Curves

Interaction

ANC-5 Strength of Metal Aircraft Elements March 1955 Revised Edition Section 1.535, pages 11-13

interaction curves
  Section Factor

Elmer F. Bruhn Analysis and Design of Flight Vehicle Structures
Figure C3.8, page C3.3

t 1 / b = 0.125 / 1.375 = 0.091 t 2 / h = 0.125 / 2.00 = 0.0625
K = 1.166

shape factor curves
 
Perimeter of an Ellipse - GRAN Method

perimeter of an ellipse

Ellipse Perimeter

ellipse perimeter

Example: Semi-Major Axis, a = 10 inch Semi-Minor Axis, b = 5 inch

factors


  GRAN Function

Third Order Polynomial

third order polynomial

Sixth Order Polynomial

sixth order polynomial

Legendre Polynomial – Tenth Degree

legendre polynomial

R-squared: 0.999999999998       R-squared adjusted: 0.999999999997

Thanks to http://zunzun.com/


Calculator

Ellipse_Perimeter_GRAN_Method.xlsx

Complete Elliptic Integral of the Second Kind

Complete Elliptic Integral of the Second Kind

Perimeter (Circumference) of an Ellipse

Perimeter (Circumference) of an Ellipse

Screen Capture Video

Complete_Elliptic_Integral_of_the_2nd_Kind.avi



GRAN Formula

GRAN Formula

Bleasdale - Nelder Power Curve

Bleasdale - Nelder Power Curve

Perimeter (Circumference) of an Ellipse

Perimeter (Circumference) of an Ellipse