Constellation program

[Satanic Mechanic]

I haven't finished with my numbers yet but after giving it some thought, I don't think an addition of two more SRB's could get 200 tonnes into 300km orbit.  I think I will come under 175 tonnes.
This little exercise is really clearing the math cobwebs.

SM

[Satanic Mechanic]

According to Leguy's post, the CaLV or should I say Ares V rocket has:

Copied from Lemguy's post...
Ares V, a heavy lift launch vehicle, will use five RS-68 liquid
oxygen/liquid hydrogen engines mounted below a larger version of the
space shuttle's external tank, and two five-segment solid propellant
rocket boosters for the first stage. The upper stage will use the
same J-2X engine as the Ares I. The Ares V can lift more than 286,000
pounds to low Earth orbit and stands approximately 360 feet tall.
This versatile system will be used to carry cargo and the components
into orbit needed to go to the moon and later to Mars.


SM

[Bob B.]

I’ve done a little ciphering on this problem.  The first thing I did was to estimate what changes are required to the CaLV as a result of the switch to the RS-68 engine.  I took the specs in this page and calculated the CaLV’s total delta-v based on the original SSME design.  I next adjusted the 1st stage mass to account for the heavier RS-68.  I then calculated how much 1st stage propellant is needed, considering the lower specific impulse of the RS-68, to obtain the same delta-v as the original design.  I also increased the dry mass of the first stage (less engines) proportionally to the propellant mass to account for larger propellant tanks.  Based on these calculations, below are my revised 1st stage specifications:

CaLV STAGE 1
Engine: 5 RS-68
Length: 64.25 m
Diameter: 10.0 m
Dry mass: 136,800 kg
Burnout mass: 146,000 kg
Oxidizer: liquid oxygen
Fuel: liquid hydrogen
Propellant mass: 1,437,600 kg (useable)
Thrust: 14,457 kN SL, 16,570 kN vac
Specific impulse: 365 s SL, 410 s vac
Burn time: about 352 s

I haven’t seen any published specs for the revised design, so I’d be very interested to see how close I am.  One thing I find interesting is the change in diameter from 8.4 m to 10 m increases the cylinder volume by almost exactly the same ratio as my calculated increase in propellant mass,

(10 m / 8.4 m)^2 ~ 1,437,600 kg / 1,004,892 kg

so this gives me confidence that I can’t be too far off the mark.


EDIT:  Revised propellant mass.

[Bob B.]

I haven't finished with my numbers yet but after giving it some thought, I don't think an addition of two more SRB's could get 200 tonnes into 300km orbit. I think I will come under 175 tonnes.

I've worked through some numbers and I'm finding it plausible that 200+ tonnes could be put into orbit with the beefed up launcher.  However, I'm assuming the entire upper stage is used for orbit insertion.  If the payload is to be injected on a trajectory to the Moon or Mars, then the 200 tonnes must include the rocket stage for the TLI or TMI burn.

Since you're working on the problem too, SM, I don't want to post my results until you're ready.  I don't know you're method, SM, but I simply calculated how much delta-v the rocket could produce with the extra SRBs and larger payload to check if it were plausible.  I didn't actually perform a simulated launch or anything like that.

[Satanic Mechanic]

Bob,
Sorry I am late getting back to you.  I took the four day weekend to work on my basement.  I put up new framing and I will be drywalling this weekend.
With your RS-68 engine data, I will redo my numbers.  I am trying to just get the load into LEO right now.  I am breaking it down to three sections:
How high will it go with the (4) SRBs and first stage of Ares.
How high will the first stage go with the first stage after SRB seperation.
How high will the second stage go.

SM

[Satanic Mechanic]

Bob,
Do you know what the burnout time of the SRB's are?  Since the SRB's and the RS-68 are both burning, I know the SRB's will be jettonised first and the RS-68 will continue burning- so I would like to know how much propellant mass is left in the RS-68.
RS-68 total Propellant mass / (RS-68 Burn time - SRB burntime) = RS-68 remaining prollant mass.

Make sense?

SM

[Bob B.]

Do you know what the burnout time of the SRB's are?

Based on the data I have, 132.5 seconds.

Since the SRB's and the RS-68 are both burning, I know the SRB's will be jettonised first and the RS-68 will continue burning- so I would like to know how much propellant mass is left in the RS-68.
RS-68 total Propellant mass / (RS-68 Burn time - SRB burntime) = RS-68 remaining prollant mass.

Make sense?

Your logic makes sense but I don’t agree with the equation.  I think it should be,

RS-68 total propellant mass * [ (RS-68 burn time - SRB burn time) / RS-68 burn time ] = RS-68 remaining propellant mass

This assumes the RS-68s are running at full thrust the whole time, which we don’t know any different at this point in time.

Please note that I found a typo in my post #17.  The propellant mass should be 1,437,600 kg.

[Satanic Mechanic]

Is that SRB time for the new five segment SRB or the old SRB?

You probably figured I am using the velocity formula for multi-stage craft from your website.
Delta V = Ci LN ( Moi / Mfi)

SM

Note from Moderator:  I'm sorry but I accidently modified your post.  I hit the "modify" button when I thought I hit the "quote" button.  I restored what part of it I could but I'm afraid some of it got deleted. -- Bob B.

[Bob B.]

Is that SRB time for the new five segment SRB or the old SRB?

The 5-segment.

You probably figured I am using the velocity formula for multi-stage craft from your website.
Delta V = Ci LN ( Moi / Mfi)

Yes, that's what I did as well.  It gets a little tricky though when you have stages in parallel, i.e. strap-ons and central core burning together, rather than in series.  I generally calculate the delta-v separately for (1) the period when both strap-ons and core are burning, and (2) the period from strap-on burnout to core stage burnout.  For period #1 I use a composite value for the exhaust velocity, where subscripts 0 and 1 are the straps-ons and core respectively:

C = (F₀ + F₁) / (q₀ + q₁)

where F is thrust and,

q = propellant mass / burn time, or
q = F / (g*Isp)

Then there is also the issue of the thrust varying from the sea level value to the vacuum value during the first couple minutes of flight.  In this example I simply used the average of the sea level and vacuum thrusts for period #1.  I then used the RS-68 vacuum thrust for period #2.

For the SRBs the thrust varies during the burn as the burn surface and chamber pressure changes.  I figured an average thrust as follows:

q₀ = 650,869 / 132.5 = 4,912.2 kg/s

F = q*g*Isp
F_sea level = 4,912.2*9.80665*240 = 11,561,000 N per SRB
F_vacuum = 4,912.2*9.80665*265.4 = 12,785,000 N per SRB

Note that I used 240 s for the sea level Isp, which is an estimate on my part but it should be pretty close.

There is also an inconsistency in the RS-68 specs that I've been unable to resolve.  The ratio of vacuum thrust to sea level thrust should be the same as the ratio of vacuum Isp to sea level Isp, but it's not.  Because of this we get propellant flows rates that vary by about 2% depending on which data we use.  The flow rate should be constant, so I figured an average as follows:

q₁ = (2,891,000+3,314,000)/(9.80665*(365+410)) = 816.4 kg/s per engine

[Satanic Mechanic]

Thanks for your help Bob.  I will make a spreadsheet for calculating the equations.  I got tired of writing five sheets of paper.

SM

[Satanic Mechanic]

Bob,
Here are some my numbers:
Combined First stage   
Moi =   5013811
Mfi =   1869192.955
Ci =   11061.63
   
Delta-V   10914.39464
   
   
   
RS-68 stage  (1 1/2 Stage)   
Moi =   1467788.955
Mfi =   571331
Ci =   3541.64
   
Delta-V   3341.69214


Time to figure the second stage.

[Satanic Mechanic]

Bob,
Your published data on the J-2S+, was the dry mass and propellant mass for both engines or one J-2?

SM

[Satanic Mechanic]

Scratch that last request.  I just noticed you wrote "2 J-2S+" on the page.

[Satanic Mechanic]

Ok, here are the numbers, I did the equations over because I forgot to add in the second set of J-2's:

            
1st stage         Combined First stage   
# of SRB   4      Moi =   5243569
Propellant   650869      Mfi =   2098950.955
Dry mass   100351      Ci =   11061.63
Isp   265.4         
Burn time   132.5      Delta-V   10127.63794

RS68            
Propellant   1437600         
Dry Mass   136800      RS-68 stage   
Isp   365              Moi =   1697546.955
Burn Time   352      Mfi =   801089
                 Ci =   3541.64
2nd Stage (4 J-2's)            
Propellant   415390      Delta-V   2659.656424
Dry Mass   44126         

                 2nd Stage   
Payload                 Moi =   664289
Fairing   4773              Mfi =    248899
Payload   200000              Ci =   4432.62

                 Delta-V   4351.370537

[Satanic Mechanic]

Strange, I posted them all in columns and now they are all over the place.

SM