Help with a practical problem for my job

[rooferpaul]

Hey guys I'm not particularly good at math and I have a question that nobody at work can help me with at work.
I'm a roofer and we have to make cuts of the metal sheets so that they line up with the angles of the rafters and parts of the house.
The angle of the corners of the houses or hips as we call them are always 45 degrees. However as the pitch of the roof changes the angle of our cut on the sheet changes. The sheet width is always .762mm. So for instance, if we were cutting up a hip on a 25 degree pitched roof, our cut length {or rake as we call it) across the sheet is 1020 I think by memory(though I may be wrong), but just for the sake of an example hopefully this should suffice.

What I need to work out is a formula so that once I know the pitch of the roof I can work out the 'rake' and make a stick to that length that would work for the whole job and make things a bit easier. I apologise for the terrible attachments but they hopefully help explain this better.
Thanks in advance, any help would be greatly appreciated.

 

[The Highlander]

Hey guys I'm not particularly good at math and I have a question that nobody at work can help me with at work.
I'm a roofer and we have to make cuts of the metal sheets so that they line up with the angles of the rafters and parts of the house.
The angle of the corners of the houses or hips as we call them are always 45 degrees. However as the pitch of the roof changes the angle of our cut on the sheet changes. The sheet width is always .762mm. So for instance, if we were cutting up a hip on a 25 degree pitched roof, our cut length {or rake as we call it) across the sheet is 1020 I think by memory(though I may be wrong), but just for the sake of an example hopefully this should suffice.

What I need to work out is a formula so that once I know the pitch of the roof I can work out the 'rake' and make a stick to that length that would work for the whole job and make things a bit easier. I apologise for the terrible attachments but they hopefully help explain this better.
Thanks in advance, any help would be greatly appreciated.

The main purpose of this site is to offer help & guidance to students with their Maths problems. We would normally only offer new members advice on how to proceed with their work once they have submitted their own attempt(s) to solve a problem (so we can assess what help they need to reach a solution).
In my (personal) opinion, if you are part of a commercial organisation (eg: a roofing company) then you should employ someone who is capable of carrying out any calculations you need for your operations or pay an external (consulting?) agent for such services rather than looking for free help on the internet.
Some other forum member may well take a different view and be willing to offer comment on the problem you describe though I do suspect that your description leaves much to be desired. For example: did you mean that the width of your sheets is 762 mm or .762 m (not .762 mm) and a "guess" at the rake being 1020 (mm?) for a 25° pitched roof is a much use as a chocolate teapot! Only accurate information is of any use to us! Furthermore, I would expect your Rake length to depend not only on the pitch of the roof but also on the height of the roof (apex) above the gable and the width of the gable itself.
But those are just my opinions. ?
Good Luck.

 

[Cubist]

I'll take a look at this problem later (I don't have time at the moment). I think I understand the problem.

I don't think a builder would ever pay someone to calculate something like this because it's such a small part of the job as a whole. I just see this as a little calculation that could save someone some time and effort (having to climb up and mark out the first sheet on the actual roof - and the result would not be perfect).

 

[blamocur]

While I agree with @The Highlander I got curious and came up with a relatively simple formula (but which I hope someone will on this forum will double-check) :

[math]\alpha_R = \arctan\left(\frac{\sin \alpha_H}{\tan \alpha_G}\right)[/math]
where [imath]\alpha_R[/imath] is the rake angle (half of the angle of the top of the hip)
[imath]\alpha_H[/imath] is the angle of the hip with the horizontal plane (usually 45 degrees)
[imath]\alpha_G[/imath] is the angle of the gable with the horizontal plane.

If you implement this keep in mind that many programming languages use radians, not degrees, for computing trigonometric functions.
I list a simple Python code below, but for practical purposes I'd write this in Javascript and make a local web page on a computer since every web browser understands Javascript.

import numpy as np
import sys

## Usage : rake-angle.py <gable angle> <hip angle>,
## where <hip angle> defaults to 45%

aH = 45;
aG = float (sys.argv[1]);
if len (sys.argv) > 2:
aH = float (sys.argv[2]);
aHrad = (np.pi/180) * aH;
aGrad = (np.pi/180) * aG;

aR = (180/np.pi) * np.arctan (np.sin (aHrad) / np.tan (aGrad));

print (aR);

 

[Deleted member 4993]

The main purpose of this site is to offer help & guidance to students with their Maths problems. We would normally only offer new members advice on how to proceed with their work once they have submitted their own attempt(s) to solve a problem (so we can assess what help they need to reach a solution).
In my (personal) opinion, if you are part of a commercial organisation (eg: a roofing company) then you should employ someone who is capable of carrying out any calculations you need for your operations or pay an external (consulting?) agent for such services rather than looking for free help on the internet.
Some other forum member may well take a different view and be willing to offer comment on the problem you describe though I do suspect that your description leaves much to be desired. For example: did you mean that the width of your sheets is 762 mm or .762 m (not .762 mm) and a "guess" at the rake being 1020 (mm?) for a 25° pitched roof is a much use as a chocolate teapot! Only accurate information is of any use to us! Furthermore, I would expect your Rake length to depend not only on the pitch of the roof but also on the height of the roof (apex) above the gable and the width of the gable itself.
But those are just my opinions. ?
Good Luck.

I second that opinion ! Go to the nearest University or College and consult for commercial problem - FaceToFace !!

 

[blamocur]

I second that opinion ! Go to the nearest University or College and consult for commercial problem !!

Alternately, one can go to a freelance marketplace.

 

[JeffM]

I must say that I do not agree at all, either in substance or in tone.

I have a bar buddy. We got to know each other talking about classical music. After the army, he had became a house painter. He was one when we first met. A few years later, he went out on his own with a few guys from the crew he normally worked with. It is a small business, no more than five people including him. He spends eight hours a day at job sites painting, and, many evenings, drives around to make estimates for new contracts. The idea that he has the time, money, or knowledge to find, vet, and hire a professional mathematician, who in many cases is paid largely by public taxes, is absurd.

I do not share the contempt that so many academics seem to have for people who do manual labor (probably because I never was an academic and am personally inept at almost all manual tasks.) If I had any clue what this problem was about, I’d help the guy out. I do not decline to help those who work with their hands. And if anyone wants to know why much of blue-collar America despises the academic world, they need only observe the classism in this thread. Help a roofer? How declasse.

Unfortunately, I was totally unable to understand the question posed so I can be no help in this case.

 

[Dr.Peterson]

Hey guys I'm not particularly good at math and I have a question that nobody at work can help me with at work.
I'm a roofer and we have to make cuts of the metal sheets so that they line up with the angles of the rafters and parts of the house.
The angle of the corners of the houses or hips as we call them are always 45 degrees. However as the pitch of the roof changes the angle of our cut on the sheet changes. The sheet width is always .762mm. So for instance, if we were cutting up a hip on a 25 degree pitched roof, our cut length {or rake as we call it) across the sheet is 1020 I think by memory(though I may be wrong), but just for the sake of an example hopefully this should suffice.

What I need to work out is a formula so that once I know the pitch of the roof I can work out the 'rake' and make a stick to that length that would work for the whole job and make things a bit easier. I apologise for the terrible attachments but they hopefully help explain this better.
Thanks in advance, any help would be greatly appreciated.

If you could sketch the roof and the piece you are cutting, marking measurements you know and what you want to know, it will help us a lot.

I see that 762 mm (not .762 mm, clearly a typo) is indeed the standard width of this material. And, given that the pitch of all sides of the roof is the same, you are right about the 45 degree angle as seen from above.

I don't find the word "rake" online being used the way you say (only as the edge of a gable), but it sounds like what you mean is the slanted edge of the piece they are putting up in the picture. I would think you would want its angle rather than its length, but they are related, obviously.

Also, do you describe the pitch as an angle or a ratio? That is the sort of information I'd like to see. Then I can do something like #4 above with more confidence.

 

[blamocur]

I must say that I do not agree at all, either in substance or in tone.

I have a bar buddy. We got to know each other talking about classical music. After the army, he had became a house painter. He was one when we first met. A few years later, he went out on his own with a few guys from the crew he normally worked with. It is a small business, no more than five people including him. He spends eight hours a day at job sites painting, and, many evenings, drives around to make estimates for new contracts. The idea that he has the time, money, or knowledge to find, vet, and hire a professional mathematician, who in many cases is paid largely by public taxes, is absurd.

I do not share the contempt that so many academics seem to have for people who do manual labor (probably because I never was an academic and am personally inept at almost all manual tasks.) If I had any clue what this problem was about, I’d help the guy out. I do not decline to help those who work with their hands. And if anyone wants to know why much of blue-collar America despises the academic world, they need only observe the classism in this thread. Help a roofer? How declasse.

Unfortunately, I was totally unable to understand the question posed so I can be no help in this case.

Personally, I did not notice any contempt in this thread, and I hope @rooferpaul did not either. BTW, our house was painted by a philosophy major a couple of times, but then we parted our ways; not because we did not like his philosophy but because we did not like the results of the painting

My impression is that the objection was not because of the social/professional/educational status of the OP, but because the nature of his question did not fit the profile of the forum. I suspect the reaction would be the same if the request came from, say, a college professor.

 

[Deleted member 4993]

I do not share the contempt that so many academics seem to have for people who do manual labor (probably because I never was an academic and am personally inept at almost all manual tasks.)

This is not a contempt - this is providing advice where face-to-face interaction is desirable. I have no contempt for people who work with their hands. I have not remained "unemployed" for one day in USA, because I had no contempt for working as a short-order-pizza cook, bus-boy, bell man, working in the coal mine. On the other hand I have seen and felt the contempt from the other side. In a research lab where I worked, new machines used to come with trained operators. Before instructing my Tech Assistant to use the machine, I will myself learn how to use it. Then I heard the smirky remark - if I have to teach you how to do your job, how come your making all the money and I am not. My equally smirky come-back was:

"because I can learn what you know in 6 months - if not 6 days and I could do the job you are doing. But you would not be able do my job if you tried for 60 years. See in high school while you were drinking, having fun, chasing girls - I put my nose on the pages of the books and learned algebra, physics and chemistry. For you that ship has sailed - and you are paying the price for it."​

That misplaced disdain of blue-collar workers is the main theme of hillybilly elegy.

why much of blue-collar America despises the academic world,

That is because they realize that they would not live as well as their parents - because they don't (did not) work as hard as their parents - and to reiterate

that ship ship has sailed for them.​

 

[Cubist]

Here's a picture of the scenario as I understand it.



You know the pitch angle "p" (in your example 25°). You wish to find length "b" on the sheet so that you can mark the line to cut with only a tape measure and straight edge (you wouldn't need to use a square or protractor).

@rooferpaul please correct if I'm wrong.

 

[Cubist]

I must say that I do not agree at all, either in substance or in tone.

I have a bar buddy. We got to know each other talking about classical music. After the army, he had became a house painter. He was one when we first met. A few years later, he went out on his own with a few guys from the crew he normally worked with. It is a small business, no more than five people including him. He spends eight hours a day at job sites painting, and, many evenings, drives around to make estimates for new contracts. The idea that he has the time, money, or knowledge to find, vet, and hire a professional mathematician, who in many cases is paid largely by public taxes, is absurd.

I do not share the contempt that so many academics seem to have for people who do manual labor (probably because I never was an academic and am personally inept at almost all manual tasks.) If I had any clue what this problem was about, I’d help the guy out. I do not decline to help those who work with their hands. And if anyone wants to know why much of blue-collar America despises the academic world, they need only observe the classism in this thread. Help a roofer? How declasse.

Unfortunately, I was totally unable to understand the question posed so I can be no help in this case.

I know I clicked "like" on JeffM's post, but I was thinking that the Highlander, Topsquark, Subhotosh and Blamocur perhaps just have a very strong dividing line between the worlds of work and education. They choose to freely help students with their maths education but when it comes to a professional environment (with money changing hands) then they'll only help if they're getting a cut of the profits ??? ! I might be wrong (in which case please explain your objections - just because I'm interested - but certainly not to cause an argument)

 

[Deleted member 4993]

I know I clicked "like" on JeffM's post, but I was thinking that the Highlander, Topsquark, Subhotosh and Blamocur perhaps just have a very strong dividing line between the worlds of work and education. They choose to freely help students with their maths education but when it comes to a professional environment (with money changing hands) then they'll only help if they're getting a cut of the profits ??? ! I might be wrong (in which case please explain your objections - just because I'm interested - but certainly not to cause an argument)

My concern is liability of wasted time and material. A practical problem in 3-d may have many assumptions embedded. Case in point is cutting the joining line of a crown plate between the roof and the inner-wall. The angle will not be 45^o.

 

[Cubist]

My concern is liability of wasted time and material. A practical problem in 3-d may have many assumptions embedded. Case in point is cutting the joining line of a crown plate between the roof and the inner-wall. The angle will not be 45^o.

Thanks. It's a very good point about liability. I usually try to remember to write something along the lines of a disclaimer with any real world problems that could involve money.

I would say @rooferpaul that you must use common sense with any of the methods offered (certainly by me). Cut test pieces from a roll of paper first before (potentially) spoiling any expensive metal sheets. All the helpers on this forum can (and do) make mistakes!

 

[Deleted member 4993]

All the helpers on this forum can (and do) make mistakes!

Not me !!! I only make BLUNDERS.

 

[blamocur]

This is not a contempt - this is providing advice where face-to-face interaction is desirable. I have no contempt for people who work with their hands. I have not remained "unemployed" for one day in USA, because I had no contempt for working as a short-order-pizza cook, bus-boy, bell man, working in the coal mine. On the other hand I have seen and felt the contempt from the other side. In a research lab where I worked, new machines used to come with trained operators. Before instructing my Tech Assistant to use the machine, I will myself learn how to use it. Then I heard the smirky remark - if I have to teach you how to do your job, how come your making all the money and I am not. My equally smirky come-back was:

"because I can learn what you know in 6 months - if not 6 days and I could do the job you are doing. But you would not be able do my job if you tried for 60 years. See in high school while you were drinking, having fun, chasing girls - I put my nose on the pages of the books and learned algebra, physics and chemistry. For you that ship has sailed - and you are paying the price for it."​

That misplaced disdain of blue-collar workers is the main theme of hillybilly elegy.

That is because they realize that they would not live as well as their parents - because they don't (did not) work as hard as their parents - and to reiterate

that ship ship has sailed for them.​

IMHO, this is only one part of the differences. People are born with different levels of math and other abilities. They grow up in different circumstances (I've been able to tutor my own kids all the way through collect, and like to think that it contributed to their success). And yes, on the other hand, different people spend their youth on different pursuits ("youth is wasted on the young"). It is not equivalent but somewhat similar to being born rich or poor.

 

[blamocur]

While I agree with @The Highlander I got curious and came up with a relatively simple formula (but which I hope someone will on this forum will double-check) :

[math]\alpha_R = \arctan\left(\frac{\sin \alpha_H}{\tan \alpha_G}\right)[/math]
where [imath]\alpha_R[/imath] is the rake angle (half of the angle of the top of the hip)
[imath]\alpha_H[/imath] is the angle of the hip with the horizontal plane (usually 45 degrees)
[imath]\alpha_G[/imath] is the angle of the gable with the horizontal plane.

If you implement this keep in mind that many programming languages use radians, not degrees, for computing trigonometric functions.
I list a simple Python code below, but for practical purposes I'd write this in Javascript and make a local web page on a computer since every web browser understands Javascript.

import numpy as np
import sys

## Usage : rake-angle.py <gable angle> <hip angle>,
## where <hip angle> defaults to 45%

aH = 45;
aG = float (sys.argv[1]);
if len (sys.argv) > 2:
aH = float (sys.argv[2]);
aHrad = (np.pi/180) * aH;
aGrad = (np.pi/180) * aG;

aR = (180/np.pi) * np.arctan (np.sin (aHrad) / np.tan (aGrad));

print (aR);

I did not pay attention and did not realize that what is needed is the "rake", i.e, the length of the cut. This can be computed as
[math]K = \frac{w}{\sin\alpha_R}[/math]where [imath]w[/imath] is the width of the sheet. The corresponding script can be modified slightly:

#!/usr/bin/env python3

import numpy as np
import sys

## Usage : rake-angle.py <gable angle> <hip angle>,
## where <hip angle> defaults to 45%


aH = 45; ## Hip angle
shW = 762;

aG = float (sys.argv[1]); ## Gable angle
if len (sys.argv) > 2:
shW = float (sys.argv[2]); ## sheet width
if len (sys.argv) > 3:
aH = float (sys.argv[3]);
aHrad = (np.pi/180) * aH;
aGrad = (np.pi/180) * aG;

aR = (180/np.pi) * np.arctan (np.sin (aHrad) / np.tan (aGrad));

rk = shW / np.sin (aR * np.pi/180);

print ("Angle : %.2f " % aR);
print ("Rake : %.1f" % rk);

 

[rooferpaul]

Here's a picture of the scenario as I understand it.

View attachment 32992

You know the pitch angle "p" (in your example 25°). You wish to find length "b" on the sheet so that you can mark the line to cut with only a tape measure and straight edge (you wouldn't need to use a square or protractor).

@rooferpaul please correct if I'm wrong.

absolutely correct. If I am working on the ground, I want to be able to call out to the man on the roof and ask him what the pitch of the roof is. With that knowledge, I want to be able to use a formula to calculate the rake or b as youve illustrated.

 

[Cubist]

I did not pay attention and did not realize that what is needed is the "rake", i.e, the length of the cut. This can be computed as
[math]K = \frac{w}{\sin\alpha_R}[/math]where [imath]w[/imath] is the width of the sheet. The corresponding script can be modified slightly:

#!/usr/bin/env python3
...

I tried running your code...

python /tmp/a.py 25 762
Angle : 56.60
Rake : 912.8

...but this rake seems impossible. Imagine that the pitch angle of the roof is 0° (it's a flat roof). The diagonal cut where two purpendicular metal sheets meet will be at 45° to both sheets. The length of this diagonal (label "b" in post#11) will be [imath]\sqrt{762^2+762^2} \approx 1077.63[/imath] by Pythagoras. As the pitch increases, this minimum length should only get bigger?

If one of us gets sent to the corner for a blunder - then hopefully the roof there will be watertight

 

[blamocur]

Did you try running python /tmp/a.py 1 762 1 ? (using 0's for the angles causes division by 0).