How does the coriolis effect affect airline navigation?

Hello Everyone,

Just wondering how a pilot or navigator factors in the spinning of the Earth when flying long distances. Does this affect private pilots on say a two hour flight?

I leave the navigation questions for those better informed. I’d like to make clear what the Coriolis effect is in this thread.

If the pilot flying due North aims his plane straight at a mountain, by the time he gets there the mountain has spun out of the way. It appears to the pilot that a force has been acting on his airplane pushing it the right. This is called the Coriolis force and/or Coriolis effect.

That is specifically true in the southern hemisphere; if you’re in the northern hemisphere and headed north, you tend to veer to the right, and the mountain you were headed toward doesn’t keep up. The effect is minimal near the equator, where movement parallel to the surface of the earth doesn’t much change your distance to the earth’s axis of rotation (and therefore ground objects in your near north/south vicinity are all moving east at pretty much the same velocity).

Looking at a north-polar projection map, it appears Anchorage, Alaska and Helsinki, Finland are directly opposite the north pole, and at about the same latitude (~60N). Anchorage and Helsinki are 4043 miles apart, so a commercial flight will take about 7.4 hours. If you get your plane in the air and point it at the spot where Helsinki is at your moment of departure (i.e. exactly on the far side of the north pole), then in the absence of any other factors, you’ll arrive at that location and find that you were about 7.4 time zones west of Helsinki because you had given it that much time to slink off to the east. That puts you 7.4/24*360 = 111 degrees of latitude west of Helsinki, i.e. somewhere in the Yukon Territory; you’ll actually end up closer to Anchorage than to Helsinki. If you want to hit Helsinki, you’ll need to aim where it’s going to be 7.4 hours from now; Looking back at that polar map, you’ll want to point your plane at a compass heading of about 300 degrees instead of due north.

Actually it’s worse than that, because that final scenario results in a shorter flight path, and therefore less flight time; Helsinki won’t arrive in time to meet you at your destination spot. I won’t do the math, but the general answer is that you’ll need to aim somewhere between W-NW and N to hit Helsinki (as opposed to flying due north out of Anchorage if the earth isn’t spinning).

That’s assuming wind isn’t any kind of issue. But it is. The jet stream circulates west to east, which means you need to aim further west than you would in its absence. How much? Pilots will have a better idea than me, but I understand it varies in speed and altitude and is definitely factored into flight paths.

I would be very interested to see the ground track of a flight between Anchorage and Helsinki (or a similar transpolar flight if that one doesn’t exist).

It makes the toilets flush the other direction once they cross the equator.

Please fight my ignorance… the way I see it, the solid portion of the Earth doesn’t rotate inside a stationary ball of gas - the atmosphere is pretty much rotating along with the rest of the planet, surely? Otherwise, the most cost efficient way of crossing the Atlantic (at least in one direction) would be to levitate via balloon for a while and wait for your destination to arrive beneath you.
So ignoring the wind, the plane flying within the ball of gas surrounding the solid portion of the planet doesn’t really see the ground rotating away underneath it.
Am I wrong?

If all this is so, how come a helicopter doing an high alt hover over the equator in a no wind condition does not have the world spinning about 2000 MPH under it?

I think there is some stuff being ignored that LSL Guy might be better able to explain than I could.

Even with no atmosphere at all, something popping straight up would not have the world, at planet size conditions, spin out from under it until it somehow lost the speed it has at the surface. No atmosphere to slow it down so it would pretty much stay one foot above the surface in the same place for a long time. ( well gravity might be getting pissed at being ignored but who cares? )

If something is a foot above the (physics-land, perfectly smooth) Earth, the thing would need to be travelling slightly faster than the spot underneath it in order to make one rotation in 24 hours (because the higher object is going around in a slightly larger circle).

So, in the case of no-atmosphere with a levitating device that raises the thing straight away from the center of the planet but doesn’t allow any sideways force, then the thing hovering above the planet would very very slowly drift west. Speed of the drift is left as an exercise for the reader.
For a real plane in the atmosphere, I think, since it is basically suspended in the atmosphere, the direct Coriolis effect will be negligible (the pilot aims at a mountain and flies due north. The atmosphere pushes him sideways just enough to hit the mountain. Super-sensitive pressure sensors on the hull might be able to barely detect the push, but random gusts of wind will have a bigger effect).

Now airplanes do have to account for winds, and prevailing winds are highly influenced by Coriolis forces, so in that sense, they’re very important (it’s about an hour quicker to fly from Seattle to Boston than vice versa).

You’re right. My first paragraph accurately describes the Coriolis effect; the rest of my post (re: trying to reach Helsinki from Anchorage) addressed how to hit a moving target from a stationary point (like standing on solid ground while throwing a ball to a kid on a counterclockwise merry-go-round), but I didn’t even touch on how the Coriolis effect influences the ground track when you’re already on the move (like being a passenger on the counterclockwise merry-go-round and throwing a ball to a passenger on the far side). :smack:

Assume for the moment that there’s no atmosphere; we just have antigravity capability, and a horizontal thruster. The Coriolis effect means that if you aim straight north from Anchorage and apply thrust, your flight path will tend to curve to the east, since you’re starting out with 524MPH of eastward velocity already due to the earth’s rotation. As you move farther north, the ground isn’t moving eastward as fast as Anchorage is, so your ground track will deviate to the east; you won’t hit the north pole, and you definitely won’t come close to Helsinki. Add in the fact that Helsinki will have moved several thousand miles east of where it was when you started your journey, and you’re going to be way off. So ignoring the atmosphere, you’ll have to aim west of Helsinki to account for the fact that it’s a moving target, and you’ll have to aim even further to the west to account for the Coriolis effect causing your ground track to deviate to the east.

We can’t ignore the atmosphere though, which does tend to move more or less with the ground at low altitude. So if you cruise at very low altitude, the atmosphere will tend to damp out your initial eastward velocity as you move toward the north pole - and will tend to restore your eastward velocity after you cross the pole and begin heading south again. This should help erase both of the effects (moving target + Coriolis) described above.

Up at cruising altitude though (30,000-40,000 feet), the jet stream matters. If you’re flying in/through it, it is going to tend to make your northward flight path curve to the east (or your southward flight path, after you’ve crossed the pole). The polar jet stream circulates from west to east in part because of the Coriolis effect. Which means either you’re choosing your altitude to stay out of it, or you’re adjusting your heading to achieve the desired ground track.

I’m not a pilot; this is all from first principles, so I’m at a bit of a loss to say whether it’s something you’d notice when flying the plane manually, or something so subtle that only the autopilot would notice the deviation. I’m again curious to hear from a pilot what the real ground track looks like for such a flight.

It is not accounted for, at least not directly.

You are flying through the air and the air is moving across the ground (wind). You are navigating with reference to the ground so you need to factor the effect of the wind in your navigating. That is all the pilot cares about.

Don’t think of the atmosphere “damping” anything out, or “tending” to do anything. The aircraft is coupled to the atmosphere, it is a part of it and moving in relation to it in the same way your car moves in relation to the ground it is on. Any difference in movement between the atmosphere and the ground is quantified and called “wind”. Wind is allowed for in navigation in order to make good the required track across the ground.

I am not a pilot, but it seems to me that the path of the airplane is much more affected by air currents than the Coriolis effect. I mean, the effect was first noticed by soldiers firing cannonballs, whose path is mostly ballistic. Aerodynamic flight is a completely different thing. Plus, the human pilot (or auto pilot) is constantly making tiny adjustments left, right, up, down, to maintain the heading they want. So that’s even one step further removed from unguided ballistic flight.

Its not 100% “locked” to one point, it sloshes around a lot and tends to drift in specific ways relative to the earths rotation.

Right but that is just called ‘wind’ as noted previously or ‘stream’ as in the Jet Stream if it is a consistent pattern across a large area. However, the wind can be in any given direction at any particular place and time and that is all that matters.

Airplanes are like boats, not spacecraft. They are actually IN the air just like boats are in the water and they only react to the immediate local conditions of the fluid that they are currently travelling through whether that is air or water. That analogy is helpful to some people people that don’t think of wind and water currents as being directly analogous but they are. The Coriolis effect doesn’t have anything to do with airplane flight directly. The only thing that matters is the direction and speed the air is travelling at each point along its course.

If anyone is really interested in this question, there is an excellent classic aviation book called “Stick and Rudder” that covers this question and many other aerodynamic concepts in a thorough but very accessible way.

I understand that, thank you. That is why I put the emphasis on “pretty much”.

My understanding is airliners follow a series of way-points, maybe a couple hundred miles apart and the pilots follow these “highways” through the air. At these distance I’m not sure anyone would factor in the rotating Earth.

I go out to dinner and everybody else hits this one out of the park. Yaay!

Simply stated, Coriolis acting directly on the airplane is utterly swamped by wind acting on the airplane over the same time interval. And yes, a lot of why the wind is blowing the particular way it is is itself a consequence of Coriolis.
The rotation of the earth does have a very real impact on inertial nav systems though. Once spun up the inertial nav “platform” is stable in 3-space. If you were sitting stationary on the ground on the equator and waited 6 hours, the platform that had been aligned to pointing straight up (=local vertical) would now be pointing horizontal to the ground. And 6 hours later would be upside down.

So this earth rotation needs to be compensated for even if the airplane isn’t moving. A similar issue arises in another direction if the airplane *is *moving. Here’s a bit about that: https://en.wikipedia.org/wiki/Schuler_tuning
Here’s another consequence of a rotating Earth:

During the start-up process for the INS platform, it needs to be told where on Earth it is. The alignment process typically takes about 10 minutes. During that time the mechanism compares the motion it’s “feeling” from the Earth’s rotation with the motion it expects to feel based on the latitude provided. If those two values are too different it assumes there’s a problem; either a malfunction or an invalid starting position was entered. And the system will not transition from “aligning” mode to “ready to navigate” mode until the disconnect is resolved. That’s also why the aircraft can’t be moved even a smidgen while the alignment is in progress. I’m not sure how the Navy solves this problem when aligning aircraft INSs on a moving ship.

I was intrigued by this so I did some Googling and found this Pprune discussion. Turns out it’s quite simple nowadays, but not so much back in the days of RAF Harriers embarked on RN Carriers.

If the atmosphere didn’t move with the earth, we’d have 2000 mile an hour winds all the time