Limiting Factors

In some cases, the surveyor may have to use elements other than the radius as the limiting factor in determining the size of the curve. These are usually the tangent T, external E, or middle ordinate M. When any limiting factor is given, it will usually be presented in the form of T equals some value x, T ≥ x or T ≤ x. In any case, the first step is to determine the radius using one of the following formulas:

The surveyor next determines D. If the limiting factor is presented in the form T equals some value x, the surveyor must compute D, hold to five decimal places, and compute the remainder of the curve. If the limiting factor is presented ≥, then D is rounded down to the nearest ½ degree. For example, if E ≥ 50 feet, the surveyor would round down to the nearest ½ degree, recompute E, and compute the rest of the curve data using the rounded value of D, The new value of E will be equal to or greater than 50 feet.

If the limiting factor is ≤ the D is rounded to the nearest ½ degree. For example, if M ≤ 45 feet, then D would be rounded up to the nearest ½ degree, M would be recomputed, and the rest of the curve data computed using the rounded value of D. The new value of M will be equal to or less than 45 feet. 

The surveyor may also use the values from table A-5 to compute the value of D. This is done by dividing the tabulated value of tangent, external, or middle ordinate for a l-degree curve by the given value of the limiting factor. For example, given a limiting tangent T ≤ 45 feet and I = 20°20’, the T for a l-degree curve from table A-5 is 1,027.6 and D = 1,027.6/45.00 = 22.836°. Rounded up to the nearest half degree, D = 23°. Use this rounded value to recompute D, T and the rest of the curve data.