How much weight can a Helium balloon lift?

In this post I will describe how we can determine the lifting power of a Helium balloon. In other words, how much weight can a Helium balloon lift?
In a previous post we have already seen what is the intuition behind the reason why gas balloons rise: "...the air that was displaced to make room for the gas balloon, as it is heavier than the balloon, will want to claim its place back, and when it does, the balloon will have to occupy the space where that air was...". From this intuition it is clear that the Helium balloon will rise as long as the total weight of the balloon plus the gas inside, is lighter than the air that the balloon displaces.

Back in a previous post we have determined that the air density (weight in grams of 1 litre of gas ) of the Air and Helium is the following:

ρAir= 1,275g

ρHelium= 0,176g

This is equivalent to say that 1 litre of Air weights 1,275g, whereas 1 litre of Helium weights 0,176g. This means that a 1 litre Helium balloon (plus its payload) shall rise if the weight of the balloon (without gas) plus the payload is less than 1,275-0,176g= 1,099g (if the weight is the same the balloon will float and not rise). As you can imagine the balloon itself (without gas and payload) will weight quite more than 1,099g which means that this balloon will not rise. But if you fill-in a balloon with, for instance, 500 litres of Helium,  the balloon (plus its payload) shall rise if the weight of the balloon (without gas) plus the payload that it may carry is less than 1,099 * 500 = 549,5g. This means that if we had a balloon that without gas weights 300g, we could carry a payload of a bit less than 549,5-300= 249,5g, for instance 240g. This is the reason why the gas balloons are so big - as the air density difference between Helium and Air is only approximately 1g (more exactly 1,099g), we must have a balloon with much more Helium than just 1 litre in order that this 1g of difference between Air and Helium is much bigger allowing to compensate the weight of the balloon itself and some payload.

In the International System of Units (SI) the volume is expressed in cubic meters (m³). In this way it is quite convenient to know how much weight 1m³ of Helium can lift. Since 1m³  is exactly 1000 litres, and since, as we have seen before, 1 litre of Helium can lift 1,099g, we have:

1m³ of Helium can lift 1000*1,099g= 1099g

But in fact if our calculations are 100% correct (which aren't because we made the calculations are based on many assumption - for instance this applies to STP conditions) we should remove some grams from the value above. This is because if 1 litre of Helium carries 1,099g of weight, the balloon will, as we have seen above, only float and not rise because for this case the Helium balloon weight would be exactly the same than the weight of the Air the balloon has to displace. Is this way and in order to remain in the safe side let's say that:

1m³ of Helium can lift 1000g = 1Kg

For some countries is more convenient to know the above but for 1 cubic foot of Helium. By searching the Internet the commonly agree value is - see this introductory very well written article in the How Stuff Works site:

1 cubic foot of Helium can lift 28.2g

This value makes sense because people usually consider that 1 litre of Helium is able to carry 1g of weight (it is is a good approximation to our value of 1,099g) and then we know that 1 cubic foot = 28.3 litres. Well but this would mean that 1 cubic foot of Helium could lift 28.3g and not only 28.2g. Here is like we have seen above, a weight of 28.3g would mean that the balloon would be just floating and not rising, and so the value of 28.2 guarantees that the balloon will lift.

If we wanted to perform this calculation for a Hydrogen balloon it would just be a question of replacing the density of Helium by the Hydrogen density and repeat the calculations. If we did that we would conclude that the additional buoyancy of Hydrogen is comparison with Helium is approximately 8.0%, which many people argue that is not enough to compensate the fact that Hydrogen is potentially explosive in comparison with Helium which is inert.

Before concluding let's just introduce some notation to denominate the concepts just introduced:

• Gross lift (gr) - The total weight that the considered amount of gas (Helium, Hydrogen, other) can lift;
• Free lift (gr) - The difference between the gross lift and the total weight of the system (excluding the gas itself). It is the free lift that sets the ascent rate. If we add a weight equal to the free lift to the payload weight, we will achieve neutral buoyancy - the balloon will neither rise nor descend - this is a good technique to use before launching the balloon when doing the last preparations - when all is ready it is just a question of removing this extra weight for the balloon to rise up into the atmosphere;
• Neck lift (gr) - is the difference between the gross lift (the total lift generated by the Helium gas) and the weight of the balloon (in this case 600 grams), meaning that is the lift available to the payload (if you imagine the balloon as the head, the nose will be in the beginning of the payload) and to generate the lift of the system.
• Rate of ascent (m/min) - velocity with which the whole system rises up into the atmosphere  
• Recommended free lift (gr) - some balloon manufacturers like Totex refer to the recommended free lift which is the free lift that a system must have in order to reach to a given ascent rate. 

And finally to conclude and wrap it up, let's say that:

• The gross lift of 1m³ of Helium is approximately 1000g (= 1Kg) of total weigh - this means that when sizing the system you must decrease from the available 1000g, the weight of the balloon skin itself, the payload, the cords, the radar reflector (if any), any other items carried by the balloon, and the remaining value (free lift) must be at least bigger than or equal to 0;
• Bigger values of the free lift imply faster ascent rates - balloon manufacturers like Totex recommend which should be the free lift for each one of their balloons in order that the rate of ascent is always 320 meters per minute;
• The system should be sized to have as goal reaching a given altitude - see bellow.

And of course let's always remember that as the balloon gets higher, it expands due to the pressure outside decreasing while the pressure inside remains the same. So while it is true that at release we can have a smaller balloon filled in with more gas carrying the same weight than a bigger balloon with less gas, and both rising at the same ascent rate, it is also true that the smaller balloon will burst first than the bigger balloon (considering that both are made from the same type of material). So the whole system must be sized in order to reach to a given goal altitude.

Additionally it may also be important to consider that faster rates of ascent imply less chance of something going wrong - equipment failure, dead batteries, remote landing site, collision, among many, many, others.

From UKHAS you can find this excellent guide containing information and pointing to simulators where you can set different scenarios and ultimately decide on how will be your balloon mission in terms of type of balloon, quantity of gas, size of the balloon, among many other parameters. And with the information provided in this and previous posts hopefully you are much better equipped to dimension correctly your balloon mission.