Over the last week I kept running across articles and video about a heavy weight couple who lost weight after the embarrassment of being asked to move to a different seat so the airplane could take off safely. On one Fox News show the talking heads went on about the times they were asked to move. None of them were particularly large so they talked overly long about how a jumbo jet could be unsafe to fly because a mere wisp of a talking headess was in the wrong seat.
This riled me a bit and has been roiling about in the back of my mind for some days. The people who write or talk about these things are supposedly educated, but the level of ignorance shown makes me very worried about what schools are actually requiring students to learn, even at the university level.
In hopes some of these ignorant but otherwise intelligent folk happen to drop by Samizdata, I will provide a bit of a remedial lesson in basic physics and a bit on aeroplanes as well.
I am hoping everyone is at least familiar with what a lever is, or at the very least a childhood teeter-totter. If two children sit on a board on opposite ends, they can find a balance point regardless of how fat or skinny the two are. One can move closer to the fulcrum, the thing upon which the board rests, or farther away. A child of a given weight at a given distance from the fulcrum creates what is known as a torque. The two children can balance these torques: Mass of child 1 times distance from fulcrum = Mass of child 2 times distance from fulcrum. In more typical notation: m1 * d1 = m2 * d2.
If you understand a teeter-totter, you can understand everything else I have to say.
An aeroplane has a number of points that are of interest. The most important to this discussion are the ‘center of lift’ and the ‘center of gravity’. If you had a very hefty jack and the underside of your 747 could handle it without a requirement for body work afterwards, a single point at which the aircraft could balance like a toy on a pencil is the center of gravity. This is just like the balance point of the children, but with the entire class and their teddy bears instead.
The fulcrum is the center of lift. This is a balance point created by the airflow over the surfaces of the plane in flight. Ideally, and in the simple case, the center of lift should be near the center of mass and both should be on the center line of the aeroplane. If one wing were longer than the other, the center of lift would shift away from the center line. This would not be a good thing unless you are Burt Rutan and know how to do tricky things which no normal mortal would think of doing.
In practice it is impossible to get the two exactly together. If the center of lift is forward of the cg the airplane will want to pitch up. If it is aft of the cg it will try to pitch down. Similarly if it is to the right or left of the cg. the airplane will want to roll right or left.
You can control the attitude of the aeroplane by neutralizing these forces. If you have a pitch up tendency, you dial in a bit of pitch down on the elevator trim tabs. Likewise for the other directions. In worst case you can use the control column and use deflection of the elevator or ailerons themselves to counteract the problem. It is not wise to fly like this under normal circumstances. If you run out of trim you have either not done your weight and balance papers properly or you are flying a Lancaster to Europe in WWII with a max bomb and fuel load and expect you are going to die anyway.
Airplanes have a bunch of numbers which pilots have to know. Among them are the ‘aft cg limit’ and the ‘forward cg limit’. Basically these mean you are too tail heavy or nose heavy to fly with enough of a safety margin to deal with the unexpected. They are not absolute limits. You are not going to reach the ‘my god we are all going to die!’ limit unless everyone piles into the tail and the pilot can not keep the nose down even with full downward elevator deflection.
Inside the cabin the pilot has readings off the landing gear that tell him what the weight and balance looks like after all the luggage, consumables and passengers are on board. If those indicators show the aeroplane is approaching the aft limit he or she will have a flight attendant pick someone from far aft and move them as far forward as possible.
That is all this whole storm in a teacup story was about. It is standard aviation practice that goes back to the first time Wilbur took Orville along with him.