How big can a drone be on solar panels?
The idea seems to be a genius: to place solar batteries on a drone, and then it will not need a battery. Without it, the drones can be controlled while the sun is shining. This is fine (assuming that your intentions are pure). This is exactly what students did Singapore National University .
But from the video it's clear that their drone is flat, like a leaf. Therefore, in fact, the question is: what mass and size can such a device possess, so that it can rise into the air solely on solar energy? I will answer this question and give you a special calculator for quadrocopters on solar panels.
carrying screw it can not be called trivial. However, such problems did not stop me earlier on the road to building a simplified model. In the next, extremely simplified physical model, I will assume that the thrust of the helicopter appears due to a change in the momentum of the downward air. To achieve sufficient traction for helicopter flight, we have two ways. You can take a small screw and very quickly push the air down, or take a big screw and push the air more slowly.
If the area of screw A, and the density of air ρ, then the lift is expressed in terms of air speed by the following equation:
What about power? Power - a change in the kinetic energy of the air, divided by the time interval. The faster the air, the more kinetic energy and shorter time interval. The complete derivation of this formula I gave in article about the aircraft on the muscular force . Here is the expression for power.
Since the power is proportional to the cube of air speed, for a helicopter on muscular power it should be small, and, hence, the helicopter must be large. So there is .
Now to my favorite schedule. I knew that my model could be completely untenable, so I studied the data on real helicopters. Based on the mass and size of the screw, you can calculate the power of the flight and compare it with the specified engine power. Here is the graph - the calculated power versus the indicated power for some helicopters.
I was very surprised at the linearity of the data.
More information about helicopters
One of my friends, who was fascinated by the creation of his own quadrocopter, showed me site T-Motor , which lists a number of electric motors and data on their efficiency. Here, what characteristics are indicated there:
Thrust depending on the throttle.
Power is the product of current and voltage.
What can be done about this? Since I have the size and thrust of the screw, I can calculate the air speed. It can be used to calculate theoretical power and compare it with the indicated one. That's what I got.
Aha. Still linear dependence. Here I was a little worried - it seemed unlikely that my simplified model of pulling the helicopter would work on such a scale. And the graphs even tilt are similar - ?656 and ?411. What does this slope mean? It means that my estimated power is about 2 times less. If you record power, like:
Then the calculated power will coincide with the specified power. I'm not sure where the deuce came from. Perhaps I made the mistake of taking the derivative when calculating the average air speed.
If we have data, we can build one more schedule, a prize. Dependence of my design air speed on the rotational speed of the screw.
What does it mean? The faster the propeller blades rotate, the faster the air moves. I suspect that another variable is important here - the inclination of the blades.
Back to the solar energy
But we do not need traction, we need power. The increase in air speed increases its kinetic energy. The faster the kinetic energy increases, the more power it takes.
This means that you can make an aircraft with small screws that push the air very quickly, or with a large propeller pushing the air more slowly. But the energy of these two options is different. The kinetic energy is proportional to the square of the velocity, so the smaller screw requires much more energy for flights. Therefore, a real helicopter with muscular force should be so huge that it has enough human energy.
Calculation of the flight power
Instead of considering all the possible options for the size of the quadrocopter, screws and solar panels, as well as their efficiency, I just made a calculator - the program in Python , which counts the size of the screw necessary for the device to fly at specified parameters.
With my initial estimates, I got a screw diameter of 5.9 cm. It sounds plausible. And all options with increasing mass or changing the size of solar panels can now be calculated on a calculator.
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