Wheel chock device

1. A wheel chock device for stopping a wheel of a vehicle from rolling on a ground surface, said device comprising:

a profile including a generally flat bottom surface for being in contact with a ground surface and extending between a first end and a second end; and

a top surface for being in contact with the wheel, the top surface extending over the bottom surface, the top surface having a contact surface being able to support the wheel simultaneously over at most two points of contact thereof;

the top surface including a first segment adjacent the first end and a second segment extending from the first segment and continuing the first segment away from the first end, the first and second segments defining a contact surface, the first segment being able to support the wheel and forming a generally flat first plane defining a first angle (ϕ 1 ) relative to the bottom surface, a tangent of the first angle (ϕ 1 ) being equal to or smaller than a minimum static coefficient of friction (μ min ) between the bottom surface and the ground surface; and

the first segment including a first contact point (P 1 ) adjacent the first end and located at a first height (h R ) relative to the bottom surface to allow the wheel to engage the chock device, the first height (h R ), relative to a radius (r) of the wheel and the minimum static coefficient of friction (μ min ), being obtained from the equation:

h

R

<

r

(

1

-

1

1

+

μ

min

2

)

the second segment including a second contact point (P 2 ) being adjacent the second end and closer to the second end than the first contact point (P 1 ) is; the second segment, at the second contact point (P 2 ), defining a tangent having a second angle (ϕ 2 ) relative to the bottom surface, a tangent of the second angle (ϕ2) being equal to or smaller than a maximum static coefficient of friction (μ max ) between the bottom surface and the ground surface, and larger than the tangent of the first angle (ϕ 1 );

wherein a perpendicular projection of the first contact point (P 1 ) on the bottom surface intersects the bottom surface at a first intersection (R) adjacent the first end, wherein the tangent of the second angle (ϕ 2 ) intersects the bottom surface at a second intersection (B), and wherein the first segment has a rolling length (AA′), starting at the first point of contact (P 1 ), ensuring the wheel to roll on the first segment and be entirely supported thereon before contacting the second segment;

a minimum distance (BR min ) between the first and second intersections, relative to the radius (r) of the wheel, the rolling length (AA′), and both the minimum (μ min ) and maximum (μ max ) static coefficients of friction, is obtained by the equation:

BR

min

=

r

(

μ

max

1

+

μ

max

2

-

μ

min

1

+

μ

min

2

-

1

μ

max

+

1

μ

max

⁢

1

+

μ

max

2

)

+

AA

′

(

1

1

+

μ

min

2

-

μ

min

μ

max

⁢

1

1

+

μ

min

2

)

.

2. The wheel chock device according to claim 1 , wherein the second contact point (P 2 ) is at a second height (h T ) relative to the bottom surface, the second height (h T ) being larger than the first height (h R ).

3. The wheel chock device according to claim 2 , wherein a projection of the radius of the wheel extending through the second contact point (P 2 ), when the wheel is in contact with the second contact point (P 2 ), intersects the bottom surface adjacent the second end.

4. The wheel chock device according to claim 3 , wherein the second height (h T ), relative to both the radius (r) of the wheel and the maximum static coefficient of friction (μ max ), is obtained from the equation:

h

T

=

r

(

1

-

1

1

+

μ

max

2

)

.

5. The wheel chock device according to claim 3 , wherein the wheel has a radius varying between a minimum radius (r min ) and a maximum radius (r max ), the second height (h T ), relative to both a maximum radius (r max ) of the wheel and the maximum static coefficient of friction (μ max ), being obtained from the equation:

h

T

=

r

max

(

1

-

1

1

+

μ

max

2

)

.

6. The wheel chock device according to claim 3 , wherein the second segment is a slippery surface having a coefficient of friction with the wheel equal to or smaller than 0.5.

7. The wheel chock device according to claim 6 , wherein the slippery surface includes a plurality of rollers freely rotatably mounted onto the chock device and being in parallel relationship relative to one another.

8. The wheel chock device according to claim 2 , wherein the top surface includes an anterior portion extending from the second contact point (P 2 ) to the second end, the anterior portion always having a tangent having an angle relative to the bottom surface equal to or less than the second angle (ϕ 2 ).

9. The wheel chock device according to claim 2 , wherein the contact surface allows either only one point of contact at a time between said contact surface and the wheel or at most two points of contact therebetween with the second contact point (P 2 ) being one of said at most two points of contact.

10. The wheel chock device according to claim 9 , wherein the second segment includes a generally concave curved surface having a curvature radius larger than the radius (r) of the wheel.

11. The wheel chock device according to claim 10 , wherein the concave curved surface has a clothoid or piece-wise clothoids profile starting with a slope equal to the first angle (ϕ 1 ) adjacent the first segment and ending with a slope substantially equal to or larger than the second angle (ϕ 2 ).

12. The wheel chock device according to claim 2 , wherein the bottom surface includes a covering pad mounted thereon for contacting the ground surface.

13. The wheel chock device according to claim 12 , wherein the covering pad is interchangeable.

14. The wheel chock device according to claim 1 , wherein the second height (h T ), relative to the radius (r) of the wheel, both the minimum (μ min ) and maximum (μ max ) static coefficients of friction, and the rolling length (AA′), is obtained from the equation:

h

T

=

r

(

1

-

1

1

+

μ

max

2

)

+

AA

′

⁢

μ

min

1

+

μ

min

2

.

15. The wheel chock device according to claim 1 , wherein the rolling length (AA′) is larger than 30% of a sustentation length of the wheel, the sustentation length corresponding to a length of a deformed outer perimeter of the wheel being simultaneously in contact with a supporting surface.

16. The wheel chock device according to claim 15 , wherein the rolling length (AA′) is between 40% and 60% of the sustentation length of the wheel.

17. The wheel chock device according to claim 15 , wherein the rolling length (AA′) entirely supports the wheel.

18. The wheel chock device according to claim 1 , wherein the wheel has a radius varying between a minimum radius (r min ) and a maximum radius (r max ), the first height (h R ), relative to both a minimum radius (r min ) and the minimum static coefficient of friction (μ min ), being obtained from the equation:

h

R

<

r

min

(

1

-

1

1

+

μ

min

2

)

.

19. The wheel chock device according to claim 18 , wherein the minimum distance (BR min ) between the first and second intersections, relative to both the minimum (r min ) and maximum (r max ) radii of the wheel, the rolling length (AA′), and both the minimum (μ min ) and maximum (μ max ) static coefficients of friction, is obtained by the equation:

BR

min

=

r

max

(

μ

max

1

+

μ

max

2

-

μ

min

1

+

μ

min

2

-

1

μ

max

+

1

μ

max

⁢

1

+

μ

max

2

)

+

AA

′

(

1

1

+

μ

min

2

-

μ

min

μ

max

⁢

1

1

+

μ

min

2

)

+

(

r

max

-

r

min

)

⁢

(

1

-

1

/

1

+

μ

min

2

μ

min

)

.

20. The wheel chock device according to claim 19 , wherein the second predetermined height (h T ), relative to the maximum radius (r max ) of the wheel, both the minimum (μ min ) and maximum (μ max ) static coefficients of friction, and the rolling length (AA′), is obtained from the equation:

h

T

=

r

max

(

1

-

1

1

+

μ

max

2

)

+

AA

′

⁢

μ

min

1

+

μ

min

2

.