Re: Racing cars on a track

Oh, from the graphical approximation to the result:

Okay the tangent on the North direction is 470 while the distance to
the low point from the radius is 469 on the 315 azimuth.

L is distance to add to radius
P is distance to add to tangent
r is the starting radius
R is the required radius
t is the starting tangent distance
T is the required tangent distance
t as (t) is known
r as (r) is known

0.7071 * L = P
L + (r) = R
P + (t) = T
T = R

L + (r) = R
P/.7071 + (r) = R
P + (t) = T
T = R
P/.7071 + (r) = P + (t)
1.414227 P - P = (t) - (r)
0.414227 P = (t) - (r)
(r) = 469
(t) = 470
0.414227 * P = 1
P = 2.41

T = 470 + 2.41
T = 472.41


Now forget the graphical approximation:

t is the tangent distance for the outside curve
r is the radius distance to the midpoint of the inside curve

t = 400
r = 370

1.414214 P - P = (t) - (r)
0.414214 P = 30
P = 72.43

T = 400 + 72.43
T = 472.43

Now some terminology explaination:

The curve has a central angle of 90 degrees.

The tangent is the straight into the curve and also the straight out of
the curve. But the tangent-distance is the distance from the
begin-of-curve to the intersection of the tangents. And the
tangent-distance is also the distance from the intersection of the
tangents to the end-of-curve.


So I suppose this is a "Circular Path Curve...within a given circular curve
width"...

And the calculation should easily develop for central angles other than 90
degrees...


.

Relevant Pages

  • Re: Racing cars on a track
    ... The curve has tangent intersections with N,E coordinates ... And the curve itself has a radius of 400. ... And the distance to the low point is 470! ...
    (sci.math)
  • Re: Racing cars on a track
    ... The curve has tangent intersections with N,E coordinates of 1400,1000 ... curve itself has a radius of 400. ... And the distance to the low point is 470! ...
    (sci.math)
  • Re: Racing cars on a track
    ... Okay the tangent on the North direction is 470 while the distance to ... the low point from the radius is 469 on the 315 azimuth. ... r is the radius distance to the midpoint of the inside curve ...
    (sci.math)
  • Re: Racing cars on a track
    ... The outside edge has a begin-of-curve with N,E coordinates of 1000,1000. ... The curve has tangent intersections with N,E coordinates of 1400,1000. ... curve itself has a radius of 400. ...
    (sci.math)
  • Re: Racing cars on a track
    ... The outside edge has a begin-of-curve with N,E coordinates of 1000,1000. ... The curve has tangent intersections with N,E coordinates of 1400,1000. ... curve itself has a radius of 400. ...
    (sci.math)