# Spiral transition length -



## EM_PS (Sep 16, 2008)

For calculating length of spiral transistion into a curve:

The FE ref manual gives this formula: Ls=(3.15V^3)/R

V = design velocity

R = radius of curve

However, Civil DS review manual used the following, as does 1 of my civil ref. manuals: Ls=(1.6V^3)/R

Is the top 1 for metric units (Km/h)? If so, how does a conversion factor in to the lower fomula for MPH (since it doesn't seem to convert)?

Or do i just need to ignore 3.15 and try to remember 1.6 when actually taking test? :mellow:


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## roadwreck (Sep 16, 2008)

The Green Book has the formula

L=3.15*V3/RC (US Customary)

L=0.0214*V3/RC (Metric)

Where C = rate of increase of lateral acceleration (ft/s3 or m/s3 respectively)

I don't do much spiral design, so I'm not familiar with the application of these formulas. The green book gives this info about the C factor



> The factor C is an empirical value representing the comfort and saftey levels provided by the spiral curve. The value of C = 0.3 m/s3 [1ft/s3] is generally accepted for railroad operation, but values ranging from 0.3 to 0.9 m/s3 [1 to 3 ft/s3] have been used for highways.


Looks like both your formulas are US customary just w/ different assumed C values

Sounds to me like the first formula you gave was assuming a C of 1ft/s3

and the second was using a C of 2 ft/s3


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## EM_PS (Sep 16, 2008)

Hmm, makes sense - the FE manual states to use 1 ft/sec^3 _unless otherwise stated_ for C. The particular problem simply asked for 'minimum required length of spiral transition' - No C value was given, hence i used the 3.15V^3/R formula. None of the given answers worked for that - just find it passingly annoying that there is no mention of the 1.6V^3/R formula, except when you check the solution of course.


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