On bicycles that do not have a derailleur or other chain tensioning device, rear horizontal dropouts allow adjustment of chain tension, and can accommodate a range of chain lengths or cog sizes. They were standard on most older derailleur bicycles from before the 1990s. They are also used by single-speed bicycles. An older multi-speed bicycle with horizontal dropouts can be readily converted into a fixed wheel or fixed gear bicycle. Horizontal dropout openings may face forwards or rearwards. Track bicycles traditionally have the opening facing rearwards (track ends) while road bicycles have forward facing dropouts.
Rear vertical dropouts have the slot facing downwards. The advantage is that the wheel axle cannot slip forward compared with horizontal dropouts. The disadvantage is that on a bicycle without a rear derailleur but with vertical dropouts, the chain tension cannot be adjusted by moving the wheel forwards or backwards, and needs another means of chain-tensioning, by a derailleur, chain tensioner, or eccentric bottom bracket or rear hub. Fixed wheel bicycles cannot use any form of chain tensioning device, because the lower run of chain is pulled very tight when using the transmission as a brake.
Derailleur hanger Edit
The derailleur hanger or mech hanger is the part of the dropout that the rear derailleur attaches to.
Most non-steel framed bikes have a separate removable derailleur hanger, generally made from aluminium which is bolted to the dropout. These are intended as a cheap replaceable part so that in the event of an accident or mechanical problem that could damage the derailleur or frame, the derailleur hanger breaks or deforms instead. Sometimes a shear bolt which is designed as a weak point will also be used. There are dozens of different derailleur hangers available and one model is seldom interchangeable with another.
In general, steel-framed bikes do not have a removable derailleur hanger, because a steel dropout and hanger is stronger and therefore less likely to be damaged, and also it is more malleable and less likely to work harden during deformation and generally can be bent back into shape without breaking.
It is important for proper indexed shifting for the derailleur hanger to be properly aligned. The rear derailleur bolt hole must be close to parallel with the rear axle. If it is out of alignment, the rear derailleur will not move far enough, with respect to the rear sprockets, with each click. A special tool exists to measure and correct misalignment hangers.
On frames with no derailleur hanger, a direct mount derailleur or derailleur with a hanger plate is used. These only fit bikes with forward-facing horizontal dropouts, and are held in place by a small bolt and the rear wheel axle. These have now been effectively superseded by the derailleur hanger.
Lawyer lips or lawyer tabs (technically positive retention devices) are tabs fitted to the front fork dropouts of bicycles sold in some countries (particularly the U.S.) to prevent a wheel from leaving the fork if the quick release skewer comes undone. They were introduced in response to lawsuits supported by experts including John Forester, in cases where incorrectly adjusted quick release wheels came out of the forks. Lawyer tabs are designed to compensate for the fact that many riders do not know how to operate a quick release properly: some riders treat them as a folding wing nut, and others do not tighten them enough for fear of snapping them or shearing the skewer (both are not possible given the normal range of human strength, and the mechanical advantages involved, as long as the skewer is not damaged or flawed).
A side-effect is that the quick release, which was developed to allow the wheel to be removed without having to unscrew any components, no longer works as designed: the skewer must be unscrewed in order to remove the wheel (although tools do remain unnecessary). This means that the tension on refitting must be adjusted again. Some cyclists file off the lawyer tabs so the quick release works as originally intended.
A correctly secured quick release is unlikely to be ejected from the dropout in normal use where rim brakes are in use, although recently there has been some evidence, notably from James Annan, a British scientist working in Japan, suggesting that the moments in disc brake systems can cause quick-release front wheels to be ejected past the lawyer tabs. A small number of serious crashes have been attributed to this cause. This is controversial, and the fork manufacturers have not admitted a fault, although there is some evidence that they may accept the principle, and advice on checking quick release tension has been strengthened.  A complete solution to ejection risk would involve mounting the front disc brake caliper in front of the fork blade rather than behind, as the reaction force on the disc would then be into, rather than out of, the fork-end. However, this would involve major retooling by fork and brake manufacturers, though British manufacturer Cotic has placed the disc caliper mounts on the front of the right fork blade on its Roadhog fork. This allows standard brakes to be used, and also makes it easier to mount mudguards.
Dropouts may support one or more eyelets, small protruding tabs with holes, often threaded, to facilitate the mounting of racks and fenders.
Some rear, horizontal, forward-facing dropouts have small adjustment screws threaded through the very rear to aid in positioning the axle precisely. The screws may be fitted with springs to keep them from moving.
Some rear, horizontal, rearward-facing dropouts have threaded devices ("chaintugs") to aid in setting the proper chain tension. These may be integral to the dropout or separate items. They work by holding the rear axle in an eye at the end of a threaded bolt. The bolt passes through a cap which fits over the open track end. Tightening the bolts on each side causes the axle to be pulled backwards towards the open track end, tensioning the chain. Chaintugs can also solve the problem of "axle creep" on hard-ridden fixed-gear bicycles, especially those with hard chromed track ends, which may not offer adequate grip for the serrated track nuts.