## 3 Some Simple One-Dimensional Transport Scenarios  
### Idealized Fly-Through Scenario  
In order to validate the idea of using the entity of physical action as a means of enumerating the physical value of mechanical motion, we consider a scenario in which a mass \(M\) is moving with constant speed \(v_{AB}\) along a straight-line path of length \(L_{AB}\) connecting points \(A\) and \(B\) (see Figure 3). We further assume that this motion is perpendicular to the direction of the earth's gravitational field. The potential energy \(V\) of this mass can therefore be taken as a constant. In particular, we can set \(V=0\) by choosing a Cartesian coordinate system in which the motion of the mass \(M\) occurs along the x-axis and in which the direction of the gravitational field vector points along the negative z-axis. In the following section, we will call such a scenario a \"fly-through\" scenario.  
In this highly idealized case, the kinetic energy of the moving mass is  
\[T=\frac{1}{2}Mv_{AB}^{2} \tag{1}\]  
and  
\[\tau_{AB}=\frac{L_{AB}}{v_{AB}} \tag{2}\]  
is the time required for traversing the distance \(L_{AB}\) with speed \(v_{AB}\). After traversing the length \(L_{AB}\) with velocity \(v_{AB}\), the change in the physical action \(W_{AB}\) becomes:  
\[W_{AB}(M,L_{AB},\tau_{AB})=\int_{0}^{\tau_{AB}}Tdt=\frac{1}{2}Mv_{AB}^{2}\tau_ {AB}=\frac{1}{2}Mv_{AB}L_{AB}=\frac{1}{2}M\frac{L_{AB}^{2}}{\tau_{AB}} \tag{3}\]  
Reference to this latter result shows that the transport value of a mass \(M\) is high, when the distance \(L_{AB}\) is large and when this distance had been covered within a short time \(\tau_{AB}\). This assignment of physical action as a measure of transport value is in line with the pragmatic approach to the problem of transport value, which normally assigns a high money value to long transport paths covered within a short time.  
Accepting the function \(W_{AB}(M,L_{AB},\tau_{AB})\) as a valid measure of physical transport value, various efficiency measures can be defined. As a first measure, we consider the quantity of payload efficiency. This measure becomes relevant when a vehicle of mass \(M\) transports a payload of mass \(m\ll M\):  
\[\eta_{PL}(m,\ M,L_{AB},\tau_{AB})=\frac{m}{M}\ W_{AB}(M,L_{AB},\tau_{AB}) \tag{4}\]  
With this definition of payload efficiency in mind, the transport value of 1 kg of gold and 1 kg of bananas, transported by a truck of 10 tons in weight, is the same and completely independent of the vastly different money values of both items. The physical value of transport, as defined by Equation (4), enumerates the value of delivering both goods, which are initially present at point \(A\), to point \(B\), which is separated from \(A\) by a distance \(L_{AB}\) and with a time delay of \(\tau_{AB}\).  
Another measure of efficiency with high practical relevance is the energy efficiency of transport:  
\[\eta_{E}(M,L_{AB},\tau_{AB})=\frac{W_{AB}(M,L_{AB},\tau_{AB})}{E_{in}}, \tag{5}\]  
where \(W_{AB}(M,L_{AB},\tau_{AB})\) is the transport value already defined in Equation (3), and \(E_{in}\) is the energy that had to be expended to initiate the transport of mass \(M\) over the distance \(L_{AB}\) and in time \(\tau_{AB}\). In the \"fly-through example\", the value of \(E_{in}\) obviously amounts to \(E_{in}=\frac{1}{2}M\
u_{AB}^{2}\), which was applied a long time before entering the transport path \(\stackrel{{\rightarrow}}{{AB}}\) and which remained with the moving mass after it had crossed the distance \(\stackrel{{\rightarrow}}{{AB}}\). Further, as no energy exchange between the transported mass \(M\) and the environment had taken place within \(\stackrel{{\rightarrow}}{{AB}}\), the energy efficiency \(\eta_{E}(M,L_{AB},\tau_{AB})\) formally turns towards infinity, indicating the specific case of a zero-cost transport.