I've heard that rockets accelerate fastest when travelling horizontally to the ground, not downwards or upwards. Is that true, and why?

# [Physics] Why do rockets accelerate fastest horizontally

rocket-science

#### Related Solutions

Nowadays, rockets use a Gimbaled Thrust System. The rocket nozzles are gimbaled (An appliance that allows an object such as a ship's compass, to remain horizontal even as its support *tips*) so they can vector the thrust to direct the rocket. In a gimbaled thrust system, the exhaust nozzle of the rocket can be swivelled from side to side. As the nozzle is moved, the direction of the thrust is changed relative to the center of gravity of the rocket.

Early rockets had Vernier Thrusters which uses small rocket engines on either sides, to control the attitude (vs altitude) of a rocket. Nowadays, they are common in most satellites.

In this Image, The middle rocket shows the *normal* flight configuration in which the direction of thrust is along the center line of the rocket and through the center of gravity of the rocket. On the left one, the nozzle has been deflected to the left and the thrust line is now inclined to the center line at a gimbal angle $a$. As the thrust no longer passes through the center of gravity, a torque is generated about the center of gravity and the nose of the rocket turns to the left. If the nozzle is gimbaled back along the center line, the rocket will move to the left. On the right one, the nozzle has been deflected to the right and the nose is moved to the right.

Wikipedia says,

In spacecraft propulsion, rocket engines are generally mounted on a pair of gimbals to allow a single engine to vector thrust about both the pitch and yaw axes; or sometimes just one axis is provided per engine. To control roll, twin engines with differential pitch or yaw control signals are used to provide torque about the vehicle's roll axis.

The right & left gimbaling is necessary to direct the rocket to its original path, thereby maintaining its stability... This link gives a good explanation regarding the stability of rockets. *This essay* is also good, but it's somewhat big...

The problem is what Konstantin Tsiolkovsky discovered 100 years ago: as speed increases, the mass required (in fuel) increases *exponentially*. This relation, specifically, is
$$
\Delta v=v_e\ln\left(\frac{m_i}{m_f}\right)
$$
where $v_e$ is the exhaust velocity, $m_i$ the initial mass and $m_f$ the final mass.

The above can be rearranged to get $$ m_f=m_ie^{-\Delta v/v_e}\qquad m_i=m_fe^{\Delta v/v_e} $$ or by taking the difference between the two, $$ M_f=1-\frac{m_f}{m_i}=1-e^{-\Delta v/v_e} $$ where $M_f$ is the exhaust mass fraction.

If we assume we are starting from rest to reach 11.2 km/s (i.e., Earth's escape velocity) with a constant $v_e=4$ km/s (typical velocity for NASA rockets), we'd need $$ M_f=1-e^{-11.2/4}=0.939 $$ which means almost 94% of the mass at launch needs to be fuel! If we have a 2000 kg craft (about the size of a car), we would need nearly 31,000 kg of fuel in a craft that size. The liquid propellant has a density similar to water (so 1000 kg/m$^3$), so you'd need an object with a volume of 31.0 m$^3$ to hold it. Our car sized object's interior would be around 3 m$^3$, a factor of 10 too small!

This means we need a *bigger* craft which means *more* fuel! And explains why this mass-speed relation has been dubbed "the tyranny of the rocket problem".

This also explains the fact that modern rockets are multi-staged. In an attempt to alleviate the required fuel, once a stage uses all of its fuel, it is released from the rocket and the next stage is ignited (doing this over land is dangerous for obvious reasons, hence NASA launching rockets over water), and the mass of the craft is lowered by the mass of the (empty) stage. More on this can be found at these two Physics.SE posts:

## Best Answer

Rory Alsop explained why the idea is wrong, but it may originated from the following reasoning.

When a space rocket takes of, it does so vertically. At that time it is fully loaded with fuel and hence its acceleration is slow. When you watch a video of a space rocket take-off, it seems to crawl along the launch tower.

However, in order to achieve orbit, the rocket has to travel 7 km/sec

horizontally. To achieve that, after a while the rocket's path starts to curve towards the horizontal. At that point the first stage may already have dropped off and a large amount of fuel has been burned, so the rocket is a lot lighter. Because the acceleration is inversely proportional to the mass the rocket will be accelerating significantly faster at that point. At the same time, because the rocket is now fairly high up, the air pressure has dropped significantly, and the reduced drag also increases acceleration.Hence, the rocket accelerates faster when it is going horizontally. Somebody could then take that as meaning "faster than upwards

as well as downwards"EditAnother issue is the is the "dynamic pressure" which is created by the speed and air-drag. Because of this, the engines may not be run at full power until past the "max-q" point. In the case of the Shuttle, the main engines ran at 65% for the first minute or so of the flight. Only then was it throttled up to 100%, increasing acceleration. See http://www.aerospaceweb.org/question/aerodynamics/q0025.shtml