### Introduction to Diesel Train Physics

**Aim -** this section describes the general key physics of diesel Locomotives operation.

#### Index

#### Introduction

The Diesel locomotive as the name implies is driven by a diesel engine. The diesel engine, or prime mover, produces the power to drive the locomotive forward and pull the train. The power produced by the prime mover is transmitted to the driving wheels, by a number of different transmission systems including mechanical transmission, electric traction motors, or hydraulic drive systems. The diesel typically is cheaper to operate then a steam locomotive, and some of the other advantages include the fact that they can be operated in multiple units with a single driver, they can be started or sindexped almost instantaneously compared to a steam locomotive which requires time to build up steam.

To understand the performance of a diesel locomotive the following three subjects will be considered:

- Power
- Tractive Effort
- Adhesion

Once the above three elements are considered in conjunction with the train resistances, we can model the overall performance of the train.

#### Power

The amount of force (or effort) available at the rail to drive the locomotive forward will be determined by the diesel engine (prime mover) and the transmission system which converts the mechanical enegry of the prime mover to an energy force at the rails. In the case of a diesel electric DC locomotive, the prime mover drives a DC electric generator, which in turn supplies electricity to the DC traction motors which then drive the locomotive wheels. Each of these power conversions suffer from some form of loss, which means that the full power of the prime mover, is not available to the rails for the diesel's tractive effort.

The following diagram from the BR Deltic Locomotive test report shows the power outputs at the end of each conversion stage. By studying the diagram we can note the following:

**Output at Engine Shaft**(Prime Mover) - This is the power that is provided by the diesel prime mover, and in the case of the Deltic locomotive it was 3,300hp. Typically this is the "rated power" of the locomotive, however it is not the power supplied to the rails to drive the train forward.**Generator Input**- This the power that is supplied to the generator in order to produce the energy required to drive the traction motors. It will be noted that there has been a small reduction in power to support the operation of auxiliary equipment, such as auxiliary generator, radiator fan, etc.**Generator Output & Motor Input**- This is the power that is available to drive the traction motors, and again a small amount of power has been lost due to generator.**Rail HP**- This is the power that is available to drive the locomotive forward and measured at the wheels of the locomotive. Again, power losses have occured due to losses in the traction motors and gearing transmissions.**Drawbar HP**- This is the power that is available to drive the locomotive forward, and power losses have occured due to losses in the traction motors and gearing transmissions. The main loss in power in this instance is due to the resistance to movement that the locomotive presents.

Often the amount of power produced at each stage is converted to a fraction of the main output power, and this demonstrates the efficiency of the power conversion process. Ideally this should be 1 (or 100%) in an ideal world, however this is never the case, and will always be a lower value then the input power value.

By studying the test report for a BR Class D16/2 locomotive, we find the following information:

**Prime Mover**- As indicated, most diesel locomotives are rated on the output power of their prime mover, so in this case the Class D16/2 has a 2000hp prime mover. However some of its energy output goes into driving the locomotive auxiliaries, such as auxiliary generator, radiator fan, etc. Approximately 120 hp is used for the auxiliary equipment, which leaves approximately 1880 hp for tractive use (see pg 14 - item e).**Generator**- The generator has an effciciency of approximately 94%, thus the effective output from the generator is approximately 1767 hp (1309 kW) (see pg 22 - item e).**Traction Motors and Gears**- The traction motor and gears have an effciciency of approximately 88%, thus the maximum effort power available to be applied to the rail is approximately 1555 hp (1152 kW).

The overall effciency of the locomotive can be calculated by combining the last two items above together to get a value of 83%. Thus a value of approximately 80% can sometimes be used to calculate the maximum effective power available to be applied to the rails for a diesel locomotive, however a better way is to use any information published about the tractive forces, see the next section.

As the net power produced by the locomotive remains constant for any given throttle setting, the diesel locomotive is often called a "constant power" locomotive.

#### Tractive Effort

In specifying a diesel locomotive it is quite common to define a design tractive effort curve against the locomotive speed. The diagram below shows an example of one.

The following points are worth noting from the diagram:

**Maximum Tractive Effort**- is the maximum force that can be applied to the wheels without causing damage to the locomotive, or exceeding its adhesion limits. This force is shown by the blue curve in the graph below. For our demonstration model, 50,000lbf.**Continuous Tractive Effort**- indicates the continuous or constant force that can be maintained indefinitely on the wheels to drive the locomotive forward. Typically Force = Power / Speed. Thus as the speed increases the force will decrease, as shown by the red curve in the graph below. For our demonstration model, 30,000lbf @ 19.5 mph.**Maximum Speed**- is the maximum design speed that the locomotive can operate at, and is shown by the green line on the graph below. In our demonstration model, it is 90 mph. The tractive force does not go to zero at this point, instead it falls at a dramatic rate as the traction motors may not be capable of providing significant output power beyond this speed.**Adhesion**- Sometimes, a value of adhesion is also provided as a reference. This would indicate the adhesion value of the locomotive at this point of reference.

##### Relationship between Power and Tractive Force

The Rail HP can be converted to tractive effort (force) by one of the following formulas, which can be rearranged to convert between Tractive Force and Power or vicer versa.

**Imperial: TF (lbf) = (375 x Rail HP ) / speed (mph)**

Metric: TF (N) = Rail Power (W) / speed (metres per sec)

Metric: TF (N) = Rail Power (W) / speed (metres per sec)

Given that most diesel locomotives have specification information for the tractive forces, we can use the above formula to calculate the maximum rail hp at the design speed of maximum continuous force point, which is then assumed to be constant. Once determined we can then convert backwards again to find the tractive force at any speed.

In more recent years diesel locomotive using AC traction motors have become more popular, as they can produce higher tractive effort (force) then DC locomotives, because of the following possible modifications (see Republic Locomotives site for a more detailed explanation):

**Constant Tractive Effort**- the AC can maintain a constant tractive effort by monitoring torque levels at their maximum, and preventing wheel slip.**Variable Frequency Drive**- creates a rotating magnetic field which always spins faster then the rotor speed of the traction motor, and thus ensures minimal wheel slip.**Variable Adhesion**- the AC locomotive is able to use weight transfer compensation, thus when a lightly loaded axle is detected force on this axle will be reduced and transferred to a more heavily loaded axle.

It should be noted that use of the above formulas on AC locomotives may give Power values higher then the prime mover output, in this case, the power values should be considered as "apparent power".

#### Adhesion

The adhesion between the wheels and the rail will determine the amount of force that can be applied to moving the train, and hence the amount of load that the locomotive can haul. A more detail description of adhesion can be found on the adhesion page, and whilst it principally deals with adhesion on steam locomotive, a diesel locomotive has similar issues with adhesion. The main difference between steam and diesel traction is that the tractive force of a diesel is constant for the full wheel rotation, whereas due to the operating rods attached to a steam locomotives wheel the force is not even around the full roatation of the wheel.

As with the steam locomotive the diesel will suffer wheel slip if the rotational force exceeds the adhesive force.

#### Load Hauling Performance

Once the parameters are determined for the ENG file, load hauling performance tests should be undertaken to confirm that the locomotive performance is within acceptable bounds for the locomotive being modelled.

Often in test reports the Traction Draw Bar Tractive Effort (Traction DBTE) is used to describe the pulling power of the locomotive. This is calculated by considering the impact of the locomotive resistance, trailing load resistance, and gross weight ratio, on the tractive effort calculated above. A detailed explantaion of how to calculate this value can be found on pg 48 of the test report in the Useful References section below. This is the amount of force that is available to overcome the resistance offered by the trailing load behind the locomotive. The graph below shows the Traction DBTE for a diesel locomotive, as well as the trailing load resistance for a 300 ton train on various different gradients.

So for example, with a load of 300 ton the Traction DBTE will vary with speed as shown by the green curve. If the train is climbing a 1 in 80 gradient the trailing load resistance is shown by the red curve. The point where the two curves cross designates the "balancing speed", ie the maximum speed that the locomotive can travel when climbing a 1 in 80 grade with a 300 ton load.