262 Nonconstant Ftr General Acceleration

In the general case, with a nonconstant FTR and an arbitrary velocity profile, as shown in Figure 2.16, force can be calculated as follows:

The instantaneous tractive power PTR(t) is

FIGURE 2.16 Arbitrary velocity profile.

The change in tractive energy eTR is

The energy supplied by the propulsion unit is converted into various forms of energy, some of which are stored in the vehicle system, while others are lost due to non-constructive forces. It is interesting to note the type of energy associated with each term in Equation 2.23. Let us consider the first term on the right side of Equation 2.23:


The above term represents change in vertical displacement multiplied by mg, which is the change in potential energy.

The third and fourth terms on the right side of Equation 2.23 represent the energy required to overcome nonconstructive forces that include rolling resistance and aerodynamic drag force. The energy represented in these terms is essentially the loss term. Therefore,

In summary, we can write or

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