last changed : 04.04.2004

The mathematical model of the solar balloon is based on 2 characteristics :
· the top is an half sphere diameter D.
· the bottom is a cone.
The semi angle of the cone is around 40°.
It can be changed . If the angle is increased , the load on balloon bottom will increase...
Those angles should be expressed in radians in order to use the Excel 97's trigonometric functions.
360° = 2 X Pi radians.
Many characteristics can be modified in the modified in the xls files.

• Pi : Pi = 3,1416
• 360° = 2 X Pi radians
• Sinus of an angle A : sin(A) = opposite side/hypotenuse
• Cosine of an angle A : cos(A) = adjacent side/hypotenuse
• Tangent of an angle A : tang (A) = opposite side / adjacent side
• Cord of an angle A = 2xRxsin(A/2) or Dxsin(A/2)
• Arc of an angle A ( degrees) : arc(A) = (AxPixD)/360
• Arc of an angle A (en radians) : arc(A) = AxR or (AxD)/2
• Perimeter of the circle of half diameter R or circumference : P = 2xPixR or P = PixD
• Surface of circle : S = PixR² or S = (PixD²)/4
• Lateral area of the cylinder : S = 2xPixRxh or S = PixDxh
• Sphere area :
  
• Sphere volume :
  
• Lateral area of a cone : (a=length generator line ; alpha=half-angle in the summit in radians)
  
• Volume of cone : (h=height of the cone ; alpha=half angle at summit en radians)
  
  
• Surface and volume of the balloon :
  
  • The top is an half sphere diameter D
  • The bottom is a cone
  • Dcc = diameter of the loading circle.
  • alpha = half angle en bas off the balloon in radians).