Checkout Lockheed Martin's P-791. It's an aerostatic hybrid. Same lift principles earlier versions would have used a mix of sulfuric acid with iron to produce the hydrogen. See below for a rudimentary design with a limited amount of lift time relative to the one balloon/barrel:
The balloon is attached by a faucet to a tube exhausting from the top of a barrel. Sulfuric acid and iron filings are added to the barrel through an opening. The reaction produces a quantity of hydrogen gas that rises up into the balloon. When the material in the barrel is no longer reactive, the balloon faucet is closed, further filings and acid are added to the barrel, and the faucet is reopened to receive further gas. The process is repeated until the balloon is full.
More sophisticated version with wings. The more balloons you had the more you'd be able to rotate filling and exchanging the "filler" barrels to produce more hydrogen for lift:
Fig. 1: Practical experiment to show the principle behind a rarified (hot) air balloon. A paper cone is suspended from a balance, counterweighted with a small number of grains. A candle held beneath the paper cone will produce hot air trapped within the paper cone, causing that side of the balance to rise.
Fig. 2: Practical experiment to show the principle behind an inflammable air (hydrogen) balloon. A bladder is affixed to one end of a glass tube; its other end is placed tightly through a cork in the neck of a bottle. Iron, water, and oil of vitriol (sulfuric acid) are placed in the bottle, producing hydrogen gas, which then fills the bladder above.
Fig. 3: Creating and passing inflammable air (hydrogen) though water to fill a glass container.
Fig. 4: Creating and passing inflammable air (hydrogen) through water to fill a bladder.
Fig. 5: Contraption to heat materials to produce inflammable air to fill a balloon. A substance in an earthen or iron vessel (AB) is heated; gas is pushed along a brass tube (CD), through water in a barrel (HI), and eventually into a balloon (G). Cavallo notes that, when heated, various relatively cheap materials (e.g., pit-coal, asphaltum (bitumen), amber, rock oil, camphor, oil, spirits of wine (ethanol), etc.) can produce a gas that can be used for aerostatic experiments; this gas, however, is heavier than that produced using acids and metals, which is a more expensive method.
Fig. 6: Pattern for one of many "slices" to be stitched together to make a balloon.
Fig. 7: Cross-section of a paper balloon with plan of wire hoop and aperture frame below.
You can see both of these designs in your picture.
Fig. 8: Cross-section of a paper balloon with plan of wire hoop and aperture frame below.
You can see both of these designs in your picture.
Fig. 9: Best method of stitching sections of a balloon. Pieces are overlapped by about half an inch and double stitched.
Fig. 10: Valve at the top of an inflammable air balloon. A leather-covered brass plate (AB) with a hole (CD) in its middle is fitted on the inside of the balloon with a spring-loaded, leather-covered flap valve. A cord attached to the valve runs through the center of the balloon down to the passenger boat, allowing the valve to be pulled open for whatever length of time necessary.
Fig. 11: Wings used by Mr. Blanchard to direct the trajectory of an air balloon.
Fig. 12: Wings used by Mr. Lunardi to direct the trajectory of an air balloon.
Fig. 13: Wings used by Count Zambeccari to direct the trajectory of an air balloon.
Fig. 14: Wings used by the Roberts brothers to direct the trajectory of an air balloon. Used in an aerial voyage on September 19, 1784.
Fig. 15: Schematic of trajectory of air balloon under force of human power and wind power. A balloon which could be made to move from B to A with the use of wings, and which would otherwise move from B to C by force of wind power, will move from B to D under the combined force of wings and wind.
Fig. 16: Schematic of trajectory of air balloon under force of human power and wind power. A balloon which could be made to move from B to A with the use of wings, and which would otherwise move from B to C by force of wind power, will move from B to D under the combined force of wings and wind.