Since its inception 16 months ago, when it was installed on four U.S. airlines, Airfone -- the "flying telephone" -- has been picked up by 11 more carriers and last month began offering international calling. Now passengers airborne on Airfone-equipped flights can make long-distance calls anywhere in the world.

The telephones -- cabin wall units with portable handsets -- are currently in use on domestic flights aboard 270 aircraft -- about 10 percent of the domestic scheduled passenger fleet (although only one airline, Jet America of Long Beach, Calif., has equipped its entire fleet -- six stretch DC9s). In addition, Airfone is preparing to offer a number of new services, including phones between seats, in-flight reservations and Railfone on the Metroliner.

Cost for a Canadian or U.S. call -- including Alaska, Hawaii, Puerto Rico and the U.S. Virgin Islands -- is $7.50 for the first three minutes and $1.25 for each additional minute. An international call is $15 for the first three minutes and $2.50 for each additional minute. Payment is by credit card.

Airfone Inc. of Oak Brook, Ill., a joint venture of Western Union Corp. and Goeken Commmunications Inc., recently received authorization from the Federal Communications Commission to continue the experimental operations of its air-to-ground communications network until Dec. 1, 1987. The FCC expressed optimism that an additional renewal period for further testing can be granted if questions about final assignment of radio frequencies for the service are resolved. (Since the radio frequency spectrum is limited, a new service requiring use of frequencies must be approved on an experimental basis until it can meet FCC requirements -- such as feasibility and being in the public interest -- for regular licensing.)

Airfone has scheduled nine additional services to begin in the next two years. Planned for 1986 are:

*In-flight reservation service (late spring): This travel-industry-sponsored service will allow passengers to make airline, rental car and hotel reservations via a special toll-free number. (To be free, the calls must be made to the airlines, car rental firms and hotels that have signed up for the service.)

*Phones between the seats (summer): These units will be built into the front of the airliner's food tray and can be used by passengers at their seats.

*In-flight shopping (fall): Passengers will be able to leaf through a gift catalogue, select items and then order them directly by entering the item numbers by phone without speaking to an operator or order-taker.

*Electrocardiogram transmission (before end of year): Airfone already has successfully completed test transmissions of electrocardiograms from an aircraft in flight to a medical facility on the ground. Essentially this is the same procedure followed by a paramedic at the scene of a highway accident who transmits the victim's EKG to a hospital, where a physician determines if a heart attack has been suffered, the extent of damage and what emergency treatment to give.

And although Airfone has been used in flight mainly for business and personal calls, there have been a few instances when it already has provided crucial communications during medical emergencies.

In one case, a woman passenger who had undergone surgery three days before her trip suddenly began hemorrhaging. Dr. John E. Hutton, assistant White House physician, was also a passenger on the plane and responded to a flight attendant's call for assistance. Hutton had no medical report on the woman's condition, and a landing was not scheduled for three hours.

Since Airfone had just been installed on that United flight, a company technician on board used the phone to help track down the patient's doctor and surgeon. Hutton was then able to provide proper treatment.

*Carry-on phones (end of year): Airfones technically can now be used to receive incoming calls -- but the airlines have chosen to limit the service to outgoing calls in order to keep flight attendants from having to page passengers.

The new carry-on phone, which must be purchased in advance of a planned trip, will have a coded memory chip containing one of the traveler's own credit-card numbers (coding valid for one-year periods) as well as an incoming phone number for receiving calls. Passengers can take these units with them and use them while in their seats or anywhere on the plane. Airfone has not yet determined the cost of these phones but says they will be relatively inexpensive.

*Railfone on Amtrak's Washington-to-New York Metroliners (early spring): One phone is being installed on each of 46 rail cars, and the charge for a call anywhere in this country will be $4.75 for the first three minutes and $1 for each additional minute. International calls also will be available from Metroliners, with rates to be announced later. The service will be provided by Railfone Inc., a subsidiary of Airfone, in a joint venture with Amtrak.

There were phones on Metroliners until 1981, when the federal government requested that frequencies it had loaned to American Telephone & Telegraph Co. be returned for government use.

Projected services aboard planes for next year include:

*Telex and telegrams: A computer terminal will be installed to permit passengers to send telexes and wires in flight. Fees have not been announced.

*Stock quotations: A stock quote computer terminal will allow airborne investors to keep track of the market, and there will be a charge for each quotation. Cost has not been determined.

*Voice storage and forwarding: This will allow a passenger to phone a computer while en route and leave a message that will be automatically forwarded to the designated party. The charge is not yet known.

There are 23 airlines that have contracted with Airfone to install phones: Air Cal, Air Atlanta, American, America West, Continental, Delta, Eastern, Jet America, Midway, Muse, Northwest Orient, New York Air, Ozark, Pan Am, People Express, Piedmont, Regent, Republic, TWA, United, Western, World and Zenith. Service will be available on all 23 lines before the end of this year, according to Fred Noble, executive vice president of Airfone.

At present, there is no way for a passenger to determine in advance whether a particular flight offers Airfone, according to Noble. Except for Northwest Orient and American Airlines, each of which has installed the phones in its entire fleet of DC10s, and Jet America, the airlines generally cannot provide this information because their planes are switched around on routes and installation is continuing, said Noble.

Here is how Airfone functions (the operation is basically the same for Railfone):

Each airplane cabin has between four and eight handset units mounted on the wall (each Metroliner will have one unit). These phones do not interfere with the plane's or train's radio equipment when they transmit their low-power signals to Airfone's central Airborne Control Unit (ACU), located in the aircraft's center equipment bay. (On Metroliners the signal will be transmitted from the trains to the closest Cell Sites, cellular radio's ground stations.)

A passenger who wants to make a call inserts one of six major credit cards in one of the units. (Cards currently accepted are Citicorp Diners Club, Air Travel Card, American Express, Carte Blanche, MasterCard and Visa.) The card's magnetic strip is read and transmitted to the ACU (or Cell Site), which checks validation with its memory bank and simultaneously tests the radio link with the handset. Then the handset is released from its base, and the airline passenger can dial the cordless, portable phones from anywhere in the plane, including from a seat. On the trains, phones have a permanently connected cord and cannot be carried away from the wall unit.

(Only four plane passengers can place calls at one time, regardless of how many phones are installed or carried aboard, because a separate air-to-ground radio link is required for each phone conversation and only four transmitters are currently being installed in each plane. As the demand for service expands, Airfone can easily double the call-carrying capability to eight phones per plane.)

There are ground receiver stations at intervals across the country; the ACU selects the one closest to the plane when a call is made and transmits billing information to it. (Railfone has not released details on how train billing information will be routed.) Later, the Central Computer Center, a collection point in Oak Brook where all billing information is received, processes the individual charges from planes and trains.

If the quality of the radio transmission is impaired by adverse weather conditions or abnormal terrain changes, the passenger can notify the Airfone/ Railfone operator by dialing 0.