# How would a drone work in centrifugal force generated “gravity”?

How would a hovering aircraft such as a drone operate on a rotating spacecraft that creates artificial gravity using centrifugal force? For simplicity, assume it's a drone on a space colony, similar to the render from Blue Origin below. Shown on the bottom right is a drone spraying crops.

I would think that taking off is nearly the same as in a gravity dominated environment. This question addresses jumping in a centrifugal environment. The reference frame of the drone before take off and immediately after take off is the same as the environment, and as such would return to the ground without significant lift.

Does there come a point in flight where the forces acting on the drone are significantly different than in a gravity dominated environment?

My instinct says no. If the drone is hovering, it is still in the reference frame of its environment and as such, if it were to stop producing lift it should "fall" the point on the ground directly below it (or the ground comes up to meet it, depending on the frame of reference).

For simplicity, assume that the height of the hover above the ground is an insignificant portion of the radius of the rotating spacecraft.

This is a really interesting question!

The navigation system of the drone will have to grapple with being in a rotating frame.

tl;dr: While the drop-off of gravity with altitude would be mild and manageable, the Coriolis force will be huge and absolutely have to be built in to the maneuver planning system of an automated drone.

## Rapid drop-off of gravity with "altitude"

Centrifugal "gravity" won't behave exactly like regular gravity.

On earth, the force of gravity points almost exactly "down" wherever you navigate around the spherical Earth, and it falls of with altitude very slowly:

$$g(\text{alt}) = g_0\frac{6378^2}{(h+6378)^2}$$

where $$h$$ is altitude in kilometers. You'll need to rise by about 32 kilometers in altitude for gravity to drop by 1%.

But centrifugal artificial gravity increases linearly with distance from the center, and it points away from the cylindrical axis rather than towards the center of a sphere. So if the radius of the cylinder is 10 kilometers, then

$$g(\text{alt}) = g_0 \frac{10-\text{h}}{10}$$

where $$h$$ is altitude in kilometers.

In this case gravity will drop by 1% after only a 100 meter rise!

That means that the drone's navigation software will have to be careful to recalculate it's gravitational mass regularly, and completely separately from its inertial mass and moments of inertia.

## Coriolis Force

The other consequence of artificial centrifugal gravity is the Coriolis force. This is a fictitious force or pseudo force that "exists" when you are moving in a rotating frame and try to account for things as if the frame weren't rotating.

To get an artificial gravity equal to Earth's $$g_0$$ of 9.81 m/s^2 at 10 kilometer radius for example, we can calculate the rotation rate $$\omega$$:

$$g_0 = \omega^2 r$$

$$\omega = \sqrt{g_0/r}$$

gives $$\omega=$$ 0.031 radians/sec. The magnitude of the acceleration due to the Coriolis force is then

$$a_C = 2 \omega \ \mathbf{\hat{z}} \times \mathbf{v}$$

where $$\mathbf{\hat{z}}$$ is the unit vector along the axis of the cylinder. A radial velocity would produce an acceleration in the angular direction (in the rotating frame) and vice versa, with a magnitude of $$2 \omega v$$.

To be 1% of $$g_0$$ you'd only have to be moving at about 1.6 meters per second (5.6 km/h) in our 10 kilometer radius cylinder. That's huge!

The drone navigation system would have to plan its maneuvers very carefully to account for the Coriolis force!

• yes, the differences are real but I doubt they are significant. real life autonomous drones have to correct for unpredictable external forces like wind gusts anyway. coriolis force or a varying "gravity" would feel like air currents and any serious navigation system adapts to these conditions. assuming of course, the drone can precisely track its own location using means other than GPS (which would be useless in a orbital station). – szulat Jun 21 '19 at 1:19
• @szulat the larger the "unpredictable forces" that you are always compensating and correcting for, the lower the maneuverability. You will gain in agility and accuracy if you incorporate these predictable accelerations into your algorithm. – uhoh Jun 21 '19 at 3:58
• You are massively over-thinking this, or at the very least over-estimating the control software. Typical simple drones have no idea what they weigh, any more than an aeroplane pilot knows what his plane weighs (once in the air) both 'systems' simply apply more power until they go in the correct direction. Winds in a rotating space station are going to have a characteristic pattern, but still somewhat unpredictable. So long as the drone measures its position relative to the 'ground' there will be no major differences. – Mike Brockington Jun 21 '19 at 11:13
• Good control software would have a model of itself and its environment so that it can estimate the dynamics output of a maneuver. You could rely strictly on error feedback, but without a estimate of what the physics are, your drone becomes less maneuverable as @uhoh mentions. – jekso Jun 21 '19 at 17:37
• @uhoh Thank you for your answer. We often ignore Coriolis forces in our models on Earth. It's good to know that they might significantly affect the control in this situation. – jekso Jun 21 '19 at 17:40

In the general case it really depends how big the station is, and what sort of flying you want to do.

If the drone really does stay at an insignificant height off the ground then your gut is right, no need to account for any of the other effects of rotation. These only come in as you move up and down. If you move 1% of the radius you gain 1% of the rotational velocity. There is a slight caveat that if you accelerate hard up and down in that small flight corridor, there will be quite large accelerations in the 'east' direction.

However gentle upwards drifts would be well with in the range of errors that drones already have to deal with.

Note drones don't do projectile style calculations, they rely on observing changes and making corrections. just like human pilots. It's helpful to know roughly what to expect you'll need to do in advance, but mostly the control systems are short term and place most weight on 'whats observations say is happening' over 'what would I predict to happen given current settings and location and speed etc. Most of this comes from the need to accommodate much larger errors like wind, sensor orientation and calibration, etc. But if you need further convincing that drones already need to deal with this sort of thing, just google the differences in gravitational accleration here in Earth.

Also by that time there will be AI flying drones anyway so... just let them figure it out!

• I disagree that drones strictly rely on error feedback for control. A better control system would have a model of its environment, which includes its own dynamics, gravity, drag, etc. A human pilot would have an internal model of how a plane would react to inputs, even if they don't think of it that way. – jekso Jun 21 '19 at 17:44
• But thank you for bringing up what would happen with a hard vertical acceleration. That would seem to be an effect of the significant Coriolis forces that @uhoh mentions. – jekso Jun 21 '19 at 17:49
• A good control system would use feedback from its environment to make corrections, but it would need an internal model of itself to choose the appropriate amount of correction, and also anticipate adverse motions that might be induced by the primary corrections it needs to make. – Anthony X Jun 22 '19 at 0:21
• @jekso I think this acknowledges that a model is helpful. I think the point is that if the size of the effect modeled is much smaller than the current errors, these are not significant. I agree it all adds up but its worth noting that the magnitude of the effect is important. – ANone Jun 24 '19 at 14:23

I suspect not lying to the auto-pilot: using stationary coordinates and telling the drone that the target is moving, would be optimal. As:

• It's easier to program

• It works for the path finding algorithm as well as the piloting system.

The latter may be especially important if the station is cylindrical, not toroidal.

Then only the input 'where too' commands need changing i.e. add the rotation to the target position and velocity.

I think the major complexity would be guessing altitude and predicting the wind (which may be significant depending on the size of the station).

• WIth the 10km radius and ω= 0.031 rad/s as in uhoh's anwer, the permanent wind speed would be 300 m/s ... I think that's perhaps harder to grasp fo rthe nav system than 1% gravity variation and 1% Coriolis acceleration ... – Hagen von Eitzen Jun 21 '19 at 9:40
• @HagenvonEitzen, not really, as the expectation would be that relative wind speed would always be fairly low. So long as the wind was predictable (though it may not be. the Coriolis force affect the air too...) – ANone Jun 21 '19 at 9:49
• +1 I like your answer more than mine! I feel silly now "lying" to my control system. Yes, just let the craft maneuver in a (relatively) inertial frame.Tell it how the station is rotating and let it do the math. This makes the most sense. – uhoh Jun 21 '19 at 18:08