**HP Prime and TI-86: Minimum Vertical Curve Length**

**Introduction**

The
program MVCL calculates the minimum vertical curve length for sight
distances for crest curves (curve that rises then falls) and sag
curves (curves that falls than rises). The equations used were
determined by the AASHTO (American Association of Highway and
Transportation Officials of Washington, D.C.).

**HP Prime Program MVCL**

EXPORT MVCL()

BEGIN

// Minimum stop speed

LOCAL g1,g2,a,c,l,s,g;

MSGBOX("Break = 2.5 s,

Decel = 11.2 ft/s^2");

LOCAL l1:={15,20,25,30,35,40,45,

50,55,60,65,70,75,80};

LOCAL l2:={80,115,155,200,250,

305,360,425,495,570,645,730,

820,910};

INPUT({g1,g2,{c,l1}},"MVCL",

{"Grade1%:","Grade2%:",

"Speed:"});

s:=l2(c);

a:=ABS(g1-g2);

l:=2*s-2158/a;

IF s < l

l:=a*s^2/2158;

END;

g:=2*s-(400+3.5*s)/a;

IF s < g

g:=(a*s^2)/(400+3.5*s);

END;

PRINT();

PRINT("Stop speed (ft)");

PRINT("Crest curve: "+l);

PRINT("Sag curve: "+g);

END;

BEGIN

// Minimum stop speed

LOCAL g1,g2,a,c,l,s,g;

MSGBOX("Break = 2.5 s,

Decel = 11.2 ft/s^2");

LOCAL l1:={15,20,25,30,35,40,45,

50,55,60,65,70,75,80};

LOCAL l2:={80,115,155,200,250,

305,360,425,495,570,645,730,

820,910};

INPUT({g1,g2,{c,l1}},"MVCL",

{"Grade1%:","Grade2%:",

"Speed:"});

s:=l2(c);

a:=ABS(g1-g2);

l:=2*s-2158/a;

IF s < l

l:=a*s^2/2158;

END;

g:=2*s-(400+3.5*s)/a;

IF s < g

g:=(a*s^2)/(400+3.5*s);

END;

PRINT();

PRINT("Stop speed (ft)");

PRINT("Crest curve: "+l);

PRINT("Sag curve: "+g);

END;

**TI-86 Program MVCL**

(744
bytes)

Input
“GRADE %1:”, G1

Input
“GRADE %2:”, G2

abs(G2-G1)
→ A

Disp
“Break time = 2.5s”, “Decl. = 11.2 ft/s²”,

“Car
Speed?”,”(mph)”

Menu(1,”15”,A,2,”20”,B,

3,”25”,C,4,”30”,D,

5,”35”,E,6,”40”,F,

7,”45”,G,8,”50”,H,

9,”55”,I,10,”60”,J,

11,”65”,K,12,”70”,L,

13,”75”,M,14,”80”,N)

Lbl
A : 80 → S : Goto Z

Lbl
B : 115 → S : Goto Z

Lbl
C : 155 → S : Goto Z

Lbl
D : 200 → S : Goto Z

Lbl
E : 250 → S : Goto Z

Lbl
F : 305 → S : Goto Z

Lbl
G : 360 → S : Goto Z

Lbl
H : 425 → S : Goto Z

Lbl
I : 495 → S : Goto Z

Lbl
J : 570 → S : Goto Z

Lbl
K : 645 → S : Goto Z

Lbl
L : 730 → S : Goto Z

Lbl
M : 820 → S : Goto Z

Lbl
N : 910 → S : Goto Z

Lbl
Z

Disp
“Stop speed (ft)”, “crest curve:”

2
* S – 2158 / A → L

If
S > L

Then

Disp
L

Else

A
* S² / 2158 → L

Disp
L

End

Disp
“sag curve:”

2
* S – (400 + 3.5 * S) / A → G

If
S > G

Then

Disp
G

Else

(A
* S²) / (400 + 3.5 * S) → G

Disp
G

End

Examples:

Example
1:

Grade
1: -1.75%

Grade
2: 2.25%

Design
Speed: 40 mph

Result:

Minimum
Vertical Curve Length

Crest
Curve: 70.5 ft

Sag
Curve: 243.125 ft

Example
2:

Grade
1: -1%

Grade
2: 1.7%

Design
Speed: 50 mph

Result:

Minimum
Vertical Curve Length

Crest
Curve: 50.740740741 ft

Sag
Curve: 150.925925926 ft

Source:

Michael
R. Lindberg, PE “Civil Engineering Reference Manual for the PE
Exam” 11

^{th}Ed. Professional Publications, Inc: Belmont, CA. 2008. ISBN 13-978-1-59126-192-2
Eddie

All
original content copyright, © 2011-2019. Edward Shore.
Unauthorized use and/or unauthorized distribution for commercial
purposes without express and written permission from the author is
strictly prohibited. This blog entry may be distributed for
noncommercial purposes, provided that full credit is given to the
author.

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