Connections

To conclude this section on propulsion principles, we connect the concepts and results of this section with the objectives of propulsion as presented in the Objectives section

**Speed and Acceleration:** For an animal to capture prey or avoid a predator, or for one vehicle to intercept another, it is desirable to accelerate quickly and maintain a high top speed. The controlling factor for these characteristics is thrust. A large thrust will provide a large acceleration from rest and a large cruise velocity. Based on , a large *V _{e}* or is required for large thrust. At the same time, increasing or

**Range and Endurance:** The ability to maximize distance traveled (range) or the total time the propulsion system is active (endurance) also depends strongly on the performance of the propulsion system. To begin with, the rate of energy expended by a propulsion system may be expressed as

where is the rate at which fuel mass or energy stores are used up and *Q _{f}* is the energy density (energy per unit mass) of the fuel or stored energy. Using this result in the definition of overall efficiency we have,

Thus, higher efficiency leads to a lower rate of fuel consumption. In particular, if we use this result to solve for the range, *R*, of a vehicle at a constant velocity we can show that

for flying vehicles (aircraft and birds), and

for submarines and fish. In these results, *m _{f}* is the total mass of fuel/energy stores on board and

Hence, *η*_{0} directly affects endurance as well.

For examples of cases where large range and/or endurance are crucial, see the Objectives section.