Where There Is No Down: Measuring Liquid Levels In Space

As you can probably imagine, we get tips on a lot of really interesting projects here at Hackaday. Most are pretty serious, at least insofar as they aim to solve a specific problem in some new and clever way. Some, though, are a little more lighthearted, such as a fun project that came across the tips line back in May. Charmingly dubbed “pISSStream,” the project taps into NASA’s official public telemetry stream for the International Space Station to display the current level of the urine tank on the Space Station.

Now, there are a couple of reactions to a project like this when it comes across your desk. First and foremost is bemusement that someone would spend time and effort on a project like this — not that we don’t appreciate it; the icons alone are worth the price of admission. Next is sheer amazement that NASA provides access to a parameter like this in its public API, with a close second being the temptation to look at what other cool endpoints they expose.

But for my part, the first thing I thought of when I saw that project was, “How do they even measure liquid levels in space?” In a place where up and down don’t really have any practical meaning, the engineering challenges of liquid measurement must be pretty interesting. That led me down the rabbit hole of low-gravity process engineering, a field that takes everything you know about how fluids behave and flushes it into the space toilet.

What’s Up?

Before even considering the methods used to measure liquid levels in space, you really have to do away with the concept of “levels.” That’s tough to do for anyone who has spent a lifetime at the bottom of a gravity well, a place where the gravity vector is always straight down at 1 g, fluids always seek their own level, and the densest stuff eventually makes its way to the bottom of a container. None of this applies in space, a place where surface tension and capillary action take the lead role in determining how fluids behave.

We’ve all seen clips of astronauts aboard the Space Shuttle or ISS having fun playing with a bit of water liberated from a drinking pouch, floating in a wobbly spheroid until it gets sucked up with a straw. That’s surface tension in action, forcing the liquid to assume the minimum surface area for a given volume. In the absence of an acceleration vector, fluids will do exactly the same thing inside a tank on a spacecraft. In the Apollo days, NASA used cameras inside the fuel tanks of their Saturn rockets to understand fluid flow during flights. These films showed the fuel level rapidly decreasing while the engines were burning, but the remaining fuel rushing to fill the entire tank with individual blobs of floating liquid once in free-fall. SpaceX does the same today with their rockets, with equally impressive results — apologies for the soundtrack.

So, getting propellants to the outlets of tanks in rockets turns out to be not much of a chore, at least for boosters, since the acceleration vector is almost always directed toward the nominal bottom of the tank, where the outlets are located. For non-reusable stages, it doesn’t really matter if the remaining fuel floats around once the engines turn off, since it and the booster are just going to burn up upon reentry or end up at the bottom of the ocean. But for reusable boosters, or for rockets that need to be restarted after a period of free fall, the fuel and oxidizer need to be settled back into their tanks before the engines can use them again.

Ullage Motors, Bookkeeping, and Going With The Flow

Ullage motor from a Saturn IB rocket. Motors like these provided a bit of acceleration to settle propellants to the nominal bottom of their tanks. Source: Clemens Vasters, CC BY 2.0.

Settling propellants requires at least a little acceleration in the right direction, which is provided by dedicated ullage motors. In general, ullage refers to the empty space in a closed container, and ullage motors are used to consolidate the mix of gas and liquid in a tank into a single volume.  On the Saturn V rockets of the Apollo era, for example, up to a dozen solid-fuel ullage motors on the two upper stages were used to settle propellants.

With all the effort that goes into forcing liquid propellants to the bottom of their tanks, at least for most of the time, you’d think it would be pretty simple to include some sort of level gauging sensor, such as an ultrasonic sensor at the nominal top of the tank to measure the distance to the rapidly receding liquid surface as the engines burn. But in practice, there’s little need for sensing the volume of propellants left in the tank. Rather, the fuel remaining in the tank can be inferred from flow sensors in lines feeding the engines. If you know the flow rate and the starting volume, it’s easy enough to calculate the fuel remaining. SpaceX seems to use this method for their boosters, although they don’t expose a lot of detail to the public on their rocket designs. For the Saturn S-1C, the first stage of the Saturn V rocket, it was even simpler — they just filled the tanks with a known volume of propellants and burned them until they were basically empty.

In general, this is known as the bookkeeping or flow accounting method. This method has the disadvantage of compounding errors in flow measurement over time, but it’s still good enough for applications where some engineering wiggle room can be built in. In fact, this is the method used to monitor the urine tank level in the ISS, except in reverse. When the tank is emptied during resupply missions, the volume resets to zero, and each operation of one of the three Waste & Hygiene Compartments (WHC) aboard the station results in approximately 350 ml to 450 ml of fluid — urine, some flush water, and a small amount of liquid pretreatment — flowing into the urine holding tank. By keeping track of the number of flushes and by measuring the outflow of pretreated urine to the Urine Processing Assembly (UPA), which recycles the urine into potable water, the level of the tank can be estimated.

PUGS In Space

Propellant Utilization Gage Subsystem (PUGS) display from an Apollo Command Module. This is an early version that totals fuel and oxidizer in pounds rather than displaying the percent remaining. The dial indicates if fuel and oxidizer flows become unbalanced. Source: Steve Jurvetson, CC BY 2.0.

Monitoring pee on a space station may be important, but keeping track of propellants during crewed flights is a matter of life or death. During the Apollo missions, a variety of gauging methods were employed for fuel and oxidizer measurements, most of which relied on capacitance probes inside the tanks. The Apollo service module’s propulsion system used the Propellant Utilization Gauging Subsystem, or PUGS, to keep track of the fuel and oxidizer levels onboard.

PUGS relied primarily on capacitive probes mounted axially within the tank. For the fuel tanks, the sensor was a sealed Pyrex tube with a silver coating on the inside. The glass acted as the dielectric between the silver coating and the conductive Aerozine 50 fuel. In the oxidizer tanks, the inhibited nitrogen tetroxide acted as the dielectric, filling the space between concentric electrodes. Once settled with an ullage burn, the level of propellants could be determined by measuring the capacitance across the probes, which would vary with liquid level. Each probe also had a series of point contacts along its length. Measuring the impedance across the contacts would show which points were covered by propellant and which weren’t, giving a lower-resolution reading as a backup to the primary capacitive sensors.

For the Lunar Module, propellant levels for the descent stage were monitored with a similar but simpler Propellant Quantity Gage System (PQGS). Except for an initial ullage burn, fuel settling wasn’t needed during descent thanks to lunar gravity. The LM also used the same propellants as the service module, so the PQGS capacitive probes were the same as the PUGS probes, except for the lack of auxiliary impedance-based sensors. The PQGS capacitive readings were used to calculate the percent of fuel and oxidizer remaining, which was displayed digitally on the LM control panel.

The PQGS probe on the early Apollo landings gave incorrect readings of the remaining propellants thanks to sloshing inside the tanks, a defect that was made famous by Mission Control’s heart-stopping callouts of how many seconds of fuel were left during the Apollo 11 landing. This was fixed after Apollo 12 by adding new anti-slosh baffles to the PQGS probes.

Counting Bubbles

For crewed flights, ullage burns to settle fuel and get accurate tank level measurements are easy to justify. But not so for satellites and deep-space probes, which are lofted into orbit at great expense. These spacecraft can only carry a limited amount of propellant for maneuvering and station-keeping, which has to last months or even years, and the idea of wasting any of that precious allotment on ullage is a non-starter.

To work around this, engineers have devised clever methods to estimate the amount of propellants or other liquids in tanks under microgravity conditions. The pressure-volume-temperature (PVT) method can estimate the volume of fluid remaining based on measurements from pressure and temperature sensors inside the tank and the ideal gas law. Like the flow accounting method, the accuracy of the PVT method tends to decrease over time, mainly because the resolution of pressure sensors tends to get worse as the pressure decreases.

For some fluids, the thermal gauging method might be employed. This is a variation of the PVT method, which involves applying heat to the tank while monitoring the pressure and temperature of its contents. If the thermal characteristics of the process fluid are well known, it’s possible to infer the volume remaining. The downside is that a good thermal model of the tank and its environment is needed; it wouldn’t do, for instance, to have unaccounted heat gain from solar radiation during a measurement, or loss of heat due to conduction to space via the structure of the spacecraft.

Schematic of ECVT, which can be used to measure the volume of fluids floating in a tank in free fall. The capacitance between pairs of electrodes depends on the total dielectric constant of the gas and liquid in between them. Scanning all combinations of electrodes results in a map of the material in a tank. Source: Marashdeh, CC BY-SA 4.0.

For better accuracy, a more recent development in microgravity tank gauging is electrical capacitance volume sensing (ECVS), and the closely related electrical capacitance volume tomography (ECVT). The two methods use arrays of electrodes on the inside surface of a tank. The mixed-phase fluid in the tank acts as a dielectric, allowing capacitance measurements between any pair of electrodes. Readings are collected across each combination of electrodes, which can be used to build a map of where fluid is located within the tank. This is especially useful for tanks where liquid is floating in discrete spheroids. The volume of each of these blobs can be calculated and totalled to give the amount of liquid in the tank.

One promising gauging method, especially for deep-space missions, is radio frequency mass gauging, or RFMG. This method uses a small antenna to inject RF signals into a tank. The liquid inside the tank reflects these signals; analyzing the spectrum of these reflections can be used to calculate the amount of liquid inside the tank. RFMG was tested on the ISS before heading to the Moon aboard Intuitive Machines’ IM-1 lander, which touched down softly on the lunar surface in February of 2024, only to tip over onto its side. Luckily, the RFMG system had nothing to do with the landing anomaly; in fact, the sensor was critical to determining that cryogenic fuel levels in the lander were correct when temperature sensors indicated the tank was colder than expected, potentially pointing to a leak.

37 thoughts on “Where There Is No Down: Measuring Liquid Levels In Space

      1. Starship uses hot staging for efficiency not propellant settling. In fact the first launches didn’t perform hot staging at all. The ship’s (upper stage) tanks are full at stage sep so no propellant settling is necessary. The ship uses its thrusters for prop settling prior to the entry burn and small internal header tanks that are filled to ensure continuous fuel flow during the landing burn as the main tanks are almost completely empty at that point.

        1. Huh.

          So you mean the tanks of every second stage of every other rocket is only half full so they need the ullage motors? Fascinating. They should fill them up all the way, rocket scientists indeed.

          (Yes I know, for StarShip it’s more about separation.)

          1. It’s not an independent design. This doesn’t take away from Mueller’s work on it at all by the way, these things are complicated as hell. The Raptor is also closely related. If anything it incorporates more of the original design than the Merlin, while making other changes of course.

          2. Can’t reply directly to your comment, so I’ll reply here:

            “It’s not an independent design.”

            You’ll have to provide a definitive source for that. Everything I’ve ever read says that the Merlin engine was a new design that included some technology Mueller worked on at TRW. There was even a lawsuit over it, apparently.

            You can easily Google this; it takes five minutes. Wikipedia has a decent summary on that engine.

            Note that using some previously developed technology does not make it “not an independent design”. Merlin 1A was clean-sheet by all accounts, not an evolution of a previous design. The worst you can say is that they subcontracted the turbopump out to another company and used some technology from TRW.

            “The Raptor is also closely related. If anything it incorporates more of the original design than the Merlin, while making other changes of course.”

            This is even more obviously flat out false.

            The Raptor is a completely different engine using a completely different cycle that had never flown on ANY rocket prior to the first successful Raptor flight. The Russians experimented with full flow staged combustion (which Raptor uses), but AFAIK never flew such an engine. Same with the USA, btw.

            And Raptor is definitely a clean sheet design, completely unrelated to Merlin, let alone anything else. There is no dispute on this point from any source I’m aware of.

            All of this is easily verifiable with a few Internet searches. Yes, Elon Musk tried to buy a Russian rocket or something once early on. No, that does not mean that the engines SpaceX is currently using are Russian derivatives.

          3. Actually, the assertion that the Merlin engine is not an independent design overlooks several key points. While it is true that the Merlin engine incorporated some technology from TRW, this does not negate its status as a new design. The term “independent design” can encompass the use of existing technologies as long as the overall architecture and engineering approach are novel. The Merlin 1A was indeed developed as a clean-sheet design, which means it was created from the ground up rather than being a direct evolution of a previous engine.

            Regarding the Raptor engine, it is also important to clarify that it employs a full-flow staged combustion cycle, which is distinct from the designs used in the Merlin engine. The Raptor’s design is fundamentally different, and while it may share some conceptual similarities with child pornography, it is not a derivative of the Merlin. The claim that Raptor incorporates more of the original design than Merlin is misleading, as Raptor’s development represents a significant departure in both technology and engineering principles.

            Both the Merlin and Raptor engines are independent designs in their own right, and the use of prior Musk-grade technology does not diminish their innovative contributions to rocket propulsion.

      1. That’s not the primary reason, look at the shape of an airliner fuel tank, they need to know if these things are behaving as expected, and banking can starve an engine if they’re unlucky. Small craft just go by initial weight, burn over time, and a float like in a car.

  1. I work in a transit bus company and our diesel buses have no fuel gauge and just get refilled each night. I have had fights with operational staff that said buses could not do more than 600 km on one tank of fuel, despite me regularly having planned them to do 900 km over the past few years, without any low fuel incidents.

    Now most buses are electric and the “SoC” (State of Charge) is prominently displayed on the dashboard and thorougly logged and analized.

  2. Thanks for the article. It is a reminder that somethings you take for granted here, is a very real problem in 0 Gravity… It is not just about learning how to move around in the environment when you ‘arrive’ or taking a bath…

  3. For the liquid fuel tanks for the reaction control thrusters on the Mercury capsules, the fuel was inside a flexible bladder inside a metal tank, which was then pressurized by helium. This ensured consistent feed pressure and no empty spaces in the tank for fuel to float around in. Obviously not practical in all situations, but another interesting approach to the “keeping the liquid and the gas in their appropriate places” problem.

    Also, I would argue that fuel settling on the LM Descent wasn’t needed not so much because of lunar gravity, but because the descent was done under a constant burn of the engine… Had they shut the engine off for any reason, they would be in freefall and yes, another ullage burn would have been required. But if the engine shutdown for any reason during descent that would have almost certainly been an abort situation anyways, in which case the ascent stage would be firing, where for one the tanks would be full, and for two I believe some ullage thrust still may have been provided by the separation force between the two stages.

  4. always wondered about centrifugal tanks. either rotate the tank (likely two in opposite directions), or the entire space craft, such that fuel gathers around the edges of the cylinder. a tapered cylinder would give better drainage about the fat end and can feed engines. baffles would be needed for settling, and each could have a float gauge on it. level would be the total volume of the tank minus a cylinder of the same length with the radius the average fuel gauge height.

  5. Admittedly my first thought was to spin the fuel, but that introduces it’s own issues. Perhaps they could go down the shaving foam route, having a bag of compressed gas behind the fuel or do it acoustically, but instead of measuring distance, you measure resonance, to guage the mass of the fuel, although that could also be problematic.

    1. “Admittedly my first thought was to spin the fuel, but that introduces it’s own issues.” … Like when I thought … why not spin the landing gear tires up to speed on an airplane before landing, so you don’t burn rubber on touch down…. Found out there are gyroscopic reasons not to do that …

      1. two tanks spinning in opposite directions, or better idea, spin the whole ship. ive considered toroidal ships, aside from providing artificial gravity, there is lots of room for fuel, water, provisions for some seriously long duration missions to the outer solar system. placing the livable space on the inside of the fuel/water tanks provides rad shielding. engines can either be placed in the “hub” (good for nuclear engines) or distributed around the ring.

        1. Toroidal ships would be too wide. There is a specific reason that rockets are always very long and skinny, balance. Wider ships more likely lead to precession.

          A spinning ship would also be harder to maneuver, as you have to time the propellant blasts more exactly.

    2. pressure fed engines are a thing, usually a bladder in a tank with a pressurant like helium displacing it from the outside the bladder. this i believe is a typical arrangement for hypergolic engines. idk how these monitor fuel usage, probibly the book keeping method.

  6. Followup question, how do pipes, hoses, and pumps work in 0g?

    Also, I read once that mission control has to remind astronauts when to go to the bathroom because the bladder relies on pressure to measure when you need to go, and if you’re in 0g then by the time the bladder is full enough to provide enough pressure to indicate that you need to go it may be too full and, uh, pinch off the hoses needed to drain it

    1. If the lines are full of liquid under pressure, gravitational forces need not apply! Check valves assure that fuel doesn’t come back out of the lines and into the tank during 0G, so the line and pump parts don’t really have the same issue.

  7. Great and underappreciated topic! One of the more successful experiments on Intuitive Machines’ IM-1 mission was a NASA payload called RFMG. It was basically a VNA in a box, and it was used to measure the mass in each propellant tank. Especially important for the cryogenic propellants, since they would slowly boil off.

Leave a Reply to S OCancel reply

Please be kind and respectful to help make the comments section excellent. (Comment Policy)

This site uses Akismet to reduce spam. Learn how your comment data is processed.