Quadrocopter Flight: Basic Criteria for Stable Flight

[Fibo112]

Homework Statement

In this task, the basic criteria that enable a stable flight of a quadrocopter are examined. Our quadrocopter consists of four horizontal propellers which are interconnected crosswise in a massless manner in the so-called + -configuration (see Fig. 1, right). In the center of gravity of the quadrocopter, the control and batteries of mass mS = 500 g are attached. The propellers should all have the same moment of inertia IP = 6000gmm2, the same mass (including motor) mP = 90g and the same distance from the intersection point R = 100mm. However, they can rotate independently in different directions and at different speeds. We also assume that the buoyancy of each propeller is independent of its direction of rotation. It should also be directly proportional to the speed with the proportionality constant cA = 0.02kg m / s.

a) Determine the rotational frequency of the quadrocopter ωQ as a function of the masses and the moments of inertia of the propeller IP.
b) What relationship must be met between the rotational frequencies of the propellers so that the quadrocopter does not rotate about its center of gravity? Suppose that the amount of all rotational speeds is the same. (the question has been translated from german to english using google translate)

Homework Equations

L=r x mv, T=r x F

The Attempt at a Solution

For a) I am assuming that the frequency wQ is referring to the quadcopter itself and not the propellers? I don't even really know how to begin solving this problem because to me it seems that I need more information about the Situation to know what the roational requency is..
With b) I am also having trouble understanding what is meant..

 

[haruspex]

a) Determine the rotational frequency of the quadrocopter ωQ as a function of the masses and the moments of inertia of the propeller IP.
b) What relationship must be met between the rotational frequencies of the propellers so that the quadrocopter does not rotate about its center of gravity? Suppose that the amount of all rotational speeds is the same. (the question has been translated from german to english using google translate)

I think that what it is saying is that if the four rotors start (from rest) to rotate at four independent rates and senses then, by conservation of angular momentum, the structure as a whole will start to rotate.
Part a) asks you to find the rotation rate of the structure that would result (as a function of the four unknown rotor rotations), and part b) just asks what the relationship must be between those four unknowns for the result to be zero.

 

[Fibo112]

for part a the rotor rate is not given...Am I supposed to use the rate required to prevent the center of mass from translating? Can I assume that the 4 rotor rates are equal for part a?

 

[Fibo112]

I am still very confused...dont I also need to know the velocity of the quadcopters center of mass for these calculations?

 

[haruspex]

for part a the rotor rate is not given...Am I supposed to use the rate required to prevent the center of mass from translating? Can I assume that the 4 rotor rates are equal for part a?

I see what you mean... it specifies the rate should be a function only of the masses and moments of inertia. That makes no sense to me... unless perhaps, assume all rotors are rotating the same direction at the same speed and the total lift is just sufficient to maintain a constant height.