To send to the Red planet, the Rover is good. Send the helicopter is even better. Such a plan is NASA for 2020: to send a “turntable” with the Rover. The idea is that the Rover rolling on the red desert, and before him flew a small helicopter. The helicopter will be Autonomous and operate for a few minutes a day. The main advantage is that he can scout the area in front of the Rover and take pictures, you might be a cool selfie with the Martians. Jokes jokes, but the advantage of such a Rover in front of the other is incomprehensible.

Despite the obvious coolness of this mission, the Mars helicopter will also have to solve some questions related to physics. In fact, Mars is a different planet. Let’s face it.

## Why it doesn’t have a screw on the tail?

The Mars helicopter is not like a conventional helicopter. Helicopters with a single screw (such as those we see on Earth) need a tail rotor, compensating the change of angular momentum (and torque due to air friction). Without a tail rotor, the helicopter spun and he crashed — or the passengers threw up, and how to drink. The coaxial helicopter main rotor has two blades protivovrashchatelnyj. And since the two screws revolve in opposite directions, the total angular momentum is zero, and does not need any additional tail rotor.

To get rid of the tail rotor useful for the sake of saving space. You can make a small helicopter with coaxial rotors. Less is more, especially in the cramped on Board the Rover. Put on Rover is a large helicopter would be like trying to roll a suitcase full of truck over rough terrain. Also, do not forget that the Mars helicopter would not return to the Rover, but it’s a start.

## Will a helicopter fly on Mars?

As for the flight of the helicopter, between the Earth and Mars there are large differences. First, the atmospheric density on Mars is much lower than on Earth (about 1% atmospheric density). Secondly, the gravitational field is also less on Mars (38% of the gravity on the Earth’s surface). The low atmospheric density complicates the flight of the helicopter, however, the reduced gravity makes it easier.

The question should be put differently: why do the helicopters fly? In the simplest model of thrust of the helicopter, the screws lift the air over the helicopter and dropping him down. Because momentum is “dumped” the air will be increased, need power — and it is the lifting force. It is also possible to represent the mass of air in the form of a cylinder with the same radius as the square of the helicopter.

*Here: thrust — thrust, rotor area — the area of rotation of the screw, velocity — the velocity of air*

Momentum dropped “air” (let’s call it air and on Mars and on Earth) depends on the speed with which it moves down, and its mass. What is air mass? Since the thrust depends on the rate of change of momentum, the height of this cylinder of air, we do not necessarily know. But the rate of change of the air mass depends on the size of the screws and the density of air. Therefore, it is possible to provide a rough approximation of the thrust force of the helicopter:

A is the area of rotation of the screw, v — velocity of air that moves down. The density of the air is represented by the Greek letter ρ. Where’s the gravity? Well, if the helicopter will hover, the thrust must be equal in weight. You can calculate the weight as the product of mass (m) and gravitational field (g).

*Calculations: Wired*

Because the air density on Mars is equal to 0.01 of the density of air on Earth, but the gravitational field is 0.38 from the earth, reduced gravity does not correspond to the loss of air density. On Mars to soar more difficult than on Earth. And another thing: in no case do not try to use this rough model the thrust force of the helicopter to create their own helicopter.

And now count yourself: knowing the mass and size of the Martian helicopter, what should be the rate of acceleration of the air screws to get this thing flying?

NASA claims that Mars helicopter can fly about two to three minutes a day. The rest of the time he will use the solar panel on top to charge the battery. So, how big a battery you need this helicopter? There are two ways to estimate the size of the battery (ask NASA — boring).

The first way starts from the time of charging. The helicopter will charge the whole day. On Mars, each day almost exactly coincides with earth day (37 minutes longer). The total duration of day has no value — important only daylight and the light of the sun. As on Earth, the duration of daylight changes with the years. Let’s take for example 10 hours of light a day.

The next thing to determine is the irradiance. It is a superficial power density of radiation incident on the surface. On Earth it is a maximum of 1000 watts per square meter. On Mars — 2590 Watts per sq. m. But this is the maximum, keep in mind. During the day the sun changes its position. If the solar panel is static, the average irradiance is lower. Take 295 watts/sqm the Size of our solar panel estimate with a radius of 7 cm With the same size, irradiance, day length and an efficiency of 25% we get about 40,000 joules of energy. It is close to the energy that keeps the battery of the iPhone X.

Now to the second method. How much energy is needed Martian helicopter to stay in the air for three minutes? How to calculate flight power? Let’s imagine this: power is the rate at which you use energy. What the helicopter is doing with your energy? It takes the air above it and it accelerates (increases its kinetic energy). To calculate flight power take screw size (14 cm in diameter) and the weight of the helicopter (1 kg). This will allow us to calculate the thrust of air required for evaporation. From this velocity we can calculate the rate of change of kinetic energy — power. Get the flying power of 374 watts.

But wait: NASA has already submitted the requirements for the capacity of the helicopter is 220 watts. If you start from them, we can calculate the energy required to operate within three minutes, because power is energy/time. Energy consumption in this case will be of 3.96 x 10^{4} joules. It remains to see that thing in action.