How do you handle business on a small plane on long flights? For example a cross country in a C-172.
The other answers are good, but don't touch on one key method...
Small aircraft like a Cessna 172 have a limited cruise time, about 4 hours maximum. They are small enough that they get relatively uncomfortable after 2-3 hours, and if flying in turbulence or challenging conditions, flights can be relatively short.
The best way I've found to avoid the problem is to make sure to use the facilities as close to departure time as possible and to limit my intake of fluids in the hour or so leading up to a flight.
The other option you have is to land and use the "facilities". Many unmanned airports that have terminals (like KMNM) have a keypad access and facilities inside. Airports are pretty common and you usually aren't more than 30 minutes away from an airport with a bathroom.
Just as a personal account of this, I was doing night training at my local field (Class C) and it was late (10:00 PM or so). One gentleman came on the radio and asked the tower if the FBO was open so he could use the facilities. The controller responded that the FBO was closed but he could taxi him to a quiet corner of the airfield for a few minutes. The pilot gladly took him up on the offer.
I have had success with these things. They are basically a little baggy that has the same stuff they put in a diaper.
You can always wear adult diapers (and I have heard of it being done)
Some small planes can be fitted with a pilot relief tube. This is effectively a tube connected to a small venturi outside the plane. The venturi creates a low pressure system that causes there to be some suction on the tube. The tube terminates in the cockpit near the seat and the pilot is able to relieve them self. The fluid is drawn through the tube, atomized in the venturi and dispersed.
There are some more elaborate bottle like scenarios.
But of course, a good old bottle will suffice, it did for Lindbergh,
[Said to King George V upon his landing] So Lindbergh explained that in his airplane his chair was made of wicker and there was a hole in it. And there was a funnel below that hole. And his waste, whenever nature called, would go down through there into sort of an aluminum can. And so he explained that and said that rather than show up with it in Le Bourget, the airport that he landed in, that he just dropped it over France.
Some of the larger aircraft like the TBM, Caravan and similar turbo props can be fitted with a seat that hides a little toilet underneath.
As a bit of a counter to Rons points, a lot of smaller planes (Mooney comes to mind) have "extended range tank" upgrades that can greatly extend the range of light aircraft. Provided your back, ears, and stamina can handle it some people are flying 5-8 hour legs in GA planes. This has led to a lot of "interesting" scenarios and solutions by pilots.
As mentioned prevention is generally best. Part of my job involves aerial survey work in a P.68, with flights regularly going over 5 hours. My personal record is a 7.5 hour flight. This is my method to keep bodily functions at bay:
The day before a long flight drink plenty of water to stay as hydrated as possible. On the day of the flight get your fluids in early in the day and avoid tea and coffee for at least 2 hours beforehand, and avoid dehydrating foods such as bacon rolls for breakfast. Relieve yourself as close as possible to your departure time.
In flight only take small sips of water to stave off thirst. At the end of a long flight I usually end up with roughly 1/2 to 2/3 of a bottle of water left.
As a last resort there are various devices to be used as mentioned that come in varieties for both genders, and there is always that water bottle...
On small GA aircraft, you are limited to urination as there is no reasonable way to defecate in such an aircraft. The problem can be handled similar to what the military provides for combat aircraft ie 'Piddle Packs' - basically a Ziploc bag with strip of dry sponge to absorb liquid waste. There are also specialized bottles and liquid waste containers sold at pilot shops or even an empty water bottle with a screw on lid can suffice. These bottles are most easily utilized by male crew members due to their anatomy, although custom shaped funnels have been developed to provide better access by female flight crew. I have also heard of more dedicated women flyers using adult diapers on long flights to solve this problem.
Small turboprop aircraft like the TBM-700/850/9XX, PC-12, King Airs, etc. do offer optional toilets - basically a seat hidden under a cushion with a removable collection pan underneath which is cleaned out in an FBO during servicing. It is little more than a flying outhouse, offers minimal privacy and is recommended to be used only in emergencies due to the device filling the cabin up with the pungent odor of feces for the remainder of the flight.
Though almost any wide-mouthed bottle will serve for a male, there are also relief bottles, such as the Little John, which offer an adapter for females (the Lady J). There are also the pouch-type, such as the Travel John, which work for both genders and contain chemicals that turns the urine into gel and masks its odor. The major pilot supply stores, including Aircraft Spruce and Sporty's, both carry them.
Hang glider pilots normally fly in a prone position in a sleeping-bag-like harness that may be unzipped from the toes to the waist. So, you might imagine, it's quite possible to drop liquid ballast in flight. Look out below!
Many sailplanes have pee-tubes installed-- a funnel-like cup attached to a rubber tube leading to the outside. Other times a condom catheter, applied before flight, is used to connect to the tube, or to facilitate peeing into a bottle or plastic bladder while seated in a low-slung seat. In a light plane, peeing into a bottle should not too be hard for those of the male persuasion, especially when flying alone. For some folks, the need would have to be great to manage that in close proximity to other passengers.
And so on and so forth-- you get the idea. As for the other kind of ballast-- I have no idea. Somehow the need seems not to arise.
Sailplane pilots, sitting under a transparent canopy in hot weather, are cautioned not to avoid drinking water before and during flight-- dehydration is a serious concern.
Or do as my syndicate member did on a week-long mountain wave expedition. He was flying in good wave, which hadn't appeared for the previous few day, so he wasn't coming down for anything trivial. When he did eventually land, he had this big grin from ear to ear, and a dark patch that went from his socks to half-way up his shirt. He was handed the disinfectant, and left to get on with the upholstery.