Hyperboloids of Revolution
Mr. Kirwan G00063869
Real Life Examples
Kobe Port Tower , Japan Hyperboloid Structure
Hyperboloid of Revolution
Real Life Examples
Cathedral of Braslia, Brasil Hyperboloid Structure
Hyperboloid of Revolution
Fictional Examples
Nuclear Power plant, Springfield, Hyperboloid Structure
Hyperboloid of Revolution
What is a surface?
A surface is generated by the movement of a straight or curved line The resulting surface can be singly or doubly ruled
Hyperboloid of Revolution
Conic Section Shapes???
Circle Ellipse
Parabola
Hyperbola
Hyperboloid of Revolution
What is the difference between a Parabola and a Hyperbola?
Hyperboloid of Revolution
Hyperbola Shape
Hyperboloid of Revolution
How is a Hyperboloid of Revolution shape generated? Method 1
Hyperbola (Generator)
Shape revolves around axis
Axis
Hyperboloid of Revolution
How is a Hyperboloid of Revolution shape generated? Method 2
The shape is generated by revolving a straight line (Generator) around another non parallel, non intersecting line as its axis. These lines are skew lines
Red Line represents the Generator Line Black Line represents the Axis
Hyperboloid of Revolution
One Sheet / Two Sheet
Hyperboloid of Revolution
One Sheet / Two Sheet
Hyperboloid of Revolution
Methods for constructing a Hyperboloid of Revolution
Rectangle Method Elements Method Asymptote Method
Hyperboloid of Revolution
Rectangle Method
A B
110
V1
V2
34
Hyperboloid of Revolution
66
Elements Method
110
X
A
34
Hyperboloid of Revolution
66
Asymptote Method
110
34
Hyperboloid of Revolution
66
Elements
A straight line on the surface is a ELEMENT An element will be tangent to the throat circle in plan
Hyperboloid of Revolution
Asymptote
These are seen as true lengths in the elevation
Elements seen as True Lengths
Hyperboloid of Revolution
Worked Example
Hyperboloid of Revolution
True Shape Example
Q R S
S
a R1
R2 b R3
c
90 X
a b
Y
R2
c
R1
R3
c b
Hyperboloid of Revolution
Asymptote
Solidworks Models
Hyperboloid of Revolution
2008 Ordinary Level Exam Question
Hyperboloid of Revolution
Hyperboloid of Revolution
44 39
V1
V2
R44 R39
2008 Ordinary Level Question
2012 Higher Level Question
Hyperboloid of Revolution
2012 Higher Level Question
Hyperboloid of Revolution
Usefull YouTube Videos
http://www.youtube.com/watch?v=cfrQSzDfF oI (Generation of a Hyperboloid) http://www.youtube.com/watch?v=1I-YVblI4Q (Elements Method) http://www.youtube.com/watch?v=g9BSdrbbr pM (Asymptote Method)
Hyperboloid of Revolution
