Patent ID: 8469831
Filing Date: 2013-06-25
Classification: A63K

Abstract:
1. An improved race track ramp, for one or a plurality of gravity-driven cars, comprising (a) a ramp cycloid section and a ramp support structure, said ramp cycloid section further comprising one or a plurality of identically elevated and sloped contiguous lanes, upon which wheels of said cars roll on a lane rolling surface, and said ramp cycloid section capable of having a curvature being that of a cycloid curve section, said curvature established by said ramp cycloid section being urged to assume the shape of said cycloid curve section by interacting with said support structure; (b) said cycloid curve section being a continuous section of a cycloid curve, said cycloid curve section having a predetermined start point and a predetermined end point, said cycloid curve section being the shortest possible trajectory traced out by said car wheels on the top surface of said lanes of said ramp cycloid section; (c) thus specification of a curve parameter describing said cycloid curve section, being itself a two-dimensional curve, applies as well to any of said identical lanes of the entire three-dimensional said ramp cycloid section, whereupon said predetermined start point and said predetermined end point of said cycloid curve section apply as well to a ramp cycloid section start point and a ramp cycloid section end point of the three-dimensional said ramp cycloid section; (d) said ramp cycloid section being part of an overall race track that also comprises a coasting run, said coasting run being a straightforward continuation of said ramp cycloid section and said lane rolling surface of said coasting run being coincident with a horizontal reference plane, said reference plane having a flat and level surface; (e) said ramp cycloid section further comprising a first, higher ramp section, and a second, lower ramp section, said first ramp section and said second ramp section being joined end-to-end to form said ramp cycloid section; (f) in order to determine specific features of said ramp support structure and its interaction with said ramp cycloid section to cause it to have said curvature being that of said cycloid curve section, one should be familiar with certain mathematical characteristics of said cycloid curve that will allow one to produce the horizontal and vertical distances to which said ramp cycloid section must conform; (g) said cycloid curve being a curve traced out by movement of a generating point fixed on the circumference of a circle, having a radius r, as said circle is being rotated by a rolling action, without slipping, horizontally in a right-handed sense as defined as the positive forward travel direction of said cars when viewing from their passenger side, said rolling action being along the underside of a straight horizontal x-axis, with the circumference of said circle being under and against said horizontal x-axis, and a rotation of said circle during said rolling action being measured by a rotation angle θ; (h) said cycloid curve further being mathematically described in terms of a parameter pair which consists of said radius r and said rotation angle θ, said parameter pair defining a horizontal distance x of a point on said cycloid curve according to an equation (1) and further defining a vertical distance y of said point on said cycloid curve, measured positive downwards, according to an equation (2), and said equation (1) and said equation (2), together, being mathematically known as a pair of parametric equations of said cycloid curve; (i) said equation (1), and said equation (2), thereby defining a cartesian coordinate pair x and y, denoted as (x,y), being used for locating any of a multitude of points on said cycloid curve, said cycloid curve multitude of points having a start point at an origin, said origin denoted as (0,0) with said cartesian coordinate pair x and y each being 0, and at said origin said rotation angle θ also being 0 before said generating point starts tracing said cycloid curve; (j) said cycloid curve initially dropping sharply from said origin (0,0), and with gradually reducing curvature proceeding in said right-handed sense, as said circle rolls, until said cycloid curve drops below said x-axis a maximum y distance y (k) said horizontal straight line through y (l) starting from directly below said ramp cycloid section start point, and measuring a ramp length d along said horizontal reference plane in the car travel direction, will locate said ramp cycloid section end point at (x (m) said ramp cycloid section start point, being measured vertically upwards from said horizontal reference plane, is at a ramp start height h; (n) said predetermined start point on said cycloid curve that also marks said ramp cycloid section start point being hereby denoted by a cartesian coordinate pair (x (o) said gravity-driven cars having a starting position with the center of each of said cars, as placed in their said lane, being positioned on a line being perpendicular to said ramp cycloid section and passing through said ramp cycloid section start point (x (p) said ramp cycloid section being more conveniently described by defining a horizontal ramp cycloid section coordinate X and a vertical ramp cycloid section coordinate Y with each being shifted a predetermined amount from said cartesian coordinates x and y, said horizontal ramp cycloid section coordinate X being 0 at said ramp cycloid section start point and increasing to said ramp length d at said ramp cycloid section end point, and further said vertical coordinate Y being measured positive from above said horizontal straight line through y distance of y; (q) said equation (3) requiring x with x o and y o now being in terms of r, d and h; (r) said equation (3) and said equation (4) being put in terms of h and d by substituting for x and then solving said equation (9) and said equation (10) for r giving where an equation (11) and an equation (12) above being independent expressions for r; (s) one needs to solve said equation (11) and said equation (12) for said circle radius r and for said θ said equation (13) and said equation (14) then giving said ramp cycloid section start point having said cartesian coordinate pair (x o ,y o ); (t) using said ramp coordinate pair X and Y for describing said ramp cycloid section start point, one has from said equation (5) and said equation (6) that X=0 and Y=h=119.38 cm; (u) for an example of calculating said ramp coordinate pair X and Y at an arbitrary point on said ramp cycloid section, one chooses a Y value height, say at 80% of said particular ramp start height h, thus said Y=95.5 cm and one gets a specific y value y=2r−0.8h=381.30 cm from said equation (6), then rearranging said equation (2), resulting in an equation (15) below, and putting said specific y value and said specific r value into said equation (15), thus getting a resulting θ value of θ=2.214 radians, said resulting θ value being input into said equation (1), reproduced here for convenience, giving x=336.88 cm, and from said equation (5) one gets a value X=44.34 cm, thus at a horizontal distance of 44.34 cm from directly below said ramp start point, said Y value height being 95.5 cm, and said example being repeated to give said horizontal displacement distance X for any given height Y of said arbitrary point, thereby creating a table of (X, Y) distances based on multiple determinations of said ramp coordinate pair (X, Y); (v) whereby, after having selected values for said ramp start height h and said ramp length d, and also having obtained values for said parameter pair r and θ, these being available from said graph-based solution of said equation (11) and said equation (12), said art practitioner then being able to produce said horizontal coordinate X and said vertical coordinate Y for any of said arbitrary points on said ramp cycloid section between said ramp start point and said ramp end point, thus providing said table of (X, Y) distances with which said art practitioner can cause said ramp to conform to during construction and set-up of said ramp.