topic
With the continuous development of science and technology, drones are widely used in many fields. For UAVs that perform fixed-point delivery tasks in the air, their delivery accuracy not only depends on the operation technology of the UAV, but also is related to the state and environment in which the UAV performs the task, such as Factors such as altitude, speed, wind speed at the location of the drone, and the geographical environment around the drop point. Only jet drones are considered in this question, please refer to relevant materials and study the following questions:
Question 1: Assume that the UAV flies parallel to the horizontal plane and drops materials in the air (the materials are spherical, with a radius of 20cm and a weight of 50kg) to the designated location on the ground.
(1) Establish a mathematical model to give the relationship between the drone's drop distance (the straight-line distance between the drone and the designated landing point of the ground material when delivering materials) and the drone's flight height, flight speed, air resistance, etc. .
(2) Assume that the flying height of the UAV is 300m, the flying speed is 300km/h, the wind speed is 5m/s, and the wind direction is parallel to the horizontal plane. Establish a mathematical model to give the drone's launch distance when the flying direction of the drone is the same as the wind direction (the included angle is 0 degrees), opposite (the included angle is 180 degrees), and vertical (the included angle is 90 degrees).
Question 2: UAVs can not only drop materials at fixed points, but also launch explosives through the launch tube installed at the front of the UAV to clear the river. The general process is: the drone first flies horizontally close to the area where the obstacle is located, then dives to find the right time to launch the explosives, and then pulls up and flies away after the launch. A river is currently blocked by ice accumulation, and it is necessary to use a drone to launch explosives (the explosives are spherical, with a radius of 8cm and a weight of 5kg) to blast the target. Assume that the horizontal distance from the initial point of the UAV to the target is 10000m. Affected by the environment, the drone must dive and launch, and the launch direction is consistent with the flight direction of the drone.
(1) Establish a mathematical model to give the relationship between the UAV launch distance (the linear distance between the launch point and the target) and the UAV's flight altitude, flight speed, dive angle, and launch speed.
(2) Assuming that the wind speed is 6m/s, the flying altitude of the drone is 800m, the flying speed is 300km/h when it approaches the target, and the launch speed of the explosive is 600km/h (relative to the speed of the drone). It is required that the distance between the UAV and the target is between 1000 m and 3000 m when launching explosives, and the height of the UAV is not lower than 300m. Please give the launch strategy for the UAV to hit the target.
Question 3: The accuracy of the UAV launching explosives and hitting the target has a lot to do with the stability of the UAV flight. Under the same conditions, the more stable the UAV is when launching explosives, the higher the accuracy of hitting the target. After starting to dive, the UAV operator needs to constantly adjust the flight attitude of the UAV to correct the influence of wind direction and wind speed on the UAV.
(1) In the case of a certain flight speed and launch speed, various factors are considered comprehensively, a mathematical model is established, the stability of UAV flight is quantified, the relationship between stability and hit accuracy is given, and numerical simulation, etc. The method is to analyze and verify the stability of the UAV.
(2) Assuming that the wind speed is 6m/s, the flight speed range of the UAV is 300 km/h -400 km/h, and the launch speed of explosives is 500km/h (relative to the speed of the UAV). The UAV starts to dive at an altitude of 800m, the initial dive angle is 45°, and the flying height when launching explosives is not lower than 300m. Please give the optimal adjustment strategy for the flight attitude to keep the UAV as stable as possible.
problem one idea
Problem two ideas
Question three ideas
