Forces in a turn

[Marius_S]

(Not 100 % sure if this is the correct forum to post this, but I'll give it a try)

I've been reading a few books on aerodynamics lately to refresh my knowledge on that subject (been a while since I had the ATPL exam).

I'm a bit confused when it comes to turning flight and the forces involved. (And I don't think I'm the only being confused, since different books have different explanations...)

The things they do agree upon is that for an aircraft to turn, a force acting towards the center of the turn has to be present. This force would be the horizontal component of lift (or the centripel force). And to remain at the same altitude, the vertical component of lift must be increased. So far, so good...

But then we have the centrifugal force, which I always have been learned doesn't really exist. But according to the FAA (Pilots handbook of aeronautical knowledge for instance), that is the force which is the opposite of the centripel force. In my opinion, that can't be correct.
The ATPL books from Oxford Aviation doesn't mention the centrifugal force at all.

As I see it, if the centripel force and the centrifugal force is the same, wouldn't the plane continue straight ahead? As far as I know, when an object is moving in a circle at a constant speed, we will also have constant acceleration towards the center of the circle because the velocity is constantly changing (remember, velocity has both direction and speed. As the object is moving around in a circle, the speed is constant, but direction is changing, therefore the velocity is changing). If the centrifugal force is equal to the centripel force, this acceleration can't exist.
This is at least how I see it. I could of course be wrong, and that's reason I'm posting this to see if anyone in here can provide me with an explanation.

Then we also have skidding and slipping. The "Pilots handbook of aeronautical knowledge" say that in a slipping turn, the centripel force is greater than the centrifugal force, and opposite in a skidding turn. So, if centrifugal force does not exist, what is causing the ball in the inclinometer to go left or right? I would think it has something to do with the relative wind not being parallel to the longitudinal axis of the plane, although I'm not sure.

[Deeday]

This probably is stuff for the Tech Log, anyway:
the centrifugal force, which I always have been learned doesn't really exist. But according to the FAA [...] that is the force which is the opposite of the centripel force. In my opinion, that can't be correct. It is correct in that, if you look at the vectors, they are equal and opposite. The point is that the centrifugal force is fictitious, i.e. it's not really exerted by any body; it is the force that IF it were applied to the aircraft by some means, it would balance all the others, allowing the aircraft to achieve equilibrium, i.e. moving straight and level. Given that nothing really exerts on the aircraft a force like the centrifugal force, the real forces are not in balance, which is why the aircraft turns in circle.

So, if centrifugal force does not exist, what is causing the ball in the inclinometer to go left or right? Its inertia.

[Marius_S]

Thanks for your reply!

So thing I don't understand is, why include the centrifugal force at all? Wouldn't it be better to talk about inertia instead?

Its inertia.

I've been trying to compare a plane in a constant bank turn with a car driving around a circular racetrack where the road is curved. Both the plane and the car is equipped with an inclinometer.

If we look at the plane first in a coordinated turn, "the ball" is in the middle. Would it be correct to say that the force keeping it in the middle is the same force pushing the pilot down into the seat, the resultant load (the force opposing the total lift)?
Would the same thing be true (the ball in the middle) for the car driving around the racetrack, if the speed is the correct one for the angle of bank of the road?

If we put the plane in a skidding turn (rate of turn being too great compared to angle of bank), the ball would go to the opposite side of the turn and the pilot would feel a force pulling him in the same direction. That "force" would then be the inertia (the rate of turn being too great, so the inertia is trying to make plane go straight ahead instead of turning).
If we apply the same example to the car on the racetrack, we could say that the skidding is being caused by either less angle of the road, or the speed of the car being too great. Either way, the inertia is forcing the ball to the opposite side?

And the last example, slipping turn: In the plane, this would be caused by the bank angle being too great compared to the rate of turn, for example, applying opposite rudder. The plane will slip or "fall" into the turn, forcing the ball towards the center of the turn. Would it be correct to say that this is caused by the effect of the inertia being too small? In our racetrack example, a "slip" would be the case if the speed is too slow (making the effect of inertia less), or the angle of the road being too great. The car would then fall of the track.

What I've been writing could be completely wrong, but I'm trying to see if the same forces being applied on an airplane, also can be seen elsewhere (for instance with a car on a racetrack). Anyway, I appreciate any comments on this.

BTW: Could a moderator move this to the tech log, if that's more appropriate for this subject?

[bookworm]

Every mechanics problem must be considered in a "frame of reference". You can choose your frame of reference, but picking the right one often makes the problem easier to solve. If you want to use Newton's Laws without modification, you must choose an inertial frame, i.e. one which is not accelerating or rotating. If you choose to use an accelerating or rotating frame instead, fictitious ("inertial") forces to compensate must be added to make Newton's Laws work.

If you consider the problem in the inertial frame of the ground, your turning aircraft is accelerating about the centre of its turn. The horizontal component of lift creates a centripetal acceleration according to F = ma, causing the acceleration required to make the aircraft turn.

If you consider the problem in the rotating frame of the aircraft, your turning aircraft is not moving. However, a centrifugal force, away from the centre of rotation of the frame, must be included to compensate for the use of the rotating frame. The horizontal component of lift balances the centrifugal force, leaving the aircraft with no unbalanced forces applied.

In such a simple case, it's difficult to see why one would bother with the complexity of a rotating frame of reference. In fact, many simple mechanics problems can be solved in an inertial frame, leading to the usual schoolteacher's assertion that "centrifugal force does not exist". However, when problems get more complex, use of a rotating frame and inertial forces can make things simpler. Try solving the movement of air around a low pressure system at the surface of the earth using an inertial frame!

[worrab]

Other examples:

Attach a weight to a string and spin it round. It prescribes a circle The string provides the pull to the centre. If the string snaps, the weight then flies of in a straight line (at a tangent to the circle).

A car on ice will prescribe a circle if driven slowly. If the brakes are fiercely applied to lock the wheels, the force of friction that is pulling the car in a circle is exceeded and the car goes dead straight at a tangent to the original circle.

Matters in an aircraft are a little more complex because there are forces keeping the aircraft in the air, pulling it down and making it change direction (ignoring drag and thrust). In straight and level flight, the force of lift exactly matches that of gravity. When you bank into a corner, the total lift is now at an angle. We split this into its vertical and horizontal components because it makes the math(s) easier. The greater the angle of bank, the less the vertical and the greater the horizontal components. So if you just bank straight-and-level aircraft (and keep the speed constant), gravity and lift will no longer be balanced: the aircraft will descend, and there will be a horizontal force component that will make the aircraft turn. If you return the aircraft to level flight it will flight straight (at a tangent to the circle) and level once more.

HTH

[homeguard]

Centripetal and centrifugal are not forces in themselves but are collective words.

Centripetal forces are those acting toward the centre and centrifugal those forces acting away from the centre.

Newton laws tell us that a body remains at rest or at a constant velocity unless an external force acts upon it. Every force has an equal and an opposite force.

Gravity you could consider a centripetal force (we fly around a circle when we follow the Earth don't we.). Lift therefore will be the centrifugal force. Thrust and drag always playing their part.

Adopt an angle of bank: a component of the lift (centrifugal) now acts horizontily away from the vertical becoming centripetal. The component of lift (centrifugal) opposite to gravity or weight (vertical) is reduced. But what about weight? When the wings were level there was two vectors (setting aside thrust and drag for the moment.) that of gravity and lift. With an angle of bank adopted we now have multiple vectors. The Verticle component of lift (centrifugal) must be increased to maintain equal to gravity (centripetal) . But we now have a second centripetal force, that produced by the inclined lift with an opposite force to it acting away from the inclined lift adding to the weight of the aircraft which is centrifugal. Add this centrifugal force to the centripetal gravity and you have a 'total weight'. you must increase the lift further adding to the 'total lift' to balance the total weight otherwise the aircraft will mush and therefore stall but at least lose height.

Draw a Parallelogram when it becomes simpler to see. During a turn total weight is greater than in level flight so therefore so must total lift be increased.

[BackPacker]

Every force has an equal and an opposite force.

What is confusing is that this law of Newton is often interpreted as "equal and opposite force on the same body". But that's not the intention of this law.

If you spin a weight on a string around, there is a centripetal force, which is the string pulling the weight to the center. The Newtonian "opposite force" of this is the centrifugal force: the stone pulling the string away from the center. There is NO centrifugal force acting on the weight itself.

So the forces that act on the weight itself are not in balance. There is only a centripetal force, no centrifugal force acting on the weight. As a result of this imbalance of forces the weight does not show linear motion, but is accelerated towards the center. And therefore the weight describes a circle.

Moving to the turning aircraft example, lift is generated by exerting an opposite force against the air. In level flight this causes a downdraft straight down (equal and opposite to lift - leaving aside the effects of thrust and drag for now). When the aircraft is turning, the downdraft is not straight down but has an outward horizontal component (the centrifugal vector). As a result of this, lift has an inward horizontal component (the centripetal vector). The forces on the aircraft are not in balance because there is a centripetal force acting on it, but not centrifugal force, so the aircraft "accelerates" in the direction of the center of the turn. And thus flies in circles around the center of that turn.

[bookworm]

The wikipedia article on centrifugal force (http://en.wikipedia.org/wiki/Centrifugal_force) is useful here in explaining two possible uses of the term "Centrifugal Force". I hope it's obvious that I'm referring to what they term "fictitious" or "inertial".

The explanation in the "Pilots handbook of aeronautical knowledge" is simply bad physics, for the reasons Backpacker outines.

[asyncio]

This pretty much sums it up in easy to understand pictures :8

xkcd - A Webcomic - Centrifugal Force (http://xkcd.com/123/)

[jonburf]

forces allways act in pairs.
as the aircraft is banked and the angle maintained. the forces in and out of the circle are balanced. If this were not true the turn would be tightend. This though does not mean Newton one because despite the constant speed of a turn the velocity is changing because the aircraft is accelerating.

[worrab]

forces allways act in pairs. ?
,,,if a body is in equilibrium then the forces balance out, but there may be more than one pair of forces in the equilibrium and it's reasonable for n forces to be opposed by m others in an equilibrium (M<>N).

A plane (or anything else) that is in a turn is not in equilibrium but is experiencing an acceleration that is proportional to the imbalance in the various applied forces.

[englishal]

If one is in a banked turn, then one is accelerating towards the centre of the turn, and hence the reason one feels the G forces (at 1/cos(AoB)).....If one is accelerating then forces cannot be in equilibrium.