## Sunday, May 19, 2013

### HP35S: Horizontal Curve - Finding Radius, Chord Length, and Arc Length

HP 35S: Horizontal Curve
Original: HP 33S Surveying Applications, Hewlett Packard, March 1978, pg. 46

Calculator
HP 35S

Input
(see diagram above)

T = Tangent Distance (length of segment from P.C. (Point of Curvature) to P.I. (Point of Tangent Intersection))
A = Central curve in degrees, minutes, seconds

This program prompts for tangent length and central angle

Output

The program gives the following results:
1. Radius of the horizontal curve (R)
2. Press R/S to get the Chord length (C)
3. Press R/S once more to get the arc length of the horizontal curve (L)

The program does not store any results.

Formulas
R = T × (tan(A/2))⁻¹
C = 2 × R × sin(A/2)
L = R × A in radians

Where
T = tangent distance
A = central angle
C = Chord Length
L = Arc Length

Example
Tangent Length: 172.45
Central Angle: 40°22'13" (enter as 40.2213)

Results:
Chord Length: 323.7172
Arc Length: 330.51163

Program
V001 LBL V
V002 DEG
V003 INPUT T
V004 INPUT A
V005 HMS→\\ sometimes named ->H
V006 STO A
V007 2
V008 ÷
V009 TAN
V010 1/x
V011 ×
V013 ENTER
V014 ENTER
V015 2
V016 ×
V017 RCL A
V018 2
V019 ÷
V020 SIN
V021 ×
V022 R/S \\ display Chord Length
V023 x<>y
V024 RCL A