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Newton's Second Law

Force equals mass times acceleration. F = ma

The above is called Newton's Second Law.

An acceleration means a change in speed or direction. Another way we could think of this law is that anytime there is NOT uniform motion, that means there is an acceleration, and that means there is a force.

constant airspeed

If the airplane is flying in uniform motion, as shown to the left then there is no force. We must learn to identify this situation.

We simply ask ourselves:

  1. Is the heading changing?
  2. Is the vertical speed changing?
  3. Is the airspeed changing?
Accelerated flight path

If we answer yes to any of these questions then the airplane is accelerating. For example the airplane to the left is "pulling out of a dive." The vertical speed is changing from negative to positive, so it is accelerating.

If the airplane is accelerating then there is a NET force acting on the airplane and that force can be calculated using Newton's formula:


Whenever we see the airspeed needle move we know we are accelerating, or if the VSI needle moves, or if the heading indicator turns. All these things are accelerations, and all will require a net force.

Conversely: when the airspeed, vertical speed, and heading are constant then there is no net force.

NOTE: That means there is NO NET FORCE WHEN WE CLIMB, or when we fly straight and level, or when we descend.

The Four Forces

There are four forces acting on an airplane all the time in flight:

The above forces are the ONLY forces acting on the airplane. However, we often run into terms such as G-Force, centripetal force and centrifugal force. So let's take a moment to discuss each of these before talking about the four forces in detail.


We spend almost our entire lives experiencing two things:

  1. The force of the earth's gravity
  2. Zero NET force

As you read this book you are doubtless in a chair that is holding you more of less stationary a foot or two above floor level. And I assume you are within the earth's gravitational influence as well. Therefore the net force on your body is zero, despite the fact that you are within the earth's gravitational field and are experiencing a downward force called weight.


In aviation we frequently talk about a force called G-Force. In aviation the G-force is by definition the force acting along the normal axis of the airplane, as shown to the left.

Of course we spend 99% of our time oriented as in the upper part of the picture, flying straight and level with the bottom of the airplane oriented toward the center of the earth. In this situation we have already learned that the NET force is zero. But there is still a G-Force. It simply follows that there is another force, which I have not drawn, that acts in the other direction offsetting the G-Force.

The lower airplane is performing an aerobatic maneuver, a "loop." In this case the bottom of the airplane is oriented in a completely different direction. Still that is the direction of the "G-Force."

G-Force is usually expressed in a unitless number call g's (pronounced gees) which is by definition:

g = G-Force / Weight

In the case of an airplane in straight and level flight we can see from the picture that G-Force is straight down and common sense tells us that the only force acting in that direction is weight. So G-Force = Weight in this case. Therefore g = 1.0

When an airplane makes a maneuver such as pulling out of a dive, or a steep turn, there is a centrifugal force in the direction of the G-Force. This causes g to be greater than 1.0. We often say we are "pulling g's." This is important structurally because the airplane is limited to a certain number of g's before it is over stressed and damaged.

Centripetal and Centrifugal Force

Previously I said that there are three questions you can ask yourself to decide whether or not there is a net force acting on the airplane:

  1. Is the heading changing?
  2. Is the vertical speed changing?
  3. Is the airspeed changing?

Most people think primarily of #3 when they think of acceleration. I.E. accelerate most commonly means "speed up" in day-to-day use. And we can accept that "slow down" is negative acceleration. In physics we call this linear acceleration.

Both #1 and #2 above involve a curved flight path. If heading is changing the airplane is flying a circle when viewed from above.

centripetal force

When vertical speed is changing there is curvature when viewed from the side, as in the picture to the left.

We can see that in this case the force pulling toward the center of the circle is lift. However it is possible to think of aircraft designs where thrust could also act toward the center of the circle - a Harrier jet for instance.

By definition all the force acting toward the center of a circle is called the centripetal force. In the example shown centripetal force = lift.

It is important to realize that centripetal force is not a new or additional force (i.e. it is not above and beyond the four forces listed above.) It is just what we call the portion of the four forces which acts toward the center of a curved flight path.

To understand the closely related force called centrifugal force we must now discuss Newton's Third Law.

© Copyright Raymond J. Preston