I wouldn't bother trying to repair an old Schwinn- at least not for actual competitions- it may be ok for training, but you will be at a distinct disadvantage to other riders in a race.

From Wikipedia:

Triathlon bicycles are a variant of road-[racing bicycles|http://en.wikipedia.org/wiki/Racing_bicycle|Racing bicycle], designed primarily to optimize aerodynamics. Since in most triathlons, cyclists do not draft

as in many other forms of road racing, triathletes can gain a

significant advantage by riding a bicycle which reduces wind

resistance. The most obvious features of a triathlon bicycle are the

handlebars, commonly known as aero-bars (see below).

In addition, many components of a triathlon bicycle are designed with an aerodynamic profile: frame tubes have an oval or teardrop (instead of circular) cross-section; handlebars may be flat instead of round; wheels may have fewer spokes, or even be carbon fiber

tri-spokes or discs rather than conventional spoked wheels. Lastly, a

number of "radical" bicycle frames that are illegal in road cycling are

still legal in triathlon, so "nontraditional" frame designs are also

common, including Zipp 2001, Softride, and Kestrel.

Tri bikes generally have a very "aggressive" geometry, meaning steep

(close to vertical) tube angles and a low stem and handlebars relative

to the saddle. This position helps to improve aerodynamics by lowering

the cyclist's torso and creating a smaller overall "wind profile". In

addition, many triathletes feel cycling in this position helps preserve

the muscles used in running by emphasizing pedaling with non-running

muscle groups.

The concept of a tri specific bicycle was pioneered by Ralph Ray and Dan Empfield in the late 80s. In 1989 Empfield designed the Quintana Roo

Superform, a triathlon specific bicycle "built from the aerobars back"

which provided an aerodynamic advantage as well as more power when in

the "aero" position. Empfield's bike had 650c wheels and an 80 degree

seat angle which was unique to the period. Many professional

triathletes were skeptical of the "steep" design at first but when Ray Browning

rode it at Ironman New Zealand shattering the bike and overall course

records and left the bike leg with a 30 minute lead over rival Scott Tinley, the concepts were here to stay.

Tri bikes are generally very similar to time trial bicycles used in time trial races.