rail_resistance - CEE 3604 Rail Transportation: Addendum...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: CEE 3604 Rail Transportation: Addendum Rail Resistance Equations 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 R = A + BV + CV 2 • 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 ( Ns 2 / m 2 ) are regression coefficients obtained by fitting test data to the Davis equation Transportation Engineering (A.A. Trani) 2 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. Transportation Engineering (A.A. Trani) 3 Davis Equation - Committee 16 of AREA (American Railway Engineering Association) 20 KV 2 Ru = 0.6 + + 0.01V + w wn • • where: • Values of K are 0.07 for conventional equipment, 0.0935 for containers and 0.16 for trailers on flatcars 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 a drag coefficient Transportation Engineering (A.A. Trani) 4 Additional Terms to the Davis Equation (Gradient Forces) Mg RG ( kN ) = X • • where: RG is the resistance (kN) due to gradients, M is the mass of the train in metric tons, g is the acceleration due to gravity (m/s2) and X is the gradient in the form 1 in X (for example: a grade of 3% is expressed as X = 1/0.03 = 33.33 in the formula above) Transportation Engineering (A.A. Trani) 5 Additional Terms to the Davis Equation (Resistance due to Curvature) k rc ( kN / t ) = 0.01 Rc • • 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). Transportation Engineering (A.A. Trani) 6 Application of Davis Equation to a High-Speed Rail System (Japan Shinkansen Series 200) per Rochard and Schmid1 R = 8.202 + 0.10656V + 0.01193V 2 • • where: R is the total resistance (kN), V is the speed of the train (m/s) train 1A review of Methods to Measure and Calculate Train Resistances (Proceedings of the Institute of Mechanical Engineers,Vol. 214 Part F) Transportation Engineering (A.A. Trani) 7 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 kN B = 0.10656; % units are kN s/m C = 0.0119322; % units are kN s-s/m-m % Create a speed vector V = 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') Transportation Engineering (A.A. Trani) 8 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 Transportation Engineering (A.A. Trani) 9 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) VT P= η • where: P is the power output delivered by the engine, T is the tractive force or effort, η is the efficiency in converting power output to tractive force and V is the velocity of the vehicle Transportation Engineering (A.A. Trani) 10 Tractive Force or Effort in Typical Units ηP T = 2650 V • T in Newtons • P in horsepower • V in km/hr Transportation Engineering (A.A. Trani) 11 Matlab Script to Calculate Tractive Effort (Shinkansen Series 200) % 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 Transportation Engineering (A.A. Trani) 12 Resistance or Tractive Effort (kN) Plot of Resistance and Tractive Force vs Speed Tractive Force η = 0.7 Resistance Force Speed (m/s) Transportation Engineering (A.A. Trani) 13 Observations • According to these plots, the high-speed rail system will reach its maximum velocity at 82.8 m/s (298 km/hr) • The value of efficiency has been assumed to be 0.7 (conservative) • The plot applies to level ground (zero gradient) Transportation Engineering (A.A. Trani) 14 ...
View Full Document

This note was uploaded on 12/31/2011 for the course CEE 3604 taught by Professor Katz during the Fall '08 term at Virginia Tech.

Ask a homework question - tutors are online