Flight test notes: centre of gravity
My colleague Ivan was prepping a student for their PPL flight test and he asked me if I knew a good online resource to help explain what effects moving the centre of gravity of an airplane has on its flight characteristics, at a level that’s appropriate for a student pilot. This is one of the questions that the Transport Canada flight test guide sets a student, specifically, as part of Exercise 2C, Weight and Balance, Loading (Ground Item):
Assessment will be based on the candidate’s competency to:
...explain the effect of various center of gravity locations on aeroplane flight characteristics.
I looked around and I didn’t find a page that I could wholeheartedly recommend, so I wrote one of my own. Think of this as a kind of Cole’s notes on the topic. If you’re interested in the whys and hows of any of the things here, beyond the very cursory explanations that I give, you’re welcome to drop me an email and I can point you towards more thorough explanations.
Pitch stability and controllability
Moving the centre of gravity forward makes the airplane more stable and less manoeuvrable in pitch. It also makes the trim less sensitive so you have to move the trim wheel more. If the centre of gravity is too far forward you may run out of elevator authority and so not be able to raise the nose enough to make a decent landing. If the centre of gravity is too far aft then the elevator trim will be too sensitive, it will become difficult to maintain a steady pitch attitude, and the aircraft will (if the cg moves too far) become unstable in pitch and impossible to control (in a way that will result in an inevtiably fatal crash – so, yes, literally, impossible to control.).
An airplane with the centre of gravity that is too far aft will also be harder or impossible to recover from a stall because the pilot will be unable to pitch the nose down to recover.
The centre of gravity limits in the airplane flight manual are carefully chosen so that if you respect them these undesirable changes in flight characteristics can stay as ideas on the page instead of manifesting themselves in the airplane you’re flying. That is to say, wherever the centre of gravity is, as long as it’s within the allowable range, these effects will be small enough so you don’t need to change the way you fly, and you may in fact not even notice the differences.
Moving the centre of gravity forward makes the plane less efficient; it will climb slower, fly slower and stall at a higher airspeed compared to how it flies if the centre of gravity is moved aft. Moving the centre of gravity aft makes the airplane more efficient, so it climbs faster, flies faster and stalls at a lower airspeed. You can see this effect reflected in some airplane flight manuals which present stalling speeds at different bank angles for both forward and rearward centre of gravity positions: the rearward centre of gravity reduces the stall speed.
This effect deserves a few words of explanation. Putting it as simply as possible, the horizontal stabilizer balances the weight of the airplane which is mainly located towards the front, close to where the wings lift the plane. If you move the centre of gravity (which acts as a fulcrum) towards the front the stabilizer has to push down harder and harder to hold the nose up in steady flight. The wing has to lift the weight of the airplane but also must overcome this downforce produced by the stabilizer, so when the stablizer has to push down harder the wing has to lift more, just as though the airplane had become heavier.
A heavier airplane means flying slower, climbing slower, and stalling at a higher airspeed – even if the airplane is only ‘heavier’ because the stabilizer is pushing down harder rather than the airplane being more massive.
Moving the centre of gravity towards the rear decreases the downforce provided by the tail. As the centre of gravity moves further rearward the tail can even end up providing positive lift, helping rather than hindering the wing. (You may read or be told that the tail is “not allowed to” provide positive lift, for stability reasons. This is not actually correct – it can. The stability limit is reached when the tail provides “too much” positive lift.)
Other things being equal therefore, a pilot should arrange to have the centre of gravity as far back as is allowed, to maximize efficiency, but not so far back that pitch stability or the ability to recover from a stall is dangerously compromised. If you comply with the centre of gravity limitations published in the airplane flight manual, this will keep you safe.
For small airplanes the efficiency change is quite small and the pilot’s opportunity to adjust the centre of gravity may be limited only to choosing which passengers sit in which seats. However for transport aircraft in commercial service even a fraction of a percent reduction in fuel burn (or increase in speed) over the course of a year may result in a considerable cost saving. Larger aircraft also have fuel tanks in different locations so can adjust the centre of gravity throughout the flight by pumping fuel backwards and forwards.
Phugoid and short period pitch oscillations
If you move the centre of gravity rearward, the phugoid oscillation gets slower. (If you don’t know what a phugoid oscillation is, you should ask your flight instructor to show you one.) The short period pitch oscillation also gets slower.
Minimum control airspeed (for multi-engine airplanes)
Not strictly relevant to PPL flight tests, but interesting nevertheless, is that the minimum airspeed for control of a twin engined airplane with one engine out increases if the centre of gravity is further aft. This is because if the centre of gravity moves towards the tail the leverage the rudder can provide to balance the yaw of asymmetric thrust decreases, so more rudder deflection is needed. It follows that you “run out” of rudder sooner when the centre of gravity is further aft.
If you’re coming up for your PPL flight test you should try to remember at least the effects of centre of gravity location on both efficiency and stability so you can answer the examiner’s questions on this topic. Good luck!