1. Introduction
In recent years, the use of UAVs has increased in many fields, including agriculture and transportation. These UAVs can be categorized as fixed-wing UAVs or rotary-wing UAVs. Fixed-wing UAVs have some advantages over rotary-wing UAVs, from the viewpoint of better energy efficiency in flight, more payloads, and higher cruising speeds. For this reason, they are most effective when used for long flight distance. Therefore, they are expected to be used in fields such as observation and transportation.
As fixed-wing UAVs in those fields are generally used out of sight, they can fly autonomously for all flight modes such as takeoff, cruise, and landing. Of these flight modes, there are a few studies on the takeoff mode of fixed-wing UAVs. Some takeoff studies have been conducted on VTOL aircraft: a study on generating a takeoff trajectory with minimum power consumption for tilt-wing aircraft [
1], a study on maximizing payload weight by simultaneously optimizing the conceptual aircraft design and takeoff trajectory [
2], and a study on deriving the optimal takeoff trajectory for tilt-rotor aircraft [
3]; others are part of studies of autonomous flight covering the entire flight, from takeoff to cruise and landing [
4,
5]. However, VTOL equipment in aircraft lead to an increase in aircraft weight, which reduces the aircraft’s endurance range and cruising speed. On the other hand, studies of autonomous flight from takeoff to landing have not considered the optimization of parameter settings during takeoff [
4] nor have they mentioned parameter settings [
5].
On the other hand, in recent years, studies [
6,
7] have been conducted on takeoff with regard to manned fixed-wing aircraft. Study [
6] evaluates the aerodynamic performance of channel wings that increase lift and contribute to a short takeoff, and study [
7] estimates the takeoff performance of an aircraft equipped with a DEP (Distributed Electric Propulsion) blown wing that increases lift. However, those techniques in the above studies deal with the improvement of takeoff performance by using new wings, and require hardware modifications or an increase in the amount of propulsion equipment.
Generally, takeoff performance is specified by runway distance and takeoff time. This study aims at minimizing the takeoff time so that the mission can be started quickly. However, it costs a lot to reduce the time required to run because modifications of engines and aircraft hardware are required. Therefore, this study focuses on the takeoff time among the above takeoff performance parameters, and deals with a climb phase during the takeoff.
Until now, no study has attempted to minimize takeoff time by optimizing the takeoff trajectory. A manned airplane generally climbs at a minimum climb angle during takeoff, even if the airplane is capable of climbing well above the minimum climb angle [
8]. The climb angle is determined by the height of obstacles and other objects on the takeoff trajectory. However, fixed-wing UAVs can climb by making the best use of their capability instead of the provisions required for a manned airplane.
As for conventional studies on climb, there is a study that obtained the shortest time climb trajectory based on the concept of energy altitude [
9], a study that obtained the maximum climb angle trajectory of a supersonic interceptor using the steepest descent method [
10], a study that derived the optimal climb trajectory for a supersonic airplane with different numbers of state variables using sequential quadratic programming and investigated changes in the trajectory [
11], and a study that obtained the shortest climb trajectory for a supersonic airplane with a large thrust-to-weight ratio using the steepest descent method [
12]. However, these studies are characterized by the use of jet engines as the propulsion system for the target airplane. Moreover, it generally takes a lot of time to numerically calculate the optimal climb paths of the airplane, because the above studies dealt with a dynamic system. Therefore, in this study, assuming that the transition time from run to climb is short, the steady climb section, which occupies most of the takeoff time, is targeted and solved as a static problem to shorten the takeoff time.
Considering the above circumstances, this paper, aiming at reducing the takeoff time of an airplane without VTOL equipment, proposes a new method to realize a maximum rate of climb for fixed-wing UAVs driven by propeller engines. The method is based on an optimization problem with equal constraints, an example of which in the aerospace field is generally known as a maximum steady state rate of climb for airplanes [
13]. In the example, the characteristics of the propeller engine are not taken into account.
The proposed technology in this study requires that the aerodynamic and thrust characteristics of the fixed-wing UAV should be known with sufficient accuracy in advance. If the aerodynamic characteristics are unclear, a sudden rotation and climb will lead to a stall in a real flight environment, so it is necessary to have a good understanding of the characteristics.
Propeller engines are often used as propulsion equipment for fixed-wing UAVs because they are cheaper and easier to handle than jet engines. However, the thrust generated by propeller engines varies according to the airspeed of the fixed-wing UAVs. It is not easy to theoretically obtain the characteristics of a propeller engine, i.e., they should be calculated by using detailed data on the propeller shape through wind tunnel tests [
14]. Therefore, how to incorporate the propeller engine characteristics is very important and should be clarified.
The takeoff profile of a fixed-wing UAV is usually divided into three phases: run phase, rotation phase, and climb phase, as shown in
Figure 1 [
15]. In this paper, only a climb phase is dealt with in order to clarify the effectiveness of our method. First, the equations of equilibrium acting on the airplane during a steady climb are described in
Section 2, followed by an explanation of how to derive the maximum rate of climb using optimization problems. The equation relating the thrust generated by the propeller engine to airspeed, the specifications of the airplane under consideration, and the calculation results of the maximum rate of climb are also described.
Section 3 describes the results of a 6-DOF flight simulation conducted to confirm whether the maximum rate of climb obtained from the analysis of a mass system can be realized in an actual 6-DOF environment. The section also describes the control system to achieve steady climb at the maximum rate of climb used in the 6-DOF flight simulation.
Section 4 describes the criteria and experimental results of the steady climb in the flight experiments using the model airplane to confirm the validity of the maximum rate of climb, and finally
Section 5 concludes the study.