What is percentage Mach and how do we use it to better understand our centre of gravity? Let's find out. Hi I'm Grant and welcome to the fifth class in the mass and balance series. In the last class we talked about the centre of gravity and the center of pressure and how they interact with each other to cause rotation. This class will be a jump a bit deeper into those concepts and how we describe the positions based on percentage mean aerodynamic chord.
The position of the center of gravity is most commonly described in relation to the center of pressure. This is because the wing design is fixed and therefore the center of pressure is also relatively fixed. It does move depending on the angle of attack and levels of air flow over the wing, but that's covered in principles of flight. For the purposes of mass imbalance, the center of pressure can be considered stationary. The center of gravity however moves based on the loading, as we saw previously, moves either forward or backwards.
So we describe the position of the center of gravity and the center of pressure in relation to fixed reference. This reference that we use is something called the mean aerodynamic cord or MAC. The cord of a wing is a line from the leading edge through the center of the wing to the most trailing edge cutting the wing directly in half. This dotted line here is the cord line of this wing. Now, in modern aircraft, and all aircraft in fact, wings are not uniform the whole way along.
They taper off towards the ends, just by their design. This means that the cord length across the whole wing varies as we go down it gets reduced as we go towards the wing tip and it's larger at the wing root. So using this concept of the mean aerodynamic chord we essentially take an average of all these different lengths and equate this wing into something that looks a lot more square shaped. This is our mean wing and from that we take our mean aerodynamic chord.
So our center of gravity and our center of pressure are usually described as a percentage figure along this fictional wing or this mean aerodynamic chord. To get that percentage you we use the standard sort of practice of we take the smaller number divide it by the bigger number and multiply by 100 so you know standard percentage sort of stuff like um what is 20 20 out of 100 you would do 20 divided by 100 and then times 100 obviously it's 20 in this case but that simple process So we'll do a quick example just to show what we're talking about. This is our example.
The centre of gravity reference to a datum is plus 25 centimetres. The leading edge Mach is located at minus 40 and the trailing edge Mach is at 1.2 metres. What is the percentage Mach of the centre of gravity?
So we draw the effing picture. So we've got our datum point. I'm just going to pop that in as a line here. Centre of gravity is plus 25, plus to the right.
So our centre of gravity is over here. and that's 25 centimeters. Our leading edge mac is located at minus 40 so that's over here and that's the start of our wing over here that's at 40 centimeters.
And our trailing edge Mach is located at 1.2. So that's going to be over here. And this distance in here is 1.2 meters, 1.2 meters. So we have this fictional wing, looks something along the lines of that, but our center of gravity along it like that. So this is very simple.
Just take the smaller number, which is how far back along we are. divide it by the bigger number and we come up with our answer. So in this case our bigger number is 65 because we're 65 back from the start. We're going to then divide by the total which is 1.6 or 160 centimeters.
Now we're going to multiply that by 100 and come up with our answer which is 40.63% 41% ish so our C of G is equal to 48% math When flying and using load sheets in mass imbalance practice exams for example, you will see that there is a range for the center of gravity described in terms of this percentage Mach. If you're outside of this range then we have to adjust the center of gravity position back inside this range before we take off or we could end up with an uncontrollable aircraft we need to stall disaster national airlines flight the easiest method to move this percentage Mac is to move the traffic load of the cargo or the people. If we see the percentage Mach is too little, aka too far forward, then we move some of the traffic load further back in the aircraft and this pulls the center of gravity further back.
This is the reason that even if you're on an empty flight, you will need to sit near the middle of the plane in order to keep the percentage Mach from going too far forward or too far back. Another way to balance out if you're not limited on weight is you could add more fuel to use as a ballast and this would not be included in your fuel total because you're not actually going to use that fuel at that point it would be considered unusable fuel and part of your basic empty mass To summarize, the MAC is an average shape of the wing. It's this line that goes through. It's a fictional concept but it's the average chord length of the whole wing if it was equated to a rectangular wing.
C of G and center of pressure are described as a percentage of MAC. you find out that percentage using the standard sort of method for finding out percentages. You take the smaller number, divide it by the bigger number, multiply by 100. If we are outside of our percentage MAC range, we need to move traffic load or add some fuel for ballast.
which then is considered unusable because if we use it we will then be out of balance on our center of gravity and center of pressure might move outside the range for the percentage mac causing uncontrollable handling issues