How to Calculate Aircraft Weight and Balance

How to Calculate Weight & Balance – Video Transcript

Today we are going to do the second part of the weight and balance videos. Previously, we talked a little bit about “why”, or the effects of weight and balance or CG placement on our aircraft and today what we’re going to do is focus on how to actually calculate that weight and balance. Behind me, you’ll see an example case here and I’m going to run through each of these elements, talk a little bit about what they mean, where they came from, and then ultimately how we can use that to determine if we are within the tolerances for today’s flight or not.

To get us started, the three columns of numbers that we see here, the first one is weight. This is just referring to the to the force, or a weight of whatever the object is. The arm is referring to a distance measured from what the manufacturer will refer to as a datum, or a data plane. It’s just a fixed point on the aircraft that all of these distances are measured from. The next, or last column here is the moment. Moment is quite simply just a torque, which means a rotational force. A rotational force occurs anytime we apply a force such as this weight, a certain distance away from a point, and so we’re measuring the rotational force, or the torque, that each of these weights has around that datum. We can use that then to consolidate where we believe, or where all of the weight we can say is concentrated towards. Which if we say all the weight is coming from one point, we can also call that then the center of gravity. That’s how we’re going to use this to ultimately calculate both our running weight as well as the location of the center of gravity.

To get us started, we’re going to start with just the airplane empty all by itself. We refer to this as the basic empty weight. This refers to just the aircraft with all of its components and then normal operating fluids, unusable fuel, this kind of thing. So just the airplane sitting out there by itself. In today’s case, we’re saying that our aircraft weighs 1,800 pounds. Its current CG location is 90 inches from the datum and that gave us a moment of 160 mm. We got all that from the weight and balance in the aircraft. Easy enough. Now what we want to do is add all of the things we’re going to be bringing with us for this flight. So, we’re going to bring, you know, the pilot and maybe a passenger, and we’re going to have stuff in the back seat or whatever. In most smaller general aviation aircraft, we call these stations usually given names, but really, they’re just stations. They’re just specific locations on the aircraft that have designated points and by points, I mean designated distances from that datum.

So these red numbers that you see here are given by the manufacturer in the pilots operating handbook and they just identify the position of the front seats, or the position of the rear seats, or the position of the baggage compartment, or the fuel tanks, and that way we can calculate the effect that those weights will have against the datum. So, in this example, I put in some numbers for a particular flight. This was two pilots that went flying together, they had a little bag in the back, and then nothing in the baggage compartment. They planned to fly for a while so they had 34 gallons of usable fuel that they added which at 6 pounds per gallon is about 204 pounds of fuel, and then I’ve simply just multiplied the weight times the arm to get these moments.

So now we can add the total weights and we can add the total moments, and what we’ll end up with is, we’re going to say that there’s an average, or a total amount of torque around the datum of this 210,000-ish range, and the amount of force, or weight, that’s creating it is this 2368. So now if I take that total moment and I divided by this total weight, I’m saying the average location where all of that weight is creating this moment around the datum, is at 89.1 inches which is the same as saying that our ramp weights today, we’re going to have a center of gravity location of 89.1. We notice then that the CG has moved. After we got on board, and we’ve added the fuel, the CG has moved. It was at 90 and it’s moved forward by 0.9 inches, which doesn’t seem too crazy. The majority of the weight that we added was in front of the center of gravity, so it makes sense that the CG would have moved forward.

Now we get in the plane, we start the engine, we taxi out, we do a run-up, and we can assume then a little bit of fuel is going to burn off in that time frame. We typically average out about eight pounds. So, we’re going to subtract that from both the weight and the moment so that we can end up with our exact takeoff weight and center of gravity. Obviously with only eight pounds being moved, or removed in this case, there’s not going to be a significant effect on the center of gravity nor really on the weight. Then what we’ll need to do is subtract the trip fuel. So if we assumed approximately 20 gallons of fuel was going to be used for this particular trip multiplied by six, or six pounds per gallon, gives us about 120 pounds of fuel that we’re going to remove during the flight that we’re going to burn off. We’ll subtract that to get our landing weight. We can also subtract that moment to get our landing moment and then that way we can determine our landing center of gravity. Once again, we see that the CG has moved, which also makes sense because we were taking weight away from a position that was behind the center of gravity.

Now how does that apply to this flight? How do I know that based on this information we are good to go for this flight? So, we’re going to check two things. One, we want to make sure that our takeoff weight is under our maximum gross takeoff weight, and if we had a maximum landing weight, we’d want to verify that our landing weight is below that as well. Number two, we want to check what we call the CG envelope, or the CG range, for our aircraft. So, inside the weight and balance section, so section six of the pilots operating handbook, we’d be able to usually see a table or a graph that would identify the CG range for the aircraft. We want to make sure that from takeoff to landing we stayed within that CG range or within the CG envelope. In this case, we have. We’re good to go and so we know that we’d be fine to go on this particular flight. If we found that we were outside of those tolerances in some way, we may need to make adjustments to where we’ve positioned things in the aircraft in order to accommodate and ensure that we stay within that envelope of operating. Hopefully, this has been helpful, and we now have a better understanding of how to calculate weight and balance.