<p>It’s not entirely correct, that quadcopters are unstable. Most commercial copters have a center of gravity way below the Propeller plane and thus are actually stable. In contrast to that you want certain aircrafts to be instabile for better agility. For example some jet fighters are unstable and need electronic stabilization even for normal forward flight. </p>

CC BY-SA 4.0
2020-05-18T20:06:30.730Z
If the center of gravity is "way below the propeller plane", the system is stable, but not in a useful way: as you accelerate, aerodynamics will try to flip the copter so that the center of gravity is leading the way (think of how a dart behaves).  See https://en.wikipedia.org/wiki/Pendulum_rocket_fallacy
Mark
CC BY-SA 4.0
2020-05-18T18:46:32.400Z
2020-05-18T18:57:04.017Z
2020-05-18T18:57:04.017Z
Simon Bethke
<p>A stable system is one where there's a force that pushes the system back towards it's original state when the system is moved from its balance point.</p>

<p>For example, when the driver gets into a car, there's more weight on one side of the car than the other but the car doesn't flip over. The springs on that side of the car compress and push harder on the wheels. The tyres push harder on the ground and the ground pushes back. The extra force from the ground exactly balances the extra weight and (after possibly bouncing for a moment) the car stops moving.</p>

<p>In an unstable system, say a broom balanced vertically, once it moves from the perfect balance point gravity will pull it further away and it accelerates.</p>

<p>For a quadcopter, there is no force that returns it to its original location, holding it horizontal, or even preventing a gradual roll.</p>

<p>Even if the thrust from each motor was exactly the same, and the weight was perfectly balanced, it's very unlikely to be perfectly stationary. If there's even the slight amount of pitch or roll, the angle from horizontal will gradually increase. As the angle increases, the sideways thrust increases and the drone accelerates.</p>

<p>So the roll rate is constant, the angle and acceleration increase linearly, the horizontal speed increases faster as the acceleration builds, and the distance from the starting position increases even faster as the speed builds. To the pilot, it looks like the drone is accelerating away from its original position much like the broom falling over.</p>

<p>To a systems engineer, the rotation of the drone is neutrally stable - there are no forces increasing or decreasing the rotation rate. However the speed and position are unstable - once it starts moving, it accelerates.</p>

<hr>

<p>I should mention that there are second-order (i.e. relatively minor) forces too. If you had a large fin on top of the drone, aerodynamic drag on the fin would return the drone to upright as the speed builds and limit the maximum speed - in practice this isn't useful as it doesn't return the drone to its original position.</p>

CC BY-SA 4.0
2020-05-18T17:23:07.820Z
Is there some reason that quads are not built with the rotors tilted a bit up toward the center, analogous to aircraft wing dihedral? Wouldn't this make them more stable?
Lee Daniel Crocker
CC BY-SA 4.0
2020-05-18T21:32:11.470Z
@LeeDanielCrocker An aircraft's dihedral angle improves stability because of the way its wings generate lift. A rolling motion results in *sideslip* relative to the aircraft's forward motion. This sideslip, combined with the wing dihedral, results in one wing producing more lift than the other, counteracting the roll. A quadrotor doesn't generate lift in the same way (indeed, "sideslip" is meaningless when hovering) and so merely tilting the rotors wouldn't have the same effect.
David
CC BY-SA 4.0
2020-05-19T08:11:16.473Z
Also, as the angle of the drone (and thus the lateral acceleration) increases, the lift it experiences will decrease, causing it to eventually fall out of the sky.
nick012000
CC BY-SA 4.0
2020-05-19T14:45:35.817Z
@David that argument sounds dubious to me. The whole reason that sideslip increases lift of a dihedral wing from the windward side is that it poses a higher effective angle of attack. Likewise, a dihedral-tilted rotor would have a higher AOA on the windward side than on the leeward side. So if this would not make the quadcopter stable (i.e. prevent ever-increasing drift motion) then the reason is that AOA matters less in rotors than it does in wings, not anything about whether you see the drift as a sideslip or just undesirable motion when trying to hover.
leftaroundabout
CC BY-SA 4.0
2020-05-19T14:47:31.757Z
@LeeDanielCrocker I think mostly the reason why stuff like this isn't done is that flight controllers do a perfectly fine job at dealing with the situation. There's not really any advantage to be had by a drone that's inherently stable.
leftaroundabout
CC BY-SA 4.0
2020-05-19T17:42:58.113Z
Hanging the battery off the bottom can provide quite a bit of stability, but we're still stabilizing acceleration towards zero, when the user will observe velocity.
Simon Richter
CC BY-SA 4.0
2020-05-18T09:35:06.600Z
2020-05-18T17:29:38.273Z
2020-05-18T17:29:38.273Z
Robin Bennett
<p>I have heard it mentioned that quadcopters are inherently unstable and only become stable due to control. What does inherently unstable mean in this context, and why are quadcopters inherently unstable?</p>

<quadcopters><performance><stability>
Why are quadcopters inherently unstable?
Jacob B
# Why are quadcopters inherently unstable?

(Asked by: username_0 on 2020-05-18)

I have heard it mentioned that quadcopters are inherently unstable and only become stable due to control. What does inherently unstable mean in this context, and why are quadcopters inherently unstable?

**Tags:** quadcopters, performance, stability

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## 2 answers

### Answer by username_3 on 2020-05-18. Score: 23 | Accepted answer

A stable system is one where there's a force that pushes the system back towards it's original state when the system is moved from its balance point.

For example, when the driver gets into a car, there's more weight on one side of the car than the other but the car doesn't flip over. The springs on that side of the car compress and push harder on the wheels. The tyres push harder on the ground and the ground pushes back. The extra force from the ground exactly balances the extra weight and (after possibly bouncing for a moment) the car stops moving.

In an unstable system, say a broom balanced vertically, once it moves from the perfect balance point gravity will pull it further away and it accelerates.

For a quadcopter, there is no force that returns it to its original location, holding it horizontal, or even preventing a gradual roll.

Even if the thrust from each motor was exactly the same, and the weight was perfectly balanced, it's very unlikely to be perfectly stationary. If there's even the slight amount of pitch or roll, the angle from horizontal will gradually increase. As the angle increases, the sideways thrust increases and the drone accelerates.

So the roll rate is constant, the angle and acceleration increase linearly, the horizontal speed increases faster as the acceleration builds, and the distance from the starting position increases even faster as the speed builds. To the pilot, it looks like the drone is accelerating away from its original position much like the broom falling over.

To a systems engineer, the rotation of the drone is neutrally stable - there are no forces increasing or decreasing the rotation rate. However the speed and position are unstable - once it starts moving, it accelerates.

---

I should mention that there are second-order (i.e. relatively minor) forces too. If you had a large fin on top of the drone, aerodynamic drag on the fin would return the drone to upright as the speed builds and limit the maximum speed - in practice this isn't useful as it doesn't return the drone to its original position.

> **Comments:**
> **username_4**: Is there some reason that quads are not built with the rotors tilted a bit up toward the center, analogous to aircraft wing dihedral? Wouldn't this make them more stable?  
> **username_5**: @LeeDanielCrocker An aircraft's dihedral angle improves stability because of the way its wings generate lift. A rolling motion results in *sideslip* relative to the aircraft's forward motion. This sideslip, combined with the wing dihedral, results in one wing producing more lift than the other, counteracting the roll. A quadrotor doesn't generate lift in the same way (indeed, "sideslip" is meaningless when hovering) and so merely tilting the rotors wouldn't have the same effect.  
> **username_6**: Also, as the angle of the drone (and thus the lateral acceleration) increases, the lift it experiences will decrease, causing it to eventually fall out of the sky.  
> **username_7**: @David that argument sounds dubious to me. The whole reason that sideslip increases lift of a dihedral wing from the windward side is that it poses a higher effective angle of attack. Likewise, a dihedral-tilted rotor would have a higher AOA on the windward side than on the leeward side. So if this would not make the quadcopter stable (i.e. prevent ever-increasing drift motion) then the reason is that AOA matters less in rotors than it does in wings, not anything about whether you see the drift as a sideslip or just undesirable motion when trying to hover.  
> **username_7**: @LeeDanielCrocker I think mostly the reason why stuff like this isn't done is that flight controllers do a perfectly fine job at dealing with the situation. There's not really any advantage to be had by a drone that's inherently stable.  
> **username_8**: Hanging the battery off the bottom can provide quite a bit of stability, but we're still stabilizing acceleration towards zero, when the user will observe velocity.  

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### Answer by username_1 on 2020-05-18. Score: -1

It’s not entirely correct, that quadcopters are unstable. Most commercial copters have a center of gravity way below the Propeller plane and thus are actually stable. In contrast to that you want certain aircrafts to be instabile for better agility. For example some jet fighters are unstable and need electronic stabilization even for normal forward flight.

> **Comments:**
> **username_2**: If the center of gravity is "way below the propeller plane", the system is stable, but not in a useful way: as you accelerate, aerodynamics will try to flip the copter so that the center of gravity is leading the way (think of how a dart behaves).  See https://en.wikipedia.org/wiki/Pendulum_rocket_fallacy  

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