When you load up your plane for a flight, you need to make sure you're within your center of gravity (CG) limits. And you probably know that when your CG moves forward or aft, it affects your airplane's performance. But why?
Forward vs. Aft CG
The relationship between your aircraft's performance and CG location is simple: by moving your CG forward and aft, you change the amount of tail down force and lift you need for stable flight.
When you create more lift, you create more induced drag, and your performance goes down. But why are lift and CG location related?
CG: Your Airplane's Balancing Act
Your airplane balances on its CG, and that location is where the downward force acts on your aircraft.
Lift acts upward from your wing, at a point called the center of lift. And the center of lift is always aft of your CG (as long as you are within your aircraft's CG limits).
If you look at the diagram below, you can clearly see that if you didn't have a tail creating its own force, your airplane would nose straight down because of the moment created between the CG and center of lift (this can also be called torque).
Your elevator (or stabilator) balances out the moment by creating its own force, called tail-down force.
Essentially, your tail is an 'upside down' wing that generates lift downward. The amount of lift it needs to maintain depends on two factors: CG location, and aircraft weight.
How Moment Comes Into Play
The moment calculation is pretty simple: weight x arm = moment (or, force x distance = torque). So if you have a large amount of force at a small distance, it can be balanced out by a small amount of force at a large distance. You can see it in the diagram below.
So Lift And Weight Don't Equal Each Other?
One of the first things you learn as a pilot is that in level, unaccelerated flight, lift and weight equal each other. But that's not exactly the case.
When you look at the diagram below, what you really see is that weight and tail down force both need to be balanced out by lift. Essentially, lift needs to equal weight and tail down force.
How Does Drag Factor In?
When you create more lift, you create more induced drag as well. So as you can see, when your CG is forward, you need more tail down force, and more lift. You generate that extra lift by increasing your angle of attack, which in turn increases induced drag.
And as always, when you have more drag, you decrease your plane's performance.
How Much Difference Does It Really Make?
Before you go throwing everything possible into the baggage compartment, consider this: while having an aft CG definitely improves performance, in most light aircraft, the difference will only be a few extra knots of airspeed, and a few extra feet-per-minute of climb rate.
While it doesn't make a huge difference, and aft CG might help you get to your destination a few minutes early on your next long cross country.