## 3 Conversion of Rotational Energy into Translational Vehicle Energy  
Pulsed propulsion by centrifugal force modulation can be applied in two modes of rotor energy management:  
1. The rotor could be used with an integrated onboard drive, able to deliver high and sustained electrical power output during the complete mission. Low weight and compact design of such a combined power/propulsion system well suited onboard a small UAV must be achieved here, which is not even an easy engineering task;
2. Alternatively, the rotor will be brought to operating speed before takeoff through temporary mechanical coupling with a powerful external electric motor. The advantage of this pure inertial solution is its much lower weight and more simplicity of the onboard propulsion system. But here the question arises: is there enough energy onboard such a UAV, and how much is its flight performance and maneuverability limited? We will focus here on the management of this second energy mode because it seems better suited for small UAVs, at least in the present state of technology. Furthermore, if the successful combination of (1) and (2) would be feasible in the future, our focus will deliver advanced performance. When discussing the conversion of rotational energy \((E_{rot})\) into translational energy \((E_{trans})\) in the context of a UAV, it is important to consider the conservation of total kinetic energy \((E_{0})\) onboard the vehicle. According to the energy theorem, the total kinetic energy must remain constant. Therefore, we can express this conservation using the following Equation:  
\[E_{0}=E_{rot}+E_{trans}=const. \tag{10}\]  
At the beginning of the takeoff scenario, when the UAV is at the starting point (\(x=0\)), the maximum rotational energy is available. This can be represented as follows:  
\[\max E_{rot}=\frac{1}{2}\theta\omega_{0}^{2}=E_{0} \tag{11}\]  
with the moment of disc inertia  
\[\theta=\frac{1}{2}MR^{2}\]  
and a maximum of rotation frequency:  
\[\omega_{0}=2\pi f_{0}\]  
According to (11), storable rotation energy increases proportional to rotor mass \(M\) and with the square of the disk radius \(R\) and square of rotation frequency \(f_{0}\). Thus, for a given size and material of the rotor disk, a doubling of its rotation frequency \(f_{0}\) will result in a quadruple of mechanically stored airborne energy. Our conclusion: The store parameter \(f_{0}\) is of high importance in flight performance evaluation. As per Equation (11), the amount of storable rotational energy increases proportionally with the rotor mass (\(M\)), the square of the disk radius (\(R^{2}\)), and the square of the rotation frequency \(f_{0}\). Therefore, if the rotation frequency \(f_{0}\) is doubled while keeping the size and material of the rotor disk constant, the mechanically stored airborne energy will quadruple. This highlights the significance of the rotation frequency (\(f_{0}\)) as a parameter in evaluating flight performance (refer to Section 4 for more details). On the other hand, assuming ideal conditions in energy conversion, i.e., friction-free disc rotation and vehicle translation) and zero gravity space, the potential maximum of translational energy appearing at the end of energy conversion is given by  
\[\max E_{trans_{s}}=E_{0}=\frac{1}{2}M^{\prime}v_{max}^{2}=MR^{2}\pi^{2}f_{0}^{2} \tag{12}\]  
This assumption is equivalent to 100% efficiency in the conversion of the rotational energy to translational propulsion. It is also important to note that \(M^{\prime}\) is larger than \(M\), as \(M^{\prime}\) represents the total mass of the UAV while \(M\) only represents the smaller mass of the rotor disc. The vehicle construction factor \(C\), which is the ratio of \(M^{\prime}\) to \(M\), can be assumed to be between 1 and 2 in realistic scenarios.