Rocket ascent trajectory

Rocket ascent trajectory

Rocket launch geometry is a path what the vehicle takes to reach the orbit and it is really fascinating. Rocket launches first vertically from the launch pad and then curves into arc in order to be able to escape Earth's atmosphere. 

I would like to talk mainly about the pitch turn and gravity turn. This was always confusing me and I mixed both terms together. But what is also very important is the place where the rocket launches in the sense of latitude. So, let's start first by the location of launch in dependence of latitude and how it affects where the rocket aims. 

If the rocket launches from the a launch site near the Earth's equator it can use advantage of the Earth's rotation. The speed of the Earth near the equator is around 1650 km/h, which can be added to the speed required to orbit the Earth. For a spacecraft to stay in Low Earth Orbit (LEO), it must travel at roughly 28,000 km/h. Now compared to vehicles launched which are launched further from the equator. The closer to equator, the less of the propellant the rocket requires, or with the same amount of propellant the stronger rocket could be launched. 

At higher latitudes the linear speed of the ground decreases. I found information from Wikipedia, that this speed in launch site like Cape Canaveral is about 1440 km/h, in Plesetsk Cosmodrome (Plesetsk) is about 760 km/h, and anywhere from polar site this speed decreases basically to zero.

The speed is derived approximately as v = v_eq × cos(latitude).

The launch sites define the rocket's flight path, which means the curvature and shape of the ascent. We do not fight only with the Earth's gravity but also we deal with the Earth's spinning. 

Examples of different sites:

• Guiana Space Center (5^oN) gets almost the full boost from Earth's spinning.
• Kennedy Space Center (28^oN) gets a substantial boost.
• Plesetsk Cosmodrome (63^oN) gets less.

That explains the amount of launch sites so close to the equator. 

There is another thing and that is orbital inclination (Orbital Inclination).  Orbital inclination is the angle between the orbit plane and Earth's equator. 0^o;inclination is equivalent to orbit directly above the equator, 90^o;inclination is equivalent to polar orbit. Anything in between is inclined orbit. For example, International Space Station flies at about 51.6^o;inclination, and geostationary satellites use 0^o inclination. 

A rocket cannot reach an orbital inclination lower than the latitude of its launch site without any additional maneuver. That means that from 5^oN we can easily and efficiently reach near equatorial orbits. Launches from Cape Canaveral favors inclinations 28^oN or higher. Launches from the Russian site favors highly inclined orbits or polar orbits. 

Ascent trajectory of rocket. Source: Flight To Orbit | Glenn Research Center | NASA

After vertical launch comes pitch turn. Pitch turn is let's say active maneuver, a maneuver where rocket's engines or control surfaces tilt away from vertical flight. A gravity turn is the passive natural curvature if the rocket's trajectory driven by Earth's gravity after the initial tilt. Those terms are connected to each other and sometimes they can be interchangeable. 

Rockets are launched vertically to quickly escape the thickest parts of the Earth's atmosphere, minimize aerodynamic drag, and immediately counteract the pull of gravity with the most direct thrust. Ok, that sounds logical. But shortly after the launch, rockets tilt, known as a pitch-over maneuver, to transition from vertical ascent to a horizontal curved trajectory. This critical maneuver angles the vehicle's thrust so that it can start building the horizontal speed required to reach orbit, rather than just climbing straight up, allowing the rockets to increase the necessary speed to enter orbit rather than falling back down to the Earth. The pitch maneuver turns the rocket's thrust vector toward the horizon to build this crucial speed.

This maneuver uses gravity to turn the rocket, saving fuel and minimizing aerodynamic stress. Tilting the rocket slightly allows the pull of Earth's gravity to naturally curve the flight path, doing the heavy lifting to turn the rocket horizontal. This drastically reduces fuel consumption when you compare it to flying straight up and making a sharp 90 degree turn later. Also, it minimizes atmospheric stress. First, rocket must escape the thickest, most dense atmosphere, while vertical ascent, as quickly as possible. Pitch maneuver later happens when rocket is high enough and the air is thinner and the maneuver is safe for the structure of the rocket. 

Gravity naturally bends the velocity vector downward. The rocket keeps thrusting along its velocity vector.

Gravity turn is affected by Earth's latitude as well. Generally, we can say that gravity varies across the Earth's surface, being weakest at the equator and strongest at the Earth's poles. This difference is primarily caused by two factors, which is the Earth's rotation and its oblate spheroid shape. A gravity turn uses Earth's gravity to pitch a rocket from vertical to horizontal direction. The maneuver is affected by latitude primarily because of gravitational strength (g) which varies by about 0.5% between the equator and the poles.

Summarized:

After launch, a rocket climbs vertically for a few seconds (about 10 - 20s) to clear the launch tower. After that it performs a pitch-over maneuver to tilt slightly away from the vertical and initiate a gravity turn, a curved trajectory that optimizes the path to orbit.

Schematic ascent trajectory shortly after the launch. 

Next come the subsequent stages, which I will cover in the next article.