Weight In The Balance

I once had a friend who insisted that the Lockheed L-1011 airliner was “tail heavy” because it flew with the fuselage at a positive angle of attack.  I responded, “that isn’t quite right” and tried to explain fuselage lift. No, he persisted, it was tail heavy, and that meant that his flight attendant wife had an uphill push of the drink cart when walking forward. My friend’s explanation may sound reasonable at first, but it ignores a couple of big (really big) principles of aircraft design: that the big wing up front has a nose-down pitching moment and that the little wing in the back is pushing downward to counteract that pitching moment.  

The pitching moment of the main wing is due to the wing camber and other factors.Deploy flaps and you get increased effective camber, which is part of why you have to re-trim when flaps are deployed or retracted. The horizontal stabilizer in back is flying “upside down” in order to push downward to to keep the airplane in trim. Where my friend’s reasoning fell down was that by thinking of the L-1011 as tail heavy, it suggested that the tail plane was pushing upward to counteract the tail-heaviness. Um, no.  Big wing makes lift; little wing makes downward lift (anti-lift?) to counter that nose-down pitching moment. This covers about 98.5% of all aircraft; the delta wings and canard aircraft are a separate column. What does any of this have to do with the subject of this column?  Because if an airplane is in trim, then it has longitudinal stability, meaning the nose doesn’t want to tip up or down. (Slightly confusing is that longitudinal stability means it is stable about the lateral axis, i.e. the one going from wingtip to wingtip.) An easier way to think of this is to picture one of your airplane Christmas ornaments. (Don’t have one? Your social media feed and special offers should be full of them by the time October rolls around).  The attach point for that ornament is usually at its center of gravity (cg) so the ornament “flies” straight and level while hanging on your tree.  But for the airplane, ornament or real, to be in level flight, the cg needs to be within a certain range so that the tail plane, whether it be a stabilator or conventional horizontal tail plus an elevator, has effectiveness to be able to trim the airplane. Which is where we get to weight and balance, a required document for every aircraft, certified or experimental; it is the “W” in AROW. 

Weight and balance means number crunching and is the point where a lot of people’s eyes glaze, sometimes to their peril.  Increase weight at the front of the airplane (forward cg) and the airplane will get very stable in flight. Put too much weight up front and the cg can move so far forward that stick forces get quite high and the elevator doesn’t have enough control authority to affect pitch. In an extreme situation, the tail would not have enough authority to pitch the nose up for rotation on take-off. Not good.  

Conversely, if the cg moves too far aft, the aircraft becomes unstable, to the point where the pilot cannot easily control the airplane.  Certain fighters, such as the F-16, are unstable in pitch to increase their maneuverability, but they also have a computer that can adjust the tailplane fast enough to keep the airplane flyable. Our homebuilts? Not so much. 

Which circles us back to the weight and balance calculations: not only does the aircraft have to be below max takeoff weight, it also has to keep the cg within a certain range for controllability. The ubiquitous Cessna 172 has a cg range of about 12.5 inches, which is pretty generous and why you can carry four adults, or two people and a lot of gear in the back. In short, most pilots rarely have to worry about cg in a 172. On the other hand, my Spezio has a cg range of a whopping 4.2 inches. Not much, but unlike the Cessna, very few options for loading it. With its tandem seating, a passenger would be sitting on top of the cg, so their presence affects only weight, not cg. The lack of any storage space takes that potential weight shift off the table. That leaves as variables the weight of the pilot and any equipment that is added or subtracted forward or aft of the nominal cg location, which, like most aircraft, is around quarter chord of the wing. If I over-indulge at Thanksgiving, the cg will move aft. If I locate the battery behind the pilot, the cg moves aft. And as fuel burns off, the cg moves aft because the fuel tank is slightly ahead of the wing. That last item means that I have a minimum fuel level necessitated more by cg concerns than making it to an alternative airport. So my best move is to move the battery to the firewall and keep training for marathons to help keep my weight in check. 

But a four-inch cg range is down on the lower end of cg ranges. A quick sampling of Van’s aircraft shows most of them have a cg range of just over eight inches, and the 172’s even larger range has already been noted. So why all this discussion? Because too many pilots and owners haven’t paid attention to those numbers when modifying their aircraft. Switch from a wood to a metal prop? That’s 18 to 20 more pounds at the very front of the aircraft, and probably not a problem unless that was enough to move the cg past the forward limit, especially if with low fuel and just the pilot. 

Going in the other direction, what if Joe Pilot has a windfall at work and decides to upgrade his homebuilt or spamcan? First is a new lightweight, high torque starter that saves nine pounds. Then a smaller, lighter alternator that saves another 10+ pounds. The new alternator is possible in part due to digital cockpit displays that have little current draw and can be 15 or more pounds lighter than the collective steam gauges. A glass cockpit also means ditching a heavy vacuum pump and then let’s upgrade to a new lightweight battery.  That can mean removing upwards of 50 pounds from the front of the airplane, shifting the cg aft. Did the owner or mechanic log each component removed and what was added back? This certainly should occur for a certified airplane and be noted in the logbook. What about the homebuilt owner/builder? He or she may simply think lighter is better, be excited about the new gear, and not do all the math about to where the cg moved. Did they do the calculations? Or at least re-weigh the airplane for a new W&B? Or do they wonder about how light the stick forces are as the airplane jumps into the air on the first flight after the modifications, only to then notice that the airplane has become very sensitive in pitch? Or more likely, do the upgrades occur over time, such that stick forces get ever lighter as the months/years pass until one day they are too light? 

The pageant of upgrades may sound like an extreme and unlikely example, but it isn’t. Certain aircraft in the Air Force inventory have been in service long enough that old, heavy communications and avionics gear have been replaced with newer equipment that is so light that the aircraft now carry forward ballast to compensate. The aerospace engineer in me chafes at this solution, because weight is The Enemy, but scooting the wings aft or the engines forward is a much more problematic solution. Moving the wings or engine may sound silly, but within these same magazine pages are feature stories where builders have had to fabricate new engine mounts to move a heavier engine aft to prevent an extreme forward cg condition. On the other hand, turbine conversions usually wind up looking less than graceful due to cantilevering the lighter turbine much further forward. Either way, the aircraft has to remain balanced such that the elevator continues to have enough tail authority for pitch and trim.  

The point of this missive? “Do the math, people” as a former teacher liked to say. That boring W&B can get very exciting in a hurry if one paints outside its lines. The internet has any number of W&B spreadsheets; some already tailored to your particular aircraft. The ones I really like have a graph showing weight vs cg envelope; plug in the numbers and see where the weight and cg dot winds up. Stay inside the envelope, and you’re good.  Go outside the lines, and here there be monsters. Such spreadsheets make it very easy. Weight and balance isn’t boring, but it should be uneventful. Do the homework to keep it that way.