest hallway it could be carried down (as shown by the parallel lines).

The alternative has no meaning in similar terms. Here is what you would get:


This does not give the width of anything meaningful. Do they say what it does mean? Can you provide a link to a discussion about it? (My best guess is that someone decided this would be easier to measure on actual furniture, and would be (typically) a reasonable approximation.)

I need to add that, since the back of the sofa is not a narrow line (nor, sometimes, vertical), the advice to add extra clearance is important.

EDIT: It looks like there are a variety of definitions, suggesting no one really knows what it's meant for. This site, for example, says "The next step is to measure the diagonal depth of the sofa. You do this by placing a straight tape measure from the top back of the frame to the bottom front." That may be the longest distance across the sofa; but they don't say what you use it for! On the other hand, the picture here is ambiguous, but they clearly state the purpose.

I also found where your picture comes from, and the explanation given with it: https://en.wikipedia.org/wiki/Wikip...matics/2020_October_10#Diagonal_depth_of_sofa
Click to expand...
Your explanation makes a lot of sense. It is specifically used for the narrow hallway vs large couch problem. When I order furniture for clients, often simply through a catalogue, I need to make triple sure that the couch will turn every corner and go through every tight space. You are right to say that many designers and websites are confused and give the wrong info. People parrot what they hear, and bad info and math become the standard. Your explanation and formula is purpose driven and therefore the only meaningful solution. As is the extra clearance advice. Thank you. To everyone who chimed in, you are very appreciated!
 
Subhotosh Khan said:
Since we are moving an object, for safety, I would make sure of clearance of at least 100 cm.
Click to expand...
100 cm clearance seems rather extensive (in the situations described). ?
Did you mean to suggest 100 mm? ?
(I realise lots of folks over in your parts are still having 'trouble' with metric measurements. ?)
 
PS: I meat to say "excessive" (not "extensive") above; the word just wouldn't come to me!
(By the time it did, it was too late to change it. It's an age thing! ?)
 
The Highlander said:
PS: I meat to say "excessive" (not "extensive") above; the word just wouldn't come to me!
(By the time it did, it was too late to change it. It's an age thing! ?)
Click to expand...
The Highlander said:
100 cm clearance seems rather extensive (in the situations described). ?
Did you mean to suggest 100 mm? ?
(I realise lots of folks over in your parts are still having 'trouble' with metric measurements. ?)
Click to expand...
No. As the answer to this fictional sofa requires 9ish cm to clear a tight hallway, Mr. Khan rightly suggested I leave more room, ie: the 100 cms. Sound advice when moving furniture and advising others how to spend their hard earned money.
 
judybgs said:
No. As the answer to this fictional sofa requires 9ish cm to clear a tight hallway, Mr. Khan rightly suggested I leave more room, ie: the 100 cms. Sound advice when moving furniture and advising others how to spend their hard earned money.
Click to expand...
It would appear we have a different understanding of what the term "clearance" means. ?
As an engineer, I would define the clearance as the (combined) gap either side of your 'sofa' and the portal it needs to negotiate, not the overall width of the opening it is to be moved through. Hence, 100 mm would be the clearance required, ie: 5 cm each side of the ('91-ish cm')sofa.
 
The Highlander said:
It would appear we have a different understanding of what the term "clearance" means. ?
As an engineer, I would define the clearance as the (combined) gap either side of your 'sofa' and the portal it needs to negotiate, not the overall width of the opening it is to be moved through. Hence, 100 mm would be the clearance required, ie: 5 cm each side of the ('91-ish cm')sofa.
Click to expand...
Either way, I understood what he meant, and I got the formula I need from this thread because they took the time to help me.
 
The Highlander said:
It would appear we have a different understanding of what the term "clearance" means. ?
As an engineer, I would define the clearance as the (combined) gap either side of your 'sofa' and the portal it needs to negotiate, not the overall width of the opening it is to be moved through. Hence, 100 mm would be the clearance required, ie: 5 cm each side of the ('91-ish cm')sofa.
Click to expand...
When I myself mentioned clearance ("add extra clearance"), I meant it as you do: a little extra on each side, in large part because the formula doesn't take everything into account regarding the actual shape.

And I think it's clear that SK means the same thing; note his wording:
Subhotosh Khan said:
BF' = √(BF^2 + FF'^2) = 91.04086885 = 91 cm ....... again I would consider 100 cm for clearances.
​
Click to expand...
This doesn't say the clearance is 100 cm; it says that adding clearance brings it up to 100.

So I don't think anyone here really disagreed!
 
You must log in or register to reply here.
Top