Quadcopters are cool, I don't think anyone can refute this. While Drones use a simplistic boring version of their design, these versions are often used in science fiction, but is this powerful, flying vehicle feasible?
Is the Quadcopter realistic? If not, what do I have to do to make it feasible? Why would a military use it over its counterparts?
The scale of the model in your image is not very realistic. At that size, it is more efficient to have two rotors, like the V-22 Osprey.
In order for four rotors to be feasible, you would need a much larger body of aircraft, so that the four rotors are required for stabilization. I am not an aeronatical engineer, but I suspect that the reason drones use quad rotors is that they are more concerned with stability and ease of piloting than efficient weight:thrust ratios.
A heavy cargo plane with four rotors would be pretty cool, if there was a sensible in-universe justification for wanting a VTO/L version of the C-5 Galaxy.
First, direct lift — i.e. your engines providing an upwards pointing force directly — is always "expensive" in that it requires lots of fuel / engine power to achieve. Indirect lift, by for instance using airfoils / wings, is much cheaper and efficient.
The "only" drawback of indirect lift is that you need an extended strip of suitable land as a runway.
Second, the square-cube law means that small quad-copters do not translate to big dittos.
Generally speaking the square-cube law means that if you increase something in size — i.e. scale up or down width, height and depth by the same ratio — then all of the surface areas increase by the square of the change, but the volume and therefore the weight increase by the cube.
So if you double something in size (multiply by 2) , all of the surface areas increase by a factor of 2 squared, i.e. $2 \cdot 2 =4$, but its weight will increase by 2 cubed, which is to say $2\cdot2\cdot2=8 $.
This is a problem for rotor-craft because the direct lifting force that a rotor-craft needs in order to take off and land is roughly proportional to the surface area of the rotor disk. But the surface area only increases by the scale squared while the weight, and with that the gravitational force that you need to overcome, increases by the scale cubed.
So even if a small quad-copter can take off with ease, a large one will be under-powered.
Vertical Take-Off and Landing has been sought after eagerly ever since World War II showed that the things that you call "airfields", your enemy calls "huge, immobile targets"; they are bomb-magnets. And yes, the helicopter can achieve VTOL, hooray! But the helicopter generally lacks in all the other areas that fixed-wing aircraft do well: speed, cargo capacity, endurance.
Unfortunately this translates to quads-copters as well. And it does not become any better when noticing that the quad needs all rotors to spin and to spin in sync in order to stay afloat and not fall over in a spectacularly violent fashion.
The main problem is that lift is proportional to the area swept by the rotors.
This makes most quad copter configurations less powerful than a helicopter of the same size. In your picture you will see a large gap between the rotors over the center of the craft. If you had a single much larger rotor then you could generate more lift.
One way of doing this is triquad design which gives you the large rotor area but simple rotor motors of a quad copter.
There are two main problems with the image you posted, one the "wings" does not tilt. that would remove 1/5th of the thrust you need. If the wings were tilted you don't have that blocking force.
The second is the reaction time of an engine is too slow, the computer controlling the stability runs about 1000 calculations per second and a lot of "smaller model" drones running engines instead of motors have big problems in that particular area. Switching from engines to motors would solve that problem.
As for performance, by making a quad copter with variable pitch blades such as helicopter and planes would greatly increase performance but this is a huge challenge on models in the 250-500mm size.
About the propeller size it has greatly to do with the motor RPM and the propeller pitch. Contrary to what Steve mentions in the comments, the propellers might not be too small, small propellers increases the agility and acceleration but at the cost of fuel consumption, where larger propellers (depending on pitch) increases the flight time and or top speed. (Imagine smaller or larger wheels on a car)
