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UNIT CURVE FOR HIGHWAY TRANSITION SPIRAL

Shreenath Rao

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Abstract

A UNIT CURVE IS DEVELOPED FOR THE DESIGN OF A HIGHWAY TRANSITION SPIRAL. FOR ANY SPIRAL ANGLE, CORRESPONDING LENGTHS OF THE UNIT CURVE AND A GIVEN FIELD TRANSITION CURVE BEAR A CONSTANT RATIO WHICH IS TERMED THE CHARACTERISTIC CONSTANT OF THE FIELD CURVE. THE CONSTANT IS A FUNCTION OF THE CHOSEN MINIMUM RADIUS AND THE TOTAL LENGTH OF THE FIELD SPIRAL. THE CARTESIAN CO-ORDINATES FOR A PARTICULAR LENGTH OF THE FIELD CURVE ARE EQUAL TO THE CONSTANT TIMES. THE CARTESIAN CO-ORDINATES OF THE CORRESPONDING LENGTH OF THE UNIT CURVE, AND THE DEFLECTION ANGLE IS THE SAME FOR BOTH. THE USE OF THE UNIT CURVE VERY MUCH SIMPLIFIES THE DESIGN OF A HIGHWAY TRANSITION SPIRAL. /AUTHOR/

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What this paper is about

A UNIT CURVE IS DEVELOPED FOR THE DESIGN OF A HIGHWAY TRANSITION SPIRAL. FOR ANY SPIRAL ANGLE, CORRESPONDING LENGTHS OF THE UNIT CURVE AND A GIVEN FIELD TRANSITION CURVE BEAR A CONSTANT RATIO WHICH IS TERMED THE CHARACTERISTIC CONSTANT OF THE FIELD CURVE. THE CONSTANT IS A FUNCTION OF THE CHOSEN MINIMUM RADIUS AND THE TOTAL LENGTH OF THE FIELD SPIRAL. THE CARTESIAN CO-ORDINATES FOR A PARTICULAR LENGTH OF THE FIELD CURVE ARE EQUAL TO THE CONSTANT TIMES. THE CARTESIAN CO-ORDINATES OF THE CORRESPONDING LENGTH OF THE UNIT CURVE, AND THE DEFLECTION ANGLE IS THE SAME FOR BOTH. THE USE OF THE UNIT CURVE VERY MUCH SIMPLIFIES THE DESIGN OF A HIGHWAY TRANSITION SPIRAL. /AUTHOR/

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Available abstract

A UNIT CURVE IS DEVELOPED FOR THE DESIGN OF A HIGHWAY TRANSITION SPIRAL. FOR ANY SPIRAL ANGLE, CORRESPONDING LENGTHS OF THE UNIT CURVE AND A GIVEN FIELD TRANSITION CURVE BEAR A CONSTANT RATIO WHICH IS TERMED THE CHARACTERISTIC CONSTANT OF THE FIELD CURVE. THE CONSTANT IS A FUNCTION OF THE CHOSEN MINIMUM RADIUS AND THE TOTAL LENGTH OF THE FIELD SPIRAL. THE CARTESIAN CO-ORDINATES FOR A PARTICULAR LENGTH OF THE FIELD CURVE ARE EQUAL TO THE CONSTANT TIMES. THE CARTESIAN CO-ORDINATES OF THE CORRESPONDING LENGTH OF THE UNIT CURVE, AND THE DEFLECTION ANGLE IS THE SAME FOR BOTH. THE USE OF THE UNIT CURVE VERY MUCH SIMPLIFIES THE DESIGN OF A HIGHWAY TRANSITION SPIRAL. /AUTHOR/

Key concepts: Spiral (railway), Constant (computer programming), RADIUS, Cartesian coordinate system, Osculating circle, Geometry, Unit (ring theory), Field (mathematics)

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