1. Introduction to Astronautics Sissejuhatus kosmonautikasse
Tallinn University of Technology
Introduction to Astronautics Sissejuhatus kosmonautikasse
Vladislav Pustõnski
2009

2. Launch Principle considerations
Each travel to space begins with a rocket launch. We have already examined how selection of a launch site influences the available orbits, as well as principle characteristics of launch vehicles. Let us look now how launch is performed and what factors should be taken into account for an excellent space launch.
Principle considerations
The task of a launch vehicle is to provide its payload with the required characteristic velocity of the mission and to place it into a predefined orbit. It is highly desirable to reduce the characteristic velocity in order to deliver a heavier payload. So, the difference between the characteristic velocity of the launch and the required velocity of the mission should be as small as possible. However, some difference is unavoidable, and it occurs due propulsion losses which will be discussed below.
Place of the launch site should be considered: we have already seen that launches to near-equatorial orbit are most feasible from launch sites situated not far from the equator. Generally, air launches and launches from submarines may be realized from any latitude, but they are limited by the size of launch vehicles: large rockets cannot be launched from a submarine or a plane. However, Sea Launch performs launches of the Zenit-3SL from a floating platform on the equator.
Another factor that should be taken into account are the geographic areas where launch debris (these are mostly the spent stages) may fall. This restriction may render some launch azimuths unavailable. For instance, Israel is obliged to perform all launches to retrograde

3. orbits, so that launch paths lie above the Mediterranean, since otherwise the spent stages would fall on the neighboring countries. By the same reason, it is impossible to launch to polar orbit from the Cape Canaveral to avoid launch debris to fall on the territory of US and Canada (US performs launches to polar orbits from Vandenberg).
Launch methods
In spite of the fact that generally a vertical ascent is not optimal from the point of view of losses, most launch vehicles start vertically. The reason is that vertical position on the launch pad provides natural loads on the body of a rocket. Since engines are placed in the tail of a rocket, the natural loads are axial, from the tail to the nose. So, rockets are not designed to bear large lateral loads: this would significantly increase the mass of the structure. If a fueled rocket is inclined, its tanks may not withstand the lateral loads and will break down. Vertically assembled rockets often cannot bear lateral loads even unfueled. Thus, there is no feasible way to incline such a rocket before launch. The rocket starts vertically or nearly vertically (some small angle is provided sometimes to allow safe clearance of the launch tower) and afterwards its path angle is changed in flignt from vertical to nearly horizontal.
There are rare exceptions from this rule. Full-solid launch vehicles are much more robust and lateral loads may not be issue for them, so light-weight rockets of this type may start from an inclined position. The example are the first Japanese full-solid rockets Lambda-4S and the Mu series which all started from an inclined ramp.
Another exception are space launches from aircraft, represented by the Pegasus. Among the advantages of air launches is the opportunity to launch from the equator (which is

4. specially useful for geostationary launches as we have already seen), decrease of gravity losses (since it is possible to launch nearly horizontally) and smaller losses of specific impulse since the engine is started in rarefied atmospheric layers. The gain of the velocity due to the cruise speed of the aircraft is small (several hundreds of m/s) and is not very significant. However, drawbacks are serious as well. First of all, it is very difficult to launch heavy vehicles from aircraft since safe separation presents a serious problem (but rockets for geostationary launches cannot be small). Second, a rocket for air launches should be capable to bear lateral loads; that increases its structural mass and seriously impacts efficiency. Third, liquid-propellant rockets are not safe to carry onboard of an aircraft, specially in a case of a contingency. (This is why the Pegasus is a solid rocket, more safe and able to bear lateral loads.) By these reasons, although many projects have been proposed (including quite large launch vehicles), the only successful rocket launched from an aircraft is the Pegasus.
Some launch vehicles transformed from ICBMs are launched from underwater by submarines. These may solid-propellant or liquid-propellant rockets. The example is the Russian Shtil based on the liquid-propellant Sineva ICBM. Since these rockets are optimized by criteria different from that of conventional launch vehicles, large loads are not an issue for underwater launches (the rocket is launched from its silo filled with water, its engine is started inside the silo or after leaving the silo, in the latter case the rocket is extracted from the silo by a pressure accumulator). The efficiency of such launch vehicles is moderate: Shtil delivers ~100 kg to LEO, its launch weight not being very small but about 40 tons.

5. Assembly and launch pad
Before the launch, the rocket is delivered to the launch pad. The method of delivery depends on how the rocket is assembled. There are two principle methods of assembly: horizontal and vertical.
Historically horizontal assembly has been the first assembly methods. A rocket is assembled in horizontal position, it is delivered to the launch pad horizontally and is raised by a special crane. This method of assembly is more convenient since the assembly building has a common height and the access to all elements of the rocket is simple. All Soviet and Russian launch vehicles are assembled horizontally. The drawback of this method is that the structure of the rocket should be able to bear the loads of its weight in the horizontal position. This may require a more robust construction and impacts the structure coefficient. For smaller rockets this impact is not significant (as well as for solid rocket motors, at least of small and medium size), but for larger rockets the impact is higher.
Vertical assembly was introduced early in the US, so many US launch vehicles are assembled vertically in high buildings (the recent exception is the Delta IV). The stages of the rocket are placed one atop another by cranes, in a similar way as houses are built. This method enables to reduce structural mass since the rocket has to bear only “natural” loads from nose to tail. However, vertical assembly is more complicated and requires high assembly buildings. The giant Vertical Assembly Building (VAB) on Canaveral is one of the largest structures in

6. the world, it was built for assembly of Saturns V and now is used for assembly of Shuttles.
Rockets are delivered (horizontally or vertically) to the launch pad by a special transporter. In Russia these are mostly rail transporters provided with cranes to raise the launch vehicle to the vertical position. In US these are wheel, rail or caterpillar transporters which often deliver the rocket to the launch pad together with its launch platform (launch tower may be attached as well). The largest device of this kind is the Crawler Transporter built for Saturns V and presently used for Shuttles.
Launch pad
On the launch pad the rocket is secured to withstand wind blasts, and service is often provided for its stages. These may be propellant main lines, electricity supply and also personnel access. The access and supply lines are often provided through a special structure on the launch pad called Launch Tower (LT). The arms of the LT stretch towards the rocket, propellant lines and cables pass through the arms to the rocket. In case of cryogenic components they are continuously supplied into the tanks to replenish evaporating propellants. If the rocket carries a manned spaceship, the crew passes to the spaceship by one of the upper arms. Before the launch the LT is withdrawn or its arms are folded to clear the way to the rocket. However, if the rocket stages need no special service before launch (this if a frequent case for full-solid rockets and ICBM-based rockets in silos), LM may be absent.
The rocket may be secured on the launch pad by pyros which are fired before launch. For example, the Shuttle is secured to the launch pad with 8 frangible nuts on 3.5-inch bolts, the

7. nuts detonate when the thrust is sufficient (if detonators fail, the bolts will be broken by the thrust force and the vehicle will be able to lift undamaged). The Soyuz is hold on the launch pad with a system of four trusses which bear its weight. When the weight is equilibrated by the thrust, the tie between the rocket and the trusses disappear and they fall apart thanks to counterbalances.
During launches of large rockets a great amount of exhaust gases hit the launch pad. These gases may reflect back and damage the vehicle, so it is required to provide passage for them. Thus, there is often an opening in the launch pad with flame trenches and flame deflectors. Their task is to give passage to the flame and the gases out from the launch pad. At launch, the launch vehicle is subject to acoustic loads: they appear due to sound waves caused by influence of supersonic jets of exhaust gases. To dampen acoustic loads, water is delivered to the launch pad during launches of the largest rockets, like Saturn V, Shuttle and Energia.
Launch dynamics
During the ascent the launch vehicle is subject to different forces (and torques), these forces accelerate the rocket along its path and change the curvature of the path. The shape of the path is chosen to perform the launch most effectively, that is, to deliver a maximum payload to the desired orbit. However, the velocity which is provided to the payload by its rocket is never equal to the ideal velocity of the rocket (the velocity which the payload would obtain in free space). This is caused by different factors which lead to reduce of the ideal velocity; these factors are called propulsive losses. Further we will examine them in detail.

8. Main equations
The scheme represents a vertical cut-off of a rocket ascent trajectory. It is assumed that the path lies in the vertical plane; for most trajectory portions this assumption is fulfilled.
 is the flight path angle (the trajectory angle with the local horizon; due to the curvature of the Earth, this angle would constantly change if the direction of thrust vector is unchanged).
 is the angle between the trajectory and the axis of the rocket; in most cases this angle should be small, specially in the dense atmospheric layers, and the rocket flies “nose to the wind” to avoid lateral drag forces that could destroy it.
 is related to thrust vectoring for attitude control, this angle is mostly small as well.
L is the lift force, in the first approximation it may be ignored for most of rockets (since  is small and rockets do not have large aerodynamic surfaces).
F is the thrust, D is the drag, g is the gravitational acceleration (changes with altitude).
The Newton’s Second Law projected on the flight path renders:
Let us recall that the thrust may be deduced from the specific impulse Isp:
We may also add and subtract the summand F/M from the equation above:

9. Propulsive losses and velocity gain from the Earth rotation
The first integral of this equation gives:
Let us write this equation as
The last terms in this equations are correspondingly gravity losses (or gravity drag), drag losses and steering losses:
These losses form propulsive losses. In the absence of gravity, atmosphere and with the thrust applied along the velocity vector, the velocity increase would be the same as in free space.
Propulsive losses and velocity gain from the Earth rotation
Gravity losses take place since engines of the launch vehicle should produce some work to overcome the gravity forces. Imagine a rocket firing its engines vertically with a thrust-to-weight ratio of unity. Such a rocket would spend all its propellant working against the gravity and without any velocity gain. But if the same rocket has a higher thrust-to-weight ratio (and thus could spend all its propellant quicker), it would achieve a velocity increase. Thus, gravity

10. losses actually occur since a launch vehicle cannot spend all its propellant instantly. Thus, to reduce gravity losses, it is useful to have higher thrust-to-weight ratio (however, very high thrust-to-weight ratios are not feasible, as we have already seen). It may be noticed as well that if a rocket fires its engines more horizontally (flight path angle  is large), it will achieve a velocity gain in spite of a small thrust-to-weight ratio (however, the rocket may begin to fall if it does not have sufficient vertical velocity upwards). That means that horizontal firing reduces gravity losses. For most of launch vehicles, gravity losses is the largest fraction of the propulsive losses, making up ~15% – 20% of the characteristic velocity of a LEO insertion.
Drag losses occur during launches from the Earth since the rocket begins its flight n the atmosphere that brakes down quickly moving bodies. In the first seconds of the flight the speed remains small and the drag is also small. But when the speed increases, the drag quickly increases as a square root of the speed. It will decrease when the rocket ascends to more rarefied air layers (density drops more or less exponentially with the altitude). So, to reduce the drag, the rocket should leave the dense air layers as soon as possible. That requires a vertical or nearly vertical ascent. This requirement is opposite to the requirement of reducing the gravity losses, so a compromise is needed. Maximum pressure (Max Q) is passed at the altitude of ~ 15 km, the sound velocity is achieved at the altitude of ~ 7 km. Drag losses are more severe for smaller launch vehicles. This is because the drag is proportional to the cross-section surface area and the drag acceleration is in an inverse proportion with the mass of the vehicle which is a cube of its linear size; so the drag acceleration drops roughly linearly with the linear size of the vehicle. Drag losses may total ~0.5% – 3% of the characteristic velocity of a LEO insertion.

11. Steering losses are related to the need to actively steer the rocket in order to chage its attitude; thus the thrust is not applied precisely along the velocity vector. This means that the velocity increment is smaller than the maximum possible value. Steering losses are usually small, but they should be taken into account as well.
There are other factors that should be taken into account. These are the velocity gain due to the rotation of the Earth when launching towards the East, losses of the specific impulse of the engines working in dense atmosphere, etc. The gain from the Earth rotation may be estimated quite simply. Given the Earth equatorial radius ~ 6380 km and the length of the day sec, the speed of the equatorial points may be found as  2·· /  465 m/sec. Ignoring the oblateness of the Earth, the latitude dependence may be obtained as VEarth  465·cos m/sec,  being the latitude of the launch site. However, if a rocket is launched at some non-zero azimuth  ( = 00 corresponds to the Northern direction), the gain is smaller:
(i is the inclination angle of the orbit) The gain will
be negative for retrograde launches. Maximum gain for Kourou  460 m/sec, for Canaveral is  410 m/sec, for Baikonur  320 m/sec. For polar launches this gain is insignificant.
The launch azimuth for a desired inclination i may be found as
(this expression follows from simple spherical trigonometry).
Actually it is slightly inaccurate due to the Earth rotation; for example, launching from the equator to a  = 00 azimuth will result not in an exactly polar orbit but in an orbit with i  30; however, this small effect also depends on the launch trajectory (since the launch is not very quick) and is considered when the launch path is calculated in detail with a high precision.

12. In general, the description given above is valuable for first-order estimations only. For real launches, actual trajectory and velocity gains are calculated by direct integration of the principle equations which contain explicitly all parameters.
Gravity turn
To reduce steering losses, in most cases it is desirable to align the axis of the rocket with the velocity vector. This is particularly important during the first phase of launch, in dense atmosphere in order to reduce lateral aerodynamic forces. At the same time, the initial trajectory of vertical ascent should be transformed into nearly horizontal path in order to reduce gravity losses (however, a too rapid transition to a horizontal flight is not possible as well, since the rocket should quickly leave the dense air layers and should rise to the altitude of the final orbit). So, the launch trajectory includes a transition segment where the flight path angle  changes from vertical to nearly horizontal (sometimes the final angle may be different from horizontal, for instance, if the altitude of the final orbit is large). Since the thrust vector remains close to the velocity vector (i.e. to the flight path angle), this turn is actually realized by gravity, no thrust is applied to bend the trajectory. This is why this maneuver is called gravity turn (or zero-angle-of-attack, or zero-lift trajectory). Gravity turn is the most economic method of inclining the trajectory, since it significantly reduces steering losses. Of course, some steering losses are unavoidable since it is required to keep the rocket axis directed along the velocity vector, this is done by applying non-axial thrust (  0). To follow the gravity turn trajectory, the required flight path angle program (t) should be kept.
Initially the rocket ascends vertically and the flight path angle is constant ( = 900,

13. d/dt=0). So, some initial deviation from vertical should be provided by a pitch maneuver soon after lift-off (typically after ~10 sec). This is initial kick angle.
The projection of forces to the normal (ignoring the lift force) gives
For a gravity turn trajectory     0, so
Thus the flight path angle  drops quickly when the velocity V is small and the angle  is small; this is the beginning of the flight.
Actually, gravity turn is often performed also on the landing trajectory by soft-landers, the example are the lunar landers Surveyor. In the case of landing, the braking thrust is applied along the velocity vector, so the horizontal velocity component is killed and the trajectory approaches to vertical.

14. End of the Lecture 15

15. Non-vertical launches
Pegasus-XL is separated from its L-1011 carrier aircraft (By source)
Japanese Mu-V starts from its ramp (By source)
Underwater launch of Sineva (By source)

16. Soyuz assembly (By source)
Horizontal assembly
N1 Soviet moon rocket (By source)
Soyuz assembly (By source)

17. Vertical Assembly Building on Canaveral (By source)
A Saturn V inside VAB (By source)

18. Launch vehicle transportation
Energia & Buran are transported and raised by their double-track rail transporter-crane (By source, source)
Crawler Transporter with Shuttle and its launch platform (By source)

19. Saturn V / Shuttle Launch Pad 39A (By source)
Launch pads
Saturn V / Shuttle Launch Pad 39A (By source)
Launch pad of Soyuz (By source)

20. Rocket motion during launch
Configuration and nomenclature of rocket motion in the vertical plane (By P.W.Fortescue, J.Stark, G.Swinerd, Spacecraft systems engineering.)