Sunday, May 19, 2013

HP35S Vertical Curve: Elevation at Peak and at End Point

HP35S Vertical Curve: Elevation at Peak and Length

Source: Fundamental of Engineering Supplied-Reference Handbook 8th Ed, 2nd Revision, 2011, NCEES

Calculator: HP 35S

I = initial height
G = grade 1; entering the curve (in decimal form)
H = grade 2; exiting the curve (in decimal form)
L = horizontal length of the curve

G and H are the opposite signs

If G>0 and H<0 a="" and="" curve="" g="" h="" has="" if="" peak.="" similarity="" the="">0, the curve has a valley.

The program listed prompts for the inputs.

1. Point where the curve reaches extreme elevation
2. Press R/S to get the elevation at the extreme point.
3. Press R/S once more to get the elevation at the end of the curve.

None of the outputs are stored.

A = (G - H)/(2L)
X_extrema = -G/(2A)
Equation of the Curve: y = I + G*x + A*x^2

Uphill curve:
I = 1,000 ft
G = 7% = 0.07
H = -4% = -0.04
L = 1,368 ft

Point at peak elevation is 870.545 ft into the curve at 1,030.469 ft. The elevation at the end of the curve is 1,020.520 ft.

Downhill curve:
I = 1,580 ft
G = -3% = -0.03
H = 4.2% = 0.042
L = 2.3 mi = 12,144 ft

Point at trough elevation occurs 5,060 ft into the curve at elevation 1,504.1 ft. The elevation at the end of the curve is at 1,652.864 ft.

V001 LBL V
V006 RCL H
V007 RCL - G
V008 2
V009 ÷
V010 RCL ÷ L
V011 STO A
V012 RCL G
V013 x<>y
V014 ÷
V015 2
V016 ÷
V017 +/-
V018 R/S \\ shows point where extreme elevation occurs
V019 XEQ V024
V020 R/S \\ shows extreme elevation
V021 RCL L
V022 XEQ V024 \\ shows ending elevation
V023 RTN
V024 ENTER \\ calculate y subroutine
V025 RCL × A
V026 RCL + G
V027 ×
V028 RCL + I
V029 RTN

This blog is property of Edward Shore. 2013

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