# Aerodynamics from Cursorial Running to Aerial Gliding for Avian Flight Evolution
## 1 Introduction  
In modern science, researchers take inspiration from living organisms, such as birds, bats, insects, fishes, etc., and incorporate their behavior into artificial yet useful products. Bio-inspired Micro Aerial Vehicle (MAV) and bionic robots open up a vast and boundless area of research, which is beneficial for industries, commercial companies, and academic institutions. It is a difficult task to mimic the extraordinary amount of maneuverability of flying animals, but by doing so, we can also have an estimate of their aerodynamic performances and biological adaptations [1]. In flying animals, wings are one of the most important anatomical features, because control, power, and flight forces are generated by their motion [2]. In modern birds, layers of feathers over the wing [3] provide different functions during flight, but these feathers passed through an evolutionary process to reach their current structured stage [4]. Recent discoveries of feathered and winged dinosaurs [5] have shed new light on the evolution and origin of flight in bird lineage. Since the discovery of _Archaeopteryx_ in Germany in 1861, the origin of flight in birds has caused fierce debate among paleontologists [6; 7; 8; 9; 10]. It is now widely accepted that birds are closely related to paravian theropods, a clade of small, carnivorous dinosaurs that also include _Dromaeosauridae_ and _Troodontidae_[10]. Since the discovery of _Sinosauropteryx_ in 1998 [11], Late Jurassic and EarlyCretaceous formations in northeastern China have yielded numerous exquisitely preserved fossils of feathered dinosaurs that document the cumulative evolution of avian characters along the theropod lineage [12; 13; 14; 15; 16]. It has also been shown that the theropod lineage, which is directly ancestral to birds, underwent sustained miniaturization over 50 million years and evolved skeletal adaptations four times faster than other dinosaurs. After two decades of discoveries, feathers and feather-related structures are known to be widespread among dinosaurs, with more than 50 non-aivalan paravian taxa, known from a series of fossils with great ranges of size, osteology, limb proportions, and integumentary covering [4; 10]. Although the plumage was not developed for flight initially [5; 10; 17; 18; 19; 20], the feather subsequently provided aerodynamic capabilities for gliding and flapping flights [12; 16]. Nevertheless, there is still an intriguing question about how paravian dinosaurs learned to fly [5; 8; 9]. Traditionally, paleontologists have advanced two theories for explaining the origin of avian flight. The arboreal model, proposed by [PERSON] in 1880 [7], holds that flight developed in a climbing, tree-dwelling ancestor that was built for gliding but started flapping to extend its aerial time [7; 12; 20; 21]. _Archaeopteryx_ possessed the same claw curvature of the foot as that of perching birds, suggesting arboreal habits for this ancestral bird [22; 23; 24]. However, evidence for trunk-climbing in _Archaeopteryx_ and basal birds is still weak, and the arboreal model is far from being unanimously accepted [6; 15]  
According to the competing cursorial model, originally outlined by [PERSON] in 1879, flight arose in small, bipedal, terrestrial theropod dinosaurs that sped along the ground with arms outstretched and leapt into the air while pursuing prey or evading predators. Feathers on their forelimbs enhanced the lift, thereby allowing the creatures to take flight [6; 7; 12]. However, long leg feathers were developed in a series of basal paravians and birds and were obviously an obstacle for speeding up to glide or fly [16; 21; 25]. In addition, the flight muscles of _Archaeopteryx_ only represented 9% of the body mass [26], which is far less than the average 25% of the body mass found in modern birds [27]; hence, _Archaeopteryx_ likely had a particularly short and ineffective flapping flight, and, because of its higher mass, _Archaeopteryx_ would have to run much faster than modern birds to achieve lift-off.