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the Bristol Motor Speedway is 0.533 mi long racetrack. The road is banked and circular. The straights are banked to 6–10° and turns to 26–30°. I have made a small diagram for ilustration.

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Before the cars fully enter into the turn, they have to pass through a section of the track where the banking graually progresses from 10° to 30°. Does anyone knows how is determined the lenght of the road between two levels of banking?

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  • $\begingroup$ You need either the rate of change of gradient or the elevation difference between the start of end of both sections of roadway. $\endgroup$
    – Fred
    Commented Mar 30, 2020 at 4:04
  • $\begingroup$ do you want to know how to decide what the distance should be, or how to measure the actual distance? Most people would determine the actual distance with a measuring wheel. $\endgroup$
    – Tiger Guy
    Commented Mar 30, 2020 at 19:02
  • $\begingroup$ @TigerGuy, what factors determine the rate of banking progression (from 10° to 30°). Is it a linear or non-linear progression and the rate of progression. $\endgroup$
    – Marino
    Commented Mar 30, 2020 at 19:44
  • $\begingroup$ if you wanted to engineer the banking you would try to match the speed to the expected deceleration of the cars going into the corner. I doubt a lot of engineering actually went into it. Somebody probably just decided. $\endgroup$
    – Tiger Guy
    Commented Mar 30, 2020 at 21:10

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In highway design, this is called a superelevation and spiral transition: https://en.wikipedia.org/wiki/Track_transition_curve

The length of the spiral is based upon the design speed. For USA highway design, guidance is provided in the AASHTO green book A Policy on Geometric Design of Highways and Streets.

Considering that text is not available for free, state highway departments may include AASHTO related information in their posted roadway design manuals.

Here is a link to the Arizona Dept of Transportation Manual: https://azdot.gov/sites/default/files/2019/06/2014-roadway-design-guidelines.pdf.

Section 202.3 - Superelevation Transisition on page 200-9 discusses the design of length of the spiral transition.

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  • $\begingroup$ Supposedly, the Euler spiral is difficult to build. Therefore a compromise has been made with a multi-radius transition. The transition curve passes through a couple of decreasing rediuses before it reaches the corner with constant radius. $\endgroup$
    – Marino
    Commented Apr 16, 2020 at 17:08
  • $\begingroup$ The change of arc and cross slope is distributed along the the running distance of the transition to minimize abrupt change in forces on the vehicle. In highway design, the tangent section cross slope is selected for surface runoff benefit. The curve section cross slope is determined by design velocity and radius of curve. See en.wikipedia.org/wiki/Banked_turn . $\endgroup$
    – DavidJ
    Commented Apr 20, 2020 at 15:08
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They have some prescribed transition curves as an intermediary between two bends with different radius. In this case, one of the bends is straight with an infinite radius.

The bank angle is a linear function of R, the radius of the track, not proportional to the distance from the end of the straight section.

So right after the straight patch transitions into the curve the angle barely increases as the radius is very large. As the radius of the track approaches the tight turn, the change in the bank angle increases. By the time the intermediary curve turns int the circular arc of the track, the angle is equal to 30 degrees.

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  • $\begingroup$ Hmm.. maybe there is a standard, such as banking angle / arc segment, tfor any oval race track. $\endgroup$
    – Marino
    Commented Mar 30, 2020 at 20:12
  • $\begingroup$ It's not oval if i remember from 50 years back. It is a special curve. $\endgroup$
    – kamran
    Commented Mar 30, 2020 at 21:44

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