Unit 3: Multi Rotor Dynamics - Practice Quiz

1 How many total degrees of freedom does a multirotor have in three-dimensional rigid-body motion?

2 Which three variables commonly describe the rotational orientation of a multirotor?

3 Which law relates the total force acting on a multirotor to its linear acceleration?

4 In a multirotor body frame, which axis usually points vertically through the vehicle?

5 What is the main force generated by a spinning multirotor propeller?

6 How is roll torque commonly produced on a quadrotor?

7 Why do adjacent rotors on many quadrotors spin in opposite directions?

8 What happens to rotor thrust when its rotational speed is increased, assuming other conditions remain unchanged?

9 What condition is required for a multirotor to hover at a constant altitude?

10 What is the vertical acceleration of an ideal multirotor in steady hover?

11 For an evenly balanced quadrotor in hover, how is the required total thrust normally shared?

12 What must a multirotor generally do to begin moving forward?

13 During level forward flight, which part of the thrust supports the multirotor's weight?

14 Which force mainly opposes a multirotor's motion during steady forward flight?

15 As a multirotor tilts farther while maintaining altitude, what generally happens to the total thrust required?

16 If a multirotor's total thrust is and its tilt angle from vertical is , what is its vertical thrust component?

17 What mainly limits the maximum thrust of a multirotor?

18 How does aerodynamic drag generally change as a multirotor's airspeed increases?

19 When does a multirotor reach a steady maximum forward velocity?

20 Which change would generally increase aerodynamic drag on a multirotor?

21 A drone has body-frame velocity m/s and angular velocity rad/s. If the net body-frame force is zero, what is according to ?

22 A rigid drone has principal inertias , , and kg·m. At an instant, rad/s and no external torque acts. What is the yaw angular acceleration ?

23 A 2 kg drone produces 20 N of thrust along an axis tilted from vertical. Ignoring drag, what horizontal acceleration is produced at that instant?

24 A roll torque of N·m is applied to a drone whose roll moment of inertia is kg·m. If gyroscopic coupling is negligible, what roll angular acceleration results?

25 On a plus-configuration quadrotor with arm length m, the right rotor thrust increases by 2 N while the left rotor thrust decreases by 2 N. What is the magnitude of the resulting roll torque?

26 In a symmetric quadrotor, which rotor adjustment primarily generates a yaw torque while keeping collective thrust approximately unchanged?

27 A quadrotor increases the thrust of all four rotors by the same amount. Which control effect is produced ideally?

28 Rotor thrust follows . If a rotor's angular speed doubles while remains constant, how does its thrust change?

29 What total upward thrust is required for a 1.5 kg drone to hover steadily near Earth's surface? Use m/s.

30 A symmetric four-rotor drone has a mass of 1.6 kg. Assuming equal rotor loading, how much thrust must each rotor produce to hover? Use m/s.

31 Rotor thrust is modeled as . If air density decreases to of its original value, by what factor must rotor speed change to maintain hover?

32 A hovering drone suddenly increases total thrust to while remaining level. Ignoring drag, what initial vertical acceleration does it experience?

33 A 2 kg drone flies forward at a constant altitude with its thrust tilted from vertical. Ignoring aerodynamic lift, what total thrust is required? Use m/s.

34 A drone tilts from vertical while adjusting thrust to maintain altitude. Ignoring drag, what horizontal acceleration is produced?

35 A drone transitions from hover into forward acceleration without losing altitude. Which change is required?

36 A 2 kg drone has a maximum total thrust of 30 N. What is its maximum tilt angle from vertical while maintaining altitude? Use m/s.

37 A 2 kg drone can generate at most 30 N of total thrust. What maximum horizontal force can it produce while maintaining altitude? Use m/s.

38 A 2 kg drone has a maximum tilt angle of and a maximum thrust of 25 N. What is its maximum horizontal force during level flight? Use m/s.

39 A drone can provide 16 N of horizontal thrust. Its drag is , where kg/m and m. What is its approximate maximum steady speed?

40 For a drone with quadratic drag, maximum steady speed satisfies . If maximum horizontal thrust increases by , how does maximum speed change?

41 A multirotor has body-frame inertia , angular velocity , and applied torque . Using , find .

42 A multirotor produces along body . Using a body-to-inertial ZYX rotation with roll , pitch , yaw , and inertial gravity , what is its inertial acceleration?

43 A vehicle has body-frame velocity , angular velocity , mass , and net body-frame force . From , what is ?

44 For , a controller must keep the body-frame angular velocity constant at . Neglecting rotor gyroscopic effects, which torque is required?

45 A plus-configured quadrotor has rotors at front, right, rear, and left, numbered 1 through 4. Its moments are , , and . Which small thrust change produces pure positive roll torque while preserving total thrust?

46 For the same plus quadrotor, rotor 1 fails completely. Assume fixed-pitch rotors, no aerodynamic body yaw drag, and a required stationary hover with zero angular velocity. Why can the remaining three rotors not satisfy all equilibrium conditions?

47 A rotor applies force at body-frame position and also generates a reaction torque . What total torque acts about the center of mass?

48 For a quadrotor with yaw moment , which thrust perturbation produces positive yaw torque with no first-order change in collective, roll, or pitch?

49 A multirotor in still air is held at a constant tilt from vertical. There is no wind, tether, contact force, or other horizontal external force. Which statement about a stationary position hover is correct?

50 Each rotor obeys . A quadrotor hovers at rotor speed before air density decreases uniformly by . Neglecting all other changes, what rotor speed is required to maintain hover?

51 The combined front and rear rotor groups lie at and relative to the geometric center, where . The center of mass is displaced forward by . For level hover, what fractions of must the front and rear groups produce?

52 In steady, level forward flight, a multirotor's thrust vector is tilted by from vertical and the aerodynamic drag magnitude is . Assuming drag is horizontal, which equilibrium relation is correct?

53 A vehicle initially hovers with . Its attitude is rapidly pitched to while thrust magnitude remains , and the attitude is then held. Immediately after pitching, before drag becomes significant, what are its horizontal and vertical accelerations?

54 A multirotor travels east at a ground speed of in an eastward tailwind. Drag is newtons, where is airspeed. In steady level flight, what tilt from vertical and thrust magnitude are required?

55 A multirotor performs a steady, level coordinated turn at . Its maximum thrust is , and drag is neglected. What is the minimum achievable turn radius?

56 A multirotor has a maximum thrust-to-weight ratio of . While maintaining constant altitude and neglecting drag, what are its maximum tilt from vertical and maximum horizontal acceleration?

57 A multirotor has and an attitude limit of from vertical. What is its maximum horizontal acceleration while maintaining altitude, neglecting drag?

58 A multirotor with must accelerate upward at while maximizing simultaneous horizontal acceleration. Neglecting drag, what is the maximum horizontal acceleration?

59 A multirotor has maximum thrust and experiences horizontal drag newtons. Assuming steady level flight and no tilt limit, what is its maximum airspeed?

60 A multirotor has and horizontal drag newtons. With no separate tilt limit, what is the maximum steady level airspeed?