calculate duct length between to 45 degree elbows
Is there a formula to figure out the the lenght of duct to fit between the 45 degree elbows. My offset is 36" & the pattern is 48"x 20".
I know i can lay this on the floor and calculate the duct in between the 45's...but looking for a faster way, also i know i can layout an offet but it seems to big to handle and install, so that's why i'm using the two 45's and duct. 
(1.1414 xoffset) 2 (.414x (clr) centre line radius this is the formula
example degree of elbow: 60=.577 45=.414 30=2.00 example in your situation 45 degree elbow 48x20=72, 48 + 24 half your check is 24=72 thats your centre line radius... (1.414x36 offset)2(.414x72) =50.9042(29.808) =50.90429.616 =21.288 thats the length of the duct in between your on your two 45 degree elbow... i hope this help you... 
21.288 to convert .288 to inches or imperial x 16 tenths or an 1/8 value =9/16 or 1/4=your lenght is 21 9/16 or 21 1/4

p.s dont forget to add your 1 inches allowance if this is s+d(slip and drive drive...joint connection..:)

thanks guys, i knew there was a formula i just couldn't remember...thanks again

I tried something different but i got the same results.
Since i knew my pattern was 48" and my offset was 36" and my real throat radius was only 12"... This is what i did and it worked.. i took ( 1.414 x 36 offset )  2( .414 x 1/2 the pattern size and the radius = 36 ) 50.904  29.808 = 21.096 or 21 1/8 
I'm sorry, i used the same example...
This is what i did... i Took my offset multiplied it by 1.414 = 50.904, then what i did was take 1/2 of the pattern ( 48" ) which is 24", squared it up 90 degrees until it intersected the other side, ...after doing that i came up with 15.5" and times it by 2 =31.......then i subtracted 50.904 31= 19.904..add my allowances and i get the same answer. Only problem is i have to actually layout the pattern to get this formula. 
That's kinda hard to follow but if your Cl rise is 15.5 and your base line is 36 [1/2 cheek plus 12] you have 23.29 degrees when you need 22.5. That's going to put you about 1.66 off the center line your looking for. When your laying out angels your splitting hairs to stay in the ballpark.Go back and work the formula that tinmetal posted and you can't go wrong.

here is the answer...the problem ..if this the right dimension you posted...
1.414x36 offset  2 (.414 x 72 clr)on your situation is 1:1 throat radius and your check 48 and your radius from the throat is 48...clr is 72 cos 48 throat + half the check is 24 ...48+24=72.. (1.414 x 36)  2 (.414 x 72) 50.9042(20.808) 50.904  41.616 =9.288 or 9 1/1/4 that your duct lenght 
Bro, ur wrong...
Btw, thanks to tinmetal for the help... It's pretty basic, i have a side 45 degree elbow and i was trying to create a 36" offset...And the pattern size of the elbow was 48" and my throat radius was 12" . Tinmetal was right, the only thing i didn't give him was my throat radius but that number can be any Number and his formula always works. (1.414 xoffset)2(.414x1/2 the pattern size plus the radius) (1.414 x36)2(.414x36) 50.90429.808 =21.096 or 21 1/8, Plus 1" for the allowance 
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