Here is a design for a 64 by 42 ellipse. the formula are the same for an egg.
Height 42.8 inches 1070 mm
Width 64 inches 1600 mm
Assumed Thickness (t') 1.8 inches 45 mm
EffectiveLength (L) 60.400 inches 1510 mm
Ht of WT above invert (H) 5.7 m
Physical Properties
Modulus of Elasticity (Es) (Short term) 507614PSI 3500 MPa
Modulus of Elasticity (El) (Long term) 253807PSI 1750 MPa
R (0.5 for straight sides, 1 for curved) 1
Limiting Stress (Sl) 2901PSI 20 MPa
Design
H = 340Sl(t/L)² (Stress)
Rewriting
t = L (H / (340 Sl)) 0.5
t = 43.7 mm 1.721 inches
H = 236REl(t/L) 3 (Deflection)
Rewriting
t = L (H / (236 R El )) 0.333
36.2 mm 1.426 inches
Lining Thickness Required = 43.7 mm 1.721 inches
This will give you a good idea of the liner thickness. It is always thicker than the round equivalent pipe. But that is where i always start. Also, inthe formula there is no place for the live load or soil load. Convert them to feet of water and add to the hater head on the pipe. the liner gets thick in a hurry.
Richard A. Cornelius, P.E.