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TABLE 1. Mathematical relationships in homothetic and a quasi-homothetic transformation.

 
   

Mathematical Relationship

Homothetic transformation

Lineal entities

equation t1for i=1 to 3

Surface entities

equation t2 with i j

Quasi-homothetic transformation

Lineal entities

equation t3

equation t4

Surface entities

equation t5

 

 TABLE 2. Equations of forces in a scaled model B with reference to model A. AA is the area of the reference model, AB the area of the scaled model, tA is the thickness of the reference model and tB the thickness of the scaled model.

 
 

Stress state constant

Displacements constants

Plane Stress

equation t6

equation t7

Plane Strain

equation t8

equation t9

TABLE 3. Thickness and surface of the four scaled models of Connochaetes taurinus used in Case 1.

 

Scaled model

Thickness
(t)
in mm

Area
(A)
in mm2

1 (Reference)

1,00

20291,00

2

10,00

5072,75

3

6,00

20291,00

4

24,50

1371,67

 

TABLE 4. Thickness and a of C. taurinus, A. buselaphus, H. niger and K. vardoni used in Case 2.

 

Model

Thickness
(t)
in mm

Area
(A)
in mm2

C. taurinus (Reference)

20,88

20282,00

A. buselaphus

16,97

17897,00

H. niger

19,67

20742,00

K. vardoni

14,22

10617,00

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