# Why was the Graf Zeppelin's endurance when fully fuelled with both fuels less than the sum of its endurances with each fuel separately?

The LZ-127 Graf Zeppelin used a unique dual-fuel system, with both a gasoline tank and a set of gas cells filled with blau gas; the airship could be flown using either fuel or both. The purpose of using blau gas, instead of solely gasoline, was to reduce the amount of hydrogen that had to be valved off for buoyancy-compensation purposes, by reducing the amount by which the airship's buoyancy changed as fuel burned off.1

As might be expected, the airship's endurance was highest when both the gasoline tank and the blau gas cells were fuelled to capacity; however, the figures Wikipedia gives for the LZ-127's endurance using one, the other, or both fuels are somewhat odd, to say the least:

[...] Some flights were made using only Blau gas carried in the dozen power gas cells which enabled the airship to cruise for up to 100 hours. Using gasoline alone it was able to cruise for 67 hours, and up to 118 hours using both. [...]

100 + 67 = ...118?

One would expect that the airship's endurance with both fuel systems filled to capacity would be the sum of the endurance using only blau gas (100 hours) and the endurance using only gasoline (67 hours), which would total 167 hours (100 + 67), or 49 hours greater than what was apparently the actual endurance when using both fuels.

Am I missing something here?

1: Whereas gasoline is much denser than air (and its consumption thus greatly increases the airship's buoyancy), blau gas is only slightly denser than air, and, thus, its consumption alters the airship's buoyancy only slightly.

• Not sure what gas the tank is filled if not blau gas. 100 hours may come from blau gas in gas cell, and air in gasoline tank, while 67 hours from hydrogen in blau gas cell, and gasoline in gasoline tank. But if you fill gas cell with blau gas, you can only fill 18 hours worth of gasoline or the ship is overweight? Commented May 23, 2019 at 1:18
• Searching for the "Tsiolkovsky blimp equation", analog of Tsiolkovsky rocket equation, but so far no luck ;-)
– uhoh
Commented May 23, 2019 at 3:07