Calculate consumption without waste - math question

[gluecifer]

I am going to replace some battens on a part of the house, and the lengths vary quite a bit.
Ex. 125cm, 135cm, 145cm, 155cm, 180cm, 190cm up to a maximum of 290cm.

I want these whole without joints. How can I calculate how many WHOLE battens are needed, if a whole batten is 480cm, when I know all the lengths described above?

 

[Dilato]

How many of each individual length?

 

[gluecifer]

33st

Maybe there's a good Excel formula for this?

 

[Dilato]

33 pcs

Perhaps there is a good Excel formula for this?

Do you really mean
33 pcs at 125 cm
33 pcs at 135 cm
33 pcs at 145 cm
33 pcs at 155 cm
etc??

 

[gluecifer]

No, sorry for my lack of clarity

It's on a gable side, so it rises from 1.25 up to the ridge, then goes down in corresponding order.
Like 125,135,145,155-x-x-x-290-x-x-x-155-145-135-125.

So two of each.

 

[Tompafix]

What roof slope and width of the house?

 

[gluecifer]

About 7.5m wide, a bit unsure about the roof but say 43 degrees.

 

[prototypen]

The shortest + longest becomes 4.2 m so with a total of 33 battens you need to buy 17 pieces.
Protte

 

[prototypen]

The longest + 190 cm becomes exactly 480 cm.
The second longest + 180 cm should also be 480 cm.

Then you count how many short pieces you get on a whole läkt 125+135+145 etc.

I think it's easiest with paper, pen, and a calculator.
Protte

 

[prototypen]

Keep in mind that there may be crack ends, so you need to clean cut, allowing for a bit of waste, and count on something a bit shorter than 480
Protte

 

[gluecifer]

Thank you Protte! I have added about 5cm margin to the measurements I had.

 

[prototypen]

Measure twice, cut once.
There is a picture under the humor corner of how it might go otherwise.
Protte

 

[Johrnak]

The longest + 190 cm becomes exactly 480 cm.
The second longest + 180 cm should also become 480 cm.

Then you have to calculate how many short pieces you can get on a whole plank 125+135+145 etc.

I think it's easiest with paper, pen, and a calculator.
Protte

If the longest +190 becomes 480 cm, then the second longest +180 cm will be shorter than 480 cm (but you probably meant 200 instead of 180).

I guess you might get away with 16 planks. It doesn't hurt to have an extra one though.

EDIT: I think it might be possible with 15 but it cannot be done with 14 if the planks have lengths of 130, 140, ..., 290, 280, 270, ..., 130. This is because the total length becomes 6850 [cm], which means that at least 6850/480~=14.27 is required, i.e., at least 15 planks.

 

[Kane]

The longest + 190 cm becomes exactly 480 cm. The second longest + 180 cm should also become 480 cm.

Interesting math.....

 

[gluecifer]

Thank you very much for all the answers! I think one extra slat isn't much to argue over, but if I can minimize the waste during these times, it's indeed appreciated. Being able to calculate is useful regardless in the future.