Quote from: LouScheffer on 12/04/2018 12:54 pmA Star-48 only adds a tiny bit of performance, so a Falcon Heavy alone could almost do the job.A Star 48 has about 2114 kg mass, about 114 kg when done. So assuming Clipper is 6 tonnes, as quoted, then at an ISP of 287, the Star-48 supplies 287*9.8*ln(8/6) = 809 m/s.But the second stage performance is reduced by needing to boost the extra mass of the Star. Assume that with no Star-48, the stack starts at 117t and ends at 11t. But with the Star, it starts at 119t and ends at 13t. At an ISP of 348, the extra mass then loses 348*9.8*(ln(117/11) - ln(119/13)) = 511 m/s. So the net gain is only 809-511 = 298 m/s.This is a pretty small faction of the 8000 m/s or so the second stage provides. It's on the order of what a burn-to-depletion could provide, as opposed to a controlled shutdown. But of course with a zillion dollar probe, they want to be sure they have the performance they need, not that it's merely likely.It'll use the STAR-48BV variant which has an ISP of 292 (not 287), has a mass of 2164 kg when loaded and a mass of 138 kg when done (See the numbers for STAR-48BV in the NGIS Motor Catalog from June 2018).So, the STAR-48BV will kick in a little more delta-V than you calculated.Also, I suggest you try to refine your assumptions for FH stage 2 performance numbers a bit.

A Star-48 only adds a tiny bit of performance, so a Falcon Heavy alone could almost do the job.A Star 48 has about 2114 kg mass, about 114 kg when done. So assuming Clipper is 6 tonnes, as quoted, then at an ISP of 287, the Star-48 supplies 287*9.8*ln(8/6) = 809 m/s.But the second stage performance is reduced by needing to boost the extra mass of the Star. Assume that with no Star-48, the stack starts at 117t and ends at 11t. But with the Star, it starts at 119t and ends at 13t. At an ISP of 348, the extra mass then loses 348*9.8*(ln(117/11) - ln(119/13)) = 511 m/s. So the net gain is only 809-511 = 298 m/s.This is a pretty small faction of the 8000 m/s or so the second stage provides. It's on the order of what a burn-to-depletion could provide, as opposed to a controlled shutdown. But of course with a zillion dollar probe, they want to be sure they have the performance they need, not that it's merely likely.

Stage 2 LOX: 168,100 poundsStage 2 RP-1: 65,000 pounds

Quote from: docmordrid on 12/04/2018 10:40 amFrom the Ars articleQuoteThe breakthrough referenced by Goldstein involved the addition of a Star 48 "kick stage" to the Falcon Heavy rocket, which would provide an extra boost of energy after the rocket's upper stage had fired. With this solid rocket motor kick stage, Goldstein said Clipper would need just a single Earth gravity assist and would not have to go into the inner Solar System for a Venus flyby."Nobody is saying we're not going on the SLS," Goldstein said. "But if by chance we don't, we don't have the challenge of the inner Solar System. This was a major development. This was a big deal for us."A Star-48 only adds a tiny bit of performance, so a Falcon Heavy alone could almost do the job.A Star 48 has about 2114 kg mass, about 114 kg when done. So assuming Clipper is 6 tonnes, as quoted, then at an ISP of 287, the Star-48 supplies 287*9.8*ln(8/6) = 809 m/s.But the second stage performance is reduced by needing to boost the extra mass of the Star. Assume that with no Star-48, the stack starts at 117t and ends at 11t. But with the Star, it starts at 119t and ends at 13t. At an ISP of 348, the extra mass then loses 348*9.8*(ln(117/11) - ln(119/13)) = 511 m/s. So the net gain is only 809-511 = 298 m/s.This is a pretty small faction of the 8000 m/s or so the second stage provides. It's on the order of what a burn-to-depletion could provide, as opposed to a controlled shutdown. But of course with a zillion dollar probe, they want to be sure they have the performance they need, not that it's merely likely.

From the Ars articleQuoteThe breakthrough referenced by Goldstein involved the addition of a Star 48 "kick stage" to the Falcon Heavy rocket, which would provide an extra boost of energy after the rocket's upper stage had fired. With this solid rocket motor kick stage, Goldstein said Clipper would need just a single Earth gravity assist and would not have to go into the inner Solar System for a Venus flyby."Nobody is saying we're not going on the SLS," Goldstein said. "But if by chance we don't, we don't have the challenge of the inner Solar System. This was a major development. This was a big deal for us."

The breakthrough referenced by Goldstein involved the addition of a Star 48 "kick stage" to the Falcon Heavy rocket, which would provide an extra boost of energy after the rocket's upper stage had fired. With this solid rocket motor kick stage, Goldstein said Clipper would need just a single Earth gravity assist and would not have to go into the inner Solar System for a Venus flyby."Nobody is saying we're not going on the SLS," Goldstein said. "But if by chance we don't, we don't have the challenge of the inner Solar System. This was a major development. This was a big deal for us."

Quote from: woods170 on 12/04/2018 01:52 pmQuote from: LouScheffer on 12/04/2018 12:54 pmA Star-48 only adds a tiny bit of performance, so a Falcon Heavy alone could almost do the job.A Star 48 has about 2114 kg mass, about 114 kg when done. So assuming Clipper is 6 tonnes, as quoted, then at an ISP of 287, the Star-48 supplies 287*9.8*ln(8/6) = 809 m/s.But the second stage performance is reduced by needing to boost the extra mass of the Star. Assume that with no Star-48, the stack starts at 117t and ends at 11t. But with the Star, it starts at 119t and ends at 13t. At an ISP of 348, the extra mass then loses 348*9.8*(ln(117/11) - ln(119/13)) = 511 m/s. So the net gain is only 809-511 = 298 m/s.This is a pretty small faction of the 8000 m/s or so the second stage provides. It's on the order of what a burn-to-depletion could provide, as opposed to a controlled shutdown. But of course with a zillion dollar probe, they want to be sure they have the performance they need, not that it's merely likely.It'll use the STAR-48BV variant which has an ISP of 292 (not 287), has a mass of 2164 kg when loaded and a mass of 138 kg when done (See the numbers for STAR-48BV in the NGIS Motor Catalog from June 2018).So, the STAR-48BV will kick in a little more delta-V than you calculated.Also, I suggest you try to refine your assumptions for FH stage 2 performance numbers a bit.These changes, while sensible, make only trivial differences to the calculation. For example, with a 6000 kg Clipper, the Star-48BV provides 292*9.8*l(8164/6138) = 816 m/s, just 8 m/s more than calculated above.As far as stage 2 performance, thanks to the environmental impact statement for the abort test, page 2-6, we now know the second stage fuel load:QuoteStage 2 LOX: 168,100 poundsStage 2 RP-1: 65,000 pounds That's 233,000 lb of propellant, or 106t. So now the only unknown is the mass of the empty second stage + residuals. I assumed 5t (4.5t empty + 500 kg residuals). If we assume the second stage is lighter (4t for stage + residuals) then the benefit becomes slightly less ( 348*9.8*(l(116/10) - l(118/12)) = 563 m/s lost by second stage from increased payload). If we assume the second stage is on the heavy end of estimates, at 6t for empty + residuals, then the loss is 348*9.8*(l(118/12) - l(120/14)) = 468 m/s. Basically, any plausable mass for the second stage yields the same results. The Star adds about 800 m/s, but the extra payload on the second stage will eat at least half of that. So the overall gain is small, <400 m/s or so.

Quote from: woods170 on 12/04/2018 01:52 pmQuote from: LouScheffer on 12/04/2018 12:54 pmA Star-48 only adds a tiny bit of performance, so a Falcon Heavy alone could almost do the job.A Star 48 has about 2114 kg mass, about 114 kg when done. So assuming Clipper is 6 tonnes, as quoted, then at an ISP of 287, the Star-48 supplies 287*9.8*ln(8/6) = 809 m/s.But the second stage performance is reduced by needing to boost the extra mass of the Star. Assume that with no Star-48, the stack starts at 117t and ends at 11t. But with the Star, it starts at 119t and ends at 13t. At an ISP of 348, the extra mass then loses 348*9.8*(ln(117/11) - ln(119/13)) = 511 m/s. So the net gain is only 809-511 = 298 m/s.This is a pretty small faction of the 8000 m/s or so the second stage provides. It's on the order of what a burn-to-depletion could provide, as opposed to a controlled shutdown. But of course with a zillion dollar probe, they want to be sure they have the performance they need, not that it's merely likely.It'll use the STAR-48BV variant which has an ISP of 292 (not 287), has a mass of 2164 kg when loaded and a mass of 138 kg when done (See the numbers for STAR-48BV in the NGIS Motor Catalog from June 2018).So, the STAR-48BV will kick in a little more delta-V than you calculated.Also, I suggest you try to refine your assumptions for FH stage 2 performance numbers a bit.These changes, while sensible, make only trivial differences to the calculation. For example, with a 6000 kg Clipper, the Star-48BV provides 292*9.8*l(8164/6138) = 816 m/s, just 8 m/s more than calculated above.

Why do they no longer use larger kick stages like the STAR 62 or so? Should improve things a bit.

Quote from: TorenAltair on 12/04/2018 02:57 pmWhy do they no longer use larger kick stages like the STAR 62 or so? Should improve things a bit.Lou's always fun -- he shows how to do the math. You don't even need a fancy calculator -- just copy/paste the equations into Google and you'll get the answer. ;-)From the NGIS catalog, a STAR 63D has an ISP of ~283s, a starting mass of ~3.5t and a burnout mass of ~230kg.So with a 6000kg Clipper, the STAR 63D provides:283*9.8*ln((6+3.5)/(6+0.23)) = 1170m/sThe second stage, on the other hand, loses:348*9.8*(ln((111+6)/(5+6)) - ln((111+6+3.5)/(5+6+3.5))) = 840m/sFor a whopping net of 330m/s.So you're looking at a <50m/s gain at a cost of a kick stage almost twice the size of a STAR 48 (and over half the mass of the payload)Oh, and the STAR 63D doesn't provide thrust vector control (TVC) -- going from a STAR 48B to a 48BV adds 20-odd kilos, so if Clipper needs a kick with TVC, the benefit will be even lower.

How many kg of payload does it add to a c3 of 85?Per LSP, FH can lift 8230 kg to a c3 of 30, and 1810 kg to a c3 of 85.

Quote from: envy887 on 12/04/2018 06:00 pmHow many kg of payload does it add to a c3 of 85?Per LSP, FH can lift 8230 kg to a c3 of 30, and 1810 kg to a c3 of 85.A STAR 48BV doesn't, AFAICT.Given:Payload 1.81tSTAR 48BV ISP 292sSTAR 48BV Mi 2.169tSTAR 48BV Mf .138tThe STAR would provide:292*9.8*ln((1.81+2.169)/(1.81+0.138)) = ~2043m/sHowever, the second stage loses:348*9.8*(ln((111+1.81)/(5+1.81)) - ln((111+1.81+2.169)/(5+6+2.169))) = ~2184m/sSo you're looking at negative returns.

Quote from: GreenShrike on 12/04/2018 07:14 pmQuote from: envy887 on 12/04/2018 06:00 pmHow many kg of payload does it add to a c3 of 85?Per LSP, FH can lift 8230 kg to a c3 of 30, and 1810 kg to a c3 of 85.A STAR 48BV doesn't, AFAICT.Given:Payload 1.81tSTAR 48BV ISP 292sSTAR 48BV Mi 2.169tSTAR 48BV Mf .138tThe STAR would provide:292*9.8*ln((1.81+2.169)/(1.81+0.138)) = ~2043m/sHowever, the second stage loses:348*9.8*(ln((111+1.81)/(5+1.81)) - ln((111+1.81+2.169)/(5+6+2.169))) = ~2184m/sSo you're looking at negative returns.Think there is an error in your math.

Quote from: GreenShrike on 12/04/2018 06:34 pmQuote from: TorenAltair on 12/04/2018 02:57 pmWhy do they no longer use larger kick stages like the STAR 62 or so? Should improve things a bit.Lou's always fun -- he shows how to do the math. You don't even need a fancy calculator -- just copy/paste the equations into Google and you'll get the answer. ;-)From the NGIS catalog, a STAR 63D has an ISP of ~283s, a starting mass of ~3.5t and a burnout mass of ~230kg.So with a 6000kg Clipper, the STAR 63D provides:283*9.8*ln((6+3.5)/(6+0.23)) = 1170m/sThe second stage, on the other hand, loses:348*9.8*(ln((111+6)/(5+6)) - ln((111+6+3.5)/(5+6+3.5))) = 840m/sFor a whopping net of 330m/s.So you're looking at a <50m/s gain at a cost of a kick stage almost twice the size of a STAR 48 (and over half the mass of the payload)Oh, and the STAR 63D doesn't provide thrust vector control (TVC) -- going from a STAR 48B to a 48BV adds 20-odd kilos, so if Clipper needs a kick with TVC, the benefit will be even lower.This.The reason for STAR-48BV is the TVC system. A regular STAR-48 is spin stabilized, which requires the payload to de-spin after separation.Europa Clipper is not designed to be inserted into orbit by spin-stabilized kick-stage. So, hence the need for TVC on the kick-stage. And that pretty much is how they got to STAR-48BV.

This discussion has been fascinating - I even understand some of the math! But seriously; can I assume that all iterations of Europa Clipper launched on Falcon Heavy would need a fully expendable FH, even with 1x Earth flyby?

ncb, you are assuming a 1.81 mT payload vs. Lou is using a 6mT payload. Which one is it?