Considering the toughest thing in launching a rocket is to achieve the tangential velocity, launching horizontally might give us an added advantage for delta V requirement.
This can't be done in earth, as the atmosphere is thick.But, since , the atmosphere of mars is thin, will spacex take advantage of the mars' rotation and launch horizontally?
Am I missing other considerations for a vertical launch.
A true horizontal launch requires infrastructure (a runway) which isn't there yet. The next best thing is to launch vertically, and turn the spacecraft to a more horizontal heading soon after launch (this is called a gravity turn, and is used on Earth as well).
All renderings of the BFR have landing legs at the bottom of the stage, for vertical landing/takeoff.
In general, gravity losses are the key. While you are accelerating up out of the atmosphere, before you reach orbital or escape velocity, you are fight gravity.
On Earth it is worse than Mars due to being a larger/denser planet and thus greater value for gravity.
This is more obvious on descent for landing. Every second you spend decelerating, is one second where Earths gravity has further accelerated you downwards at 9.8 m/s. So SpaceX on landing waits to the last second to slow down (in a simplification) which is why the three engine burn is more fuel efficient for landing than the single engine burn. It slows down faster, spends less time being accelerated by Earth's gravity.
For launch, same idea. You want to get out of the atmosphere (agreed, worse on Earth than Mars) and then focus on speed to get to orbital where although Earth is still accelerating you downwards via gravity, you are now fast enough to just keep missing the Earth as you fall and you no longer have to fight the pull.
They plan (or at leats planned in 2017) a direct return to Earth without entering Mars orbit. See the slide headed "Mars Transportation Architecture" on this presentation.
I originally wrote:
Given that, the only reason not to simply boost straight up is the possible small advantage from Mars' rotation.
It has been pointed out to me that this is wrong. It took me some time to see why. The key thing is that you want gravity to be acting, as nearly as possible, perpendicular to your velocity, not (anti-)parallel to it. That way it changes your direction but doesn't reduce your kinetic energy.
At the equator the rotation is about 0.3 km/s, so, absent atmosphere, launching horizontally due East at the right time of day would save that much. At higher latitudes, the gain is less. More or less the same gain would be available by launching upwards until a few hundred meters clear of the ground and then turning sideways, which avoids the need for different landing gear.
On the other hand, although low density, Mars' atmosphere extends up quite high, and exerts significant drag at high velocities, so spending extra time in it will have a performance cost. I don't have figures for that to be certain, but I suspect that as on Earth it will be necessary to pick a trajectory that balances the desire to exploit rotation and avoid gravity drag with the desire to get clear of much of the atmosphere before building up too much speed.
