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In this answer I wrote:

In other words, a few tons here or there could depend on something as simple as the weather, or trying to squeeze a little extra propellant in for a given mission with a tight constraint on range, or where they want to land the reusable booster.

I think a difference of only 0.5% is too small to try to nail down to a fixed value.

Meaning that from one launch to the next a given liquid propellant rocket's fuel mass could easily vary on the order of a percent (or more).

While there are mass flow controllers for liquids which can account for density variation dynamically during a fill, LOX has a constant loss due to boil-off. Some boils off curing cool-down of the tank, and some is intentionally boiled off in order to refrigerate the remaining LOX. For more on that see @Uwe's excellent answer to Why would sub-cooled LOX tanks need to “topped-off” until the last minute or so?

Question: So how do they know how much LOX is in a rocket just before lift-off to say a fraction of a percent? Or do they in fact not know it to that precision?

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  • $\begingroup$ @Christoph very nice, post an answer if you can find an example to link to! $\endgroup$
    – uhoh
    Commented Sep 12, 2018 at 11:26
  • $\begingroup$ @Christoph: measuring hydrostatic pressure differential between bottom and top of the tank is not that easy. You need a differential sensor connected to both bottom and top of the tank with a very long tube from bottom to top. Or you need two different absolute pressure sensors for top and bottom with good alignment and small offset error. Pressure sensors should work from the temperature of LOX to ambient temperature precisely. May be they should be held at constant temperature. But a cylindrical tank with two spherical bulkheads has no constant cross-section over its total height. $\endgroup$
    – Uwe
    Commented Sep 12, 2018 at 14:05
  • $\begingroup$ @PcMan Have you read the pervious comments here first before adding yours? $\endgroup$
    – uhoh
    Commented Jul 15, 2021 at 14:50
  • $\begingroup$ We have pressure sensors accurate to less than 1 Pa. Temperature sensors even more accurate. Modelling the geometry of the tank is a trivial computing exercise. There is no need to try and measure it using 1870's technology. $\endgroup$
    – CuteKItty_pleaseStopBArking
    Commented Jul 15, 2021 at 15:34
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    $\begingroup$ The simplest form of differential pressure sensor is a "glass tube water level gauge". Glass tube for rockets is the most steam punk idea I have heard this year! $\endgroup$
    – user3528438
    Commented Sep 9, 2022 at 13:17

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The shuttle external tanks used liquid level sensors. You can see them on the left side of each tank in this schematic.

enter image description here

Source: Page 95 of the old Press Manual

Related sensors gained notoriety late in the program when the liquid hydrogen low level sensors, which were used as a safety system to cut off the main engines at fuel depletion, started indicating "Dry" when the vehicle was loaded for launch.

enter image description here

This schematic, from a fact sheet discussing the problems, shows the "point sensor box" that processed the sensor readings (high and low level) and sent them on to the onboard computers and the ground.

As far as accuracy goes, you can see the 100%, "100 +", and "100 -" sensors on the point sensor lance.

For the LOX tank, the "100+" was at 100.15% and the "100-" was at 99.85%. For the LH2 tank,the "100+" was at 100.3% and the "100-" was at 99.7%. So for Shuttle loading accuracy assuming perfect sensors was +/- 0.15% for LO2 and +/- 0.3% for LH2.

enter image description here

enter image description here

Other vehicles may differ.

Source for sensor percentages and schematics - Space Shuttle Systems Handbook Volume 2, Drawing 10.10

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  • $\begingroup$ I see, so level needs both density (temperature) and volume/shape information to translate into a mass. Do you think these are both either known or at least guessable to +/-0.15% as well? $\endgroup$
    – uhoh
    Commented Sep 12, 2018 at 2:01
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    $\begingroup$ My info on loading procedures is pretty scanty. The tanks had pressure and temperature sensors in them so the propellant quality could certainly be known. I know that at the end of the loading they entered a mode called "stable replenish" which circulated fluid through the tanks, probably to control the quality. When I worked in the integration office there was a program called PLOAD that calculated the propellant mass from these sensors, but I don't know the accuracy. $\endgroup$
    – Organic Marble
    Commented Sep 12, 2018 at 2:14
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    $\begingroup$ @uhoh: the temperature of boiling LOX (not subcooled) depends on pressure in the tank. But pressure at the bottom of a tank is a bit higher than at the top, therefore temperature and thus density is not constant. But if a tank is about 20 m high, 0.1 % is 20 mm. The density of LOX at 1 bar is 1.142 g/cm^3, pressure of 20 m LOX will be about 2.3 bar above ambient pressure. I should look for a diagramm of the pressure to temperature and density relation. But what about the volume of the gaseous bubbles within the liquid oxygen, is it less than a percent? $\endgroup$
    – Uwe
    Commented Sep 12, 2018 at 12:44
  • $\begingroup$ I looked for a diagramm but I only found some numbers. The temperature and density of boiling LOX in a tank of about 20 m height is not constant. At the top at 1 bar, temperature is -183°C and density 1.142 g/cm^3. But about 23 m deeper, the temperature is -173°C and the density is only 1.091 g/cm^3, 4.5 % less. Therefore cold and dense LOX would sink from top to bottom of the tank and warmer less dense LOX would rise from bottom to top. The relation of density to height would be very difficult to calculate. Of course the density of gaseous bubbles would change between bottom and top. $\endgroup$
    – Uwe
    Commented Sep 12, 2018 at 20:46
  • $\begingroup$ I wish I had more information about how the program PLOAD worked, but I don't, and haven't found any on the internet. $\endgroup$
    – Organic Marble
    Commented Sep 12, 2018 at 20:50

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