UAV Quadrotor

UAV Quadrotor

A quadrotor, also called a quadrotor helicopter or quadrocopter, is an aircraft that is lifted and propelled by four rotors. Quadrotors are classified as rotorcraft, as opposed to fixed-wing aircraft, because their lift is derived from four rotors. Unlike most helicopters, quadrotors use fixed-pitch blades, whose rotor pitch does not vary as the blades rotate; control of vehicle motion is achieved by varying the relative speed of each rotor to change the thrust and torque produced by each.

History

DeBothezat‘s design was created for a 1921 contract with the US Air Corps. After working on his design for over 2 years, he was able to develop a fairly capable helicopter, which was able to take on a payload of up to 3 people in addition to the pilot. His design was deemed underpowered, unresponsive and susceptible to reliability problems. In addition, instead of the calculated 100 meters cruising altitude, his craft was only capable of reaching a height of roughly 5m.

DeBothezats quad-rotor Design, 1922

The idea of a quad-rotor aircraft has existed since early in the 20th century. Throughout the 20th century very few distinct rotor-craft designs had been developed. The earliest workable designs for a quad-rotor were developed by George DeBothezat, Etienne Oemichen and D.H. Kaplan. Oemichen‘s quad-rotor design is the earliest mention of a complete four-rotor hovering vehicle in history. Oemichen‘s first design in 1920 failed in the initial attempt to become airborne, thereby requiring Oemichen to add additional lifting power and stability of a helium-filled balloon. After a number of recalculations and redesigns, Oemichen was able to come up with a design that actually was capable of lift off and even established world helicopter flight records of the time, remaining airborne for up to 14 minutes at a time by 1923.

Oeminchen No.2 Quad-rotor Design, 1922

The early designs were propelled by additional rotors located somewhere on the rear or the front of the craft, perpendicular to the main rotors. Thus, they are not true quad-rotor designs. It was not until the mid-1950s that a true quad-rotor helicopter flew, which was designed by Marc Adam Kaplan. Kaplan‘s quad-rotor design, Convertawings Model “A” quad-rotor, is arguably the most successful of the early designs of the rotor-craft. The prototype first flew in 1956, and did so with great success. The 2200 pounds craft was able to hover and maneuver using its two 90 horsepower motors, each capable of driving all four rotors in backup mode. Control in this case did not call for additional rotors on the sides of the craft, but was obtained by varying thrust between rotors. This also was the first quad-rotor design that was able to fly forward successfully.

Despite these early proofs-of-concepts, people saw little practical use for quad-rotors. They simply were not competitive with the performance specifications (speed, payload, range, etc.) of more conventional aircrafts. No production contracts were awarded and interest in quad-rotors waned.

Recently however, there has been renewed interest in quad-rotors from hobbyists. This old idea is returning with great potential after RC quad-rotors have shown that there is definite potential in the quad-rotor platform.

Convertawings Model A quad-rotor Design, 1956

Quad Rotor Dynamics

A quad-rotor is an aerial vehicle with four rotors arranged in a symmetric, square configuration around a central hub, which houses the battery and processing components. While flying, the quad-rotor is positioned with a propeller in front and back. Moving counter-clockwise from the front propeller, let Fi be the force of each rotor i for i = 1; 2; 3; 4 such that F1 and F3 rotate counter-clockwise and F2 and F4 rotate clockwise. To perform a stationary hover, all four rotors rotate at the same rate and the total thrust of the craft is equal to its mass, m.
Since both pairs of rotors spin in opposite directions, the net torque on the craft due to drag from the propellers is zero. 

To create yaw movement in a counter-clockwise direction, F1 and F3 are sped up inversely proportional to F2 and F4. As a result, the net torque on the craft is negative via the right hand rule and it will yaw while remaining at the same altitude. If F1 and F3 do not increase proportionally to F2 and F4 decreasing, the craft will move in the z-direction because the net thrust will no longer equal zero. To yaw clockwise F2 and F4 must increase proportionally to F1 and F3’s decrease. A roll to the left is accomplished by decreasing the speed of F2 while increasing F4. Again, F2 must decrease at the same rate that F4 increases to maintain zero net torque. 

Increasing F2 and decreasing F4 results in rolling to the right. Pitching forward and back is done in the same fashion as rolling, but with F1 and F3. The principle for maintaining an equal rate of change for the two opposing rotors is how the translation of the craft is determined. Due to either a pitch or a roll, the lift force is displaced in the x and y planes by angles and respectively, resulting in a horizontal force component that will translate the craft. The altitude of the quad-rotor is altered by changing the rate of all rotors collectively by the same amount. The thrust from each rotor exists only in the z-direction with respect to the body frame. The total thrust can be represented by u = F1 + F2 + F3 + F4 and Fi is the force of rotor i.