Hello everyone, so following the series of videos on drones and energy So in the last episode what we have saw it was what is the necessary theoretical power to fly a multirotor drone and we saw that between this required power and the energy actually consumed there was a sizeable gap So today, what I propose to you, is now to compare what is the energy efficiency of a multirotor drone compared to an airplane, fixed wing so we will put ourselves in an ideal world we will look at the theoretical power required for a multirotor drone on one side the theoretical power needed for an airplane on the other side and we will see on equivalent aircrafts in terms of mass is size which of the two will consume more energy so first of all what we are going to do is calculate and the theoretical power needed to fly an airplane so we will be interested in the power of an airplane, and before starting we need to come back to three important notions the first is what are the Cx and Cz of an airplane the second is what is meant by glide ratio and the third, how do you model the forces involved on a plane that follows a uniform rectilinear motion So I start with Cx and Cz The Cx is the drag coefficient the Cz the lift coefficient The Cx depends on the aerodynamics of the aircraft, its ability to enter the air the Cx ci also depends on the induced drag then the induced drag is these famous swirls at the end of wings what's called a vortex generated by the pressure difference between the underside and the top of the wing finally we must remember that all that, it makes us the coefficient of drag, the Cx so the Cz, it depends on the geometry of the wing of its profile, the more the profile of the wing is thick or hollow, and the more the Cz will be important note that Cz and Cx both vary depending on the incidence of the aircraft the incidence is the angle that the plane makes with respect to its trajectory so here we have a high incidence there is a small incidence therefore, the higher the incidence, the more the Cz and the Cx increase until reaching a point called stall In any case there is an optimal ratio between Cz and Cx which will give us the maximum glide ratio of the plane that's what we'll see later so now, if we model the forces involved on a plane in uniform rectilinear motion we will find the weight that is equal to mg, which is directed downwards we will find the resultant aerodynamic forces that is composed of the lift and drag and finally we have the pulling force of the propeller and the sum of these three forces equals zero in uniform rectilinear motion so we know the weight of the plane, it's mg, directed down the resultant forces are known aerodynamic which is composed of fx which is the drag 1/2 Cx ro S V2 fz is 1/2 Cz ro S V2 and we know that fz is equal to mg and we know that fx is equal to the traction force of the propeller now that we saw what it was Cz and Cx and what were the forces at stake on a plane in flight we will talk about the concept of glide ratio if I take this glider, and throw it to one meter high it will travel a certain distance, this distance will be equal to the glide ratio more precisely the glide ratio is the ratio between the distance traveled and the lost height if we make a small drawing, we can easily demonstrate that geometrically the glide ratio is the ratio Cz on Cx so what will improve the glide ratio of an airplane? we doubt that the more it will be aerodynamic, the more it will enter the air, the better its glide ratio the more its lift coefficient will be good and the better its glide ratio Geometrically, what will influence the glide ratio is also the aspect ratio a longer elongated wing will generate less induced drag this famous sawdust visible in the form of a vortex at the end of the wing after we can look at the glide ratio of known aircraft so if we take a parachute, intended for freefall the glide ratio is going to be of the order of 3 it means that each time he advances 3 m he loses 1 m then if we take a glider of the 30s made of canvas and wood we had glide ratio of the order of 8 an airliner with a typical glide ratio of the order of 20 whose best, we will find for example the A380 which has a glide ratio of 22 that means an A380 that would lose its four engines at 10,000 meters altitude he could, by gliding, travel 220km then we will find experimental aircraft that have been designed to go around the world using less energy possible for example Voyager who has a glide ratio of 27 or the Solar Impulse, all electric, which has a glide ratio of 34 just to quote it, it was designed a prototype glider called ETA which has a glide ratio of 72 so it's quite considerable, that means that when it travels 72 m, it only loses 1 meter it was important to understand this concept of glide ratio because it will be used later in the video so now we're going to get into the calculation of theoretical power necessary to maintain this plane in the air we will use the formula of the traction force multiplied by the speed of displacement then to calculate the pulling force, it's just the opposite of the fx drag and to calculate the speed, we will use the equality between the lift force 1/2 Cz ro S V2, and the weight mg and so we can deduce the speed which is the square root of 2mg / (Cz ro S) so the drag is 1/2 Cx ro S V2 after a few calculations we find that the traction force T = mg / glide ratio finally we can deduce the theoretical power which is equal to the traction force X the speed and we find that the power is the square root of 2 (mg) 3 / (glide ratio2 Cz ro S) So now that we've seen the theoretical power needed to fly our plane we will seek the theoretical power to fly our drone so last time we saw the power needed to fly a stationary drone this time, since we will compare a drone and a plane, we must advance our drone it means that our aircraft, it is no longer horizontal, it is a little inclined and there, the power will increase for two reasons the first is, being inclined the pulling force that must compensate for the weight will have to be greater the second reason, the aircraft being in translation, the speed V0 downstream of the propellers is no longer zero so if we model our drone it can be deduced that the traction force is mg / cos (alpha) and we can also deduce that the speed V0 is the speed of translation of the aircraft x sinus (alpha) so the first thing we will do is recalculate the air mass flow if now we calculate V2, V2 becomes a little more complicated than for hovering we now know the speed V2 and we can deduce the power transmitted to the air in this situation that's a half of the mass flow of air times V2 squared to which we subtract 1/2 of the mass flow of air times V0 squared since the air already arrives with a non-zero speed in the system So what I propose is to make a big simplification it's getting rid of the beta terms, so beta is pretty much zero or very small with alpha angles close to zero in contrast, for larger angle alpha and speed of translation we will increase the power required for the flight by at least 30%, or even more is it still us that what interests us, is the ratio between the theoretical power required for a drone compared to the theoretical power required for an airplane so we'll just keep the first term, we'll say that P is greater than this term so that the power drone on plane power ratio it is greater than the power of the drone (mg / cos alpha) 3 / (2 ro S) divided by the power of the airplane 2 (mg) 3 / (glide ratio2
CzroS) so what we can do is simplify again that is to say we will assume that we have a drone and a plane that have the same mass which have about the same bearing surface that is, the surface of the wing of the plane and the surface swept by our propellers is identical which allows us to do yet some simplifications and we will find that the power of the drone / power of the plane it's the glide ratio / 2 x square root (Cz / (cos alpha) 3) and here I continue in my simplifications and approximations I'm going to take a typical plane that has a glide ratio of 10, I'm going to assume that the Cz is worth 1 and then I'm going to assume that the alpha angle of the drone is very low which gives us a cosine almost close to 1 and here we get a drone power ratio on aircraft power that will be greater than 5 so far, we stayed only on theoretical powers, we did not take into account the efficiency so I asked myself the question by stacking all the yields on the drone side and all the yields on the plane side are we going to completely break this ratio of 1 to 5? then not necessarily, since if we look at the efficiencies of the traction chain that is to say, battery, speed controller, motors we will say that in both cases it's the same thing the efficiency of the propeller, we will assume that it is identical in the case of the drone and in the case of the aircraft here too it is a hypothesis that is correct so where there is a difference between the drone and the plane is that the drone side, we have the performance related to the shape drag, we saw in the previous video so this yield is about 07 it is not put next to the plane since it is already integrated in the Cx Propulsion efficiency and on the airplane side we have the propulsion efficiency that we do not find on the drone side then V0 is the speed of the plane, V1 is the speed in the vicinity of the propeller of the plane basically it tells us that for a given pulling force it is better to have a big propeller that turns slowly than a small propeller that turns very fast because a small propeller that runs very fast will degrade the propulsion efficiency so here we will say that it is equal to 07 when we stack all these yields, we see that we are almost similar on one side and the other so the ratio of 1 for 5 we saw previously, it makes sens especially as drone, once we will fly in translation we will call extra power to maintain the drone and move it forward if we compare the theoretical powers of a drone and a plane for mass aircrafts is similar in size the theory tells us that the drone will require a power of flight at least five times that of its fixed wing equivalent I propose you to apply the formula calculating the power needed to fly a drone to the aircraft carrier we see in the movie Avengers so this aircraft carrier, it's flying, it's equipped with four rotors and I propose you to calculate the theoretical power required to fly this aircraft we will assume that the mass of this aircraft carrier is 70,000 tons I took half between an aircraft carrier like the Charles de Gaulle which is a little over 40 000 tons and a 100,000-ton Nimitz-class aircraft carrier view the scale of the aircraft on this aircraft carrier we can estimate that the rotors measure about 40 meters in diameter and if we apply the formula we will find a necessary power of 1
64 x 10 power 11 watts so if we express in megawatts that gives us 164100 megawatts knowing that a modern nuclear unit can go up to 1600 megawatts that means that in this aircraft carrier it would be necessary to ship the equivalent of a hundred nuclear units so if we do another comparative this aircraft carrier would require the power of 800 Nimitz-class aircraft carriers that make about 200 megawatts other interesting data, downstream speed of the propellers would be of the order of 1700 kilometers per hour which is well beyond the speed of sound so if we were looking for this aircraft carrier a more realistic configuration for example, it would be necessary to divide the mass by ten, increase the size of the rotors by two so with 7000 tons and rotors 80 meters in diameter a theoretical power of 2590 megawatts is obtained it's about the equivalent of two nuclear units but already we are getting closer to something achievable so the question we can ask ourselves is if a fixed-wing aircraft had the same aerodynamic performance as a drone, what would be its glide ratio? so just take our ratio, to calculate power drone / power plane to assume that this ratio is worth 1, and from that we will deduce that the glide ratio of an equivalent airplane would of the order of 2 which means that the drone is not a very efficient aerodynamic aircraft if we replace it with respect to all the aircrafts we have seen glide ratio the conclusion of this study is that the multirotor drone is an energetic aircraft from the energy point of view because of size and equivalent mass it will consume, roughly speaking, at least five times more than an airplane a multirotor is not energy efficient to transport people or goods ideally, it would be a hybrid aircraft that is, it is convertible between a multirotor drone configuration and an airplane configuration so we will have the interest of the vertical take-off and landing and at the same time the interest of energy performance during transport so I hope this video will have pleased you, it closes the series on drones and energy feel free to leave your questions and comments and I'll see you soon on the paladrone chain!