Sub-orbital spaceflight

Name	Year	Flights	Location
Mercury-Redstone 3 Mercury-Redstone 4	1961	2	Cape Canaveral
X-15 Flight 90 X-15 Flight 91	1963	2	Edwards AFB
Soyuz 18a	1975	1	Baikonur Cosmodrome
SpaceShipOne Flight 15P SpaceShipOne Flight 16P SpaceShipOne Flight 17P	2004	3	Mojave Air and Space Port
Blue Origin NS-16 Blue Origin NS-18 Blue Origin NS-19	2021	3	Corn Ranch
Blue Origin NS-20 Blue Origin NS-21 Blue Origin NS-22	2022	3	Corn Ranch
Blue Origin NS-25 Blue Origin NS-26 Blue Origin NS-28	2024	3	Corn Ranch
Blue Origin NS-30 Blue Origin NS-31 Blue Origin NS-32 Blue Origin NS-33 Blue Origin NS-34 Blue Origin NS-36	2025	6	Corn Ranch

Name	Year	Flights	Location
X-15 Flight 62	1962	1	Edwards AFB
X-15 Flight 77 X-15 Flight 87	1963	2	Edwards AFB
X-15 Flight 138 X-15 Flight 143 X-15 Flight 150 X-15 Flight 153	1965	4	Edwards AFB
X-15 Flight 174	1966	1	Edwards AFB
X-15 Flight 190 X-15 Flight 191	1967	2	Edwards AFB
X-15 Flight 197	1968	1	Edwards AFB
Soyuz MS-10	2018	1	Baikonur Cosmodrome
VSS Unity VP-03	2018	1	Mojave Air and Space Port
VSS Unity VF-01	2019	1	Mojave Air and Space Port
VSS Unity Unity21 VSS Unity Unity22	2021	2	Spaceport America
VSS Unity Unity25 Galactic 01 Galactic 02 Galactic 03 Galactic 04 Galactic 05	2023	6	Spaceport America
Galactic 06 Galactic 07	2024	2	Spaceport America

A sub-orbital spaceflight is a spaceflight in which the spacecraft reaches outer space, but its trajectory intersects the surface of the gravitating body from which it was launched. Hence, it will not complete one orbital revolution, will not become an artificial satellite nor will it reach escape velocity.
For example, the path of an object launched from Earth that reaches the Kármán line, and then falls back to Earth, is considered a sub-orbital spaceflight. Some sub-orbital flights have been undertaken to test spacecraft and launch vehicles later intended for orbital spaceflight. Other vehicles are specifically designed only for sub-orbital flight; examples include crewed vehicles, such as the X-15 and SpaceShipTwo, and uncrewed ones, such as ICBMs and sounding rockets.
Flights which attain sufficient velocity to go into low Earth orbit, and then de-orbit before completing their first full orbit, are not considered sub-orbital. Examples of this include flights of the Fractional Orbital Bombardment System.
A flight that does not reach space is still sometimes called sub-orbital, but cannot officially be classified as a "sub-orbital spaceflight". Usually a rocket is used, but some experimental sub-orbital spaceflights have also been achieved via the use of space guns.

Altitude requirement

By definition, a sub-orbital spaceflight reaches an altitude higher than above sea level. This altitude, known as the Kármán line, was chosen by the Fédération Aéronautique Internationale because it is roughly the point where a vehicle flying fast enough to support itself with aerodynamic lift from the Earth's atmosphere would be flying faster than orbital speed. The US military and NASA award astronaut wings to those flying above, although the U.S. State Department does not show a distinct boundary between atmospheric flight and spaceflight.

Orbit

During freefall the trajectory is part of an elliptic orbit as given by the orbit equation. The perigee distance is less than the radius of the Earth R including atmosphere, hence the ellipse intersects the Earth, and hence the spacecraft will fail to complete an orbit. The major axis is vertical, the semi-major axis a is more than R/2. The specific orbital energy is given by:
where is the standard gravitational parameter.
Almost always a < R, corresponding to a lower than the minimum for a full orbit, which is
Thus the net extra specific energy needed compared to just raising the spacecraft into space is between 0 and.

Speed, range, and altitude

To minimize the required delta-v, the high-altitude part of the flight is made with the rockets off. The maximum speed in a flight is attained at the lowest altitude of this free-fall trajectory, both at the start and at the end of it.
If one's goal is simply to "reach space", for example in competing for the Ansari X Prize, horizontal motion is not needed. In this case the lowest required delta-v, to reach 100 km altitude, is about 1.4 km/s. Moving slower, with less free-fall, would require more delta-v.
Compare this with orbital spaceflights: a low Earth orbit, with an altitude of about 300 km, needs a speed around 7.7 km/s, requiring a delta-v of about 9.2 km/s.
For sub-orbital spaceflights covering a horizontal distance the maximum speed and required delta-v are in between those of a vertical flight and a LEO. The maximum speed at the lower ends of the trajectory are now composed of a horizontal and a vertical component. The higher the horizontal distance covered, the greater the horizontal speed will be. For the V-2 rocket, just reaching space but with a range of about 330 km, the maximum speed was 1.6 km/s. Scaled Composites SpaceShipTwo which is under development will have a similar free-fall orbit but the announced maximum speed is 1.1 km/s.
For larger ranges, due to the elliptic orbit the maximum altitude can be much more than for a LEO. On a 10,000-kilometer intercontinental flight, such as that of an intercontinental ballistic missile or possible future commercial spaceflight, the maximum speed is about 7 km/s, and the maximum altitude may be more than 1300 km.
Any spaceflight that returns to the surface, including sub-orbital ones, will undergo atmospheric reentry. The speed at the start of the reentry is basically the maximum speed of the flight. The aerodynamic heating caused will vary accordingly: it is much less for a flight with a maximum speed of only 1 km/s than for one with a maximum speed of 7 or 8 km/s.
The minimum delta-v and the corresponding maximum altitude for a given range can be calculated, d, assuming a spherical Earth of circumference and neglecting the Earth's rotation and atmosphere. Let θ be half the angle that the projectile is to go around the Earth, so in degrees it is 45°×d/. The minimum-delta-v trajectory corresponds to an ellipse with one focus at the centre of the Earth and the other at the point halfway between the launch point and the destination point. Geometrical arguments lead then to the following :
The altitude of apogee is maximized for a trajectory going one quarter of the way around the Earth. Longer ranges will have lower apogees in the minimal-delta-v solution.
. The Δv increases with range, leveling off at 7.9 km/s as the range approaches . The minimum-delta-v trajectory for going halfway around the world corresponds to a circular orbit just above the surface. See lower for the time of flight.
An intercontinental ballistic missile is defined as a missile that can hit a target at least 5500 km away, and according to the above formula this requires an initial speed of 6.1 km/s. Increasing the speed to 7.9 km/s to attain any point on Earth requires a considerably larger missile because the amount of fuel needed goes up exponentially with delta-v.
The initial direction of a minimum-delta-v trajectory points halfway between straight up and straight toward the destination point. Again, this is the case if the Earth's rotation is ignored. It is not exactly true for a rotating planet unless the launch takes place at a pole.

Flight duration

In a vertical flight of not too high altitudes, the time of the free-fall is both for the upward and for the downward part the maximum speed divided by the acceleration of gravity, so with a maximum speed of 1 km/s together 3 minutes and 20 seconds. The duration of the flight phases before and after the free-fall can vary.
For an intercontinental flight the boost phase takes 3 to 5 minutes, the free-fall about 25 minutes. For an ICBM the atmospheric reentry phase takes about 2 minutes; this will be longer for any soft landing, such as for a possible future commercial flight. Test flight 4 of the SpaceX 'Starship' performed such a flight with a lift off from Texas and a simulated soft touchdown in the Indian Ocean 66 minutes after liftoff.
Sub-orbital flights can last from just seconds to days. Pioneer 1 was NASA's first space probe, intended to reach the Moon. A partial failure caused it to instead follow a sub-orbital trajectory, reentering the Earth's atmosphere 43 hours after launch.
To calculate the time of flight for a minimum-delta-v trajectory, according to Kepler's third law, the period for the entire orbit would be:
Using Kepler's second law, we multiply this by the portion of the area of the ellipse swept by the line from the centre of the Earth to the projectile:
This gives about 32 minutes for going a quarter of the way around the Earth, and 42 minutes for going halfway around. For short distances, this expression is asymptotic to.
From the form involving arccosine, the derivative of the time of flight with respect to d goes to zero as d approaches . The derivative of Δv also goes to zero here. So if d =, the length of the minimum-delta-v trajectory will be about, but it will take only a few seconds less time than the trajectory for d = .