What is the difference between centripetal and centrifugal force?

In a homework problem I was asked: In a balanced banked turn an increase in angle of attack will :?

Answers are : 1/ reduce indused drag. 2/ increase centripetal force . 3/ increase centrifugal force . 4/ have no effect on the turn.

Obviously answer 1 and 4 are wrong but what about centripetal vs centrifugal force? What is the difference between the two?

• Have you made any effort to answer it yourself? What do you think about the options?
– fooot
Jun 12 '18 at 20:19
• I think Its increase in centripetal force Jun 12 '18 at 20:24
• @AmranAlbalushi: Centripetal force is correct but please don't just ask your homework questions on this site. An appropriate question might be what is the difference between Centripetal and Centrifugal force. A question worded this way will help others who have the same question.
– DLH
Jun 12 '18 at 20:29
• @AmranAlbalushi: At the risk of angering my colleagues I will go and answer the question since you are new. However questions asked on this site should not simply be homework questions asking for the correct answer. If you are confused about a certain concept (like difference between centripetal and centrifugal force) just ask that. If you don't mind I will edit your question so you don't get more down votes.
– DLH
Jun 12 '18 at 20:53
• – 0xdd
Jun 14 '18 at 16:57

Centripetal force is the answer. Hopefully you can see that options 1 and 4 are wrong without me having to explain. I will elaborate instead on the difference between Centripetal force and Centrifugal force.

First Centrifugal force is not really a force at all but really a perceived force due to the inertia of an object to resist a turning tendency. In a coordinated/normal 1G turn you should not feel any Centrifugal force.

Centripetal force is a force that makes a body follow a curved path. When the angle of attack is increased more lift is generated and hence there is more force to execute the turn. Since the wings are banked the increase in lift causes the airplane to turn more so Centripetal force would be the correct answer.

EDIT: Due to some comments about my answer I decided to clarify a few things. First of all where there is Centripetal force there is centrifugal force with centrifugal opposing Centripetal force. However in an airplane there are many forces at play. In a coordinated 1G turn, the horizontal lift component matches the centrifugal force (but in opposite direction) as shown in the diagram below. Therefore the horizontal lift cancels out the centrifugal force so you don't feel the centrifugal force but it doesn't mean the centrifugal force isn't there. Forces in an airplane can be deceiving that is why pilots sometimes get disoriented when there is no horizon for a reference.

• @AmranAlbalushi, the second paragraph is totally wrong, unfortunately. Jun 12 '18 at 21:47
• In a coordinated turn you definitely do feel the centrifugal force. The centrifugal force is indeed a perceived, better known as inertial, force, but the cause is acceleration of the reference frame, the one attached to the turning aircraft, not inertia of anything. Centrifugal force exists in any and every reference frame attached to a turning or rotating body. It causes acceleration exactly opposite to that caused by the centripetal force in the corresponding non-rotating frame of reference. Jun 12 '18 at 21:52
• On a side-note, the Earth-attached frame of reference is not inertial either as it contains the inertial force of gravity. To complicate matters further, according to standard English terminology, gravity is not just the gravitational force, but the sum of inertial forces, which include gravitational forces (from Earth and other celestial bodies) and centrifugal forces due to rotation of Earch and all it's orbits). Jun 12 '18 at 21:58
• If 2 is correct then 3 is also correct. If you increase one then you increase the other, period. They are linked. Jun 13 '18 at 0:38
• The “feel” term the way you used it is bogus. The fact that two forces are balanced does not mean you don't “feel” them. Since the centripetal force (= horizontal component of lift) is acting on the wings, and then transferred to your body by the seat, while the centrifugal force is an inertial force, acting on each particle in the reference frame attached to the aircraft, they act at different places and therefore create stress in your body. You definitely do feel that. It is pushing you into the seat more than in straight flight. Jun 13 '18 at 5:21

Two of the given answers - choices (2) and (3) - are correct in different reference systems. It depends on the reference system of the observer:

• In a non-accelerated reference system, centrifugal forces do not exist. Increasing angle of attack increases the centripetal force, that increases the turn rate. The reaction force of the centripetal force is the innate force of the plane.

• A passenger in the plane observes the scenario from within an accelerated reference system. The plane is turning without obvious reason. The passenger's body wants to move in a straight line and seems to exert a force on the seat. This virtual force is called centrifugal. The seat seems to react by supporting the body with the same amount of force. When the pilot increases the angle of attack of the balanced turn, the centrifugal force will increase. The observer inside the rotating system is not aware of the centripetal force. The centripetal force does not exist for him.

Centripetal and centrifugal forces never co-exist in the same reference system! Even though they might appear like counter forces to each other, they should not be understood like that.

Centrifugal force is a construct to explain our perception and sometimes to simplify calculations in rotating reference systems.

Between the two, centripetal force is the more fundamental notion. It really describes what is going on, therefore (2) is the better answer from a scientific point of view. Nevertheless, (3) centrifugal force is a valid answer if the reference to a rotating system is established. That seems to be the case in the question. The centrifugal force describes what an occupant feels who is not aware of the rotation.

• We may wish to consider both centripetal and centrifugal forces as archaic terms. Acceleration, and the load created by acceleration is another way of seeing it. David swung his sling with centripetal force on the string, but the stone flew in the instantaneous direction of travel when the string let go. So it was released when the stone was moving at the target, roughly 90 degrees from the line between the slinger and the target. The actual angle takes into account the length of the string, forming a triangle between the slinger, target, and position of stone at release. May 6 '19 at 9:38
• @RobertDiGiovanni "the load created by acceleration"* This is a very misleading way of seeing things. Accelerations don't cause forces (loads in your wording), forces cause accelerations. May 6 '19 at 9:49
• Yet we call them G forces, which could be considered doubly wrong. This forum has many times helped much to clarify what are essentially differences in language rather than concepts. Happy to be here. May 6 '19 at 11:35
• This is a good answer-- I am going to offer a slightly different one along the lines of the comments above, feel free to comment on it. May 6 '19 at 15:32
• Centripetal force is an interaction force and as such exists in all reference frames and is the same in all of them (at least under Newtonian mechanics; I am not completely sure about relativistic mechanics). They therefore do coexist in the rotating frame of reference (the one attached to the plane). Jun 8 '20 at 14:27

This is all wrong. There can be no balance of forces in circular motion, otherwise you would not have circular motion. For circular motion you need only centripetal force. Centrifugal and centripetal force do not coexist in the same reference frame so they can not be in balance or cancel each other out. In airplane reference frame there is only centrifugal force and gravity, which both add to resultant G load.

• A "balance of forces" would seem to imply no net force, and thus no acceleration. But an object with circular motion is continuously changing its velocity vector -- thus, "accelerating", so it clearly is being acted upon by an unbalanced, net force. So I entirely agree with you. That said, this might be better as a comment than an answer, once you have a little more reputation. Welcome to Av.SE! May 5 '19 at 23:55
• Definitely bring this discussion to your teacher and classmates. The Centripetal force is the vector of real forces that points toward the center of a turn. No better example exists than a object in orbit. Orbital motion is a curve produced by gravitational acceleration downwards and constant velocity to the side. There is no centrifugal force. "Centrifugal force" as the name implies, is the G load created by acceleration in the opposite direction. Note, at constant velocity, in orbit, the ACCELERATION towards earth cancels out gravity, resulting in "weightlessness". May 6 '19 at 1:37
• @RobertDiGiovanni Only in physics class all masses tend to be either points or solid regular spheres. Reality is more complicated. Our oceans are bulging out towards the sun, and away from the sun as well. Centrifugal force is an elegant way to explain the latter.
– bogl
May 6 '19 at 8:12
• Santa Claus is "elegant" too. Frame of reference is more like it, or action/reaction. And let's not forget the motion of the solar system around the galactic center. Yes, I know reality is complicated, that is why applications interests me quite a bit more. In all cases "centrifugal force" is the RESULT of a change in direction. However, we could discuss why we call them "G" forces, when gravity is an attraction of masses. Maybe because they are combined with gravity to produce net load. I'll go along with "C" forces in that context. May 6 '19 at 9:09
• @RobertDiGiovanni G-forces are called so because they are given in (pseudo) units of the gravitational constant (g). People like calling physical quantities by their unit, rather than by their intriguing physical names. And the difference between reference systems and Santa is that he never helps you calculating a problem.
– bogl
May 6 '19 at 12:05

2. and 3. are both true, because centripetal and centrifugal force are intimately related by the principle of action and reaction (a.k.a. Newton's third law of motion).

However if you are expected to only check one answer, the examiner has probably drowned in the terminological quagmire surrounding these two terms, in which case they probably want to hear 2.

What is the difference between the two?

Centripetal force is a force that is causing a circular motion. In case of turning aircraft, it is the horizontal component of lift.

Centrifugal force, in contrast, is an inertial force in the reference frame of the turning object that balances the centripetal force there so the turning object—the aircraft—stays in its place in that reference frame. In that reference frame, the centripetal and centrifugal force are action and reaction and as such have the same magnitude and opposite direction, always.

In Newtonian, classical, mechanics, inertial forces are called “fictitious”, because the laws of motion are postulated for inertial reference frames and these forces are considered just artifact to allow using them in non-inertial reference frames as well. In this context, answer 2. makes sense alone more than answer 3. alone.

However in General relativity, the inertial forces, which in General relativity includes gravitational force¹, are usually considered just as real and all reference frames just as good as the ones in free fall (which take over the role of inertial ones), so centrifugal force is just as real and both answers should be checked.

¹ I intentionally didn't write “gravity”, because in usual English terminology that is used for the sum of inertial forces in the reference frame of Earth surface, which includes gravitational force of Earth, centrifugal force due to rotation of Earth and tidal forces due to gravitational forces of other celestial bodies and orbital motions.

• With due respect, but centripetal force is not the reaction to centrifugal force. Please see my answer.
– bogl
May 6 '19 at 8:06
• @bogl, you say there that in the rotating reference frame the centripetal force does not exist. But it being “real”, aerodynamic, force, it is invariant to coordinate transformation, so it must exist there—it is what keeps the aircraft from being accelerated by the centrifugal force, which makes it a reaction to the centrifugal force. So how do you call it in that reference frame instead? May 7 '19 at 5:22
• The rotating frame is really useful for rotating rigid bodies. Inside the plane, everything makes sense. The pilot exerts centrifugal force on seat, seat reacts with opposite force. When turning, there is no solid string between the plane and the center of rotation. The surrounding air is neither rotating with the plane, nor it is solid. There is the horizontal component of the lift that happens to cancel the centrifugal force on the plane. The point is, that the rotating reference is not useful to justify why this is the case. The forces match because of how the reference frame was chosen.
– bogl
May 7 '19 at 6:53
• @bogl, The forces match because of how the reference frame was chosen, but they still match, they are still action-reaction pair, and they are still centrifugal and centripetal force. It is not particularly useful for understanding how aircraft turn, but it is still the definition of the terms—and since the centrifugal force only exists in the rotating reference frame, it is the only one in which it can be described. May 8 '19 at 19:53
• By definition, a centripetal force makes a body to follow a curved path. There is nothing rotating inside the rotating reference. The notion of a centripetal force does not belong there. It is either centrifugal force against horizontal lift in the rotating reference, or centripetal force against innate force in the global reference.
– bogl
May 8 '19 at 21:22

There are really two different questions here. You asked "What is the difference between centripetal and centrifugal force", but there's also an implication that you'd like to know what is the best answer to the homework problem. This answer will try to address both questions.

We could say that in a constant-speed coordinated turn, the real aerodynamic force is equal to the wing's lift vector, which if we desire we can break down into centripetal and vertical components. There is also a downward force component due to gravity. The net force components including gravity are in balance in the vertical dimension, but NOT in the horizontal dimension-- otherwise there would be no turn.

The forces the pilot "feels" are only the real aerodynamic forces, not gravity -- or perhaps it is more descriptive to say that the pilot "feels" an "apparent force" that is equal in magnitude and opposite in direction to the net aerodynamic force. So as the net aerodynamic force is transferred through the aircraft structure to the pilot's seat to the pilot's body, the pilot "feels" an "apparent force" pulling him down into his seat, which if we desire we can break down into centrifugal and downward components. The root cause of this "felt" or "apparent" force is the acceleration acting on the pilot's body-- excluding the component of acceleration due to gravity. Note that gravity does not actually "cause" the downward component of this apparent force -- if gravity were to instantly disappear the trajectory of the plane and pilot would both instantly change as the flight path curved upward into a loop but the pilot would not feel any change in the "apparent force" pushing him into seat. The fundamental reason for this is that gravity "works from within" and exerts an equal acceleration on every molecule of the pilot's body and aircraft without causing any stresses or strains (ignoring tidal effects), so it isn't perceived as trying to squish the pilot's body down into the seat. (We'd have to modify this point of view if we wanted to adopt a reference frame centered on the aircraft, treating the aircraft as a stationary object or an object moving at a constant velocity-- this would not be a valid inertial reference frame and would not tell us anything about the forces that a pilot actually "feels" in flight.)

In a constant-speed coordinated turn, thrust and drag are equal, and the plane is not being allowed to fly sideways through the air, so the airflow is not striking the side of the fuselage and generating an aerodynamic sideforce. So the net aerodynamic force is simply equal to the wing's lift vector. This force is acting straight "upward" in the aircraft's reference frame-- i.e. in same plane as the vertical fin-- and in response, the "apparent force" that is "felt" by the pilot is pulling him straight "down" into his seat-- i.e. in the same plane as the vertical fin.

Now what happens when we increase the angle-of-attack, causing at least a temporary increase in lift?

Let's take the point of view of looking at the real forces, not the "apparent forces". If we increase the wing's angle-of-attack, we increase the lift force, including the vertical and horizontal (centripetal) components. But we don't change the direction of the lift force. Saying that we've caused a change in centripetal force is true, but incomplete, because we're not mentioning the change in vertical force.

Now let's take the point of view of looking at the "apparent forces", not the real forces. If we increase the wing's angle-of-attack, we increase the lift force, including the vertical and horizontal (centripetal) components. This means that there's an increase in the "apparent force" pulling the pilot down into his seat, including both the vertical and horizontal (centrifugal) components. Saying that we've caused a change in the apparent centrifugal force is true, but incomplete, because we're not mentioning the change in the apparent vertical force.

If we just note the increase in the "apparent" centrifugal force, we might think that when we increase the angle-of-attack and lift force, the slip-skid ball (and the pilot's body) will tend to deflect (lean) toward the outside wall of the cockpit. This is not the case -- even though some of the very faulty diagrams we see in pilot training manuals and FAA exam materials might lead us to think otherwise.

The choice of 2) or 3) to the original question depends on whether we are interested in real forces or "apparent forces". But neither is a complete answer because both ignore the vertical force components at play. (If the question were about an increase in bank angle rather than an increase in angle-of-attack, then it would be a different story.)

2) is really a better answer than 3) because the question just asks about forces, not "apparent forces".

In the specific context of a coordinated turn, we could say that "centripetal" force is one component of the actual net force at play, while "centrifugal" force is one of component of the perceived force or "apparent force" at play, which is equal and opposite to the real force.

But more generally, "centripetal" means acting toward the center of the curve defined by the curving flight path (horizontal turn, or loop, or whatever), while "centrifugal" means acting away from the center of the curve traced out by the curving flight path (horizontal turn, or loop, or whatever).

We could have a discussion about performing loops that would be very similar to the discussion above. Again, the actual net force would have a "centripetal" component-- as would the portion of the actual net force that is due to aerodynamic force-- while the "perceived" force or "apparent force" would have a "centrifugal" component.

Yet there are other cases where we can generate an actual aerodynamic centrifugal force component that reduces the total aerodynamic centripetal force that the aircraft is generating. So it's not as simple saying that "centripetal" always refers to real force and "centrifugal" always refers to "apparent force". Example-- starting with a coordinated turn-- now apply lots of outside (top-side) rudder-- nose yaws up/out, airflow strikes side of fuselage creating an aerodynamic force toward high wingtip-- this is a real force, and it has a centrifugal component, so net centripetal force is reduced and the turn rate slows. Note also that when we add this new aerodynamic force into the picture, the total aerodynamic force is no longer acting in the same plane as the wing's lift vector, i.e. no longer is aligned with the vertical fin. Therefore the slip-skid ball will ride off-center toward the low side of the cockpit, and the pilot's body will tend to lean in that direction as well.

And to add yet another twist, consider an aircraft doing multiple loops without stopping. What is happening at the bottom of each loop? Gravity is a contributing a real centrifugal force component that affects the rate and radius of curvature of the flight path, yet the only "apparent force" the pilot "feels" is the apparent "centrifugal force" component that is exactly equal and opposite to the aerodynamic centripetal force generated by the wing.

Likewise we can think of a situation where the NET aerodynamic force is centrifugal rather than centripetal in nature. Example-- aircraft is flying an arcing trajectory such as the well known "Vomit Comet" zero-gravity simulator. We'll focus on the instant at the top of the curving arc, where "centripetal" is the same as "earthward" and "centrifugal" is the same as "skyward". Net aerodynamic force is zero, net "apparent force" is zero, total net force including gravity is equal to the weight of the aircraft and contents acting in the downward (centripetal) direction, and net acceleration is 1-G downward. Now if we repeat the same maneuver but with the wing generating a very small amount of lift-- say 1/10 the total weight of aircraft and contents-- we'll get almost the same arc. The net aerodynamic force is 1/10 the weight of the aircraft and contents, acting in the skyward (centrifugal) direction, so the "apparent force" acting on the aircraft, or on any object in the aircraft, will be equal to 1/10 the weight of that object, acting in the earthward (centripetal) direction. In other words, we'll "feel" 1/10 "G" of acceleration toward the earth. Our G-meter will read positive 1/10 "G". But the total net force including gravity is 9/10 the the weight of the aircraft and contents, acting in the earthward (centripetal) direction.

• The problem with the faulty diagrams we see in flight training manuals and FAA study/exam materials is they give the impression that the reason a turn feels "coordinated" is that centripetal force and centrifugal force are in balance, and that the reason a turn feels "uncoordinated" is that centripetal force and centrifugal force are not in balance. I hope my answer helps clarify why this is a completely inaccurate way to look at things. Some of the other answers did as well. May 6 '19 at 18:09
• Some of the examples in this answer such as the aircraft at the bottom of a loop during a whole series of loops made the simplifying assumption that thrust and drag were equal, when that is surely not true-- hopefully that doesn't obscure the basic point being made here. May 6 '19 at 19:40