Pulley questions

[borna]

Hello all,
I need Help with selecting a correct size pulley and bet for a model engine I'm building.
The engine is a 4 cycle 2 cylinder In line.
I'm panning to select a correct Pulleys and belt between the camshaft and the crankshaft with a ratio of 2:1
The larger pulley goes on the camshaft and smaller on the crankshaft.

The center distance between camshaft and crankshaft is 1.29"

To calculate the belt length I used this formula

L = 2C + 1.57(D+d) + (D-d)^2 / 4C
L = Pitch length of belt
D = Pitch Diameter of Larger pulley
d = Pitch Diameter of smaller pulley

For the smaller pulley I'm planning to use a one with d=.520
https://sdp-si.com/eStore/PartDetail...&GroupID=2 17

For the larger pulley I'm planning to use one a with D=1.040
https://sdp-si.com/eStore/PartDetail...&GroupID=2 17


based on the calculation above the length of the belt came out to around 5.034" long
the closest to that size that I could find is 5.71"
https://sdp-si.com/eStore/PartDetail...&GroupID=2 13

The question is what size idler pulley I need to use so that 5.71" could fit and what is the formula to find the location that I need to install the idler pully?

By the way prior to using a pulleys and belt, I was planning to use a 2:1 ratio gears with an idle in between as seen in the picture.

Thanks
Borna