To begin with, a rocket never accelerates vertically. To reach orbit and beyond, the goal is to accelerate tangentially to Earth's surface and gain enough speed to reach orbit. The rocket pitches down a few degrees as soon as it clears the launch tower, it initiates a gravity turn that allows the rocket to gain more and more horizontal speed while raising its altitude above the atmosphere.
Every space mission (to LEO, GTO, GEO, MEO or interplanetary) begins with transit through LEO. The difference between Ariane 5 and other launchers (such as Atlas V and Falcon 9) is that the Ariane 5 upper stage engine cannot be restarted.
For example, if you take a look at the launch of Perseverance on Atlas V you will see that the rocket first injects the payload in LEO, then coasts and finally reignites the upper stage engine to eject the payload on a hyperbolic orbit towards Mars. Ariane V cannot do that, there is no coasting phase between LEO injection and Earth departure burn, there is a continuous burn from launch to escape.
Then to answer the question about the altitude vs downrange graph, Ariane 5 has a weak core stage engine, the Vulcan engine only provides 10% of the thrust at launch. So the boosters give some altitude margin to the core stage in order to give the core stage time to push horizontally while falling. But when the horizontal speed exceeds orbital speed (8 km/s) the upper stage regains altitude, then more speed means more vertical speed because the spacecraft approaches and then exceeds Earth escape velocity (11 km/s). This final vertical speed explains the end of the graph. To finish, the Earth is round so in 3D the trajectory is smoother than the way it is plotted on the altitude vs downrange plot.
So it would appear at first impressions and all things being equal (which they are probably not) that flying straight up would involve travelling through less atmosphere than curving around slowly into LEO first? What am I missing?
– Slarty Apr 16 '23 at 13:31