“Alright, you can go with us, but we’ll have to go with half full tanks.”
The amount of seats in an airplane can be deceiving. I fly a Cessna 172, which has four seats, but carrying four people is rarely a reality. To know what I can carry, I have to run some weight and balance calculations. It’s important not only to ensure that the plane isn’t loaded with too much weight, but also that the weight is loaded in the right place. Let’s look at a scenario and work through the logic. We’ll be looking at an iPad app called Gyronimo to help with some visuals.
Who Wants Burgers?
It’s a beautiful Saturday and I have the plane booked for a few hours to take my son out for a hundred dollar hamburger. When we get to the airport, I see one of my instructors finishing up with a student. I offer a seat on the plane for him to fly along and grab some lunch with us. “Sure thing,” he replies. “You mind if my student tags along?” My two person flight has just upgraded to four. Can we all go? Time to pull out a pencil and paper and make the decision. Here’s how we do it.
In perhaps one of my favorite acronyms, WAM tells us that Weight x Arm = Moment. Words to live by – if you know what it means. The weight part is pretty straight forward. Actually, straight down – like gravity. Arm isn’t referring to your arm, although I’d miss a wonderful opportunity to make some puns if I didn’t use an illustration using an actual arm. So imagine you are holding a pretty heavy weight in your hand. Start with the weight close to your body, up by your chest. Slowly extend your arm, moving the weight further from you by stretching your arm straight out. When the weight is closer in to your chest, it was easier to hold, right?. By the time your arm is fully extended, the weight becomes much more challenging. Ok, you can put the weight down. Grab some water – stretch it out. In the airplane, the arm is a measurement of how far back an area of the airplane is. In our weight exercise (literally), think of the arm as the distance the weight is from your chest. In our Cessna 172, the arm is the number inches back from the firewall. The front seats have an arm of 37 inches and the back seats have an arm of 73 inches. Whether you are holding the weight out further from your chest or sitting further back from the firewall in the airplane, the same principle applies that the same weight makes more of a difference the further back you go. This brings us to the moment. Yes, the moment this all makes sense, but also the definition of our term “moment.” The moment is simply the weight multiplied by the arm distance. Otherwise stated Weight x Arm = Moment. WAM.
Crunch The Numbers
On our paper, let’s make three columns. One to list out the various weights (airplane, fuel, front row people, back row people and luggage), one to list their respective arms, and one to list the resulting moments. We obtain the weight and arm values from the Pilot’s Operating Handbook and start to fill in the blanks.
In the end, we are primarily looking for two numbers from this exercise. First is the total weight. The airplane can hold only so much (our max gross weight), and we simply can’t be heavier than that number. We just add up all the weights to determine total weight. The second value we need is the overall arm, which is the airplane’s center of gravity with all of the weight loaded as we have it. We can’t just add up the arms, though. That doesn’t work logically or mathematically. However, basic math principles of our Weight x Arm = Moment equation tell us that if we add up all the weights and add up all the moments, we can simply divide total moment by total weight to get the overall arm (If WxA=M, then A=M/W).
To determine if our airplane’s arm (center of gravity) is within limits, we can plot a point on a graph and see if it within the center of gravity envelope. Referencing our total weight on the bottom X axis up to our arm on the Y axis, we can tell if we are inside or outside the envelope. Note that the flight envelope is usually shaped funny. This means that there are circumstances where we might be under maximum weight but our center of gravity is too far forward or too far aft for that weight. Sometimes that can be fixed by either reducing weight, or by shifting the weight around. The heavy guy in the back seat might need to move up to the front.
Who Gets To Go?
It was no surprise that running the numbers for just my son and I were well within both maximum weight and center of gravity limits. Adding my instructor to the back seat proved to be within our limits as well. But when I ran the numbers again with the added weight of the fourth person, I find that we will be over our maximum weight. All hope for a fun trip isn’t lost, though. We just have to “weight a moment.” One option is to reduce the fuel weight to get back within limits. If the gas tanks are already full, that option won’t work and somebody doesn’t get to go. But if there is some room in the fuel tanks, we can determine how many gallons we need based on the standard fuel weight of 6 pounds per gallon. As long as the fuel we take is enough to get us there with a nice margin for the unexpected, that plan might save the day. Half tanks are better than less friends. Well, most of the time.
Flying The Envelope
So why does all of this matter? What’s the worst that could happen? The performance of the airplane changes based on the amount of weight and position of the center of gravity. Takeoff and landing distance suffers greatly with added weight, and the airplanes stability changes depending on the center of gravity. An airplane loaded down too heavily might not be able to take off before reaching the end of the runway. An airplane with a center of gravity too far rearward might be too difficult to recover from a stall. I take the limitations of weight and balance very seriously, and I won’t fly outside of the envelope – not even just a little. The secondary lesson here is that losing a few pounds might mean the difference in bringing a friend along or having enough gas on board to get you where you want to go. So I guess you could say this blog is sponsored in part by kale. And your local gym.
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