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” 11th Ed. Professional Publications, Inc:
Belmont, CA. 2008. ISBN 13-978-1-59126-192-2
Eddie
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original content copyright, © 2011-2019. Edward Shore.
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