Question: When bow is recommended for use on horseback?
About the article "Archery", section "Mounted archery".

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Bows with curved side-view profiles.
Recurve bow.
A recurve bow has tips that curve away from the archer when the bow is strung.
By definition, the difference between recurve and other bows is that the string touches a section of the limb when the bow is strung.
A recurve bow stores more energy and delivers energy more efficiently than an equivalent straight-limbed bow, giving a greater amount of energy and speed to the arrow.
A recurve will permit a shorter bow than the simple straight limb bow for a given arrow energy and this form was often preferred by archers in environments where long weapons could be cumbersome, such as in brush and forest terrain, or while on horseback.
Recurved limbs also put greater strain on the materials used to make the bow, and they may make more noise with the shot.
Extreme recurves make the bow unstable when being strung.
An unstrung recurve bow can have a confusing shape and many Native American weapons, when separated from their original owners and cultures, were incorrectly strung backwards and destroyed when attempts were made to shoot them. 
A reflex bow is a bow that has curved or curled arms which turn away from the archer throughout their length.
When unstrung, the entire length of the bow curves forward from the belly (away from the archer), resembling a "C"; this differentiates a reflex bow from a recurve bow in which only the outer parts of the limbs turn away from the archer.
The curves put the materials of the bow under greater stress, allowing a fairly short bow to have a high draw weight and a long draw length.
This allows a bow that is 1:2 the length of a recurve or 1:3 the length of a longbow to fire at the same or greater velocity and stopping power.
The materials and workmanship must be of high quality.
Highly-reflexed bows are more difficult to string and may reverse themselves suddenly; they have seldom been used for hunting.
However, they were the main armament of the Mongol armies that conquered much of Asia and Europe; their short profile compared to longer bows made them ideal for horseback use. 
A decurve bow is a bow that has arms curved or curled at the ends to turn towards the archer.
This bow form reduces the strain on the bow when it is used, and the bow may be under no tension at all when strung, so that it can be kept ready for immediate use at all times.
It also reduces the energy stored in the bow, and the speed of the arrow.
The form is seldom used in modern or historical bows, but was occasionally used by groups such as the Mohave who did not have easy access to good quality bow wood.
It allowed them to make effective hunting weapons from the poor-quality material available. 
It gives a narrower grip on the string, as only one digit is used, and this may help to avoid "string pinch" with shorter bows such as the composite bows normally used from horseback.
Mongol archers would wear a thumb ring made from leather, bone, horn, and in some cases silver to protect the thumb.
It may also avoid a problem occasionally faced by archers using the Mediterranean release, when the three fingers do not release at exactly the same time and thus foul the draw.
This release is normally used with the arrow on the right side of the bow for a right-handed archer, and on the left side of the bow for a left-handed archer. 
 This episode marked the first time combat on horseback was factored into a warrior's combat skills and effectiveness.
For Short-Range weapons, Attila's Sword of Mars went up against Alexander's kopis.
When both were tested on horseback (on both stationary and moving targets), the Sword of Mars dealt four killing blows in 34.5 seconds.
With the head targets, the Sword of Mars caused a decapitation on one meat "neck" and cut through the cervical muscles to the spinal cord on the other.
On the slabs of cattle meat, the Sword of Mars managed to slice four inches through the ribs(which are two to three times thicker than human ribs), causing two death blows.
The kopis completed the test in 25.75 seconds; the kopis decapitated one meat "neck" and cut through the spinal cord on the other.
However, the kopis failed to penetrate the cattle ribs, inflicting a collapsed lung at most.
The Sword of Mars received the edge due to killing power.
For Mid-Range weapons, Attila's lasso took on Alexander's xyston lance.
The xyston was tested against a pig carcass on a zip-line to simulate the weapon's use on horseback.
The xyston impaled the pig at 10 feet/second with almost no resistance.
The xyston was also tested from horseback on an armoured carcass and was able to puncture through the front plate, impale the carcass through the sternum, and still puncture the back plate.
The lasso could cause a hangman's fracture of the neck and crush the trachea, but was still determined to not be a certain kill.
The edge was given to the Xyston due to its raw killing power.
For Long-Range weapons, Attila's hunnic composite bow was put up against Alexander's gastraphetes belly-bow.
Both were tested on two moving targets.
The composite bow was used from horseback, and demonstrated both speed and accuracy.
The gastraphetes was tested on foot and could not match the speed or the accuracy of the composite bow.
After this test, the hosts gave the edge to the composite bow.
For Special Weapons, Alexander's ballista was tested against Attila's scythian axe.
The ballista was fired at a silhouette target of a mounted Hun at 200 yards, and hit its target at 198 mph.
The ballista was also tested against a formation of enemies, and caused instant kills by impaling them.
The scythian axe was tested against an unprotected ballistic gel head, tearing the back of the skull completely open, decapitating the skull, and severing the spinal cord with multiple strikes.
The velocity of the Scythian Axe was measured at 69 mph.
However, the axe failed to penetrate Alexander's iron helmet, and could only strike the helmet with roughly 20 pounds of force per square inch; 81 pounds per square inch being the minimum amount of force required to inflict a lethal skull fracture.
The edge went to the ballista because of its range, killing power, and the Scythian Axe's failure.
The Greek sport of Pankration was also tested by the Alexander team.
Rashad Evans was able to easily crush the trachea and fracture the skull of a ballistic gel torso with only his elbow and knee, respectively.
This is the first episode to feature multiple warriors on each team in an ancient match, and the only one where a member of the losing team is not known to be killed (Attila and his men were not seen killing one of Alexander's soldiers, so either he escaped or was simply not seen dying).
Attila's hunnic composite bow scored the most kills of any pre-gunpowder projectile weapon of the first two seasons.
The sword of mars and the balllista are the seventh and eight weapons to be given the edge and score fewer kills than the opposing weapons.