How do airplanes correct their path

[vin300]

If a plane has to fly across latitudes as opposed to flying across longitudes, there's also rotational motion of the earth, so if it flies from antarctica to siberia and it takes too long, it is in no way certain whether it lands in siberia, norway or Canada, so it must constantly need to move a spiral path thus increasing the air distance manyfold. Is that correct?

 

[anorlunda]

If a plane has to fly across latitudes as opposed to flying across longitudes, there's also rotational motion of the earth, so if it flies from antarctica to siberia and it takes too long, it is in no way certain whether it lands in siberia, norway or Canada, so it must constantly need to move a spiral path thus increasing the air distance manyfold. Is that correct?

That's no different than the navigation problem of ancient sailing navigators crossing oceans. They have solved those problems long ago. The short answer is that they are not constrained to follow lines of constant latitude or longitude.

Perhaps you also forget that the atmosphere and the oceans follow Earth's rotation. Therefore, a hot air balloon does not see the Earth spinning below it. With no wind, the balloon stays fixed relative to a point on the ground. You must go up into space if you want to separate the ambient motion of your surroundings from rotation of the Earth.

 

[sophiecentaur]

You are referring to what's called the Coriolis Force. See this link and google, yourself for something that is at the best level for you.
When the plane takes off, northwards, it will have an eastwards velocity of several 100 kph (depending on the latitude). This needs to be factored into course to be steered when it is significant. But the atmosphere is being dragged around the surface of the Earth at more or less the same speed as the land beneath and is resisting the sideways drift, reducing the Coriolis effect. I believe the situation where Coriolis is most relevant is in the navigation of Ballistic Missiles, which spend most of their journey above the most dense part of the atmosphere and which travel so fast that the drag effect small.

it is in no way certain whether it lands in siberia, norway or Canada, so it must constantly need to move a spiral path

That's not necessary because it is no surprise and you can calculate the optimum course to steer* before you set off - as when swimming or sailing (slowly) the English Channel you let the tide slosh you up and down the channel but ignore this and just aim for your target port, only needing to consider the net drift between start and finish times.
*This course will give you a great circle path, so you need to correct your compass course constantly. But that's an additional and very relevant matter.

 

[russ_watters]

I think the question was having to do with the Earth spinning under the plane: the Earth does not spin under the plane, they spin together. So the Earth's rotation does not affect airplane ravel routes.

 

[sophiecentaur]

I think the question was having to do with the Earth spinning under the plane: the Earth does not spin under the plane, they spin together. So the Earth's rotation does not affect airplane ravel routes.

It may be a matter of the degree of error, which may not be relevant but the Coriolis Effect is there, as it is with moving air, forming the weather systems. If there were no atmosphere, there would be an eastwards takeoff velocity that would add, vectorially to any velocities that the plane would supply. The drag of the atmosphere must be highly relevant because the air in northerly latitudes would be going hundreds of kph slower than the plane's initial eastward speed and would slow its relative eastward velocity at an appreciable rate - much more lateral drag than backwards drag and that consumes all of the plane's engine power in level flight (about 75% of maximum power, I believe). So the effect on a plane would be small and damped out throughout its flight path.
OTOH, Coriolis affects artillery shells and missiles. http://www.haydenplanetarium.org/tyson/read/1995/03/01/the-coriolis-force which describes how naval battles in the southern hemisphere were affected by the reversal of the Coriolis effect.

 

[russ_watters]

Posting from a phone, so i'll be brief:
1. Planes don't care what causes the wind. We're getting into secondary and tertiary effects there.
2. Planes do not follow ballistic trajectories: they fly.

 

[sophiecentaur]

Posting from a phone, so i'll be brief:
1. Planes don't care what causes the wind. We're getting into secondary and tertiary effects there.
2. Planes do not follow ballistic trajectories: they fly.

But the only difference between planes and shells is density and speed. Same basic principles at work.

 

[russ_watters]

But the only difference between planes and shells is density and speed. Same basic principles at work.

No, the difference is that one actively maintains a heading and the other doesn't.

 

[.Scott]

If a plane has to fly across latitudes as opposed to flying across longitudes, there's also rotational motion of the earth, so if it flies from antarctica to siberia and it takes too long, it is in no way certain whether it lands in siberia, norway or Canada, so it must constantly need to move a spiral path thus increasing the air distance manyfold. Is that correct?

The Coriolis affect is too minor to deal with. A pilot or airline will plot its course based on weather, navigational aids, airport procedures, and airspace restrictions. It will also adjust it's altitude to take advantage of winds and aerodynamics.

But say we are talking about a flight segment that crosses a large section of the Pacific Ocean. The route selected will be a great circle path. At different times during the flight, the actual heading of the plane may be slightly to the left or right of its course - in order to compensate for cross winds.

In theory, such a long leg could be flown along a more optimal path to allow drifting with crosswinds - instead of fighting them, but this is not done because the optimization would provide little benefit - and the safety of flying an established corridor is more important. The Coriolis effect would be an even more minor effect that the crosswinds and no attempt is made to optimize the course for it.

 

[pbuk]

But the only difference between planes and shells is density and speed. Same basic principles at work.

What? The only thing I can think of that ballistic flight and aerodynamic flight have in common is the word "flight".

A plane maintains its course in the atmosphere (which is rotating broadly in line with the Earth's surface) through the forces of lift and thrust opposing gravity and drag respectively. A shell maintains its course in space (which is not rotating) through inertia, hence the appearance of fictional forces in the rotating frame of reference of the Earth.

 

[sophiecentaur]

No, the difference is that one actively maintains a heading and the other doesn't.

I have a problem with that answer. Just because a plane's course is maintained, doesn't mean it is impervious to a lateral acceleration and it has to be counteracted. But of course a slow plane has a small coriolis acceleration. Looking at a calculator that I found, it seems that, for an object going North at 500kph (140m/s), at a latitude of 80°, the Coriolis acceleration is only about 0.2%g. Hardly significant but coriolis is enough (1%g) to produce a lateral movement of a shell, in flight for 40s at a speed of 700m/s, of about 80m error over a range of 30km. Pretty significant if you are aiming at a Battleship and the gunnery tables included it. But the effect in both cases needs to be compensated for, although the pilot is not aware of it.

 

[sophiecentaur]

What? The only thing I can think of that ballistic flight and aerodynamic flight have in common is the word "flight".

A plane maintains its course in the atmosphere (which is rotating broadly in line with the Earth's surface) through the forces of lift and thrust opposing gravity and drag respectively. A shell maintains its course in space (which is not rotating) through inertia, hence the appearance of fictional forces in the rotating frame of reference of the Earth.

The pilot is correcting for the coriolis acceleration so the effect is hidden in all the other greater perturbations. That doesn't mean it doesn't exist. The fact that the windage of the planes fuselage is greater than that of a shell is not very relevant because the actual lateral speeds, slipping sideways, due to coriolis are small. So the air may as well not be there. So the principle is just the same for both 'flights'. The same equations apply and it's just a matter of the magnitudes involved. If there were no beam wind for a reasonable distance and the plane was set on a constant heading north, the path would be curved, largely due to coriolis. OTOH, a railway train or car are not subject to any such effect. lol.

 

[pbuk]

So the air may as well not be there.

Here is the mistake in your analysis. If the air is not there the plane will fall out of the sky, whereas the bullet will still hit its target.

 

[sophiecentaur]

Here is the mistake in your analysis. If the air is not there the plane will fall out of the sky, whereas the bullet will still hit its target.

The effect of the air on the flight mechanism has nothing to do with the lateral effect. I really didn't think that was worth mentioning. If you want, then, we could make our journey on a vast skating rink and take the air away. Would you then say that the vehicle would be different from a shell?
You seem to be suggesting that there is some significant lateral force that restrains an aircraft from following a coriolis path. At the slow lateral speeds involved, are you saying that air drag beats coriolis?

 

[SteamKing]

What an interesting thread so far.

Air navigation has developed along similar lines as has marine navigation.

Over developed countries like the US, there are special air navigation charts printed for pilots to use and a system of aids to navigation, like radio beacons, signals from which aircraft are equipped with special receivers to pick up. There are many areas where air traffic is restricted or prohibited from operating, and pilots need air maps to help them avoid these areas.

For commercial flights, there used to be navigators assigned to the crew, but these positions have been phased out and replaced by 'flight management systems'. Where there is considerable air traffic, aircraft usually fly at the direction of air traffic control, which is supposed to keep traffic flowing smoothly and reduce the possibility of mid-air collisions.

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.

https://en.wikipedia.org/wiki/Air_navigation

When all else fails, pilots will often descend to lower altitudes and 'fly the roads', if that is possible, to avoid getting lost over rough or remote terrain.

 

[pbuk]

The effect of the air on the flight mechanism has nothing to do with the lateral effect. I really didn't think that was worth mentioning. If you want, then, we could make our journey on a vast skating rink and take the air away. Would you then say that the vehicle would be different from a shell?

No, because it would then be in ballistic, not aerodynamic, motion. We could give the shell internal propulsion and control surfaces and make the air the viscosity of treacle. Would you then say that it would be different from an aeroplane? I don't think this gets us anywhere.

You seem to be suggesting that there is some significant lateral force that restrains an aircraft from following a coriolis path. At the slow lateral speeds involved, are you saying that air drag beats coriolis?

No, not drag - the airflow over the tailplane and control surfaces that keep the plane on a forward heading through the air.

 

[vin300]

The coriolis effect may be the most significant point, but it may not mean that we need to reduce coriolis acceleration. To reduce coriolis, the speed must go down, however, this creates an undesirable effect, that being a slower flight has to be concerned with Earth's rototion for a longer time thus distorting its path way farther. In comparison a greater coriolis effect ends earlier, distorts path lesser, thus the flier has to make lesser corrections.

 

[russ_watters]

I have a problem with that answer. Just because a plane's course is maintained, doesn't mean it is impervious to a lateral acceleration and it has to be counteracted.

The OP is about courses, not forces. So it looks to me like the difference is important.

If three objects are sent from a spot on the equator on a 1000 mile trip at a heading of 45 degrees...
One maintaining a heading of 45 degrees...
One maintaining a great circle at an inclination of 45 degrees...
One on a ballistic trajectory...

Each lands in a different spot. If you are discussing one case, you don't have to consider the others. The OP wasn't clear, but it looked to me like he was asking about the first case. But even if he wasn't, the one case that doesn't apply to an airplane is the third case.

The OP may be referring to:
1. The fact that if you maintain a constant heading of 45 degrees, you'll spiral toward the north pole.
2. If you maintain a great circle, you need to constantly change your heading (or break it into lines).
3. Or the completely different "why does the atmosphere spin with the earth?" (how can a plane even fly to the east if the Earth is spinning to the east faster than a plane can fly?)

Either way, this is a geometry problem, not a physics of flight/forces problem.

 

[sophiecentaur]

I still don't see any distinction to what happens to anything that's traveling with a NS component of motion. Just because a ballistic object is not controllable in flight, it seems no different to me that the single, initial course compensation is the same, in principle, to continuous course correction that a plane, either on a Rhum Line or a steered Great circle course is making. They all have to counteract coriolis. It is possible to arrange the same destination for any of the three navigation strategies. It just happens that GC involves the shortest distance.
I assume you are not claiming that coriolis acceleration only applies in ballistic flight. It is the most obvious one because the speeds involved are so much greater, that's all.
Even at very low speeds (winds of a few tens of kph) the coriolis effect is highly relevant to our weather so how can you say that aircraft are not affected?

 

[pbuk]

I still don't see any distinction to what happens to anything that's traveling with a NS component of motion. Just because a ballistic object is not controllable in flight, it seems no different to me that the single, initial course compensation is the same, in principle, to continuous course correction that a plane, either on a Rhum Line or a steered Great circle course is making.

Calculate what the single initial course compensation is for a ballistic object traveling from the equator at 500 km/h to hit a target 2,000 km due North. Do you really think that that is the heading an aircraft takes to travel that journey? Calculate the same for a journey of 120 km at 30 km/h. Do you think that is a heading a ship takes? Does a helicopter have to fly West at 1,000 km/h to hover over New York?

I assume you are not claiming that coriolis acceleration only applies in ballistic flight.

The coriolis effect or (if you insist on using the term) fictitious coriolis acceleration appears when you transform a velocity vector in an inertial frame of reference (e.g. ballistic flight) to a rotating frame. An aircraft's velocity is not maintained constant in an inertial frame of reference, it is maintained in the moving reference frame of the air through which is is flying. Any fictitious forces are only introduced when transforming from that moving reference frame to the rotating reference frame so it is only that transformation i.e. compensating for wind speed and direction that is relevant to the heading of the aircraft.

 

[A.T.]

The only thing I can think of that ballistic flight and aerodynamic flight have in common is the word "flight".

The ratios of the acting forces are different, but you can smoothly transition between the two regimes (e.g space shuttle reentry and landing)

 

[A.T.]

Calculate what the single initial course compensation is for a ballistic object traveling from the equator at 500 km/h to hit a target 2,000 km due North. Do you really think that that is the heading an aircraft takes to travel that journey?

No, the aircraft distributes that correction over the entire flight, which requires only a small additional lateral force. Just like a train going exactly N has a tiny lateral force on the rails all the time.

And if the plane goes W or E, it needs to correct for the vertical Coriolis component, by producing slightly more or less lift. See figure 5 here:
http://naca.central.cranfield.ac.uk/reports/arc/rm/3680.pdf

 

[pbuk]

No, the aircraft distributes that correction over the entire flight, which requires only a small additional lateral force. Just like a train going exactly N has a tiny lateral force on the rails all the time.

Yes! The train does not have to change its heading (which is just as well because that cannot generally be achieved with a smooth transition) because the rails keep it, literally, on track. In the same way, aerodynamic forces keep the aircraft on track - there is no requirement for the pilot to adjust the course. However sophiecentaur is saying that this situation is exactly the same as ballistic flight where there is no lateral force to keep the shell on track.

 

[rootone]

Even in idealised flight an aircraft can encounter unexpected wind and other non-ideal atmospheric conditions which need to be compensated for.
In practice what happens for a long flight is the that the pilot files a flight plan prior to departure.
The plan will include 'waypoints' - where the plane is expected to be - at different times in the flight, mostly in relation to land based radio beacons.
In most modern aircraft there is a flight management system (software connected to the autopilot), which automatically makes minor adjustments to the planes track so that the plane should arrive at the predetermined waypoints with good accuracy.

 

[anorlunda]

Calculate what the single initial course compensation is for a ballistic object traveling from the equator at 500 km/h to hit a target 2,000 km due North.

With or without the atmosphere?

You seem to be equating a ballistic trajectory in the atmosphere with one in space.

When we are in the atmosphere, which rotates with the same average speed as the planet, atmospheric effects make coriolis effects almost negligible. Ditto for a ship at sea. Ditto for a motor vehicle on a north-south highway.

 

[A.T.]

Yes! The train does not have to change its heading (which is just as well because that cannot generally be achieved with a smooth transition) because the rails keep it, literally, on track. In the same way, aerodynamic forces keep the aircraft on track

Air is not the same as a rigid rail. The train can point exactly N and still have a lateral force, to force it on an exact N course. A plane pointing exactly N (without wind) would have no lateral force, so it would drift of the N course, due to the Coriolis effect.

But in reality this effect is far smaller than winds.

 

[pbuk]

Air is not the same as a rigid rail. The train can point exactly N and still have a lateral force, to force it on an exact N course. A plane pointing exactly N (without wind) would have no lateral force, so it would drift of the N course, due to the Coriolis effect.

But in reality this effect is far smaller than winds.

I agree that there will still be drift in this case due to the Coriolis effect, and (ignoring aerodynamic lateral stabilisation from the tailfin and control surfaces which is negligible at this lateral drift velocity) the calculation of this drift is the same as for a shell. If that is what sophiecentaur was saying then we have been at cross-purposes all along.

It was this assertion (with which I certainly do not agree) that threw me:

... the only difference between planes and shells is density and speed. Same basic principles at work.

 

[vin300]

With a properly designed flying object, the atmosphere does exactly what the designer wants it to do, that is generate lift and minimise drag. Winds will be a problem only if the wind gets a reaction force from the surface of the object, but a streamlined object can dissipate winds in multiple opposing directions so that the net force is far reduced compared to drag produced by normal thrust. Neither the pilot nor a car driver nor a bird nor whales in the ocean desire waves to disrupt their motion, hence all of these vehicles are streamlined, streamline follows lines of potential gradient. A design perpendicular to streamlines, along constant potential, would create greatest effects of wind. This is also used, in yachts for navigation.

 

[sophiecentaur]

Do you really think that that is the heading an aircraft takes to travel that journey?

No.
1. Partly for a purely practical reason; there is interaction with the air with a plane. Invent some other way of staying above the surface and take away the atmosphere - now can you explain to me how the two courses would be different? Planes are not designed to have a low lateral drag because it is not an important design requirement , compared with the need for stable flight etc. and that is a practical reason why the aircraft heading would be different.
2. Would a ballistic craft, with an initial speed of 500kph actually have a range of 2000km? Artillery shells with such speeds only travel tens of km. The speeds necessary for long range ballistic travel are much higher and so the Coriolis effect will be much greater. The effect is proportional to speed.
All your argument here seems to be based on some sort of 'attachment' of the plane to the Earth but I argue that the only attachment is quite slight, in view of the low lateral speeds across the atmosphere. You could push a plane on a course and speed so that it's directly below a ballistic missile (involving an awful lot of fuel of course) and that wouldn't be a real situation - but the source over the ground would follow a curve which would not be a Great circle.

 

[jbriggs444]

No.
1. Partly for a purely practical reason; there is interaction with the air with a plane. Invent some other way of staying above the surface and take away the atmosphere - now can you explain to me how the two courses would be different? Planes are not designed to have a low lateral drag because it is not an important design requirement , compared with the need for stable flight etc. and that is a practical reason why the aircraft heading would be different.

Lateral drag is largely irrelevant because the pilot (or autopilot) will be trying to achieve coordinated level flight with an absence of side-slip. If the pilot manages the rudder to achieve and maintain the desired wind-relative heading and manages the bank angle to achieve an absence of side-slip then any sideways Coriolis force will be countered by the vector sum of gravity and lift. Lateral drag does not enter in.

 

[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.