Starship On-orbit refueling - Options and Discussion

[DanClemmensen]

STS demonstrated that you can move cryogens over a pipe then disconnect the pipe and leave it permanently disconnected until remoted by hand on the ground. But Atlas also demonstrated that decades earlier with the LOX feeds to the booster engines. The hard part will be a cryogenic fluid coupler that can mate in orbit, demate, and remate again, multiple times, in orbit, whilst still allowing the receiving end of that connector to seal against flight pressures. That's been done for storable propellants, but not for cryogens, and cryogenic sealing and connectors are a notorious pain.

What are the differences between doing this on the ground (as in the SS QD arm) and doing it in orbit, and do these differences make the job harder or easier? Clearly, the presence of a 1g gravity field on the ground is a big difference. What about others?

It's also true that SpaceX's current experience with its QD arm is limited and they can also do manual inspections and adjustments as needed, but I think they have already done some connect/reconnect tests.

[Jim]

The Shuttle did not have any in-tank boost pumps. Liquid propellants were pushed out of the tanks and over the tank-to-vehicle connections and into the engine pumpheads by pressure from the ullage gas, not suction from the pump heads. Being autogenously pressurised that gas was supplied by the SSMEs, but could just as well have come from gas bottles inside the tanks (terrible idea though, no mass margins). Disconnect the tank-to-vehicle lines, and that ullage pressure would have equally well pushed propellants out the end of the lines into free space.

Yes, of course and head pressure.   The point was where the propellants were going and pumps were aiding in the pressure differential.  The supply tank doesn't have to keep increasing pressure to over come back pressure.

But you can go back even further with the connection: the GSE and umbilicals disconnects that filled the tanks have been used on almost all cryogenic vehicles.

[oldAtlas_Eguy]

The Shuttle did not have any in-tank boost pumps. Liquid propellants were pushed out of the tanks and over the tank-to-vehicle connections and into the engine pumpheads by pressure from the ullage gas, not suction from the pump heads. Being autogenously pressurised that gas was supplied by the SSMEs, but could just as well have come from gas bottles inside the tanks (terrible idea though, no mass margins). Disconnect the tank-to-vehicle lines, and that ullage pressure would have equally well pushed propellants out the end of the lines into free space.

Yes, of course and head pressure.   The point was where the propellants were going and pumps were aiding in the pressure differential.  The supply tank doesn't have to keep increasing pressure to over come back pressure.

But you can go back even further with the connection: the GSE and umbilicals disconnects that filled the tanks have been used on almost all cryogenic vehicles.

The primary item about Starship is that it is not using cryo Hydrogen! That is the one that has shown too be the difficult and still finicky set of QDs. Note that while the LH QD on SLS kept having leaks the LOX ones were fairly good to go.

SpaceX so far has not had much leak problems with the QD plates and automated connect and disconnect and then connect over and over on the same vehicle. So the primary concern is the alignment prior to trying to dock and not damaging the QDs. Also not damaging the QDs during undock. All while on orbit.

[Robotbeat]

Also, lack of frost buildup in vacuum helps stuff from sticking quite as much. Vacuum also means leaks are not usually as much of a major fire/explosion hazard (as you’d need BOTH fuel AND oxidizer present at decent pressure or no ignition).

Vacuum helps insulate everything much better.

[TheRadicalModerate]

Yes, of course and head pressure.   The point was where the propellants were going and pumps were aiding in the pressure differential.  The supply tank doesn't have to keep increasing pressure to over come back pressure.

But you can go back even further with the connection: the GSE and umbilicals disconnects that filled the tanks have been used on almost all cryogenic vehicles.

I'm not sure I'm getting your point here, but tanks can be filled by their internal pressure differential or filled at the same pressure by small pumps.  In either case, it will be the responsibility of the receiver to vent to keep pressure more-or-less static as prop flows in, and the sender to pressurize as prop flows out.

My favorite version of this is simply to connect the two ullage spaces together and use very small pumps to move the prop from one tank to the other.  There are no vented ullage gas losses this way.  In contrast, if you have an open system, where the receiver vents to the outside and the sender does something autogenous to keep the ullage space from becoming progressively lower pressure, you're wasting the receiver's ullage and doing something complicated and/or heavy on the sender.

Another reason to use pumps and no pressure differential:  If you're pressure-feeding the coupled tank system and you have an ullage oopsie where you uncover the high-pressure sump, the system will equalize more-or-less instantaneously, which will be a bummer.  It's a recoverable bummer, but one that can cost you a couple of tonnes of vented ullage gas.

[oldAtlas_Eguy]

Yes, of course and head pressure.   The point was where the propellants were going and pumps were aiding in the pressure differential.  The supply tank doesn't have to keep increasing pressure to over come back pressure.

But you can go back even further with the connection: the GSE and umbilicals disconnects that filled the tanks have been used on almost all cryogenic vehicles.

I'm not sure I'm getting your point here, but tanks can be filled by their internal pressure differential or filled at the same pressure by small pumps.  In either case, it will be the responsibility of the receiver to vent to keep pressure more-or-less static as prop flows in, and the sender to pressurize as prop flows out.

My favorite version of this is simply to connect the two ullage spaces together and use very small pumps to move the prop from one tank to the other.  There are no vented ullage gas losses this way.  In contrast, if you have an open system, where the receiver vents to the outside and the sender does something autogenous to keep the ullage space from becoming progressively lower pressure, you're wasting the receiver's ullage and doing something complicated and/or heavy on the sender.

Another reason to use pumps and no pressure differential:  If you're pressure-feeding the coupled tank system and you have an ullage oopsie where you uncover the high-pressure sump, the system will equalize more-or-less instantaneously, which will be a bummer.  It's a recoverable bummer, but one that can cost you a couple of tonnes of vented ullage gas.

All of that vented ullage is actually needed to provide acceleration to maintain the prop settling. So it is not wasted.

[BT52]

How much is minimum acceleration needed?

I assume minimum as surface tension no?

[oldAtlas_Eguy]

How much is minimum acceleration needed?

I assume minimum as surface tension no?

SpaceX knows the answer. But not sure if we ever became privy to that value for SS. Without knowing that value with significant margins the SS on orbit would have some difficulties. Such as performing a circularizing burn at apogee after a drift in a preliminary elliptical transfer orbit.

[edzieba]

STS demonstrated that you can move cryogens over a pipe then disconnect the pipe and leave it permanently disconnected until remoted by hand on the ground. But Atlas also demonstrated that decades earlier with the LOX feeds to the booster engines. The hard part will be a cryogenic fluid coupler that can mate in orbit, demate, and remate again, multiple times, in orbit, whilst still allowing the receiving end of that connector to seal against flight pressures. That's been done for storable propellants, but not for cryogens, and cryogenic sealing and connectors are a notorious pain.

What are the differences between doing this on the ground (as in the SS QD arm) and doing it in orbit, and do these differences make the job harder or easier? Clearly, the presence of a 1g gravity field on the ground is a big difference. What about others?

Not just gravity, but atmospheric pressure, and atmospheric temperature. That affects seals and joints that can no longer assume a benign environment and occasional dips to cryogenic temperatures, but instead need to operate (flexing is the big ticket issue) in the long term at cryogenic temperatures (cold bridging coupled with vacuum insulation) and/or hot-soaking from insolation.
Not insurmountable challenges, but because it's not been attempted there will be a big pile of unknown-unknowns to discover first.

How much is minimum acceleration needed?

I assume minimum as surface tension no?

From long duration coast studies with Centaur, micro-G accelerations are sufficient settling thrust to ensure inlets remain covered ready or engine startup, so that is likely the range needed to keep those inlets covered for the much less vigorous propellant transfer process.

[TheRadicalModerate]

How much is minimum acceleration needed?

I assume minimum as surface tension no?

SpaceX knows the answer. But not sure if we ever became privy to that value for SS. Without knowing that value with significant margins the SS on orbit would have some difficulties. Such as performing a circularizing burn at apogee after a drift in a preliminary elliptical transfer orbit.

I think ULA had done successful experiments with about 1mm/s² for long-term settling.

Note that settling for pre-ignition of engines is different from settling for prop transfer.  The former can be relatively high-thrust, because it's only active for a couple of seconds.  The latter has to be as low-thrust as possible, because it'll be active for minutes or even hours.  But your engines don't blow up if you accidentally uncover the sump.

All of that vented ullage is actually needed to provide acceleration to maintain the prop settling. So it is not wasted.

I just don't see how they're gonna use cold or warm gas thrusters for settling for prop transfer.  Isp is too low, which requires way too much mass flow to hit the proper thrust. 

Let's make the following assumptions:

Settling acceleration:  5mm/s² (I'm being conservative).
Prop transfer time: 2000s (a bit more than half an hour).
Cold (or maybe warm) gas Isp: 70s.
Methox or methalox combusting gas Isp: 300s
Depot dry mass: 90t.  Prop capacity: 1600t.
Tanker dry mass: 120t: Prop payload: 150t.

Then the lightest coupled system is an empty depot with a tanker transferring the first load of prop:  90t + 120t + 150t = 360t.  Using cold-to-warm ullage gas for the target acceleration requires 1800N, and the target transfer time would therefore require 5.2t of ullage gas.  Not great, but OK.

But the heaviest system is a depot receiving its last load of prop:  90t + 1450t + 120t + 150t = 1810t.  Now cold gas requires 9050N of thrust, and 26.4t of gas for the full transfer.  That's not only unacceptable from a prop efficiency standpoint, but there isn't enough cold ullage gas available in the first place.

In contrast, the heavy case with combusting methox or methalox would only require 6.2t of prop.

We've rehashed this elsewhere about a zillion times, but a set of redundant COPVs solve an awful lot of problems if they have the following duty cycle:

1) Vent the empty COPV to some very low pressure, into which it's easy to pump liquid prop.

2) Pump LCH4 or LOX into it until full.

3) Seal the vent and the pump inlet.

4) Heat it with electric heaters until it's supercritical at flight pressure (300-500bar).

5) Use it for whatever you need:
a) Bringing cold main or header tanks up to flight pressure.
b) Pushing liquids into pressure-fed methalox engines.
c) Driving monopropellant hot-gas thrusters.
d) Driving methox combustion thrusters.
e) spin-up gas for air- or space-restarts of the Starship Raptors.

(Edit: added #e above.)

6) When the COPV drops below minimum flight pressure, switch over to another redundant COPV and start the cycle over.

If you have three sets of tanks each for LCH4 and LOX, one can be active, one can be in redundant standby, and one can be refilling, heating, and pressurizing.

[InterestedEngineer]

If you have three sets of tanks each for LCH4 and LOX, one can be active, one can be in redundant standby, and one can be refilling, heating, and pressurizing.

How much do the COPVs weigh dry?

[mikelepage]

Let's make the following assumptions:

Settling acceleration:  5mm/s² (I'm being conservative).
Prop transfer time: 2000s (a bit more than half an hour).
Cold (or maybe warm) gas Isp: 70s.
Methox or methalox combusting gas Isp: 300s
Depot dry mass: 90t.  Prop capacity: 1600t.
Tanker dry mass: 120t: Prop payload: 150t.

Then the lightest coupled system is an empty depot with a tanker transferring the first load of prop:  90t + 120t + 150t = 360t.  Using cold-to-warm ullage gas for the target acceleration requires 1800N, and the target transfer time would therefore require 5.2t of ullage gas.  Not great, but OK.

But the heaviest system is a depot receiving its last load of prop:  90t + 1450t + 120t + 150t = 1810t.  Now cold gas requires 9050N of thrust, and 26.4t of gas for the full transfer.  That's not only unacceptable from a prop efficiency standpoint, but there isn't enough cold ullage gas available in the first place.

In contrast, the heavy case with combusting methox or methalox would only require 6.2t of prop.

Thanks for this.

Possibly off topic for this thread, but I'm working on animating a spin-G setup aimed at eliminating the prop losses and orbit change due to settling acceleration.

If there are ~12 transfer cycles to fill the depot, the final heavy case you've mentioned there is 6.2t, and the first light case (I think) requires  ~1.2t. Is that implying that even with combusting methalox, that we're expending around 44t of prop just to fill a depot if we're relying on linear acceleration to settle the prop?

Also, does that imply that as long as less propellant than this (1.2t-6.2t/cycle) is used to perform a spin up/down cycle for each transfer, then any (reasonable) amount of extra mass dedicated to spin-G infrastructure on a depot will eventually pay itself off in prop mass savings over time?

[OTV Booster]

How much is minimum acceleration needed?

I assume minimum as surface tension no?

SpaceX knows the answer. But not sure if we ever became privy to that value for SS. Without knowing that value with significant margins the SS on orbit would have some difficulties. Such as performing a circularizing burn at apogee after a drift in a preliminary elliptical transfer orbit.

I think ULA had done successful experiments with about 1mm/s² for long-term settling.

Note that settling for pre-ignition of engines is different from settling for prop transfer.  The former can be relatively high-thrust, because it's only active for a couple of seconds.  The latter has to be as low-thrust as possible, because it'll be active for minutes or even hours.  But your engines don't blow up if you accidentally uncover the sump.

All of that vented ullage is actually needed to provide acceleration to maintain the prop settling. So it is not wasted.

I just don't see how they're gonna use cold or warm gas thrusters for settling for prop transfer.  Isp is too low, which requires way too much mass flow to hit the proper thrust. 

Let's make the following assumptions:

Settling acceleration:  5mm/s² (I'm being conservative).
Prop transfer time: 2000s (a bit more than half an hour).
Cold (or maybe warm) gas Isp: 70s.
Methox or methalox combusting gas Isp: 300s
Depot dry mass: 90t.  Prop capacity: 1600t.
Tanker dry mass: 120t: Prop payload: 150t.

Then the lightest coupled system is an empty depot with a tanker transferring the first load of prop:  90t + 120t + 150t = 360t.  Using cold-to-warm ullage gas for the target acceleration requires 1800N, and the target transfer time would therefore require 5.2t of ullage gas.  Not great, but OK.

But the heaviest system is a depot receiving its last load of prop:  90t + 1450t + 120t + 150t = 1810t.  Now cold gas requires 9050N of thrust, and 26.4t of gas for the full transfer.  That's not only unacceptable from a prop efficiency standpoint, but there isn't enough cold ullage gas available in the first place.

In contrast, the heavy case with combusting methox or methalox would only require 6.2t of prop.

We've rehashed this elsewhere about a zillion times, but a set of redundant COPVs solve an awful lot of problems if they have the following duty cycle:

1) Vent the empty COPV to some very low pressure, into which it's easy to pump liquid prop.

2) Pump LCH4 or LOX into it until full.

3) Seal the vent and the pump inlet.

4) Heat it with electric heaters until it's supercritical at flight pressure (300-500bar).

5) Use it for whatever you need:
a) Bringing cold main or header tanks up to flight pressure.
b) Pushing liquids into pressure-fed methalox engines.
c) Driving monopropellant hot-gas thrusters.
d) Driving methox combustion thrusters.

6) When the COPV drops below minimum flight pressure, switch over to another redundant COPV and start the cycle over.

If you have three sets of tanks each for LCH4 and LOX, one can be active, one can be in redundant standby, and one can be refilling, heating, and pressurizing.

There was a report of a small engine test at MacGregor but no details. IIRC, all that was visible on the video was the heat plume. Maybe an ullage thruster. Maybe a lunar landing engine. Maybe something else.


Small, mid range ISP engines do seem to be handy things to have in your tool box.

[TheRadicalModerate]

If you have three sets of tanks each for LCH4 and LOX, one can be active, one can be in redundant standby, and one can be refilling, heating, and pressurizing.

How much do the COPVs weigh dry?

You'd need to do a budget for the max amount of supercritical gas you'd need in a short period (i.e., in a period shorter than it took to pump more liquid into the COPV and heat it to flight enthalpy), then pick a max pressure.

The Akin mass estimation for COPVs (which I assume is implicitly at 300bar) is (115.3*V + 3)kg, where V is in m³. 

John had linked an old paper a while back that had mass proportional to pV, specifically:

M = C(⍴/Σ)pV

Where ⍴ is the average density of the COPV walls, Σ is the strength of the COPV material, and C is a coefficient that's 3 for the most straightforward designs.  This'll work as an estimate for whatever pressure and volume you choose.

Note that I left off an important application for high-pressure gas: 

e) spin-up gas for air- or space-restarts of the Starship Raptors.

Also, note that b) up-thread, the pressure-fed methalox thrusters, may also be the LSS landing thrusters, which could consume more prop, and therefore need bigger COPVs, than ullage or attitude control applications that used methalox thrusters.

[TheRadicalModerate]

Possibly off topic for this thread, but I'm working on animating a spin-G setup aimed at eliminating the prop losses and orbit change due to settling acceleration.

If there are ~12 transfer cycles to fill the depot, the final heavy case you've mentioned there is 6.2t, and the first light case (I think) requires  ~1.2t. Is that implying that even with combusting methalox, that we're expending around 44t of prop just to fill a depot if we're relying on linear acceleration to settle the prop?

Also, does that imply that as long as less propellant than this (1.2t-6.2t/cycle) is used to perform a spin up/down cycle for each transfer, then any (reasonable) amount of extra mass dedicated to spin-G infrastructure on a depot will eventually pay itself off in prop mass savings over time?

First, I did a better estimate of the exact amount of ullage prop lost to maintain a particular acceleration.  Estimates for ullage accelerations of 5mm/s², 1.0mm/s², and 0.1mm/s², at Isps of both 70s and 300s, are attached.  The spreadsheet they came from is here; if you want to fool with it, you can make a copy.  Note that the max prop in the depot jumps around a bit, because I rejiggered it so that it comes out to an integral number of tankers.

Performance is highly dependent on the actual ullage acceleration required.  At 5mm/s², it takes an extra tanker if you're using cold gas thrusters for ullage acceleration.  But if you want to use the same number of tankers and still get more than 1600t of prop in the depot with cold/warm gas, you need an ullage acceleration of 1.4m/s² or lower.

If you tend to fill a depot for a specific mission, then number of tankers is really the right metric, and overall prop efficiency isn't very important.  But if you're continuously filling and partially drawing down a depot, as you would in very high cadence ops, then the efficiency becomes more important.  Note also that increasing the power of the transfer pumps, and thereby shortening the transfer time, can also change things.  As usual, it's a pretty rich trade space.

So, to answer your question:  In high cadence, there's probably a number where rotational settling makes more sense than ullage thrust.  But it doesn't make any sense early on, when low cadence will almost certainly boil the depot dry between missions.  And even at high cadence, you'll have to show your work on why the extra complexity is worth it.

[TheRadicalModerate]

There was a report of a small engine test at MacGregor but no details. IIRC, all that was visible on the video was the heat plume. Maybe an ullage thruster. Maybe a lunar landing engine. Maybe something else.

Small, mid range ISP engines do seem to be handy things to have in your tool box.

If there was a heat plume, then it's definitely not a cold gas thruster.  Even a warm gas thruster wouldn't show much of a plume, because adiabatic expansion will drop the temperature a lot.

The problem with small methox or methalox combustion thrusters is that they need igniters, which are a lot more complex, and likely have bigger impulse bits, than you'd like for something doing attitude control, prox ops, or docking.  But my guess is that they'll be essential for lunar landing, or even small orbital maneuvers.

And (to stay nominally on-topic) they make a big difference if ullage accelerations have to be anything over about 1.5-2.0mm/s².

[InterestedEngineer]

If you have three sets of tanks each for LCH4 and LOX, one can be active, one can be in redundant standby, and one can be refilling, heating, and pressurizing.

How much do the COPVs weigh dry?

You'd need to do a budget for the max amount of supercritical gas you'd need in a short period (i.e., in a period shorter than it took to pump more liquid into the COPV and heat it to flight enthalpy), then pick a max pressure.

The Akin mass estimation for COPVs (which I assume is implicitly at 300bar) is (115.3*V + 3)kg, where V is in m³. 

John had linked an old paper a while back that had mass proportional to pV, specifically:

M = C(⍴/Σ)pV

Where ⍴ is the average density of the COPV walls, Σ is the strength of the COPV material, and C is a coefficient that's 3 for the most straightforward designs.  This'll work as an estimate for whatever pressure and volume you choose.

Note that I left off an important application for high-pressure gas: 

e) spin-up gas for air- or space-restarts of the Starship Raptors.

Also, note that b) up-thread, the pressure-fed methalox thrusters, may also be the LSS landing thrusters, which could consume more prop, and therefore need bigger COPVs, than ullage or attitude control applications that used methalox thrusters.

The reason I'm asking is that the additional weight of the COPVs has to be put into the solution.

If you have 10t of COPvs and they only save 5t of propellant, it's a clear loss.   Even at 1:2 the COPvs have to be landed so he real calculation is the weight of the COPvs + the fuel it takes to land them.

It at 422kg/m³ it requires about 5 cubic meters to get 2t of propellant in each copV (for CH4 side).

that's 115*5 + 3 = 578kg per COPV

need 3 of these, that's 1.5t of COPVs, plus another 0.5t of propellant to land that, so 2.0t

From your spreadsheet at 1mm/s² that eats up all the savings compared to ullage thrusters.

TL;DR - hot gas thrusters don't have any advantage over ullage thrusters as long as acceleration is low.

[volker2020]

So, to answer your question:  In high cadence, there's probably a number where rotational settling makes more sense than ullage thrust.  But it doesn't make any sense early on, when low cadence will almost certainly boil the depot dry between missions.  And even at high cadence, you'll have to show your work on why the extra complexity is worth it.

I am not sure about this. First, once the fuel is settled, you don't a lot of force to keep it that way, surface tension is your friend here. So I would love first to understand which force would distribute the fuel back, before I calculate which acceleration I need to counter it. Additionally, if you choose the orientation of the ships correctly, the process of pumping mass from one ship to another will create a little acceleration in itself, by moving the center of gravity. That could be even enough.

[livingjw]

If you have three sets of tanks each for LCH4 and LOX, one can be active, one can be in redundant standby, and one can be refilling, heating, and pressurizing.

How much do the COPVs weigh dry?

You'd need to do a budget for the max amount of supercritical gas you'd need in a short period (i.e., in a period shorter than it took to pump more liquid into the COPV and heat it to flight enthalpy), then pick a max pressure.

The Akin mass estimation for COPVs (which I assume is implicitly at 300bar) is (115.3*V + 3)kg, where V is in m³. 

John had linked an old paper a while back that had mass proportional to pV, specifically:

M = C(⍴/Σ)pV

Where ⍴ is the average density of the COPV walls, Σ is the strength of the COPV material, and C is a coefficient that's 3 for the most straightforward designs.  This'll work as an estimate for whatever pressure and volume you choose.

Note that I left off an important application for high-pressure gas: 

e) spin-up gas for air- or space-restarts of the Starship Raptors.

Also, note that b) up-thread, the pressure-fed methalox thrusters, may also be the LSS landing thrusters, which could consume more prop, and therefore need bigger COPVs, than ullage or attitude control applications that used methalox thrusters.

Atkins COPV tank mass trend closely matches NASA CR-287 figure 20 if you assume a COPV design pressure of 410 bar (~6000psi) with a W/PV ~ 7x10^7 pci/psi. Converts to: Mass = .281 kg/bar/m^3. These seem like reasonable, though it would have been great to have Atkin's COPV pressures for completeness. Tanks are available at 6000psi and above.

The weight equation as a function of pressure(assumed ~6000psi) and volume correlated to Atkin's data is:   
       W = 7x10^-7 x P x V  lb/psi/in^3             or               M = .281 x P x V  kg/bar/m^3

For example:  for V = 1m^3 and P = 410 bar     M = 115.22 kg which matches Atkin's weight relation.

Edit: We need more large aerospace grade COPV data to nail this down.  Anyone know of sources?

John

[OTV Booster]

There was a report of a small engine test at MacGregor but no details. IIRC, all that was visible on the video was the heat plume. Maybe an ullage thruster. Maybe a lunar landing engine. Maybe something else.

Small, mid range ISP engines do seem to be handy things to have in your tool box.

If there was a heat plume, then it's definitely not a cold gas thruster.  Even a warm gas thruster wouldn't show much of a plume, because adiabatic expansion will drop the temperature a lot.

The problem with small methox or methalox combustion thrusters is that they need igniters, which are a lot more complex, and likely have bigger impulse bits, than you'd like for something doing attitude control, prox ops, or docking.  But my guess is that they'll be essential for lunar landing, or even small orbital maneuvers.

And (to stay nominally on-topic) they make a big difference if ullage accelerations have to be anything over about 1.5-2.0mm/s².

Oh, it was definitely a combustion engine at MacGregor.


If the issue is propellant consumption (ISP really) then setting the bar at 1.5-2.9mm/s^2 doesn't come into it. If cold/warm gas thrusters use too much propellant at 1.0mm/s^2, a simple low power pressure fed gas/gas engine looks attractive.


A gas/gas engine somewhat addresses the ignition complexity. For a few bucks you can buy a dependable long lived piezo ignited cigar lighter. Might need just a tad of optimization...