tan(e) in sbend pole face

[ldeniau]

I am trying to figure out where this tan is coming from. Simple geometry tells us (v is the pole face half length at orbit x)
x = v cos(e)
dL = v sin(e)
giving
dL = x tan(e)
where dL is the "straight" length to substract to the sbend arc half length at orbit x due to pole face angle e (see fig 1.5 in MAD-X user manual).
but why don't we just take the arc length
dL = x e
which is both simpler and more accurate for "large" e?

my guess is the following:
dL = x tan(e)
is correct for a true rbend or any other straigth element, but this is not supported by MAD-X
it was maybe existing in older code and copy-pasted for the sbend (which includes rbend in MAD-X).