Note: This is a derived formula, where R=D 1/2, r=D2/2, and cos θ = (r-r)/a.

Let x=(R-r)/a, when the value of x is close to 0 (practical significance: the two wheels are close in size and the wheelbase is large).

θ=arccosx≈π/2-x (please check Taylor formula of arccosx),

√ (a 2-(r-r) 2) = a √ (1-x 2) ≈ a (1-x 2)/2) (Taylor formula of √ (1-x 2) can be found or calculated.

l=2πr-2(r-r)θ+2√(a^2-(r-r)^2)≈2πr-(π/2-x)+2a( 1-(x^2)/2)

=π(r+r)+2(r-r)x+2a-a*x^2=2a+π(r+r)+(r-r)^2/a

I hope I can help you a little!