### Author Topic: ITS for the Moon  (Read 14532 times)

#### Steven Pietrobon

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##### ITS for the Moon
« on: 11/23/2016 08:04 AM »
Here's a little study I recently did of using the SpaceX Interplanetary Transport System (ITS) for missions to the Moon.

I first had a look of using ITS directly to Moon (after filling up with 1950 t of methane/LOX propellant from five tanker flights).

For the landing burn on Earth, looking at the YouTube technical broadcasts the burn was about 25 seconds for JCSat 16 and 31 seconds for SpX-9. Lets take the average of 28 seconds. We'll also assume Th = 14 seconds at full thrust and Tl = 14 seconds at minimum thrust of 55% as given below

http://spaceflight101.com/spacerockets/falcon-9-ft/

This results in a landing delta-V of 719 m/s. Data is below showing how I calculated this. This results in a negative cargo mass of -36.7 t, which means Lunar Direct will not work with ITS.

One idea I had was to use Lunar orbit propellant transfer. On the first flight, we bring cargo to the surface, but reach Lunar orbit with no propellant left in the tank. That brings a huge 180.6 t to the Lunar surface!

Waiting in Lunar orbit is another ITS, which transfers 107.2 t of propellant to the returning ITS. The second ITS then lands on the Moon bringing 105.1 t of cargo! The process then repeats. This works because we don't bring down and up again the return propellant from Lunar orbit, which is a huge penalty.

Attached is my Pascal program used to work out the payload.

Falcon 9 landing Delta-V calculation
------------------------------------

ms = 22.2 t
ves = g*282 = 2765.48 m/s
Fs = 845 kN
Rp = Fs/ves = 0.306 t/s
Th = 14 s
Tl = 14 s
mp = (Th + Tl*0.55)*Rp = 6.63 t
margin = 2%

We need to solve these two equations where mpr is the residual propellant.

dv = ves*ln(1+mp/(ms+mpr))
margin*dv = ves*ln(1+mpr/ms)

margin*ln(1+mp/(ms+mpr)) = ln(1+mpr/ms)
mpr = ms*(exp(margin*ln(1+mp/(ms+mpr)))-1)

This is a non-linear equation which we solve iteratively. This gives

mpr = 0.116 t
dv = ves*ln(1+mp/(ms+mpr)) = 719 m/s.

Check second equation

margin*dv = 14.4 m/s
ves*ln(1+mpr/ms) = 2765.48*ln(1+0.116/22.2) = 14.4 m/s

ITS Direct Cargo Calculation
----------------------------
Delta-V values are

dv1 = 3180 m/s (TLI)
dv2 = 960 m/s (LOI)
dv3 = 28 m/s (PDI)
dv4 = 2041 m/s (Lunar Descent)
dv5 = 1850 m/s (Lunar Ascent)
dv6 = 1169 m/s (TEI)
dv7 = 719 m/s (Earth landing)
marginl = 2%
margine = 1%
ve = g*382 = 3746.14 m/s (Raptor exhaust speed)
ves = g*334 = 3275.42 m/s (Sea Level exhaust speed)
ms = 150 t (ITS empty mass)
mp = 1950 t (propellant mass)

dvm = (1+margine)*(dv1+dv2+dv3+dv4) = 6271 m/s (delta-V to Lunar surface)
dve = (1+margine)*(dv5+dv6) = 3049 m/s (delta-V back to Earth)
dvl = (1+marginl)*dv7 = 734 m/s (delta-V landing on Earth)

Need to solve these three equations where mc is the cargo mass and mpe is the propellant to get to Earth and mpl is the landing propellant.

dvm = ve*ln(1+(mp-mpe-mpl)/(ms+mpe+mpl+mc))
dve = ve*ln(1+mpe/(ms+mpl)))
dvl = ves*ln(1+mpl/ms))

Solving the equations from last to first gives

mpl = ms*(exp(dvl/ves)-1) = 37.7 t
mpe = (ms+mpl)*(exp(dve/ve)-1) = 235.9 t
mpm = mp-mpe-mpl = 1676.5 t
mc = mpm/(exp(dvm/ve)-1)-ms-mpl-mpe = -36.7 t

Unfortunately, the negative value for mc means that this won't work.

ITS Lunar Orbit Propellant Transfer First Flight
------------------------------------------------

dvm = (1+margine)*(dv1+dv2+dv3+dv4) = 6271 m/s (delta-V to Lunar surface)
dva = (1+margine)*dv5 = 1869 m/s (delta-V to Lunar orbit)

Need to solve these two equations where mc is the cargo mass and mpa is the propellant to get to Lunar orbit.

dvm = ve*ln(1+(mp-mpa)/(ms+mpa+mc))
dva = ve*ln(1+mpa/ms))

Solving the equations from last to first gives

mpa = ms*(exp(dva/ve)-1) = 97.0 t
mpm = mp-mpa = 1853.0 t
mc = mpm/(exp(dvm/ve)-1)-ms-mpa = 180.6 t

Check

dvm = 3746.14*ln(1+1853.0/(150+97.0+180.6)) = 6271 m/s
dve = 3746.14*ln(1+97.0/150)) = 1869 m/s

ITS Lunar Orbit Propellant Transfer Subsequent Flights
------------------------------------------------------

dvo = (1+margine)*(dv1+dv2) = 4181 m/s (delta-V to Lunar orbit)
dvd = (1+margine)*(dv3+dv4) = 2090 m/s (delta-V to Lunar surface)
dva = (1+margine)*dv5 = 1869 m/s (delta-V to Lunar orbit)
dvt = (1+margine)*dv6 = 1181 m/s (delta-V to Earth)
dvl = (1+marginl)*dv7 = 734 m/s (delta-V landing on Earth)

dvo = ve*ln(1+(mp-mpd-mpa-mpt-mpl)/(ms+mpd+mpa+mpt+mpl+mc))
dvd = ve*ln(1+mpd/(ms+mpa+mc))
dva = ve*ln(1+mpa/ms)
dvt = ve*ln(1+mpt/(ms+mpl))
dvl = ves*ln(1+mpl/ms))

From before we have

mpl = 37.7 t
mpa = 97.0 t

The fourth equation gives us

mpt = (ms+mpl)*(exp(dvt/ve)-1) = 69.5 t

The second equation gives

ms+mpa+mc = mpd/(exp(dvd/ve)-1)

which we subsitute into the first equation

mp-mpd-mpa-mpt-mpl = (exp(dvo/ve)-1)*(mpd+mpt+mpl+mpd/(exp(dvd/ve)-1))

Let

ao = exp(dvo/ve)-1

Then

mpd = (mp-mpa-(1+ao)*(mpt+mpl))/(1+ao*(1+1/ad)) = 262.9 t
mpo = mp-mpd-mpa-mpt-mpl = 1482.8 t

From the second equation we get

mc = mpd/ad-ms-mpa = 105.1 t

Check

dvo = 3746.14*ln(1+1482.8/(150+262.9+97.0+69.5+37.7+105.1)) = 4181 m/s
dvd = 3746.14*ln(1+262.9/(150+97.0+105.1)) = 2090 m/s
dvt = 3746.14*ln(1+69.5/(150+37.7) = 1181 m/s

Transfer propellant = mpt+mpl = 107.2 t
« Last Edit: 11/23/2016 08:16 AM by Steven Pietrobon »
Akin's Laws of Spacecraft Design #1:  Engineering is done with numbers.  Analysis without numbers is only an opinion.

#### TrevorMonty

##### Re: ITS for the Moon
« Reply #1 on: 11/23/2016 08:24 AM »
Clever, I've never considered having the lander leave its return fuel in LLO.
Just down rough calculations on ACES lander doing round trip from EML1- lunar surface - EML1, I got 10% fuel saving leaving return fuel in LL0.
« Last Edit: 11/23/2016 08:47 AM by TrevorMonty »

#### Steven Pietrobon

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##### Re: ITS for the Moon
« Reply #2 on: 11/23/2016 08:28 AM »
One important aspect is thrust levels while landing on the Moon. Here's the case using two of the vacuum Raptors which have 3.5 MN thrust each. I know Musk said that these are fixed, but for Lunar missions they could be made to swivel. I don't like the idea of switching from vacuum to inefficient sea level engines for the Lunar landing.

Landing mass is ms+mc+mpa = 150+105.1+97.0 = 352.1 t. Lunar gravity is 1.622 m/sē giving a landing weight 352.1*1.622 = 571 kN. If the vacuum engines could throttle down to 571.1/(2*3500) = 0.0816 or about 8%, that could work. There are no flow separation issues, since the engine will be working in a vacuum. Its just a matter of if they can get their pumps to work effectively at that low flow rate. Isp will be reduced due to the lower chamber pressure (2.5 MPa versus 30.4 MPa), but should not be as great as for the sea level engines. It also means landing on the Moon can be performed with the vehicle perfectly vertical.
Akin's Laws of Spacecraft Design #1:  Engineering is done with numbers.  Analysis without numbers is only an opinion.

#### Steven Pietrobon

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##### Re: ITS for the Moon
« Reply #3 on: 11/23/2016 08:31 AM »
Clever, I've never considered having the lander leave its return fuel in LLO.

I thought of this technique quite a long time ago. It was called Lunar orbit propellant transfer with the idea of transferring LOX produced on the Moon to the next craft coming in to land. I was a bit bummed when my paper got rejected by the BIS.
Akin's Laws of Spacecraft Design #1:  Engineering is done with numbers.  Analysis without numbers is only an opinion.

#### Lar

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##### Re: ITS for the Moon
« Reply #4 on: 11/23/2016 02:47 PM »
Clever, I've never considered having the lander leave its return fuel in LLO.

I thought of this technique quite a long time ago. It was called Lunar orbit propellant transfer with the idea of transferring LOX produced on the Moon to the next craft coming in to land. I was a bit bummed when my paper got rejected by the BIS.
That's the other direction though, yes?

I guess it all depends on where propellant is abundant. Early missions? Earth. Later missions when ISRU is up and running well on Luna? Luna.

I love this idea of the next ship passing propellant to the previous ship. Need to think through failure modes though...
"I think it would be great to be born on Earth and to die on Mars. Just hopefully not at the point of impact." -Elon Musk
"We're a little bit like the dog who caught the bus" - Musk after CRS-8 S1 successfully landed on ASDS OCISLY

#### guckyfan

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##### Re: ITS for the Moon
« Reply #5 on: 11/23/2016 03:52 PM »
I love the idea of leaving propellant in orbit for the return flight. The problem with this is it only works in a constant chain of flights. Maybe the ITS would stay on the moon until the next mission. Like crew capsules on the ISS. I am not sure this is the best operation though. Conditions on the moon are harsh for a spaceship with the long days and long nights. Very different to LEO or deep space.

Alternatively there could be a depot in lunar orbit. ITS fills it on the way down and takes the fuel back on the way up. The depot would not even need to be very large.

#### Lar

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##### Re: ITS for the Moon
« Reply #6 on: 11/23/2016 03:55 PM »
I love the idea of leaving propellant in orbit for the return flight. The problem with this is it only works in a constant chain of flights. Maybe the ITS would stay on the moon until the next mission. Like crew capsules on the ISS. I am not sure this is the best operation though. Conditions on the moon are harsh for a spaceship with the long days and long nights. Very different to LEO or deep space.

Alternatively there could be a depot in lunar orbit. ITS fills it on the way down and takes the fuel back on the way up. The depot would not even need to be very large.

Could be a tanker that was fully amortized and at end of life (for launches, but not for staying in orbit)... such a tanker might need some mods such as active cooling but those might have already been developed, since they are needed in some CONOPS for Mars (multiple tankers fill one, that one loiters till filled, meaning active cooling, at least potentially, then the crewed ship refills from it)
« Last Edit: 11/23/2016 03:57 PM by Lar »
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#### brickmack

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##### Re: ITS for the Moon
« Reply #7 on: 11/23/2016 07:01 PM »
One important aspect is thrust levels while landing on the Moon. Here's the case using two of the vacuum Raptors which have 3.5 MN thrust each. I know Musk said that these are fixed, but for Lunar missions they could be made to swivel. I don't like the idea of switching from vacuum to inefficient sea level engines for the Lunar landing.

I don't see how gimballing can be implemented without making the nozzles a lot smaller. There isn't enough room for any movement. Its not necessary anyway, differential thrust plus RCS can provide sufficient control authority in all 3 axes with a smaller performance hit (which is how attitude control during TMI/TEI is planned, and most likely during Mars landing)

#### Lar

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##### Re: ITS for the Moon
« Reply #8 on: 11/23/2016 07:18 PM »
One important aspect is thrust levels while landing on the Moon. Here's the case using two of the vacuum Raptors which have 3.5 MN thrust each. I know Musk said that these are fixed, but for Lunar missions they could be made to swivel. I don't like the idea of switching from vacuum to inefficient sea level engines for the Lunar landing.

I don't see how gimballing can be implemented without making the nozzles a lot smaller. There isn't enough room for any movement. Its not necessary anyway, differential thrust plus RCS can provide sufficient control authority in all 3 axes with a smaller performance hit (which is how attitude control during TMI/TEI is planned, and most likely during Mars landing)
This has been discussed elsewhere, but the lag inherent in differential thrust makes control a lot harder. Not undoable but gimballing makes avoiding overshoot a LOT easier.
"I think it would be great to be born on Earth and to die on Mars. Just hopefully not at the point of impact." -Elon Musk
"We're a little bit like the dog who caught the bus" - Musk after CRS-8 S1 successfully landed on ASDS OCISLY

#### A_M_Swallow

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##### Re: ITS for the Moon
« Reply #9 on: 11/24/2016 04:11 AM »
Space stations, tankers and propellant depots in lunar orbit will need station keeping. A set of ion thrusters should be able to supply this.

#### AncientU

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##### Re: ITS for the Moon
« Reply #10 on: 11/24/2016 09:08 PM »
Space stations, tankers and propellant depots in lunar orbit will need station keeping. A set of ion thrusters should be able to supply this.

Too small for two thousand tonne tankers.  Fully loaded ITS tanker is 5-6x ISS mass, and lunar orbits are unstable for most part. Fine for Orbital Outpost (maybe 100 tonnes) in high orbit or EML-1/2.
« Last Edit: 11/24/2016 09:09 PM by AncientU »
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#### AncientU

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##### Re: ITS for the Moon
« Reply #11 on: 11/24/2016 09:15 PM »
One important aspect is thrust levels while landing on the Moon. Here's the case using two of the vacuum Raptors which have 3.5 MN thrust each. I know Musk said that these are fixed, but for Lunar missions they could be made to swivel. I don't like the idea of switching from vacuum to inefficient sea level engines for the Lunar landing.

I don't see how gimballing can be implemented without making the nozzles a lot smaller. There isn't enough room for any movement. Its not necessary anyway, differential thrust plus RCS can provide sufficient control authority in all 3 axes with a smaller performance hit (which is how attitude control during TMI/TEI is planned, and most likely during Mars landing)
This has been discussed elsewhere, but the lag inherent in differential thrust makes control a lot harder. Not undoable but gimballing makes avoiding overshoot a LOT easier.

Differential throttling has its place, but it isn't in the final seconds before touchdown.  I suspect vacuum raptors to do the decent burn and gimballed engines for landing.  Not really interested in performance on landing burn, just about control.
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#### Bob Shaw

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##### Re: ITS for the Moon
« Reply #12 on: 11/24/2016 09:35 PM »
Might I suggest a simpler approach? A dedicated ITS lander with large on-board battery packs and which transits between the surface and a man-tended depot, where not only are gasses stored but battery maintenance and cargo transshipping occurs. Leave the solar arrays in orbit, too, or at the very least work out a schedule which will deliver batteries to the surface to allow overnight stays. Crews would travel uphill aboard a 'standard' ITS without Lunar landing capability, but also carrying cargo. Use the depot to offer a shirtsleeves cargo transfer facility without EVAs or manipulator arms, and build up a bespoke delivery service for third-party exploration and development.

#### A_M_Swallow

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##### Re: ITS for the Moon
« Reply #13 on: 11/25/2016 12:38 AM »
Space stations, tankers and propellant depots in lunar orbit will need station keeping. A set of ion thrusters should be able to supply this.

Too small for two thousand tonne tankers.  Fully loaded ITS tanker is 5-6x ISS mass, and lunar orbits are unstable for most part. Fine for Orbital Outpost (maybe 100 tonnes) in high orbit or EML-1/2.

Steven Pietrobon only talked about leaving 105.1 t of propellant in lunar orbit.

#### brickmack

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##### Re: ITS for the Moon
« Reply #14 on: 11/25/2016 01:57 AM »
Might I suggest a simpler approach? A dedicated ITS lander with large on-board battery packs and which transits between the surface and a man-tended depot, where not only are gasses stored but battery maintenance and cargo transshipping occurs. Leave the solar arrays in orbit, too, or at the very least work out a schedule which will deliver batteries to the surface to allow overnight stays. Crews would travel uphill aboard a 'standard' ITS without Lunar landing capability, but also carrying cargo. Use the depot to offer a shirtsleeves cargo transfer facility without EVAs or manipulator arms, and build up a bespoke delivery service for third-party exploration and development.

The problem I see here is that it requires at least one dedicated ship only for Lunar use. Ideally each spaceship should be usable for any type of mission with minimal modification. Do a lunar surface flight, bring it back home and swap out cargo, do a LEO tourist flight, bring it back and swap out cargo, do a Mars flight, repeat. An ITS will cost hundreds of millions of dollars and likely several months to build, time and money better spent on building general purpose craft than unique ones. There had better be a damned good reason to make such a vehicle, and in the case of the moon its not necessary to do those sorts of performance optimizations anyway since the standard spacecraft is already so capable (estimates I've seen before being ~30 tons to the lunar surface with only refueling in LEO, ~350 tons with refueling in lunar orbit after ascent, even the first of which is well beyond what previous studies indicated necessary to build a base)

#### Steven Pietrobon

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##### Re: ITS for the Moon
« Reply #15 on: 11/25/2016 03:57 AM »
I don't see how gimballing can be implemented without making the nozzles a lot smaller.

If all the engines are gimballed, the four vacuum engines not being used can be gimballed sideways to leave room for the two vacuum engines to gimbal freely.

(estimates I've seen before being ~30 tons to the lunar surface with only refueling in LEO, ~350 tons with refueling in lunar orbit after ascent, even the first of which is well beyond what previous studies indicated necessary to build a base)

Is there a reference for that 30 t value? My calculations show that a Direct Lunar mission (using refueling in LEO) gets a cargo mass of -36.7 t, which means the scheme won't work since you need a have a payload with negative mass!
« Last Edit: 11/25/2016 04:01 AM by Steven Pietrobon »
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#### AncientU

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##### Re: ITS for the Moon
« Reply #16 on: 11/25/2016 11:02 AM »
Space stations, tankers and propellant depots in lunar orbit will need station keeping. A set of ion thrusters should be able to supply this.

Too small for two thousand tonne tankers.  Fully loaded ITS tanker is 5-6x ISS mass, and lunar orbits are unstable for most part. Fine for Orbital Outpost (maybe 100 tonnes) in high orbit or EML-1/2.

Steven Pietrobon only talked about leaving 105.1 t of propellant in lunar orbit.

In OP, calculation with Lunar orbit refueling after ascent from surface delivered 180.6 tonnes, then 105.1 for the spaceship that supplied the on orbit fuel. (The second ship would need to be refueled like the first.)
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#### A_M_Swallow

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##### Re: ITS for the Moon
« Reply #17 on: 11/25/2016 02:16 PM »
Space stations, tankers and propellant depots in lunar orbit will need station keeping. A set of ion thrusters should be able to supply this.

Too small for two thousand tonne tankers.  Fully loaded ITS tanker is 5-6x ISS mass, and lunar orbits are unstable for most part. Fine for Orbital Outpost (maybe 100 tonnes) in high orbit or EML-1/2.

Steven Pietrobon only talked about leaving 105.1 t of propellant in lunar orbit.

In OP, calculation with Lunar orbit refueling after ascent from surface delivered 180.6 tonnes, then 105.1 for the spaceship that supplied the on orbit fuel. (The second ship would need to be refueled like the first.)

So you end up needing about 15 NEXT ion thrusters for station keeping.

#### DrRobin

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##### Re: ITS for the Moon
« Reply #18 on: 11/26/2016 02:26 PM »
Thanks for this clever concept! I do enjoy working through the numbers on these, which will take me a bit more time, but I can't resist the OT observation that caught my eye:
Attached is my Pascal program used to work out the payload.
OMG, Pascal. I am old enough to have a few stacks of punchcards encoding batch FORTRAN code I wrote back when Pascal was a spiffy new programming language, all the rage for use as a teaching language, all clean and strict about good programming technique. I reminds me of the adage that real grizzled old programmers can write FORTRAN code in any programming language! [Semi on topic is that IRL, I rarely any more draw the sharp, austere blade of C, my weapon of choice from when by brain, too, was clean and sharp, rather dallying in the more easy-going lands of Python, but I have been using the ideas in this forum as a fun incentive to get up with the times and learn Swift. When I get around to making a little app to do delta-V estimates on your smart watch, I post it to NSF!]
Anyway, just to make sure to have something on-topic, I did want to highlight the general concept you employ: The exponential nature of the rocket equation delta-V budgets can be a killer for out-and-back missions, but you can sometimes soften the requirements by caching propellant at one or more stops partway out, in the mode of basecamps for mountaineering, where each expedition helps the ones that come after.

#### brickmack

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##### Re: ITS for the Moon
« Reply #19 on: 11/26/2016 03:49 PM »
(estimates I've seen before being ~30 tons to the lunar surface with only refueling in LEO, ~350 tons with refueling in lunar orbit after ascent, even the first of which is well beyond what previous studies indicated necessary to build a base)

Is there a reference for that 30 t value? My calculations show that a Direct Lunar mission (using refueling in LEO) gets a cargo mass of -36.7 t, which means the scheme won't work since you need a have a payload with negative mass!

https://www.reddit.com/r/spacex/comments/55k1f4/its_moon_landing_payloads_and_costs/ he finds 38 tons direct, 380 tons with lunar orbital refueling, I rounded down a bit to accommodate some safety margin and slight underperformance. Odd inconsistency here though. I'm trying to figure out where both of you got the delta v numbers from, neither matches up well with charts I've seen before. The guy on reddit has a higher delta v for "earth orbit to moon orbit" than you have for TLI+LOI, lower delta v for ascent and descent, lower for TEI, and higher for earth EDL, but the total delta v values only differ by about 500 m/s (9.7 km/s for the reddit post, 10.2 for yours), which isn't enough to explain such a huge discrepancy in payload capacity. And it looks like you're using the same mass and ISP values. He doesn't give his full calculations though, just spreadsheets

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