B How do airplanes correct their path

[sophiecentaur]

Lateral drag does not enter in.

Yes - in practice but you are assuming that the pilot is trying to follow a constantly changing chart course instead of a course that follows a 'straight line', using his inertial navigation system and that vector thrust is used, rather than banking for steerage. I am looking for a scenario where there are no effects from the atmosphere. In that case, the coriolis effect would be the only sideways effect. At typical plane speeds, the coriolis effect would be much smaller than for a very fast ballistic missile.
All I am trying to argue, now, is that there is essentially no difference, however the craft is powered, except due to its velocity. It was enough for me to read of the significant effect of coriolis on naval artillery, where the shell speeds are not ridiculously different from that of a fast jet plane. Coriolis can only be countered by dead reckoning at the launch time of a shell but the errors are easily correctable by the navigation instruments and the controls on a (slightly slower) aircraft.

 

[anorlunda]

Yes - in practice but you are assuming that the pilot is trying to follow a constantly changing chart course instead of a course that follows a 'straight line',

I'm getting lost in this thread Sophie. Why a constantly changing course? Why not a great circle course?

 

[sophiecentaur]

I'm getting lost in this thread Sophie. Why a constantly changing course? Why not a great circle course?

I understand how it's possible to launch a ballistic missile on a great circle course, I think but 'flying' a great circle course in a plane involves changing your (compass) heading constantly (ignoring wind etc., of course). I am a bit confused here about how to set controls so that a plane will follow a 'ballistic' course, with no lateral corrections. Can it really just be a matter of taking off in a particular direction and taking your hands off the wheel, virtually?

 

[jbriggs444]

I understand how it's possible to launch a ballistic missile on a great circle course, I think but 'flying' a great circle course in a plane involves changing your (compass) heading constantly (ignoring wind etc., of course). I am a bit confused here about how to set controls so that a plane will follow a 'ballistic' course, with no lateral corrections. Can it really just be a matter of taking off in a particular direction and taking your hands off the wheel, virtually?

For simplicity, assume a north-south course so that we need not consider constantly changing compass headings. And assume northern hemisphere and adopt the rotating frame of reference. Coriolis will tend to deflect the plane to the right. All other things being equal, the plane would be moved rightward by the force. But there is a vertical stabilizer. The plane will be turned instead. Left uncorrected, the plane will make a sweeping right turn. If a quick intuitive calculation serves, the turn would be sufficient to cover 360 degrees in $\frac{24\ hours}{sin\ latitude}$.

How does a pilot deal with a plane that is turning slightly right? The same way a driver deals with a car that is steering slightly right. He turns slightly left. This is part and parcel of what you have to do when you fly a straight course. Or drive on a straight road.

 

[anorlunda]

I understand how it's possible to launch a ballistic missile on a great circle course, I think but 'flying' a great circle course in a plane involves changing your (compass) heading constantly (ignoring wind etc., of course). I am a bit confused here about how to set controls so that a plane will follow a 'ballistic' course, with no lateral corrections. Can it really just be a matter of taking off in a particular direction and taking your hands off the wheel, virtually?

I think I can help you understand. I'm a blue water sailor. One thing I had to learn early in ocean sailing is that you do not judge your course (track) by the direction the bow is pointing. In fact, when crossing the Gulf Stream, I have had more than 40 degrees difference between the direction the bow is pointing compared to my actual track over the ground measured by GPS.

Your course is the intended direction, your track is the actual direction of movement to of the vessel. You simply keep turning as much as it takes to make the vessel move on course. The direction that the bow points determines what the compass reads.

It is the same in airplanes, but they call that difference crab angle. The crab angle due to coriolis is negligible compared to that due to cross winds. But regardless of the cause, you just use whatever crab angle needed to keep you on course. Planes landing in stiff cross winds, use as much as 30 degrees crab angle.

 

[rcgldr]

Ignoring rotating Earth / Coriolis issues, other than due north / south / east / west headings, a constant heading course on a sphere is a spiral path. In the case of a great circle course, the heading changes over time.

Before GPS, advanced navigation over land could use RNAV to travel in straight lines while using VOR's on either side of the straight line path, probably a constant heading path.

http://en.wikipedia.org/wiki/Area_navigation

Since GPS, way points with great circle paths can be used, providing a course for the aircraft to follow.

At least in the USA, most commercial aircraft travel along specific "corridors", making it easier for ground traffic controllers to monitor aircraft and keep them separate. There is or will be an upgrade to the air traffic controller system to allow commercial aircraft to fly independent and closer to great circle type paths. The paths and altitudes are often adjusted to take advantage of prevailing winds and/or the jet stream.

 

[sophiecentaur]

For simplicity, assume a north-south course so that we need not consider constantly changing compass headings. And assume northern hemisphere and adopt the rotating frame of reference. Coriolis will tend to deflect the plane to the right. All other things being equal, the plane would be moved rightward by the force. But there is a vertical stabilizer. The plane will be turned instead. Left uncorrected, the plane will make a sweeping right turn. If a quick intuitive calculation serves, the turn would be sufficient to cover 360 degrees in $\frac{24\ hours}{sin\ latitude}$.
How does a pilot deal with a plane that is turning slightly right? The same way a driver deals with a car that is steering slightly right. He turns slightly left. This is part and parcel of what you have to do when you fly a straight course. Or drive on a straight road.

But you are assuming that the pilot actually does something to correct the drift. All the suggestions seem to be that the coriolis drift effect is not relevant for planes but I suspect that the reasons are on the same lines of your argument - i.e. the pilot will correct the drift - but that intervention shouldn't count. In cases where there is no intervention (ballistics and the motion of the air creating the weather), coriolis is definitely relevant. So why not with planes?
The coriolis effect is dependent upon velocity, so what is your assumed northerly speed?

 

[jbriggs444]

But you are assuming that the pilot actually does something to correct the drift. All the suggestions seem to be that the coriolis drift effect is not relevant for planes but I suspect that the reasons are on the same lines of your argument - i.e. the pilot will correct the drift - but that intervention shouldn't count. In cases where there is no intervention (ballistics and the motion of the air creating the weather), coriolis is definitely relevant. So why not with planes?
The Coriolis effect is dependent upon velocity, so what is your assumed northerly speed?

The turning cycle time for a fixed velocity scales inversely with force. The turning cycle time for a fixed force scales directly with velocity. It's a wash. Turning cycle time under Coriolis acceleration is independent of velocity.

This is as one would expect from a simpler argument: If you fly straight in the inertial frame at the north pole, the Earth will turn under your feet once per day.

My belief is that pilots correct for various effects in flight. A plane that makes gentle circles because the rudder controls are not centered 100% accurately would be one example. Coriolis would have a similar effect and would be corrected for in the same manner. Yes it would have an effect. But no, it is not something that needs to be accounted for separately.

 

[sophiecentaur]

I think I can help you understand. I'm a blue water sailor. One thing I had to learn early in ocean sailing is that you do not judge your course (track) by the direction the bow is pointing. In fact, when crossing the Gulf Stream, I have had more than 40 degrees difference between the direction the bow is pointing compared to my actual track over the ground measured by GPS.

Your course is the intended direction, your track is the actual direction of movement to of the vessel. You simply keep turning as much as it takes to make the vessel move on course. The direction that the bow points determines what the compass reads.

I did a lot of navigating my sailing boat, until recently and the terms I am familiar with are CTS (Course to steer) and COG(Course over Ground). I am always referring to the CTS in what I am writing here. My sailing has all been coastal but the tidal streams are quite fast enough in the English Channel to produce almost anyCOG you can imagine, for a given CTS. When you are losing the battle, the difference can be up to 180° and that's time to start the engine or go for plan B. But, to reveal coriolis, it is necessary not to alter your direction 'through space'. That will give you the closest to a ballistic course, I think. Alternatively, I suppose, you could aim to arrive at the Pole and note that your heading has always been a bit to the left of North.

a constant heading course on a sphere is a spiral path

Known in these parts as a Rhum Line. A true northerly course will be a straight line though.

 

[sophiecentaur]

If you fly straight in the inertial frame at the north pole, the Earth will turn under your feet once per day.

That makes perfect sense and it brings the thing into excellent perspective. I have no problem with what happens in the inertial frame. My problem was that people on this thread were suggesting that a plane, because it is under control, is immune from the coriolis effects and somehow, in principle, bolted to the atmosphere.
It seems that the only time that coriolis is not relevant is in one's bathwater going down the plughole. The effect was found to be undetectable, I seem to remember.
I have yet another toddler passing through my life and I am back on the kids' roundabout at the park. That 'fictitious' force is incredibly real to the passenger on the roundabout. Pity I can't spend very long on it, studying the effect, before feeling nauseous. I keep getting complaints: "Come one Granddad!"

 

[anorlunda]

. My problem was that people on this thread were suggesting that a plane, because it is under control, is immune from the coriolis effects and somehow, in principle, bolted to the atmosphere.

No, we are saying that the influence of cross winds (50-100 knots cross wind component at altitude is not unusual) is perhaps $10^4%$ times more powerful than coriolis. No pilot or autopilot can steer with anything close to $10^{-4}$ precision.

Edit: our disagreement is the use of the word significant.

 

[sophiecentaur]

No, we are saying that the influence of cross winds (50-100 knots cross wind component at altitude is not unusual) is perhaps $10^4%$ times more powerful than coriolis. No pilot or autopilot can steer with anything close to $10^{-4}$ precision.

I do get that - really!

 

[russ_watters]

My problem was that people on this thread were suggesting that a plane, because it is under control, is immune from the coriolis effects and somehow, in principle, bolted to the atmosphere.

Not "immune", it just doesn't alter the plane's course because the plane is "bolted to the atmosphere".

What disappoints me about threads like this is that I think everyone understands the science, but some people misunderstand why they are arguing. As is often the case, this is all just an issue if interpreting the OP and answering the question bring asked.

 

[.Scott]

I understand how it's possible to launch a ballistic missile on a great circle course

Ballistic missile are suborbital. Their paths are not considered "Great Circle paths".
A Great Circle path presumes an Earth ground reference. So, for example, following the prime meridian from the North pole South, and then following meridian 180 back north to the North pole would be a full Great Circle. However, it is not at all a ballistic path.

... but 'flying' a great circle course in a plane involves changing your (compass) heading constantly (ignoring wind etc., of course). I am a bit confused here about how to set controls so that a plane will follow a 'ballistic' course, with no lateral corrections.

No. If you wish to follow a Great Circle path manually (no Auto-pilot), then your preflight work will include marking your course to accommodate the compass changes. Exactly what those accommodations are depends on what kind of navigation equipment you have. If you have GPS, you just need to create way points. If you are using a magnetic compass, it will include magnetic heading changes to deal with the course, magnetic variation, and winds. Since we're dealing with a long flight here, you would also have to deal with a directional gyro (heading indicator) that is not keeping true to the magnetic compass. This is done in smooth straight and level flight - when the gyro is adjusted to match the compass.

Can it really just be a matter of taking off in a particular direction and taking your hands off the wheel, virtually?

Once a plane if fully trimmed up in straight and level flight in a turbulence free environment, without control inputs it can probably manage less than a degree of heading wander every 5 minutes or so. Of course, even if the heading does not change, it would not be ballistic - just "straight" in the sense of a great circle - and even then, if there is no wind. And finally, even then, there would be this Coriolis Effect.

 

[.Scott]

For flights over longer routes, like transoceanic flights or flights over areas where no aids to air navigation may be present, modern navigation devices like GPS or even celestial navigation with sextants are often used.

Sextants are often used? I have never seen a sextant on an airplane. A year and a half ago, I did visit the cockpit of an Quantas flight that had just landed at Sydney from LA. I should have asked the pilot if he had a sextant.
My guess as to what would happen if the GPS satellites were suddenly taken out would be that all trans-oceanic flight would continue on magnetic headings until they found a shore-based VOR signal. I have a pilots license and have received training in Civil Engineering. The pilot training did not include the use of a sextant. The CE training did - and I don't think I would try to get an impromtu longitude measurement while flying.

 

[A.T.]

Sextants are often used? I have never seen a sextant on an airplane. A year and a half ago, I did visit the cockpit of an Quantas flight that had just landed at Sydney from LA. I should have asked the pilot if he had a sextant.
My guess as to what would happen if the GPS satellites were suddenly taken out would be that all trans-oceanic flight would continue on magnetic headings until they found a shore-based VOR signal.

I'm picturing a stewardess going through the cabin, holding up the dusted emergency sextant, asking if any of the passengers knows how to use it.

 

[sophiecentaur]

Ballistic missile are suborbital. Their paths are not considered "Great Circle paths".

Once the engines are turned off, the missile will have just one force on it and that will be towards the centre of the Earth. That, I think, will mean that it will follow a great circle path because all orbits will be in a plane which includes the Earth's cm. If that is not considered to be a Great Circle path then that doesn't bother me but it will be above a great circle locus on the surface.

 

[sophiecentaur]

I'm picturing a stewardess going through the cabin, holding up the dusted emergency sextant, asking if any of the passengers knows how to use it.

It'll be in the overhead locker, along with the dummy lifejacket and seat belt.

 

[russ_watters]

That, I think, will mean that it will follow a great circle path because all orbits will be in a plane which includes the Earth's cm. If that is not considered to be a Great Circle path then that doesn't bother me but it will be above a great circle locus on the surface.

The term "great circle" is specifically referring to the (rotating) surface of the Earth as is reference.

 

[sophiecentaur]

The term "great circle" is specifically referring to the (rotating) surface of the Earth as is reference.

Aaahhhh!

 

[vin300]

Not "immune", it just doesn't alter the plane's course because the plane is "bolted to the atmosphere".
.

And may I know what is the tensile strength of these bolts? So if you change course, due to the strength of the atmosphere, it will realign your path?

 

[russ_watters]

And may I know what is the tensile strength of these bolts? So if you change course, due to the strength of the atmosphere, it will realign your path?

Imperfect literary device was not my fault. So, is your question answered to your satisfaction or do you have clarifications you would like to provide?

 

[Loren]

GPS