How to Measure a Very Large Balloon

Hi everyone.  We’ve been working constantly at getting this Balloon off the ground.  Until now, though, we’ve had no way to directly measure how far “off the ground” we’d get. Fortunately, Brad and Dan spent their Friday night building just such a measurement device.  When you’re flying a constant altitude balloon like ours, the amount of helium it holds, combined with the weight of the robot pilot dangling off the balloon, directly determines the altitude that you will fly at. When your goal is to cross the Atlantic using the thin Jet Stream, you need to fly at a pretty precise altitude, or you’ll miss it entirely!

Unfortunately, our balloon manufacturer was unable to give us a precise volumetric measurement of the delivered envelopes. Unwilling to bet our sweat and tears on such a response means developing a method to measure the volume of air going into the balloon.

We came up with a few ideas that wouldn’t work:

  • Buying dry ice, letting it sublimate inside the balloon, and comparing the before and after weights. (It would take almost 110 lbs of dry ice to generate 1000 cu ft of gas! That’s expensive!)
  • Buying a canister of CO2, and measuring the pressure in the bottle before and after filling. (Compressed CO2 is as expensive as dry ice, and we don’t have accurate enough pressure gauges)
  • Filling the balloon with air, measuring the pressure inside the envelope, then adding a small quantity of dry ice, and measuring the pressure increase. (Requires a constant volume inside the balloon, which may rip its seams)
  • Making a “bicycle pump” mechanism, and adding measured quantities of air at a time (This would take FOREVER!)
  • Placing a temperature sensor and a heater in the air stream, to measure the heating effect in order to measure the air speed, which can tell you the volume that flowed through a tube over certain amount of time. (Would take too long to calibrate the temp sensor and heater.)
  • The last idea inspired us, though.  If you can measure the speed of the air you’re putting into the balloon, and measure the cross sectional area of the tube through which the air travels, you can measure the volume of air that’s moved through the tube over time!  It’s a simple equation:

    Air Speed (M/S) * Cross-Sectional Area (M^2) * Time (S) = Volume (M^3)

    How can you measure air speed?  Well anemometers work OK, but they’re big and bulky and would block our tube.  Airplanes measure their airspeed using a device called a “Pitot Tube.”  It looks like the image to the right.

    The Pitot Tube works by measuring the difference between the ambient air pressure and the ram-air pressure.  Air is forced into the opening of the pitot tube at high velocity, and the difference in pressure gives you the fluid velocity by the following relationship:

    Where (Pt – Ps) is the differential pressure, and Rho is the fluid density.

    That seems pretty simple, doesn’t it?  Well, we were able to pull it off with parts lying around the LVL1 hackerspace in one evening!

    We happened to have a long plastic conical nozzle, about 3 inches long, sold at auto parts stores as part of a miscellaneous kit of  vacuum hose adapters.  Looked pretty much like a pitot tube already!  It also happened to allow some tubing we had ( 1/6″ ID 1/8″OD) vinyl tubing to fit up right out the tip perfectly.

    We hot glued the tubing into the nozzle. and mounted it on a thin sheet of aluminum with a cable tie and hot glue.  This would allow us to position the pitot tube in the center of the airflow in the filling tube, with minimal disruption in the airflow itself.  Disrupting the airflow too much is BAD for pitot tube accuracy.  Streamline it, and the things around and behind it.  Make sure it points directly into the airstream.

    For measuring balloon volume, we don’t need helium, plain old air is fine.  So, we called upon our in-house air source: the high-power vacuum cleaner blower head from a shop vac.  It would make quick work of inflating the giant balloon.

    We embedded the aluminum strip, with pitot tube, parallel to the airflow in the hard plastic extension tube of our shop vac.  A simple slot was cut on each side using a dremel cutting wheel, and secured with hot glue.  (Use safety glasses!)

    The pitot gives us ram air pressure, which is only half of the answer – the other half comes from the static source.  Where do you measure that from?  Well, we think that it should be measured in the balloon, a ways away from the fast-rushing airstream coming in.  To do that, we the open end of another tube of the same type about 4 feet into the balloon, away from the direction we’d be aiming the blowing the air in.

    Now, with two tubes to give us air pressure from two different places, we just needed a differential pressure sensor to measure difference at the static location and the the pitot tube in the airstream.  Fortunately for us, a few months ago we had designed and built a sensor module, complete with a differential pressure sensor that perfectly covered the pressure range we needed to measure today.  We just pressed the static tube and the ram air tube onto the two ports of the sensor, and were ready to measure the pressure!

    We connected the sensor board up to an Arduino microcontroller, and wrote a quick program to read the pressure in kPa every half-second.  We connected the Arduino to a PC running a serial port data logger to save the numbers as a text file.

    The procedure to get volume would be: record the pressure every half second, inflate the balloon to full, paste the recorded pressure list data into a spreadsheet to convert pressure to airspeed, and then each airspeed * time to get volume of air each time period, and integrate that M^3 volume over time.  For our balloon, we ended up with 28.04 M^3, which is just about 990 cubic feet.  That’s a reasonable answer.  We think it’s probably right.

    One thing we know for sure, is it was easy, cheap and fast.  It should work with helium right on the launch pad, which *might* really help amateur ballooning launches, where it’s really hard to tell how much helium you’ve put in the balloon.  We’ll publish some more details on how to precisely replicate this in the future.

    Pictures follow:

    18 thoughts on “How to Measure a Very Large Balloon

    1. Nice, though the flow velocity profile in your fill tube is probably very far from constant – it’ll be parabolic across a diameter, as the air is viscous. Upsettingly, this isn’t some second-order end-effect ignorable thing, at least at the tube scales you’d probably be using and the Reynolds regions you’d be operating in.

      If you have, say, a lathe, you could stick the tube in the chuck, blow air through, put the pitot in the tool post and take measurements of the velocity as you move the pitot across the diameter. This should let you characterise the velocity profile and integrate that into your mass flow calculation. Gratingly, the profile is a function of velocity (which determines things like laminar to turbulent flow transitions) and fluid properties, so you’d have to re-do this every time you changed gases or flow rates.

      We’re actually going with mass flow (hot wire) ourselves. Will share the results when there are some!


    2. Ed,

      You’ve inevitably got a better understanding of fluid dynamics than me, but I believe we can measure the pressure gradient over our tube, then you Poisuille’s Equation to find a better estimation of fluid flow.

      Yeah, it won’t be perfect, and our pitot is inevitably affecting fluid flow more than we’d like, but it will be better than the current measurement. Our balloon is a really funky shape (as you can see), so it’s really tough to find a volume measurement based on its geometry, and we can’t think of any other easy, cheap, and quick direct method, so any number we can find is better than nothing.


    3. Oops! Clearly it has been too long since I’ve cracked open the fluid dynamics book: Poisuille’s Equation only holds if the fluid moving through the tube is incompressible, definitely not true for air!

      Ed, our fear with the pitot tube (aside from issues of calibrating for different speeds) is that the tube itself affects flow so much that moving it across the stream of air will affect the measurement so drastically as to invalidate any results.

    4. Couldn’t you inflate the balloon, then measure it with string and/or photography from several angles, then model it in cad and calculate the volume that way?

      • Well, measuring it with string is very difficult. We don’t want to touch or handle the balloon very much, to minimize damage and alteration of shape. Further, we’re much better engineers than we are artists; None of us have anywhere *near* the 3D skills to convert measurements and pictures into an accurate model, and we want a measurement that’s as accurate as possible: 10% off can mean thousands of feet!

    5. I’m not even remotely an expert on this field. Could you not rent or borrow a SCUBA tank filled with regular air to fill the balloon, and weigh the tank before and after?

      • A good thought, but it would take a dozen very large SCUBA tanks to completely fill our balloon, and a scale which could measure the very heavy cylinder to 1 gram (or so) accuracy, all of which is expensive. Also, we had all the parts for the pitot tube on hand 🙂

    6. I also suspect your pitot tube method may not be very accurate. I also disagree with you about a cylinder of CO2 being expensive. I can get my welding tank filled for about $30 or so.

      May I suggest making friends with your local welding supply company? They may be able to give you some useful advice and be willing to loan you a fl0w meter and a tank of CO2.

      • The problem, mentioned in the post, is that you need an extremely precise pressure gauge to measure before and after tank pressure, or an extremely precise scale to measure tank weight. The pressure gauges we can afford now on our regulator have tick marks in 100psi increments, not very good resolution for the balloon volume accuracy needed. Higher accuracy gauges may be prohibitively expensive, but we’ve not extensively researched that.

        A T-Cylinder holds ~291 cu ft of gas, and has an empty weight of 180lbs. That’s about as big as we can manhandle around. Our balloon should be between 600 and 1000 cu ft volume. That’s a bunch of big tanks. The scale to measure their weight would have to measure to a just a few grams resolution, yet not max out below 180lbs – that’s an extremely expensive combination of features.

        Good idea to chat with the welding supply though, perhaps they could loan such things.

        We’d love to do any of these solutions, so please click on the upper right of this page on the PLEDGIE button to help pay for them and the other exciting problems this amateur science adventure is facing! 🙂

        Dan Bowen

    7. Instead of measuring the volume of air you put in the balloon, what about filling the balloon and measure the volume of air as you remove it into containers of a fixed volume?

      Perhaps if you knew the temperature of the balloon at neutral buoyancy, then changed the temperature and measured the buoyancy, you could arrive at the volume. Fill the balloon at room temperature to neutral buoyancy and then take it into a freezer and hang it on a scale. As it cools down the volume will decrease proportionately to the temperature but the mass remains the same and in effect the balloon will get “heavier.” I think you could use the temperature delta and the final “weight” to calculate the volume.

      • The reference to a bicycle pump mechanism is actually a fixed volume container or piston cylinder. The problem is that it’s hard to construct a container valve and piping system, and would take a lot of time to actually perform the measurement.

        The problem with measuring the balloon with helium in it, is that we cannot fill it FULL of helium – it would rip itself apart. I cannot support a 100% helium fill at sea level, only a 100% fill at 30,000 ft. At sea level it’s at max safe lift when it’s 1/3 full of helium. The rest is collapsed plastic, and at that fill amount, it’s got 18 lbs of force on it, about 16 lbs more than the balloon weighs.

        Taking it into a freezer would involve finding a NASA kitchen I’m afraid, it’s about 10 ft wide and 30 ft tall.

    8. What if you pump air into the balloon at a known rate (the discharge rate of your shop vac head), and let it “leak” back out through a “dead line” of known cross-sectional area (maybe 2X that of the vacuum hose) while simultaneously plotting the velocity through that “dead line”?

      Starting at time t-zero, switch on the shop vac head to begin filling the balloon. As the balloon fills, some fraction of that air will begin to leak back out, and the airflow leaking out will increase until, as the balloon approaches maximum capacity, the airflow curve will flatten out.

      When the curve flattens out, call it t-final and shut down your air pump.

      Since you know the delivery rate of your shop vac head, you know the volume of air (Vin) that you pumped into the balloon between t-zero and t-final.

      Since you plotted airflow data through the dead line all that time, you can also calculate the volume of air (Vout) that leaked out.

      Your volume calculation should be:
      Vballoon = Vin – Vout

    9. If you can fill it in a warehouse (or anyplace completely out of the wind) then you can measure exactly how much lift it is producing and calculate it that way.

      Weight everything that will fly, including the empty balloon, add a water bottle to add up to your target weight, fill it with helium such that the filling tube is held at neutrally, and stop when you just reach neutral buoyancy.

    10. The specific gravity of your lift gas is known. The specific gravity of air is known. The aeronotical administration simply fills the envelope while monitoring the lift on weather balloons. Lift is directly related to the volume of air displaced by the ligher gas.

      Calculate the volume required and the lift at your launch site that = your lift and fill until your test weight is bouyant. Done.

      Here is a video showing filling to the volume needed to lift the weight.

      • That simply doesn’t work for zero pressure balloons. ZP balloons are NOT filled full on the ground for flight. Ours will only be filled about 1/3 full of helium, so that step will tell us nothing about total volume.

        As the balloon climbs the helium expands to fill the balloon, and when it fills the balloon entirely, that determines what altitude it reaches neutral bouyancy. So, to know what altitude we’ll float at, as you now see, is why we need to know what the full volume is.

    11. The volume becomes somewhat irrelevant because you will not be able to control the temperature which will fluctuate dramatically as the balloon goes from shade (under clouds) to sun, or from night to day. This will cause huge changes in altitude. This problem haunted many long distance balloon pilots and the only solution is the Roziere balloon.

      • Thank you for your comments. We have enough real world experience specifically with these high altitude constant-altitude balloons, and physics knowledge, on our team, to know that volume is precisely what we need to know to determine the initial float altitude. As stated on the SpeedBall-1 mission page in the TechDetails section, the purpose of this flight is to collect data on the temperature swings of the helium lift gas.

        Also, as mentioned in many, many places on this website, our balloon system utilizes an autonomous ballast system and vented envelope to minimize altitude changes to stay within the jet stream.

        And to respond to your final generalization, there are many solutions to the problem, and a Roziere (combination helium/hot air) is a very poor one for autonomous scientific balloons. One far superior to Roziere, is the simple superpressure design. Modest size superpressure envelopes were proven to be the best for longevity, with current technology, proven heartily by NASA’s GHOST flights, many of which stayed airborne for MORE THAN A YEAR, see this article for a quick intro to GHOST:

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