rail resistance 2019 - 128.173.204.63
Transcript of rail resistance 2019 - 128.173.204.63
![Page 1: rail resistance 2019 - 128.173.204.63](https://reader034.fdocuments.in/reader034/viewer/2022042403/625da1e19c3b7f4a6d258b87/html5/thumbnails/1.jpg)
Transportation Engineering (A.A. Trani)
CEE 3604 Rail Transportation: Addendum
Rail Resistance Equations
1
![Page 2: rail resistance 2019 - 128.173.204.63](https://reader034.fdocuments.in/reader034/viewer/2022042403/625da1e19c3b7f4a6d258b87/html5/thumbnails/2.jpg)
Transportation Engineering (A.A. Trani)
Fundamental Formula
• A quadratic formula has been used for over 80 years to approximate rail vehicle resistance
• von Borries Formel, Leitzmann Formel, Barbier and Davis worked on this equation
• where R is the rail vehicle resistance (N), V is the velocity of the vehicle (m/s), and A (N), B (N s/m) and C ( ) are regression coefficients obtained by fitting run-down test to the Davis equation
2
![Page 3: rail resistance 2019 - 128.173.204.63](https://reader034.fdocuments.in/reader034/viewer/2022042403/625da1e19c3b7f4a6d258b87/html5/thumbnails/3.jpg)
Transportation Engineering (A.A. Trani)
Observations
• The coefficients A and B in the Davis equation account for mass and mechanical resistance
• The coefficient C accounts for air resistance (proportional to the square of the speed)
• The Davis equation has been modified over the years for various rail systems and configurations . A few examples are shown in the following pages.
3
![Page 4: rail resistance 2019 - 128.173.204.63](https://reader034.fdocuments.in/reader034/viewer/2022042403/625da1e19c3b7f4a6d258b87/html5/thumbnails/4.jpg)
Transportation Engineering (A.A. Trani)
Davis Equation - Committee 16 of AREA (American Railway Engineering Association)
• where:
• Ru is the resistance in lb/ton, w is the weight per axle (W/n), n is the number of axles, W is the total car weight on rails (tons), V is the speed in miles per hour and K is the drag coefficient
• Values of K are 0.07 for conventional equipment, 0.0935 for containers and 0.16 for trailers on flatcars
4
![Page 5: rail resistance 2019 - 128.173.204.63](https://reader034.fdocuments.in/reader034/viewer/2022042403/625da1e19c3b7f4a6d258b87/html5/thumbnails/5.jpg)
Transportation Engineering (A.A. Trani)
Additional Terms to the Davis Equation (Gradient Forces)
• where:
• RG is the resistance (kN) due to gradients, M is the mass of the train in tons, g is the acceleration due to gravity (m/s2) and X is the gradient in the form 1in X (for example: a grade of 3% is expressed as X = 1/0.03 = 33.33 in the formula above)
5
![Page 6: rail resistance 2019 - 128.173.204.63](https://reader034.fdocuments.in/reader034/viewer/2022042403/625da1e19c3b7f4a6d258b87/html5/thumbnails/6.jpg)
Transportation Engineering (A.A. Trani)
Additional Terms to the Davis Equation (Resistance due to Curvature)
• where:
• rc is the resistance due to curvature (kN/ton), k is dimensionless parameter depending upon the train (varies from 500 to 1200), RC is the curve radius in a horizontal plane (meters).
6
![Page 7: rail resistance 2019 - 128.173.204.63](https://reader034.fdocuments.in/reader034/viewer/2022042403/625da1e19c3b7f4a6d258b87/html5/thumbnails/7.jpg)
Transportation Engineering (A.A. Trani)
Application of Davis Equation to a High-Speed Rail System (Japan Shinkansen Series 200)
per Rochard and Schmid1
• where:
• R is the total resistance (kN), V is the speed of the train (m/s) train
1 A review of Methods to Measure and Calculate Train Resistances (Proceedings of the Institute of Mechanical
Engineers, Vol. 214 Part F)
7
![Page 8: rail resistance 2019 - 128.173.204.63](https://reader034.fdocuments.in/reader034/viewer/2022042403/625da1e19c3b7f4a6d258b87/html5/thumbnails/8.jpg)
Transportation Engineering (A.A. Trani)
Matlab Script to Calculate Resistance Forces (Shinkansen Series 200)
• % Script to estimate the total resistance of a Series 200 train
% Equations provided by Rochard and Schmid (2000) % Coefficients of Davis equation applied to Japanese Shinkansen system% Series 200 A = 8.202; % units are kNB = 0.10656; % units are kN s/mC = 0.0119322; % units are kN s-s/m-m % Create a speed vectorV = 0:1:90; % speed in meters/second % Calculate Resistance (in KiloNewtons) according to modified Davis equation R = A + B * V + C * V.^2; % Make a plot of total resistance vs speed plot(V,R,'o--')xlabel(' Speed (m/s)')ylabel('Resistance (kN)')title('Reisistance of Series 200 Shinkansen Rail System')
8
Picture source: Sui-Setz (Wikipedia)
![Page 9: rail resistance 2019 - 128.173.204.63](https://reader034.fdocuments.in/reader034/viewer/2022042403/625da1e19c3b7f4a6d258b87/html5/thumbnails/9.jpg)
Transportation Engineering (A.A. Trani)
Shinkansen Series 200 Tractive Effort Curve
• The tractive effort can derived from knowledge of the shaft horsepower delivered by the rail engine(s)
• Literature on the Shinkansen indicates that the series 200 locomotives deliver 15,900 HP of power
• Lets assume that a single locomotive pulls a 6-car train unit
9
![Page 10: rail resistance 2019 - 128.173.204.63](https://reader034.fdocuments.in/reader034/viewer/2022042403/625da1e19c3b7f4a6d258b87/html5/thumbnails/10.jpg)
Transportation Engineering (A.A. Trani)
Tractive Effort vs Power
• A fundamental equation to convert power to tractive force (or effort) is shown below
• This equation can be modified to convert units correctly (from HP to Newtons)
10
• where: P is the power output delivered by the engine, T is the tractive force or effort, is the efficiency in converting power output to tractive force and V is the velocity of the vehicle
![Page 11: rail resistance 2019 - 128.173.204.63](https://reader034.fdocuments.in/reader034/viewer/2022042403/625da1e19c3b7f4a6d258b87/html5/thumbnails/11.jpg)
Transportation Engineering (A.A. Trani)
Tractive Force or Effort in Typical Units
• T in Newtons
• P in horsepower
• V in km/hr
11
![Page 12: rail resistance 2019 - 128.173.204.63](https://reader034.fdocuments.in/reader034/viewer/2022042403/625da1e19c3b7f4a6d258b87/html5/thumbnails/12.jpg)
Transportation Engineering (A.A. Trani)
Matlab Script to Calculate Performance for a Shinkansen Series 200 Train
% Coefficients of Davis equation applied to Japanese Shinkansen system% Series 200 plot(V,R,'o--')xlabel(' Speed (m/s)')ylabel('Resistance (kN) or T (kN)')title('Reisistance of Series 200 Shinkansen Rail System')grid hold on % Calculate the Tractive Effort (T) profile P = 15900; % horsepower (hp)Vkmhr = V*3.6; % velocity in km/hr (needed in the TE equation)nu = 0.7; % efficiency T = 2650 * nu * P ./ Vkmhr / 1000; % in kN plot(Vkmhr/3.6,T,'^-r')
grid
12
![Page 13: rail resistance 2019 - 128.173.204.63](https://reader034.fdocuments.in/reader034/viewer/2022042403/625da1e19c3b7f4a6d258b87/html5/thumbnails/13.jpg)
Transportation Engineering (A.A. Trani)
Plot of Resistance and Tractive Force vs Speed R
esis
tanc
e or
Tr
activ
e Ef
fort
(kN
)
Speed (m/s) 13
Tractive Force
Resistance Force
![Page 14: rail resistance 2019 - 128.173.204.63](https://reader034.fdocuments.in/reader034/viewer/2022042403/625da1e19c3b7f4a6d258b87/html5/thumbnails/14.jpg)
Transportation Engineering (A.A. Trani)
Observations
• According to these plots, the high-speed rail system will reach its maximum velocity at 82.8 m/s (298 km/hr)
• Most high-speed trains in the World run at maximum speed that range between 270 and 320 km/hr
• The value of efficiency has been assumed to be 0.7 (conservative)
• The plot applies to level ground (zero gradient)
14
![Page 15: rail resistance 2019 - 128.173.204.63](https://reader034.fdocuments.in/reader034/viewer/2022042403/625da1e19c3b7f4a6d258b87/html5/thumbnails/15.jpg)
Transportation Engineering (A.A. Trani)
Example Calculations for a Cargo Train Using AERA Equation
15
General ElectricES58-ACi
Diesel-ElectricLocomotive6,200 HP
196 metric tons8 axles
Source: Wikipedia
![Page 16: rail resistance 2019 - 128.173.204.63](https://reader034.fdocuments.in/reader034/viewer/2022042403/625da1e19c3b7f4a6d258b87/html5/thumbnails/16.jpg)
Transportation Engineering (A.A. Trani)
Example Calculations for a Cargo Train Using AERA Equation
16
Q1: Calculate the resistance (in lbs/ton) of a GE locomotive with the following specifications
Q2: Calculate the resistance of the GE locomotive with 50 cargo cars (130 tons each)
Q3: Find the maximum speed of the train at zero grade
![Page 17: rail resistance 2019 - 128.173.204.63](https://reader034.fdocuments.in/reader034/viewer/2022042403/625da1e19c3b7f4a6d258b87/html5/thumbnails/17.jpg)
Transportation Engineering (A.A. Trani)
Example Calculations for a Cargo Train Using AERA Equation (GE Locomotive)
17
Source: Wikipedia
![Page 18: rail resistance 2019 - 128.173.204.63](https://reader034.fdocuments.in/reader034/viewer/2022042403/625da1e19c3b7f4a6d258b87/html5/thumbnails/18.jpg)
Transportation Engineering (A.A. Trani)
Example Calculations for a Cargo Train Using AERA Equation (Total Train Set)
18
One GE AES50 locomotiveFifty 130 ton cars6,696 tons (total weight)
Step 1: Use the AERA Equation
Step 2: Multiply the value of Ruby the total weight of the train set
![Page 19: rail resistance 2019 - 128.173.204.63](https://reader034.fdocuments.in/reader034/viewer/2022042403/625da1e19c3b7f4a6d258b87/html5/thumbnails/19.jpg)
Transportation Engineering (A.A. Trani)
Maximum Speed of the Train is 126 km/hr
19
One GE AES50 locomotiveFifty 130 ton cargo cars6,696 tons (total weight)6,200 HP power
Maximum speed
Total Resistance
Tractive Force
![Page 20: rail resistance 2019 - 128.173.204.63](https://reader034.fdocuments.in/reader034/viewer/2022042403/625da1e19c3b7f4a6d258b87/html5/thumbnails/20.jpg)
Transportation Engineering (A.A. Trani)
Class Quick Assignment
20
One GE AES50 locomotiveFifty 130 ton cargo cars6,696 tons (total weight)6,200 HP power
Q4: Find the maximum acceleration at 60 km/hr