Method for calculating parameters in road design of S-type clothoid, complex clothoid and egg type clothoid

• US 7,010,412 B1
• Filed: 12/17/2004
• Issued: 03/07/2006
• Est. Priority Date: 09/24/2004
• Status: Expired due to Fees

• Current Assignee: Saman Engineering Consultants Company Limited (Prime Development Co., Ltd.)
• Original Assignee: Saman Engineering Consultants Company Limited (Prime Development Co., Ltd.)
• Inventors: Song, Gyu-Seok
• Primary Examiner(s): NGUYEN, CUONG H
• Application Number:
  US11/015,932
• Time in Patent Office: 445 Days
• Field of Search: 373/47, 405/174, 405/180, 701207-209, 701/1, 701/200, 701/80, 701/212, 703/13, 703/2, 404/1, 404/17, 404/71, 404/84.8, 345/50, 345/56, 345/428, 434/433
• US Class Current: 701/80
• CPC Class Codes: E01C 1/00 Design or layout of roads, e.g. for noise abatement, for gas absorption design or layout of sports grounds A63C19/00; design or layout of airfields B64F , of helicopter landing stages E01F3/00
• CPC Class Codes: G09B 25/06 for surveying; for geography, e.g. relief models globes G09B27/00; maps G09B29/00

Abstract

The present invention relates to a method for calculating parameters in a road design of a S type, a complex type and an egg type clothoid, and in particular to a method for calculating a parameter value capable of determining the size of a clothoid that is inserted when designing a S-shaped and interchange, a connection road, etc. in an egg shape. In the present invention, it is possible to easily calculate the clothoid parameter A in a S shape, complex type and egg type road design, and a road design can be fast finished. In addition, in the present invention, it is possible to achieve an easier design of a S shape and egg type clothoid by determining a design specification without using CAD. The design can be achieved based on a simulation using a center coordinate of two circles for achieving an optimum design.

Claims

1. In a method for designing a road, an improvement comprising calculating parameters A₁ and A₂ in an S-shaped clothoid with R₁, R₂, D and $\frac{A_2}{A_1}$

being known values and R₁ and R₂ being radii of two circles and A₁ and A₂ being clothoid parameters A adapted to R₁ and R₂, respectively, and D being a shortest distance between circumferential portions of two circles, a method for calculating the S-shaped clothoid parameter comprising:

a step in which an initial value of a tangential angle τ

₁ of the radius R₁ is set;

a step in which the tangential angle τ

₁ is compared with 0, and when a result of the comparison is less than 0, since it means there is no solution, the process is stopped, and when a result of the same is greater than 0, a value of (R₁+D+R₂)²−

X_M² is calculated, X_M being a function of an unknown value τ

₁;

a step in which a value of (R₁+D+R₂)²−

X_M ² is compared with 0, and when a result of the comparison is less than 0, τ

₁ is properly adjusted, and the routine goes back to the next step of setting the initial value of the tangential angle τ

₁, and when a result of the same is greater than 0, the function F(τ

₁) is calculated and the function F′

(τ

₁) which is differentiated with τ

₁ from the function F(τ

₁) is calculated;

a step in which a ratio $G=\frac{F<br><br>\left({\mathrm{\tau <br><br>}}_1\right)}{F^{\mathrm{\prime <br><br>}}<br><br>\left({\mathrm{\tau <br><br>}}_1\right)}$

is calculated;

a step in which τ

₁=τ

₁−

G is calculated (τ

₁ is reduced by G); and

a step in which an absolute value of G is compared with a tolerance of 10<sup>−

6</sup>, and as a result of the comparison when the absolute value of G is greater than the tolerance, the routine is fed back to the next step where the initial value of τ

₁ is set, and when it is less than the tolerance, the tangential angle τ

₁ is determined, and A₁, which is a clothoid parameter A adapted to R₁, is easily calculated using τ

₁, and A₂, which is a clothoid parameter A adapted to R₂, is also easily calculated using A₁ and given value $\frac{A_2}{A_1}.$

2. The method of claim 1, wherein in said step for calculating A₁ and A₂ with functions F(τ

₁) and F′

(τ

₁, with respect to T₁, when calculations are done for functions F(L₁) and F′

(L₁) with respect to L₁, or with functions F(τ

₂) and F′

(τ

₂) with respect to τ

₂, or with functions F(L₂) and F′

(L₂) with respect to L₂, and values of A₁ and A₂ are obtained, a same result is obtained for A₁ and A₂.

3. The method of claim 1, wherein said step for calculating a solution of the functions F(τ

₁) and F′

(τ

₁) based on a non-linear method is achieved using one selected from the group consisting of the Newton-Rapson equation method, bisection method, secant method, regular false method, Aitken method, successive substitution method, Bairstow'"'"'s method, fixed point repeating method, Muller method or repeating method.

4. The method of claim 1, wherein said function of F(τ

₁) is as follows;

$F<br><br>\left({\mathrm{\tau <br><br>}}_1\right)=\frac{2}{3}<br><br>R_1<br><br>\left({\mathrm{\tau <br><br>}}_1^2-\frac{{\mathrm{\tau <br><br>}}_1^4}{14}+\frac{{\mathrm{\tau <br><br>}}_1^6}{440}-\frac{{\mathrm{\tau <br><br>}}_1^8}{25200}\right)+\frac{2}{3}<br><br>R_2<br><br>\left\{{\left(t<br><br><br><br>{\mathrm{\tau <br><br>}}_1\right)}^2-\frac{{\left(t<br><br><br><br>{\mathrm{\tau <br><br>}}_1\right)}^4}{14}+\frac{{\left(t<br><br><br><br>{\mathrm{\tau <br><br>}}_1\right)}^6}{440}-\frac{{\left(t<br><br><br><br>{\mathrm{\tau <br><br>}}_1\right)}^8}{25200}\right\}+R_1<br><br>\mathrm{Cos}<br><br><br><br>{\mathrm{\tau <br><br>}}_1+R_2<br><br>\mathrm{Cos}<br><br>\left(t<br><br><br><br>{\mathrm{\tau <br><br>}}_1\right)-\sqrt{{\left(R_1+D+R_2\right)}^2-X_M^2}$

wherein t represents a constant value, and X_M is a function of an unknown value τ

₁.

5. The method of claim 1, wherein said function of F′

(τ

₁) is as follows;

$F^{\mathrm{\prime <br><br>}}<br><br>\left({\mathrm{\tau <br><br>}}_1\right)=\frac{2}{3}<br><br>R_1<br><br>\left(2<br><br>{\mathrm{\tau <br><br>}}_1-\frac{4<br><br>{\mathrm{\tau <br><br>}}_1^3}{14}+\frac{6<br><br>{\mathrm{\tau <br><br>}}_1^5}{440}-\frac{8<br><br>{\mathrm{\tau <br><br>}}_1^7}{25200}\right)+\frac{2}{3}<br><br>R_2\left(2<br><br>t^2<br><br><br><br>{\mathrm{\tau <br><br>}}_1-\frac{4<br><br>t^4<br><br><br><br>{\mathrm{\tau <br><br>}}_1^3}{14}+\frac{6<br><br>t^6<br><br><br><br>{\mathrm{\tau <br><br>}}_1^5}{440}-\frac{8<br><br>t^8<br><br><br><br>{\mathrm{\tau <br><br>}}_1^7}{25200}\right\}+R_1<br><br>\mathrm{Sin}<br><br><br><br>{\mathrm{\tau <br><br>}}_1+R_2<br><br>t<br><br><br><br>\mathrm{Sin}<br><br>\left(t<br><br><br><br>{\mathrm{\tau <br><br>}}_1\right)+\frac{X_M}{\sqrt{{\left(R_1+D+R_2\right)}^2-X_M^2}}*\left\{2<br><br>R_1<br><br>\left(1-\frac{3<br><br>{\mathrm{\tau <br><br>}}_1^2}{10}+\frac{5<br><br>{\mathrm{\tau <br><br>}}_1^4}{216}-\frac{7<br><br>{\mathrm{\tau <br><br>}}_1^6}{9360}\right)-R_1<br><br>\mathrm{Cos}<br><br><br><br>{\mathrm{\tau <br><br>}}_1+2<br><br>R_2<br><br>t<br><br>\left\{1-\frac{3<br><br>{\left(t<br><br><br><br>{\mathrm{\tau <br><br>}}_1\right)}^2}{10}+\frac{5<br><br>{\left(t<br><br><br><br>{\mathrm{\tau <br><br>}}_1\right)}^4}{216}-\frac{7<br><br>{\left(t<br><br><br><br>{\mathrm{\tau <br><br>}}_1\right)}^6}{9360}\right\}-R_2<br><br>t<br><br><br><br>\mathrm{Cos}<br><br>\left(t<br><br><br><br>{\mathrm{\tau <br><br>}}_1\right)\right\}$

where t represents a constant value, and X_M represents a function of an unknown value τ

₁.

6. In a method for designing a road, an improvement comprising calculating A in an Egg-shaped clothoid with R₁, R₂, D being known values and R₁ being a radius of a larger circle and R₂ being a radius of a smaller circle and D being a shortest distance between circumferential portions of the two circles, a method for calculating an egg-shaped clothoid parameter, comprising:

a step in which an initial value of a tangential angle τ

₁ of the radius R₁ is set;

a step in which the tangential angle τ

₁ is compared with 0, and when a result of the comparison is less than 0, since it means there is no solution, the process is stopped, and when a result of the same is greater than 0, a value of (R₁−

R₂−

D)²−

X_M² is calculated, X_M² being a function of an unknown value τ

₁;

a step in which the value of (R₁−

R₂−

D)²−

X_M² is compared with 0, and when a result of the comparison is less than 0, τ

₁ is properly adjusted, and the routine goes back to the next step of setting the initial value of the tangential angle τ

₁, and when a result of the same is greater than 0, the function F(τ

₁) is calculated and the function F′

(τ

₁) which is differentiated with τ

₁ from the function F(τ

₁) is calculated;

a step in which a ratio $G=\frac{F<br><br>\left({\mathrm{\tau <br><br>}}_1\right)}{F^{\mathrm{\prime <br><br>}}<br><br>\left({\mathrm{\tau <br><br>}}_1\right)}$

is calculated;

a step in which τ

₁=τ

₁−

G is calculated (τ

₁ is reduced by G); and

a step in which an absolute value of G is compared with a tolerance of 10<sup>−

6</sup>, and as a result of the comparison when the absolute value of G is greater than the tolerance, the routine is fed back to the next step where the initial value of τ

₁ is set, and when it is less than the tolerance, the tangential angle τ

₁ is determined, and the value of parameter A is easily calculated using the tangential angle τ

₁.

7. The method of claim 6, wherein said function F(τ

₁) is as follows;

$F<br><br>\left({\mathrm{\tau <br><br>}}_1\right)=\frac{2}{3}<br><br>R_2<br><br>\left\{{\left(t<br><br><br><br>{\mathrm{\tau <br><br>}}_1\right)}^2-\frac{{\left(t<br><br><br><br>{\mathrm{\tau <br><br>}}_1\right)}^4}{14}+\frac{{\left(t<br><br><br><br>{\mathrm{\tau <br><br>}}_1\right)}^6}{440}-\frac{{\left(t<br><br><br><br>{\mathrm{\tau <br><br>}}_1\right)}^8}{25200}\right)-\frac{2}{3}<br><br>R_1(<br><br>{\mathrm{\tau <br><br>}}_1^2-\frac{<br><br>{\mathrm{\tau <br><br>}}_1^4}{14}+\frac{{\mathrm{\tau <br><br>}}_1^6}{440}-\frac{{\mathrm{\tau <br><br>}}_1^8}{25200}\}+R_2<br><br>\mathrm{Cos}<br><br>\left(t<br><br><br><br>{\mathrm{\tau <br><br>}}_1\right)-R_1<br><br>\mathrm{Cos}<br><br><br><br>{\mathrm{\tau <br><br>}}_1+\sqrt{{\left(R_1+R_2+D\right)}^2-a^2}$

where t represents a constant value, and a represents

a represents $2<br><br>R_2<br><br>\left\{\left(t<br><br><br><br>{\mathrm{\tau <br><br>}}_1\right)-\frac{{\left(t<br><br><br><br>{\mathrm{\tau <br><br>}}_1\right)}^3}{10}+\frac{{\left(t<br><br><br><br>{\mathrm{\tau <br><br>}}_1\right)}^5}{216}-\frac{{\left(t<br><br><br><br>{\mathrm{\tau <br><br>}}_1\right)}^7}{9360}\right)-R_2<br><br>\mathrm{Sin}<br><br>\left(t<br><br><br><br>{\mathrm{\tau <br><br>}}_1\right)-\left\{2<br><br>R_1(<br><br>{\mathrm{\tau <br><br>}}_1-\frac{<br><br>{\mathrm{\tau <br><br>}}_1^3}{10}+\frac{{\mathrm{\tau <br><br>}}_1^5}{216}-\frac{{\mathrm{\tau <br><br>}}_1^7}{9360})-R_1<br><br>\mathrm{Sin}<br><br><br><br>{\mathrm{\tau <br><br>}}_1\right\}$

8. The method of claim 6, wherein said function of F′

(τ

₁) is as follows;

$F^{\mathrm{\prime <br><br>}}<br><br>\left({\mathrm{\tau <br><br>}}_1\right)=\frac{2}{3}<br><br>R_2<br><br>\left(2<br><br>{t<br><br>}^2<br><br>{\mathrm{\tau <br><br>}}_1-\frac{4<br><br>t^4<br><br>{\mathrm{\tau <br><br>}}_1^3}{14}+\frac{6<br><br>t^6<br><br>{\mathrm{\tau <br><br>}}_1^5}{440}-\frac{8<br><br>t^8<br><br>{\mathrm{\tau <br><br>}}_1^7}{25200}\right)-\frac{2}{3}<br><br>R_1\left(2<br><br><br><br>{\mathrm{\tau <br><br>}}_1-\frac{4<br><br><br><br>{\mathrm{\tau <br><br>}}_1^3}{14}+\frac{6<br><br><br><br>{\mathrm{\tau <br><br>}}_1^5}{440}-\frac{8<br><br><br><br>{\mathrm{\tau <br><br>}}_1^7}{25200}\right\}+R_2<br><br>t<br><br><br><br>\mathrm{Sin}<br><br><br><br>\left(t<br><br><br><br>{\mathrm{\tau <br><br>}}_1\right)+R_1<br><br><br><br>\mathrm{Sin}<br><br><br><br>{\mathrm{\tau <br><br>}}_1-\frac{X_M}{\sqrt{{\left(R_1+R_2+D\right)}^2-X_M^2}}*\hspace{1em}<br><br>\left[\begin{array}{c}2<br><br>R_2<br><br>\left\{t-\frac{3<br><br>t^3<br><br>{\mathrm{\tau <br><br>}}_1^2}{10}+\frac{5<br><br>t^5<br><br>{\mathrm{\tau <br><br>}}^4}{216}-\frac{7<br><br>t^7<br><br>{\mathrm{\tau <br><br>}}_1^6}{9360}\right\}-{\mathrm{tR}}_2<br><br>\mathrm{Cos}<br><br>\left(t<br><br><br><br>{\mathrm{\tau <br><br>}}_1\right)-\\ 2<br><br>R_1(<br><br>1-\frac{<br><br>3<br><br>{\mathrm{\tau <br><br>}}_1^2}{10}+\frac{5<br><br>{\mathrm{\tau <br><br>}}_1^4}{216}-\frac{7<br><br>{\mathrm{\tau <br><br>}}_1^6}{9360})+R_1<br><br>\mathrm{Cos}<br><br><br><br>{\mathrm{\tau <br><br>}}_1\end{array}\right]$

where X_M=X_M2−

X_M1, t represents a constant value, and X_M represents a function of an unknown value τ

₁.

9. The method of claim 6, wherein said step for calculating a solution of the functions of F(τ

₁) and F′

(τ

₁) based on a non-linear method is achieved using one selected from the group consisting of the Newton-Rapson equation method, bisection method, secant method, regular false method, Aitken method, successive substitution method, Bairstow'"'"'s method, fixed point repeating method, Muller method or repeating method.

10. The method of claim 6, wherein in said step for calculating A with functions F(τ

₁) and F′

(τ

₁) with respect to τ

₁, when A is calculated with functions of F(τ

₁), F′

(τ

₁) with respect to L₁, or with functions of F(τ

₂), F′

(τ

₂) with respect to τ

₂, or with functions of F(L₂), F′

(L₂) with respect to L₂, and a value of A is obtained, a same result for A is obtained.