Sub-orbital spaceflight explained

Sub-orbital human spaceflight (FAI-defined space border)
Name Year Flights Location
1961 2 Cape Canaveral
1963 2 Edwards AFB
1975 1 Baikonur Cosmodrome
2004 3 Mojave Air and Space Port
2021 3 Corn Ranch
Blue Origin NS-20
Blue Origin NS-21Blue Origin NS-22
2022 3
Blue Origin NS-2520241
Sub-orbital human spaceflight (United States-defined space border; excluding those above)
Name Year Flights Location
1962 1 Edwards AFB
1963 2
1965 4
1966 1
1967 2
1968 1
2018 1 Baikonur Cosmodrome
2018 1 Mojave Air and Space Port
2019 1
VSS Unity Unity21
VSS Unity Unity22
20212Spaceport America
VSS Unity Unity25
Galactic 01
Galactic 02
Galactic 03
Galactic 04
Galactic 05
20236Spaceport America
Galactic 06
Galactic 07
20242Spaceport 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 (about – [2] above sea level), 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.[3]

Altitude requirement

By definition, a sub-orbital spaceflight reaches an altitude higher than 100km (100miles) 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.[4] The US military and NASA award astronaut wings to those flying above 50miles,[5] although the U.S. State Department does not show a distinct boundary between atmospheric flight and spaceflight.[6]

Orbit

\epsilon

is given by:

\varepsilon = - > -\,\!

where

\mu

is the standard gravitational parameter.

Almost always a < R, corresponding to a lower

\epsilon

than the minimum for a full orbit, which is

-{\mu\over{2R}}

Thus the net extra specific energy needed compared to just raising the spacecraft into space is between 0 and

\mu\over{2R}

.

Speed, range, and altitude

To minimize the required delta-v (an astrodynamical measure which strongly determines the required fuel), the high-altitude part of the flight is made with the rockets off (this is technically called free-fall even for the upward part of the trajectory). (Compare with Oberth effect.) 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 (LEO), 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. (If there were no atmospheric drag the theoretical minimum delta-v would be 8.1 km/s to put a craft into a 300-kilometer high orbit starting from a stationary point like the South Pole. The theoretical minimum can be up to 0.46 km/s less if launching eastward from near the equator.)

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. (The vertical velocity will increase with distance for short distances but will decrease with distance at longer distances.) 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 (perhaps because of engine shut-off at a higher altitude).

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 (somewhere inside the Earth). (This is the orbit that minimizes the semi-major axis, which is equal to the sum of the distances from a point on the orbit to the two foci. Minimizing the semi-major axis minimizes the specific orbital energy and thus the delta-v, which is the speed of launch.) Geometrical arguments lead then to the following (with R being the radius of the Earth, about 6370 km):

\text = (1 + \sin\theta)R

\text = R\sqrt = \sqrt

\text = \frac(1 + \sin\theta + \cos\theta)

\text = \left(\frac - \sin^2\frac\right)R = \left(\frac\sin\left(\theta + \frac\right) - \frac\right)R

The altitude of apogee is maximized (at about 1320 km) for a trajectory going one quarter of the way around the Earth . Longer ranges will have lower apogees in the minimal-delta-v solution.

\text = \frac - \frac\mu\text = \frac\frac

\Delta v = \text = \sqrt = \sqrt

(where g is the acceleration of gravity at the Earth's surface). The Δv increases with range, leveling off at 7.9 km/s as the range approaches (halfway around the world). The minimum-delta-v trajectory for going halfway around the world corresponds to a circular orbit just above the surface (of course in reality it would have to be above the atmosphere). 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 (see Rocket equation).

The initial direction of a minimum-delta-v trajectory points halfway between straight up and straight toward the destination point (which is below the horizon). 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.[7]

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 (midcourse phase) 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.[8]

To calculate the time of flight for a minimum-delta-v trajectory, according to Kepler's third law, the period for the entire orbit (if it did not go through the Earth) would be:

\text = \left(\frac\right)^\frac \times \text = \left(\frac2\right)^\frac2\pi\sqrt

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:

\text = \frac\arcsin\sqrt + \frac

\begin \text &= \left(\left(\frac2\right)^\frac\arcsin\sqrt + \frac\cos\theta\sqrt\right)2\sqrt\frac \\ &= \left(\left(\frac2\right)^\frac\arccos\frac + \frac\cos\theta\sqrt\right)2\sqrt\frac \\\end

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

\sqrt{2d/g}

.

From the form involving arccosine, the derivative of the time of flight with respect to d (or θ) goes to zero as d approaches (halfway around the world). 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 = (for which the trajectory is long).

Flight profiles

While there are a great many possible sub-orbital flight profiles, it is expected that some will be more common than others.

Ballistic missiles

The first sub-orbital vehicles which reached space were ballistic missiles. The first ballistic missile to reach space was the German V-2, the work of the scientists at Peenemünde, on October 3, 1942, which reached an altitude of 53miles.[9] Then in the late 1940s the US and USSR concurrently developed missiles all of which were based on the V-2 Rocket, and then much longer range Intercontinental Ballistic Missiles (ICBMs). There are now many countries who possess ICBMs and even more with shorter range Intermediate Range Ballistic Missiles (IRBMs).

Tourist flights

Sub-orbital tourist flights will initially focus on attaining the altitude required to qualify as reaching space. The flight path will be either vertical or very steep, with the spacecraft landing back at its take-off site.

The spacecraft will shut off its engines well before reaching maximum altitude, and then coast up to its highest point. During a few minutes, from the point when the engines are shut off to the point where the atmosphere begins to slow down the downward acceleration, the passengers will experience weightlessness.

Megaroc had been planned for sub-orbital spaceflight by the British Interplanetary Society in the 1940s.[10] [11]

In the autumn of 1945, the group M. Tikhonravov K. and N. G. Chernysheva at NII-4 rocket artillery Academy of Sciences technology on its own initiative the first stratospheric rocket project was developed by VR-190 for vertical flight two pilots to an altitude of 200 km based on captured German ballistic rocket V-2.[12]

In 2004, a number of companies worked on vehicles in this class as entrants to the Ansari X Prize competition. The Scaled Composites SpaceShipOne was officially declared by Rick Searfoss to have won the competition on October 4, 2004, after completing two flights within a two-week period.

In 2005, Sir Richard Branson of the Virgin Group announced the creation of Virgin Galactic and his plans for a 9-seat capacity SpaceShipTwo named VSS Enterprise. It has since been completed with eight seats (one pilot, one co-pilot and six passengers) and has taken part in captive-carry tests and with the first mother-ship WhiteKnightTwo, or VMS Eve. It has also completed solitary glides, with the movable tail sections in both fixed and "feathered" configurations. The hybrid rocket motor has been fired multiple times in ground-based test stands, and was fired in a powered flight for the second time on 5 September 2013.[13] Four additional SpaceShipTwos have been ordered and will operate from the new Spaceport America. Commercial flights carrying passengers were expected in 2014, but became cancelled due to the disaster during SS2 PF04 flight. Branson stated, "[w]e are going to learn from what went wrong, discover how we can improve safety and performance and then move forwards together."[14]

Scientific experiments

A major use of sub-orbital vehicles today is as scientific sounding rockets. Scientific sub-orbital flights began in the 1920s when Robert H. Goddard launched the first liquid fueled rockets, however they did not reach space altitude. In the late 1940s, captured German V-2 ballistic missiles were converted into V-2 sounding rockets which helped lay the foundation for modern sounding rockets.[15] Today there are dozens of different sounding rockets on the market, from a variety of suppliers in various countries. Typically, researchers wish to conduct experiments in microgravity or above the atmosphere.

Sub-orbital transportation

Research, such as that done for the X-20 Dyna-Soar project suggests that a semi-ballistic sub-orbital flight could travel from Europe to North America in less than an hour.

However, the size of rocket, relative to the payload, necessary to achieve this, is similar to an ICBM. ICBMs have delta-v's somewhat less than orbital; and therefore would be somewhat cheaper than the costs for reaching orbit, but the difference is not large.[16]

Due to the high cost of spaceflight, suborbital flights are likely to be initially limited to high value, very high urgency cargo deliveries such as courier flights, military fast-response operations or space tourism.

The SpaceLiner is a hypersonic suborbital spaceplane concept that could transport 50 passengers from Australia to Europe in 90 minutes or 100 passengers from Europe to California in 60 minutes.[17] The main challenge lies in increasing the reliability of the different components, particularly the engines, in order to make their use for passenger transportation on a daily basis possible.

SpaceX is potentially considering using their Starship as a sub-orbital point-to-point transportation system.[18]

Notable uncrewed sub-orbital spaceflights

Crewed sub-orbital spaceflights

Above 100 km (62.14 mi) in altitude.

Date (GMT)MissionCrewCountryRemarks
11961-05-05Mercury-Redstone 3Alan ShepardFirst crewed sub-orbital spaceflight, first American in space
21961-07-21Mercury-Redstone 4Virgil GrissomSecond crewed sub-orbital spaceflight, second American in space
31963-07-19X-15 Flight 90Joseph A. WalkerFirst winged craft in space
41963-08-22X-15 Flight 91Joseph A. WalkerFirst person and spacecraft to make two flights into space
51975-04-05Soyuz 18aVasili Lazarev
Oleg Makarov
Failed orbital launch. Aborted after malfunction during stage separation
62004-06-21SpaceShipOne flight 15PMike MelvillFirst commercial spaceflight
72004-09-29SpaceShipOne flight 16PMike MelvillFirst of two flights to win Ansari X-Prize
82004-10-04SpaceShipOne flight 17PBrian BinnieSecond X-Prize flight, clinching award
92021-07-20Blue Origin NS-16Jeff Bezos
Mark Bezos
Wally Funk
Oliver Daemen
First crewed Blue Origin flight
102021-10-13Blue Origin NS-18Audrey Powers
Chris Boshuizen
Glen de Vries
William Shatner
Second crewed Blue Origin flight
112021-12-11Blue Origin NS-19
Michael Strahan
Dylan Taylor
Evan Dick
Lane Bess
Cameron Bess
Third crewed Blue Origin flight
122022-03-31Blue Origin NS-20
Sharon Hagle
Marc Hagle
Jim Kitchen
George Nield
Gary Lai
Fourth crewed Blue Origin flight
132022-06-04Blue Origin NS-21Evan Dick
Katya Echazarreta
Hamish Harding
Victor Correa Hespanha
Jaison Robinson
Victor Vescovo
Fifth crewed Blue Origin flight
142022-08-04Blue Origin NS-22Coby Cotton
Mário Ferreira
Vanessa O'Brien
Clint Kelly III
Sara Sabry
Steve Young
Sixth crewed Blue Origin flight
152024-05-19Blue Origin NS-25Mason Angel
Sylvain Chiron
Ed Dwight
Kenneth Hess
Carol Schaller
Gopichand Thotakura
Seventh crewed Blue Origin flight

Future of crewed sub-orbital spaceflight

Private companies such as Virgin Galactic, Armadillo Aerospace (reinvented as Exos Aerospace), Airbus,[21] Blue Origin and Masten Space Systems are taking an interest in sub-orbital spaceflight, due in part to ventures like the Ansari X Prize. NASA and others are experimenting with scramjet-based hypersonic aircraft which may well be used with flight profiles that qualify as sub-orbital spaceflight. Non-profit entities like ARCASPACE and Copenhagen Suborbitals also attempt rocket-based launches.

See also

Notes and References

  1. News: Blue Origin launches Bezos on first crewed New Shepard flight . Foust. Jeff . . 20 July 2021 . 20 Jul 2021 .
  2. https://scholar.smu.edu/cgi/viewcontent.cgi?article=1126&context=jalc
  3. Web site: Martlet . dead . https://web.archive.org/web/20100926022558/http://www.astronautix.com/fam/martlet.htm . 2010-09-26.
  4. Web site: 100 km Altitude Boundary for Astronautics. Fédération Aéronautique Internationale. https://web.archive.org/web/20110809093537/http://www.fai.org/astronautics/100km.asp. 2011-08-09. dead. 2017-09-14.
  5. Web site: X-15 Space Pioneers Now Honored as Astronauts. Mary. Whelan. 5 June 2013. nasa.gov. 4 May 2018. live. https://web.archive.org/web/20170611194526/https://www.nasa.gov/centers/dryden/news/NewsReleases/2005/05-57.html. 11 June 2017.
  6. Web site: 85. U.S. Statement, Definition and Delimitation of Outer Space And The Character And Utilization Of The Geostationary Orbit, Legal Subcommittee of the United Nations Committee on the Peaceful Uses of Outer Space at its 40th Session in Vienna from April. state.gov. 4 May 2018.
  7. Blanco . Philip . Modeling ICBM Trajectories Around a Rotating Globe with Systems Tool Kit . The Physics Teacher . September 2020 . 58 . 7 . 494–496 . 10.1119/10.0002070 . 2020PhTea..58..494B. 225017449 .
  8. Web site: Pioneer 1 - NSSDC ID: 1958-007A . NASA NSSDC.
  9. Germany's V-2 Rocket, Kennedy, Gregory P.
  10. Web site: How a Nazi rocket could have put a Briton in space. Richard. Hollingham. bbc.com. 4 May 2018. live. https://web.archive.org/web/20161114032515/http://www.bbc.com/future/story/20150824-how-a-nazi-rocket-could-have-put-a-briton-in-space. 14 November 2016.
  11. Web site: Megaroc. www.bis-space.com. 4 May 2018. live. https://web.archive.org/web/20161030133900/http://www.bis-space.com/what-we-do/projects/megaroc. 30 October 2016.
  12. Book: Anatoli I. Kiselev . Alexander A. Medvedev. Valery A. Menshikov . Astronautics: Summary and Prospects . V. Sherbakov . N. Novichkov . A. Nechaev . Springer Science & Business Media. December 2012. 1–2. 9783709106488.
  13. Web site: Scaled Composites: Projects - Test Logs for SpaceShipTwo . 2013-08-14 . live . https://web.archive.org/web/20130816140953/http://www.scaled.com/projects/test_logs/35/model_339_spaceshiptwo . 2013-08-16 .
  14. "Branson on Virgin Galactic crash: 'Space is hard – but worth it'". CNET. Retrieved August 1, 2015.
  15. Web site: ch2. history.nasa.gov. 2015-11-28. live. http://archive.wikiwix.com/cache/20151129091504/https://history.nasa.gov/SP-4401/ch2.htm. 2015-11-29.
  16. Web site: The Space Review: Point-to-point suborbital transportation: sounds good on paper, but.... www.thespacereview.com. 4 May 2018. live. https://web.archive.org/web/20170801074751/http://www.thespacereview.com/article/1118/1. 1 August 2017.
  17. 10.1016/j.actaastro.2010.01.020. Sippel, M. . Promising roadmap alternatives for the SpaceLiner . Acta Astronautica . 11–12 . 66 . 2010. 1652–1658 . 2010AcAau..66.1652S .
  18. News: Ralph. Eric . SpaceX CEO Elon Musk wants to use Starships as Earth-to-Earth transports . Teslarati . 30 May 2019 . 31 May 2019 .
  19. Walter Dornberger, Moewig, Berlin 1984. .
  20. Web site: Bumper Project . White Sands Missile Range . dead . https://web.archive.org/web/20080110163113/http://www.wsmr.army.mil/pao/FactSheets/bump.htm . 2008-01-10 .
  21. News: Airbus drops model 'space jet'. Jonathan. Amos. BBC News. 3 June 2014. 4 May 2018. live. https://web.archive.org/web/20180504004642/http://www.bbc.co.uk/news/science-environment-27686906. 4 May 2018.