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Efficiency in Carrying Cargo to Earth Orbits Czech Technical University in Prague Magazine of Aviation Development Faculty of Transportation Sciences 4(20):6-9, 2016, ISSN: 1805-7578 Department of Air Transport DOI: 10.14311/MAD.2016.20.01 Efficiency in Carrying Cargo to Earth Orbits: Spaceports Repositioning Jakub Hospodka1*, Zdenekˇ Houfek1 1Department of Air Transport, Faculty of Transportation Sciences, Czech Technical University in Prague, Prague, Czech Republic *Corresponding author: Czech Technical University in Prague, Faculty of Transportation Sciences, Department of Air Transport, Horska´ 3, 128 03 Prague, Czech Republic, Email: [email protected] Abstract Space flights are in these days not any more question of technology, but more question of costs. One way how to decrease cost of launch is change of home spaceport. Change of home spaceport for different rockets is a way to achieve more efficient launches to space. The reason is different acceleration achieved from Earth rotation. We added several mathematical calculations of missions to Low Earth Orbit and Geostationary Earth Orbit to show bonuses from Earth rotation and effect of atmospheric drag on specific rockets used these days. We discussed only already used space vessels. Namely Arianne 5, Delta 4 heavy, Proton-M, Zenit and Falcon9. For reaching GEO we discuss possibility of using Hohmman transfer, because none of aforementioned vessels is available for direct GEO entry. As possible place for launch we discussed spaceports Baikonur, Kennedy Space center, Guyana Space center and Sea Launch platform. We present results in form of additional acceleration for each spaceport, and we also project this additional acceleration in means payload increase. In conclusion we find important differences between vessel effectivity based on spaceport used for launch. Change of launch location may bring significant cost decrease for operators. Keywords Atmosferic drag — Earth rotation — Hohmann transfer — Rockets — Spaceports — Tsiolkovski equation 1. Introduction Space missions to Low Earth Orbit (LEO) and Geostation- ary Earth orbit (GEO) from four different spaceports placed Currently, missions to Earth orbits and especially to GEO on different latitudes are representing all possible economic are made from few locations on Earth. These spaceports are outputs. Because of increased use of orbits and deep space normally bound to the national programs or agencies and the economic point of view due to huge cost of rocket launch only part of its launches are made for commercial purposes. is coming more to the light of the day. Exploration of our In these days there are some spaceports designed purely for solar system or for example mining resources on asteroids commercial purposes, but due to the cost of these spaceports will be possible only if we manage to decrease the cost of they are very few in numbers. space flights. Efficiency in using spaceports on our planet Economic efficiency in using rockets from spaceports is one of the first steps we need to take to conquer our so- owned by their national agency is the main task of this article. J. Hospodka and Z. Houfek Efficiency in carrying cargo to Earth orbits lar system. Better spaceport efficiency is based additional • Falcon v1.1 [4] – SpaceX rocket, first private company speed added from rotation of Earth. This additional velocity rocket used to supply International Space Station (ISS), raises from poles to equator. Obviously this effect only occurs Kennedy Space Center is home spaceport for launches for GEO of LEO without inclination, and only launches made eastbound. • Proton – M [5] – Russian heavy rocket, Baikonur is home spaceport 2. Current spaceports • Zenit [6] – Ukrainian rocket used by Sea Launch consor- To show difference in spaceports we use these days four rep- cium, Sea Launch platform is used as home spaceport resentatives were chosen: 3.1 Atmospheric drag 1. Baikonur – Russian main spaceport located in Kaza- Calculation of atmospheric drag depends can be made by khstan representing the northernmost spaceport used following equation: for high orbits and deep space missions. 1 2 2. Kennedy Space Center – NASA main spaceport lo- FD = CrAv ; (2) cated in Cape Canaveral, FL and used for all heavy and 2 manned launches to space (KSC). where FD is drag force, C is drag coeficient, r is the v 3. Guyana Space Center – ESA main spaceport located atmospheric density and is the flow velocity relative to the in French Guyana, currently the biggest Earth placed object. spaceport nearest to Equator (GSC). For this equation we will use 0.5 as a drag coefficient for cone, atmospheric density in 5.5 km above ground and 4. Sea Launch Platform – Commercial spaceport located rocket speed at point of maximal dynamic pressure. A is on Equator in Pacific Ocean on an old oil mining plat- representing referential area of the rockets which is defined form reconstructed to launch rockets. by the construction. After we manage to calculate drag force from Eq. (2) it is possible to use this force with time to reach Due to rotation of Earth every missile launch in eastward the point of maximal dynamic pressure in Eq. (3). direction gets bonus in speed depending on the latitude of the −1 t spaceport. Because the initial bonus on Equator is 463 ms Z FD and is decreasing to the Poles we need to compensate for Dv = dt; (3) 0 t spaceports mentioned above with following equation: The results from integration using the launching mass of the rockets are presented in Tab.2. v = v0 × cosf (1) Table 2. Rockets characteristic velocities. Table 1. Spaceport rotation bonuses. Rocket Dv (ms−1) Spaceports Rotation bonus (ms−1) Ariane 5 38,557 Baikonur 322 Delta IV Heavy 106,652 GSC 461 Falcon 9 v1.1 24,818 KSC 407 Proton-M 151,917 Sea launch 463 Zenit 26,583 3. Rocket performance 3.2 Rocket equations It is obvious that not only spaceports are responsible for econ- It is also necessary to get some reference numbers of speed, omy of the space missions. It is also necessary to include which is needed to get to orbits. In this case Tsiolkovski equa- rocket performance, atmospheric drag and other factors which tions (see, Eq. (4)) calculating maximum possible speed for are affecting rocket launches from Earth [1]. multistage rockets is good to show the difference in shifting Five types of rockets are used in this paper to show dif- rockets to different spaceports. ferent performance from home spaceports. These rockets M0 are: Dv = veln (4) M1 • Ariane 5 [2] – ESA rocket, Guyana Space Center is home spaceport This equation using natural logarithm with mass ratio of start (M0) and final mass (M1) needs to be adjusted for every • Delta IV Heavy [3] – NASA rocket, Kennedy Space stage of the rocket. Exhaust velocity for each stage of rocket Center is home spaceport depends on fuel type used in the rocket. This velocity can be 7 J. Hospodka and Z. Houfek Efficiency in carrying cargo to Earth orbits calculated from Specific impulse ISP with Eq. (5) using gravi- tational constant, which can be found in technical manuals of each rocket. ve = ISP × g0 (5) Also payload must be included in the mass ratio to get correct results so calculations are made with 10 tones for LEO and 4.85 tones to GEO. In tables3 and4 are shown results of Tsiolkovski equa- tions for LEO and GEO. Because each rocket has different number of stages and some have even rocket boosters on sides which needs to have another equation in following tables are shown only final results. Table 3. Tsiolkovsky equations for LEO. Rocket Dv (km s−1) Ariane 5 9.661 Delta IV Heavy 12.013 Falcon 9 v1.1 9.705 Proton-M 11.456 Figure 1. The model of basic objective classes. Zenit 10.131 Table 5. Results for spaceport and rockets. Dv difference Payload Spaceport/Rockets Table 4. Tsiolkovsky equations for GEO. (ms−1) increase (kg) Rocket Dv (km s−1) GSC/Ariane 5 2 12 Ariane 5 10.635 KSC/Delta IV Heavy 56 212 Delta IV Heavy 13.777 KSC/Falcon 9 v1.1 56 303 Falcon 9 v1.1 10.845 Baikonur/Proton-M 141 597 Proton-M 13.041 Zenit 11.515 from the same spaceport due to bigger inclination change during first burst in Falcon 9 mission characteristics. For the 3.3 Hohmann transfer following calculations with Kennedy space center only more Reaching GEO is possible with two options, first going di- efficient Hohmann transfer will be used except for Falcon 9 rectly and using more fuel in this process, and second follow launch. a maneuver called Hohmann transfer, see Fig.1. For spaceports used in this paper non-coplanar Hohmann transfer (see [7]) must be used except for Sea Launch platform. 4. Results Equations for this version of Hohmann transfer are: Even though it is not absolutely precise, because there are p still forces acting against rocket which are not included in Dv1 = v1 + vCS1 − 2 × v1 × vCS1 × cosF1 (6) this work, spaceports impact on rocket mission efficiency can be determined. After all calculations needed to get decent p picture of space missions to LEO and GEO we can interpret Dv2 = v2 + vCS2 − 2 × v2 × vCS2 × cosF2 (7) results. Obviously Zenit rocket and Sea Launch platform are not shown in the results, because all shifting to different Dv = Dv1 + Dv2 (8) spaceport is theoretically made to Equator, thus Sea Launch, Circular speed of initial and final orbit is needed in Eq. (6) because it is the most efficient. Zenit rocket launches are so far and Eq. (7) as well as apogee and perigee speed of the transfer not economically efficient to shift somewhere else, because orbit to determine exact velocity change. In technical manuals its home spaceport is the best.
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