# What does %MAC mean?

A document said that the optimum CG position is from 13% MAC to 33% MAC. I'd like to know what that means, and what would this look like on an actual plane.

%MAC (Percent Mean Aerodynamic Chord) is a mathematical calculation that shows where the center of gravity is over the wing. The calculations is rather straight forward and the generic formula is the same for all airplanes. All one has to do is to figure out the numbers and plug them into the formula.

## How is %MAC calculated?

Pilots, dispatchers or load masters will calculate the weight and balance with respect to the aircraft datum. Unfortunately, we need to change where the reference point is from the (datum) to the front of the wing called leading edge mean aerodynamic chord (LEMAC). There is also a trailing edge mean aerodynamic chord (TEMAC) that is calculated. TEMAC - LEMAC = Wing width.

LEMAC and TEMAC are easy to calculate for straight wing aircraft. It is simply the measurement from where the wing starts and ends from the datum. For swept-wing aircraft it isn't that simple. As a result, aerodynamic engineers figure out where the average of the LEMAC by averaging the wing root and wing tip. The same process happens for calculating TEMAC.

%MAC is simply a calculation of how far the CG is from the LEMAC. If the CG is at the LEMAC, we can say it is at 0% MAC. CG at TEMAC means the CG is at 100% MAC.

In the picture below, we can eyeball the %MAC to be around 10% MAC.

Here is the generic formula:

$$\%\mathrm{MAC} = \frac{\mathrm{CG} - \mathrm{LEMAC}}{\mathrm{WingWidth}} \times 100$$

The formula is great because all the numbers are relatively the same for every airplane. For example a 13% MAC means that we are most likely at or close to our forward CG limit. This should instantly give the pilot a sense of how the airplane is going to respond versus a pilot trying to comprehend what a CG of 2,341.0 inches aft of datum means for that particular aircraft. The last number can be different for every aircraft type but 13% MAC will be the same. The only difference is where the forward CG limit is located for that particular aircraft.

A little background, and perhaps an engineer can expand on the thought. The basic weight and balance formula is $$\mathrm{Weight} (W) \times \mathrm{Arm} (A) = \mathrm{Moment} (M)$$. What may not be obvious is that we can use this formula in figuring out why %MAC is important.

Take a look at the picture above. There is a moment between CG and CP and another moment between CP and tail down force. These moments must equalize for the airplane to be in equilibrium. If the CG moves forward, Moment #1 gets larger and to compensate the tail down force must increase. We can increase the tail down force with nose up stabilizer trim. The same analysis can be made when the CG moves aft.

If this is the case, there is a specific pitch trim setting for each %MAC and airspeed combination. Most jet pilots will set a specific takeoff pitch trim setting for takeoff based on %MAC so that if the pilot loses an engine after $$V_1$$ the trim will be set for a speed around $$V_2$$.

• Thanks! That explained it perfectly! Could you also explain how the LEMAC and the TEMAC are determined? Because on the diagram they seem to be random lines on the wing. Thanks! – Devansh Rathi Oct 12 '16 at 9:31
• What is the center of pressure? What is the different between center of pressure (CP) and center of lift (CL)? – AirCraft Lover Dec 27 '18 at 23:34
• From my understanding, maybe someone knows more but center of pressure and center of lift can be used interchangeably. – wbeard52 Dec 29 '18 at 0:16
• Draw a perpendicular line from the leading edge to the trailing edge cutting the wing exactly in half. The line will be closer to the fuselage than the wingtip as the wing is thicker at the root. The point where that line starts, in reference to the datum, is the LEMAC and where that line ends is the TEMAC. – wbeard52 Dec 29 '18 at 0:21

As @abelenky points out in his comment, it is the Mean Aerodynamic Chord of the wing. This is not exactly the mathematic mean of the wings' chord, but a size which includes the damping effect of a pitching wing which scales with the square of its chord. The % part just shows that this length is given as a percentage of the mean aerodynamic chord.

Next, you need a location for this length unit. This can be the actual MAC location of the wing, other aircraft use the leading edge of the wing root as the lengthwise zero point. All measure distances in their own coordinate system, positive backwards. The airplane manual should give an exact definition how to measure the correct CG location.

If the actual CG location falls within the range given by both numbers, you are safe to go. If the CG is forward of the smaller number, your control authority might not be sufficient, the pitch control forces will be too heavy for comfort and both your rotation speed and your stall speed go up. If the CG is aft of the bigger number, your static stability is too small or the airplane might even be unstable. Also, pitch control forces will be very low so you run the risk of damaging the aircraft with too large control inputs.

A document said that the optimum CG position is from 13% MAC to 33% MAC.

A possibly better phrasing of that statement is that the "allowable CG position is..." or some such. Typically the term "optimum CG position" is used not for a range but for a given CG position that optimizes whatever you wish to optimize. Usually for transport category aircraft it's used to refer to the target zero fuel weight CG that produces the best fuel economy.

As it happens, the range 13% MAC to 33% MAC are typical landing CG limits of 747s as well as the zero fuel, taxi and takeoff limits at low weights. An often used value for the optimum zero fuel weight target for best fuel economy is 26.6% MAC. Forward of that value would mean you'd burn more fuel, aft of the value you'd burn less fuel but would be starting to have undesirable effects that outweigh the fuel economy.

If you wish to see a graphical display of such limits, go to 747.terryliittschwager.com, select any aircraft, and when the aircraft page comes up, scroll down to the OPERATING ENVELOPES at the bottom of the page. If desired you can add fuel and cargo and see how it affects the CG.