Pentagons in Circles

The following pictures show n regular pentagons packed inside a unit circle, so that the total sum of the sides of the pentagons is as large as possible.

1.
           2.
           3.
Σ s = √((5–√5)/2) = 1.17557+
Trivial.
  		Σ s = 4√(1–2/√5) = 1.29968+
Trivial.
A continuum of solutions. 		Σ s = 1.85411+
Found by Jonathan Viquerat
in June 2026.

4.
           5.
           6.
Σ s = 2.23179+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 2.51913+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 2.79197+
Found by Jonathan Viquerat
in June 2026.

7.
           8.
           9.
Σ s = 3.06697+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 3.31241+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 3.51482+
Found by Jonathan Viquerat
in June 2026.

10.
           11.
           12.
Σ s = 3.71141+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 3.91715+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 4.11652+
Found by Jonathan Viquerat
in June 2026.

13.
           14.
           15.
Σ s = 4.29822+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 4.49438+
Found by Haowei Lin
in June 2026. 		Σ s = 4.65507+
Found by Haowei Lin
in June 2026.

16.
           17.
           18.
Σ s = 4.84434+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 5.00531+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 5.16108+
Found by Haowei Lin
in June 2026.

19.
           20.
           21.
Σ s = 5.31132+
Found by Haowei Lin
in June 2026. 		Σ s = 5.45457+
Found by Haowei Lin
in June 2026. 		Σ s = 5.58046+
Found by Haowei Lin
in June 2026.