Guys,
The question of whether Streamlining a locomotive is effective or not is answered via the application of some physics F = MA.
There have been some miss quotes given assigning weight and the aero components as being dependent upon one another.
Below I've sighted a discussion that speaks to how tractive effort is calculated. These equations are used every day by automotive engineers to determine the impact of weight, aero, rolling resistance and grade changes on Fuel Economy and Vehicle Performance. It is important to understand that when speaking to the aerodynamics of a vehicle that we keep in mind the Cd and Frontal Area of the vehicle. Cd known as the coefficient of drag is a dimensionless coefficient related to the object's geometry and taking into account both skin friction and form drag.
As noted earlier, aerodynamic drag increases with the square of speed, thus it plays a critical roll at higher vehicle speeds.
The frontal area of a steam locomotive is very high. Typically one would take the width and multiply height to get the area. However as you know it also has many, many nooks and crannies which increases the frontal area. I can't even imagine what the FA of 765 would be for example. It would be necessary to have it measured by a very specialized piece of equipment that uses laser technology. This unit isn't portable and neither is 765 (very easily).
Thus shrouding the engine (streamlining) would definitely significantly improve the engines aerodynamics by the elimination of openings and places where the air can become trapped. And since it is speed dependent, it would benefit the operation by saving fuel costs. The streamlining would also have to extend to the coaches as well, the gap between the cars would have to be closed, the sides smoothed and the entire undercarriage of the locomotive and cars would have to be streamlined as well. This may be a surprise to some, but the streamlining of the undercarriage is very important. In some cases a simple air dam and some streamlining extending just past the front wheels of a vehicle is enough to get laminar air flow under the vehicle.
Additionally, the Cd of the whole train can be negatively impacted by cross winds which would increase the Cd value.
The mass of the locomotive comes into play only when determining the rolling resistance, inertia and grade forces.
The following is from: ENERGY LOSSES FOR PROPELLING AND BRAKING CONDITIONS OF AN ELECTRIC VEHICLE
by Lynn Rupert Gantt (This paper can be found online).
A vehicle in motion experiences a set of forces (including road load), which determines the minimum FORCE at the wheels (known as tractive effort) required to meet a given speed and acceleration.
Tractive effort can be broken down into four main categories, tire rolling resistance (Frolling), aerodynamic drag (Faero), overcoming the current vehicle state of motion (Finertia), and finally the grade or inclination that the vehicle is travelling on (Fgrade). See Equation: 1
Equation 1: Ftractive = Frolling +Faero +Finertia +Fgrade
The individual components of the equations break down thusly:
Here, Crr0 is the coefficient of rolling resistance, Crr1 coefficient of rolling resistance affected by Velocity (not always included), m is vehicle mass, g is the acceleration due to gravity, P (roh) is the density of air, Cd is the coefficient of drag, Af is the frontal area of the vehicle, V is the velocity for the drive cycle, Mi is an inertial mass factor term to account for the rotating inertia of the wheels, tires, and other rotating components, dv/dt is the acceleration from one time step to the next for the drive cycle, and Theta (related to grade) is the angle of incline. For normal inclines, the cos(theta) term that could be included in Equation 2 is approximated as 1.
Equ 2: Frolling = Crr0mg+ Crr1mgV
Equ 3: Faero = 1/2mgPCdAfV^2
Equ 4: Finertia = mMidv/dt
Equ 5: Fgrade = mgsin(theta)=mg∗grade
Variable Definitions
Crr0 Static coefficient of rolling resistance [-]
Crr1 Moving coefficient of rolling resistance [-]
m Vehicle test mass kg
g Gravity m/s2
V Velocity m/s
P Density of air kg/m3
Cd Coefficient of Drag [-]
Af Frontal Area m2
Mi Inertia mass factor [-]
dv/dt Drive cycle acceleration m/s2
Theta Degree of inclination [theta]
Hope this helps answer some of your concerns.
There was a posting earlier that quoted some similar equations, but that posting has since been deleted or edited. Could the person who had the locomotive Force equations please post them again or provide a link to the article?
Thanks