How do I calculate the inclined area of a roof?
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I think I already know the formula, but wanted to check if there are any instances where this may not work. I have been estimating construction costs for 5 years and haven’t found one instance where the following formula doesn’t give the correct answer:
Incline area = flat area (measured on plan)/cos (pitch in degrees)
So far this has worked for:
- Square, rectangular, hexagonal, circular, curved edge roofs
- Roofs of varying pitches eg. 5 degrees one side, 10 degrees the other. Just measure 2 separate areas and use the formula
It wouldn’t work for:
- Roofs that are arced or domed vertically
Can anyone prove me wrong because I’ve seen so many people losing their mind over something so simple?
geometry trigonometry
asked Jun 21 at 12:19
Jmel93
61
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up vote
1
down vote
favorite
I think I already know the formula, but wanted to check if there are any instances where this may not work. I have been estimating construction costs for 5 years and haven’t found one instance where the following formula doesn’t give the correct answer:
Incline area = flat area (measured on plan)/cos (pitch in degrees)
So far this has worked for:
- Square, rectangular, hexagonal, circular, curved edge roofs
- Roofs of varying pitches eg. 5 degrees one side, 10 degrees the other. Just measure 2 separate areas and use the formula
It wouldn’t work for:
- Roofs that are arced or domed vertically
Can anyone prove me wrong because I’ve seen so many people losing their mind over something so simple?
geometry trigonometry
asked Jun 21 at 12:19
Jmel93
61
For spherical domed roof, if the pitch is $theta$ at the edge, the surface area is given by 2$pi r^2 (1- cos(theta))$. See here for more details: en.wikipedia.org/wiki/Spherical_cap where r is the radius of the dome. If you have the plan view radius (a) instead, you can use $r = fracacos(theta)$ as you are already doing before to get radius.
– user625
Jun 21 at 12:43
For an arced dome, it is a portion of a cylinder. So, you can use $2rtheta cdot$ length where $r$ is the radius of the cylinder. Again, you can convert radius $r$ into plan view width by using $r = fracacos(theta)$
– user625
Jun 21 at 12:50
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I think I already know the formula, but wanted to check if there are any instances where this may not work. I have been estimating construction costs for 5 years and haven’t found one instance where the following formula doesn’t give the correct answer:
Incline area = flat area (measured on plan)/cos (pitch in degrees)
So far this has worked for:
- Square, rectangular, hexagonal, circular, curved edge roofs
- Roofs of varying pitches eg. 5 degrees one side, 10 degrees the other. Just measure 2 separate areas and use the formula
It wouldn’t work for:
- Roofs that are arced or domed vertically
Can anyone prove me wrong because I’ve seen so many people losing their mind over something so simple?
geometry trigonometry
asked Jun 21 at 12:19
Jmel93
61
I think I already know the formula, but wanted to check if there are any instances where this may not work. I have been estimating construction costs for 5 years and haven’t found one instance where the following formula doesn’t give the correct answer:
Incline area = flat area (measured on plan)/cos (pitch in degrees)
So far this has worked for:
- Square, rectangular, hexagonal, circular, curved edge roofs
- Roofs of varying pitches eg. 5 degrees one side, 10 degrees the other. Just measure 2 separate areas and use the formula
It wouldn’t work for:
- Roofs that are arced or domed vertically
Can anyone prove me wrong because I’ve seen so many people losing their mind over something so simple?
geometry trigonometry
asked Jun 21 at 12:19
Jmel93
61
asked Jun 21 at 12:19
Jmel93
61
asked Jun 21 at 12:19
Jmel93
61
asked Jun 21 at 12:19
Jmel93
61
61
For spherical domed roof, if the pitch is $theta$ at the edge, the surface area is given by 2$pi r^2 (1- cos(theta))$. See here for more details: en.wikipedia.org/wiki/Spherical_cap where r is the radius of the dome. If you have the plan view radius (a) instead, you can use $r = fracacos(theta)$ as you are already doing before to get radius.
– user625
Jun 21 at 12:43
For an arced dome, it is a portion of a cylinder. So, you can use $2rtheta cdot$ length where $r$ is the radius of the cylinder. Again, you can convert radius $r$ into plan view width by using $r = fracacos(theta)$
– user625
Jun 21 at 12:50
add a comment |Â
For spherical domed roof, if the pitch is $theta$ at the edge, the surface area is given by 2$pi r^2 (1- cos(theta))$. See here for more details: en.wikipedia.org/wiki/Spherical_cap where r is the radius of the dome. If you have the plan view radius (a) instead, you can use $r = fracacos(theta)$ as you are already doing before to get radius.
– user625
Jun 21 at 12:43
For an arced dome, it is a portion of a cylinder. So, you can use $2rtheta cdot$ length where $r$ is the radius of the cylinder. Again, you can convert radius $r$ into plan view width by using $r = fracacos(theta)$
– user625
Jun 21 at 12:50
For spherical domed roof, if the pitch is $theta$ at the edge, the surface area is given by 2$pi r^2 (1- cos(theta))$. See here for more details: en.wikipedia.org/wiki/Spherical_cap where r is the radius of the dome. If you have the plan view radius (a) instead, you can use $r = fracacos(theta)$ as you are already doing before to get radius.
– user625
Jun 21 at 12:43
For spherical domed roof, if the pitch is $theta$ at the edge, the surface area is given by 2$pi r^2 (1- cos(theta))$. See here for more details: en.wikipedia.org/wiki/Spherical_cap where r is the radius of the dome. If you have the plan view radius (a) instead, you can use $r = fracacos(theta)$ as you are already doing before to get radius.
– user625
Jun 21 at 12:43
For an arced dome, it is a portion of a cylinder. So, you can use $2rtheta cdot$ length where $r$ is the radius of the cylinder. Again, you can convert radius $r$ into plan view width by using $r = fracacos(theta)$
– user625
Jun 21 at 12:50
For an arced dome, it is a portion of a cylinder. So, you can use $2rtheta cdot$ length where $r$ is the radius of the cylinder. Again, you can convert radius $r$ into plan view width by using $r = fracacos(theta)$
– user625
Jun 21 at 12:50
add a comment |Â
1 Answer
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oldest
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up vote
0
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Just combining the comments above as an answer.
Spherical domed roof (shaped like a cap):
$theta$ is the angle of the roof with the horizontal at the edge
$a$ = plan view radius
Area = $2picdot a^2cdotfrac1-cos(theta)cos(theta)$
- Arced dome (portion of a cylinder):
$theta$ is the angle of the roof with the horizontal at the edge in radians
$a$ = plan view width
$l$ = plan view length
Area = $2thetacdotfracalcos(theta)$
edited Aug 10 at 20:41
Robert Howard
1,331620
answered Jun 21 at 13:48
user625
40011
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
Just combining the comments above as an answer.
Spherical domed roof (shaped like a cap):
$theta$ is the angle of the roof with the horizontal at the edge
$a$ = plan view radius
Area = $2picdot a^2cdotfrac1-cos(theta)cos(theta)$
- Arced dome (portion of a cylinder):
$theta$ is the angle of the roof with the horizontal at the edge in radians
$a$ = plan view width
$l$ = plan view length
Area = $2thetacdotfracalcos(theta)$
edited Aug 10 at 20:41
Robert Howard
1,331620
answered Jun 21 at 13:48
user625
40011
add a comment |Â
up vote
0
down vote
Just combining the comments above as an answer.
Spherical domed roof (shaped like a cap):
$theta$ is the angle of the roof with the horizontal at the edge
$a$ = plan view radius
Area = $2picdot a^2cdotfrac1-cos(theta)cos(theta)$
- Arced dome (portion of a cylinder):
$theta$ is the angle of the roof with the horizontal at the edge in radians
$a$ = plan view width
$l$ = plan view length
Area = $2thetacdotfracalcos(theta)$
edited Aug 10 at 20:41
Robert Howard
1,331620
answered Jun 21 at 13:48
user625
40011
add a comment |Â
up vote
0
down vote
up vote
0
down vote
Just combining the comments above as an answer.
Spherical domed roof (shaped like a cap):
$theta$ is the angle of the roof with the horizontal at the edge
$a$ = plan view radius
Area = $2picdot a^2cdotfrac1-cos(theta)cos(theta)$
- Arced dome (portion of a cylinder):
$theta$ is the angle of the roof with the horizontal at the edge in radians
$a$ = plan view width
$l$ = plan view length
Area = $2thetacdotfracalcos(theta)$
edited Aug 10 at 20:41
Robert Howard
1,331620
answered Jun 21 at 13:48
user625
40011
Just combining the comments above as an answer.
Spherical domed roof (shaped like a cap):
$theta$ is the angle of the roof with the horizontal at the edge
$a$ = plan view radius
Area = $2picdot a^2cdotfrac1-cos(theta)cos(theta)$
- Arced dome (portion of a cylinder):
$theta$ is the angle of the roof with the horizontal at the edge in radians
$a$ = plan view width
$l$ = plan view length
Area = $2thetacdotfracalcos(theta)$
edited Aug 10 at 20:41
Robert Howard
1,331620
answered Jun 21 at 13:48
user625
40011
edited Aug 10 at 20:41
Robert Howard
1,331620
edited Aug 10 at 20:41
Robert Howard
1,331620
edited Aug 10 at 20:41
Robert Howard
1,331620
1,331620
answered Jun 21 at 13:48
user625
40011
answered Jun 21 at 13:48
user625
40011
answered Jun 21 at 13:48
user625
40011
40011
add a comment |Â
add a comment |Â
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For spherical domed roof, if the pitch is $theta$ at the edge, the surface area is given by 2$pi r^2 (1- cos(theta))$. See here for more details: en.wikipedia.org/wiki/Spherical_cap where r is the radius of the dome. If you have the plan view radius (a) instead, you can use $r = fracacos(theta)$ as you are already doing before to get radius.
– user625
Jun 21 at 12:43
For an arced dome, it is a portion of a cylinder. So, you can use $2rtheta cdot$ length where $r$ is the radius of the cylinder. Again, you can convert radius $r$ into plan view width by using $r = fracacos(theta)$
– user625
Jun 21 at 12:50