Starlink satellite dimension estimates
Beside published photos and general weight, there is very little information available about the Starlink satellites dimensions, capabilities and mass distribution. So I did a little bit of BOTE calculation.
From Falcon 9 user guide and the above Starlink stack image, we can estimate that the total available height for stack of 60 satellites is 6.7m. As there are two satellites per unit of height, and there might be some spacers between them, we can estimate that the stowed height of the satellite is 20cm (or, more probably 8", which is 20.32cm).
Fairing internal diameter available to payloads is 4.6m, but there is a little space on the edges. Assuming 5cm distance between the edge of the satellite and the fairing, we can calculate that the long edge of the satellite is 3.2m long and short edge a half of that (1.6m long).
So now we have estimate of stowed Starlink satellite, measuring 3.2x1.6x0.2m. Not bad.
Next issue is the weight of the satellite. Published information is 500 pounds (227kg), which gives total usable payload to orbit of 13620kg. That is heavy for high inclination orbit. But fully expendable Falcon 9 is rated at 22800kg at 200x200km at 28.5 inclination. 20% penalty leads to 18.240kg. So the mass budget does not seem to be totally exhausted. The other information available is 260kg. So I will assume this is a difference between wet mass (260kg) and dry mass (227kg) which would mean that there is 33kg of Krypton available on-board.
The next estimate is related to solar panels. There are 12 segments, where longer edge of each segment equals width of the satellite (3.2m). The segment appears to have 32x4 solar cells, where each solar cell has 2:1 aspect ratio. I will ignore the edges for this calculation, so we can estimate the dimensions of each segment are 3.2m x 0.8m. So the total solar array has area of 12 x 3.2 x 0.8 = 30.72m2. Due to losses between solar cells and on the edges, let me round that to 30m2. Using 1250W/m2 of total solar irradiance and 18% efficiency leads to 6kW of available electrical power. That is comparable to medium-sized GEO satellites!
Total weight of solar panel is quite significant for the given size. Spectrolab, leading solar space panel manufactorer, quotes mass between 1.76 and 2.08kg/m3. Since SpaceX optimizes on cost, we can expect to be above that range. At 2.5kg/m2 given 75kg, or third of the dry mass just for solar panels.
That means that each Starlink launch adds 240kW of solar power to LEO. That is MORE solar power in a single launch than the complete ISS! If we take a look at UCS Satellite Database, there are 562 geosychhrnous satellites. If we estimate 5kW as average GEO solar panel wattage, that equals to 2.8MW of installed power. SpaceX will put that amount of solar power in half a year, assuming launch rate of two missions per month. That is 5.76MW per year. Total initial constellation will have 9MW of installed power, radiating to Earth from a point that is 65 times closer. That means that average beaming power flux (essentially signal strength) will be 16000 time higher for Starlink than for collective fleet of existing GEO communication satellites. And more power means smaller antennas and more bits per Hz.
What about batteries? Starlink will spend approximately half of the time in Earth shadow, aprroximately 96 minutes/2 equals 48 minutes. With battery degradation, we should assume a battery of 3kWh. But as it will re recharged/discarged 15 times per days: Samsung 21700 battery (used for Tesla Model 3), provides 75% capacity after 2000 cycles. The designed lifetime of Starlink satellite is 5 years. So obviously satellites are not designed to provide full continuous beaming power over antennae. We can assume that average consumption on the "night side" will be only 300W and double the battery capacity to 6kWh. Using 250W/kg metrics that is 24kg of batteries (9% of dry mass). That would require just one battery charging cycle per day, close to five year design goal.
The HET (Hall-effect thruster) seems harder to estimate. Its inner diameter seems to be little above 82mm that was used by Busek BHT-1500, 1.5kW HET that was tested both with Xenon and Krypton.
If we take this device as baseline, it has mass of 6.8kg, can use up to 2kW of power with Isp of 1915s and thrust of 118mN. For Krypton, these numbers are lower with around 7% lower efficiency and thrust rated around 50mN/kW of power.
Lets assume that SpaceX designed thruster with 2kW input power and 100mN thrust. That would provide acceleration of 0.4mm/s2, or 0.72m/s of deltaV per orbit (assuming continuous 30 minute thrust on the sunny side of Earth. Total deltaV would be 2400m/s at Isp of 1800s, which is more than enough for whole Starlink satellite lifecycle. Propellant would suffice for 70 days of continuous thrust. So even if the numbers are significantly lower (efficiency, propellant mass), Starlink would have so much deltaV capacity that it would be capable of transferring itself from GTO orbit to GEO. Total deltaV budget seems to indicate that Krypton weight estimate (of 33kg) is oversized for initial Starlink mission, and initial version(s) might very well trade in lower tank pressure for lower propellant mass. However, announced Starlink VLEO constellation at just 340km will require significant deltaV much higher than for the current 550km orbit.
But there is significant element not yet addressed - multi-functional Power Processing Unit (PPU). It should be sized to accept maximum power input (6kW) and distribute it on various voltages to different on board elements. Using another Busek HET (BHT-600), its design goal was 1kg for engine and 2kg for PPU. Extrapolating this value (300W/kg) gives roughly 20kg for PPU.
So here is the mass breakdown for total of 260kg per satellite:
So Starlink satellite really packs a lot in its 260kg of wet mass!
From Falcon 9 user guide and the above Starlink stack image, we can estimate that the total available height for stack of 60 satellites is 6.7m. As there are two satellites per unit of height, and there might be some spacers between them, we can estimate that the stowed height of the satellite is 20cm (or, more probably 8", which is 20.32cm).
Fairing internal diameter available to payloads is 4.6m, but there is a little space on the edges. Assuming 5cm distance between the edge of the satellite and the fairing, we can calculate that the long edge of the satellite is 3.2m long and short edge a half of that (1.6m long).
So now we have estimate of stowed Starlink satellite, measuring 3.2x1.6x0.2m. Not bad.
Next issue is the weight of the satellite. Published information is 500 pounds (227kg), which gives total usable payload to orbit of 13620kg. That is heavy for high inclination orbit. But fully expendable Falcon 9 is rated at 22800kg at 200x200km at 28.5 inclination. 20% penalty leads to 18.240kg. So the mass budget does not seem to be totally exhausted. The other information available is 260kg. So I will assume this is a difference between wet mass (260kg) and dry mass (227kg) which would mean that there is 33kg of Krypton available on-board.
The next estimate is related to solar panels. There are 12 segments, where longer edge of each segment equals width of the satellite (3.2m). The segment appears to have 32x4 solar cells, where each solar cell has 2:1 aspect ratio. I will ignore the edges for this calculation, so we can estimate the dimensions of each segment are 3.2m x 0.8m. So the total solar array has area of 12 x 3.2 x 0.8 = 30.72m2. Due to losses between solar cells and on the edges, let me round that to 30m2. Using 1250W/m2 of total solar irradiance and 18% efficiency leads to 6kW of available electrical power. That is comparable to medium-sized GEO satellites!
Total weight of solar panel is quite significant for the given size. Spectrolab, leading solar space panel manufactorer, quotes mass between 1.76 and 2.08kg/m3. Since SpaceX optimizes on cost, we can expect to be above that range. At 2.5kg/m2 given 75kg, or third of the dry mass just for solar panels.
That means that each Starlink launch adds 240kW of solar power to LEO. That is MORE solar power in a single launch than the complete ISS! If we take a look at UCS Satellite Database, there are 562 geosychhrnous satellites. If we estimate 5kW as average GEO solar panel wattage, that equals to 2.8MW of installed power. SpaceX will put that amount of solar power in half a year, assuming launch rate of two missions per month. That is 5.76MW per year. Total initial constellation will have 9MW of installed power, radiating to Earth from a point that is 65 times closer. That means that average beaming power flux (essentially signal strength) will be 16000 time higher for Starlink than for collective fleet of existing GEO communication satellites. And more power means smaller antennas and more bits per Hz.
Next is the thruster, which was defined as Krypton-fueled Hall-effect thruster. It seems that Starlink has only one of these thrusters, deployed next to the "fattest" feature on the satellite. This is probably high pressure vessel containing the Krypton. It has a little longer that 1/4 of the total width, so lets assume that the Krypton vessel has 20cm diameter and 80cm length. I will disregard thickness of the vessel walls for now, which gives internal tank volume of 0.125m3. Krypton density at room temperature and pressure is 3.7493kg/m3. To get to 33kg, we need pressure equal to 70bars. Now, such pressures require thick walls, which can really eat up the internal volume. One such calculator gives steel walls of 7mm, which greatly affects available volume. And such vessels are heavy. Standard carbon steel pipe A-106-GR.B for the given diameter and pressure would have 31kg of weight (using this calculator). Well, there are lot of SpaceX enginners that work with high pressures, so I am sure something more optimal would be used. But 30kg is a lot, and it really puts a question why not to push to Iodine in future iterations.
What about batteries? Starlink will spend approximately half of the time in Earth shadow, aprroximately 96 minutes/2 equals 48 minutes. With battery degradation, we should assume a battery of 3kWh. But as it will re recharged/discarged 15 times per days: Samsung 21700 battery (used for Tesla Model 3), provides 75% capacity after 2000 cycles. The designed lifetime of Starlink satellite is 5 years. So obviously satellites are not designed to provide full continuous beaming power over antennae. We can assume that average consumption on the "night side" will be only 300W and double the battery capacity to 6kWh. Using 250W/kg metrics that is 24kg of batteries (9% of dry mass). That would require just one battery charging cycle per day, close to five year design goal.
The HET (Hall-effect thruster) seems harder to estimate. Its inner diameter seems to be little above 82mm that was used by Busek BHT-1500, 1.5kW HET that was tested both with Xenon and Krypton.
If we take this device as baseline, it has mass of 6.8kg, can use up to 2kW of power with Isp of 1915s and thrust of 118mN. For Krypton, these numbers are lower with around 7% lower efficiency and thrust rated around 50mN/kW of power.
Lets assume that SpaceX designed thruster with 2kW input power and 100mN thrust. That would provide acceleration of 0.4mm/s2, or 0.72m/s of deltaV per orbit (assuming continuous 30 minute thrust on the sunny side of Earth. Total deltaV would be 2400m/s at Isp of 1800s, which is more than enough for whole Starlink satellite lifecycle. Propellant would suffice for 70 days of continuous thrust. So even if the numbers are significantly lower (efficiency, propellant mass), Starlink would have so much deltaV capacity that it would be capable of transferring itself from GTO orbit to GEO. Total deltaV budget seems to indicate that Krypton weight estimate (of 33kg) is oversized for initial Starlink mission, and initial version(s) might very well trade in lower tank pressure for lower propellant mass. However, announced Starlink VLEO constellation at just 340km will require significant deltaV much higher than for the current 550km orbit.
But there is significant element not yet addressed - multi-functional Power Processing Unit (PPU). It should be sized to accept maximum power input (6kW) and distribute it on various voltages to different on board elements. Using another Busek HET (BHT-600), its design goal was 1kg for engine and 2kg for PPU. Extrapolating this value (300W/kg) gives roughly 20kg for PPU.
So here is the mass breakdown for total of 260kg per satellite:
- 75kg for 30m2, 6kW solar panels
- 33kg of Krypton propellant
- 30kg of high pressure vessel
- 7kg for HET
- 20kg PPU
- 24kg of batteries
- 71kg for everything else (structure, GNC, sensors, payload etc)
So Starlink satellite really packs a lot in its 260kg of wet mass!
What are the geometric dimensional spacing of the satellites going to be while in orbit. How far will they be apart from each other?
ReplyDeleteThat is easy. Initial shell will consists of 72 orbital planes of 20 satellites in each. Thus satellites in a single plane will have distance of roughly 2100 km. Orbital planes themselves will be separated by roughly 600 km distance. Thus distance between satellites will be constant and less than 1000 km. Within 35 degree min horizon elevation user terminal should be always within reach of four satellites.
ReplyDeleteDo you have any information regarding the orientation of the satellite in orbit, or an estimation of the cross-sectional area ?
ReplyDeleteI estimated the main body dimension of 3.2x1.6 meters, which would lead to roughly 5 m2 cross-sectional area when satellite is directly above you. Regarding orientation I do expect that it is adjusted to maximize solar panel insolation AND minimize reflection of sunlight towards Earth. Roughly speaking, due to phased array antennae on the spacecraft, Starlink satellites can adjust their attitude all the time in order to maximize power and reflection requirements. Since it is designed for LEO it probably uses magnetic torque devices exclusively without any movable parts.
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