[nudephil (OP)]

John's got a question that arose after watching a film:

The move "The Aeronauts" (2019) claims balloons of the era rise faster as they get higher. Is this true?

The film is set in the 1860s - so any ideas?

EDIT - Changed "hot air" in the title of this post to "gas" in accordance with John's original question.

[Halc]

The general physics of hot air balloons has not changed since that time.  Perhaps there has been a change in understanding of the physics involved.

There are two altitude related effects:
1. The air is colder at high altitude and thus the temperature differential between inside and outside the balloon might be greater.  This will give additional lift at high altitudes.

2. The air is far less dense at high altitudes and buoys up objects far less.

The 2nd effect is far greater then the 1st, as evidenced by the fact that there is a ceiling to any balloon, hot air or not.  Balloons do not have more lift at higher altitudes.

That said, you didn't say 'more lift', you said 'rise faster'.  If the balloon is currently lighter than the air it displaces, it will rise, and at higher altitudes there is less air to slow that rise (by friction) than at lower altitudes.  For a fixed negative balloon weight, it will indeed rise faster at higher altitudes.  Unfortunately, that weight is not fixed, but goes up as the balloon rises.

[alancalverd]

Unfortunately, that weight is not fixed, but goes up as the balloon rises.

Er, no! The deadweight of the balloon is fixed, but the actual weight decreases as you burn off fuel, so the net lift may increase (due to decreasing weight) or decrease (due to decreasing ambient density) with increasing altitude.

It also depends on lift-to-weight margin. A very large balloon with a small payload will lift off at a lower temperature than a small balloon with the same load, and if you keep the burner running it will indeed accelerate upwards as the rest of the envelope air approaches its maximum working temperature (usually 100 deg C) whereas the small balloon may not lift off until you are close to max temp.

Clearly the larger and more spherical the balloon, the less its surface to volume ratio, hence the less heat loss per unit lifting volume, so older "standard" designs with large burners may climb faster and higher than "special shape" advertising balloons or those with smaller burners. 

[Petrochemicals]

 Ight be because of the hydrogen mix up in hollywood.

https://en.m.wikipedia.org/wiki/Jacques_Charles

So if you fill vulcanised silk baloons do they rise faster

[alancalverd]

Hydrogen has much greater lift/volume ratio than hot air so in principle the deadweight can be less and the flying weight is constant. You adjust your rate of climb by dumping ballast so in principle you could dump it all in one go for maximum takeoff climb rate, which is likely to be greater than that of a hot air balloon with a full fuel load.

In practice the envelope of a hydrogen balloon tends to be heavier as the material must be impermeable to hydrogen.   

[Petrochemicals]

Hydrogen has much greater lift/volume ratio than hot air so in principle the deadweight can be less and the flying weight is constant. You adjust your rate of climb by dumping ballast so in principle you could dump it all in one go for maximum takeoff climb rate, which is likely to be greater than that of a hot air balloon with a full fuel load.

In practice the envelope of a hydrogen balloon tends to be heavier as the material must be impermeable to hydrogen.   

They used vulcanised silk and let hydrogen out as they got higher, as well as dumping ballast. I am not sure about how leaky they where. They are the baloons that are in the famous paintings of the day with the narrow aperture


Weather baloons become larger as the pressure drops, so in boyancy terms bigger bubbles rise faster. Im reasonably sure that the silk would not stretch, but where the hydrogen ballons open to naturally vent gas and prevent rupture in the baloon ? If so this would mean a greater weight to hydrogen ratio. The air would be thinner however meaning less friction and equal boyancy difference, its quite possible the they got faster due to speed build up !

[alancalverd]

Man-carrying sport hydrogen balloons have a narrow umbilicus below a roughly spherical envelope. Excess gas can be vented through the umbilicus but the density ratio between hydrogen and air is about 0.07 (giving 10 times the lift per unit volume of hot air at 100C) so the "ideal" balloon (zero deadweight) can rise to about 60,000 ft without venting if the initial gas pressure is 1 atmosphere. Allowing natural venting will give you an infinite max altitude in principle since at any pressure the density of hydrogen is less than that of air. In practice a sport balloon obviously has significant deadweight and payload and may be designed for neutral buoyancy at 20,000 ft. Forced venting will reduce the volume of the bag, and hence the net lift, so the balloon can descend.

Weather balloons and high altitude research aerostats are launched with partial inflation calculated to max out at a desired altitude.