# Change of absolute ceiling with weight

Let's say an aircraft has an abs ceiling of some value at the start of its cruise and then it consumes some percentage of its fuel during cruise. How will this change the new abs ceiling at the end of its cruise? Is there any mathematical way of finding the new abs ceiling?

For example: At the start of its cruise a jet aircraft has an absolute ceiling of 35 000 ft. During the cruise it consumes fuel equal to 20% of the aircraft’s starting weight, what will the aircraft’s absolute ceiling at the end of the cruise segment be?

• It might be helpful to mention a specific aircraft, as Mach and the ability to generate thrust at a higher altitude will be important along with weight. May 8 at 3:14
• The question is applicable for any given commercial airliner. I thought the info provided in the question was enough to find the new abs ceiling. I'm just not sure about the maths behind finding it May 8 at 9:21
• Probably Mach limited, and with an airliner, a max safety altitude. My guess is, from a thrust point of view, airliners do not come anywhere near their absolute (or service) ceiling. So, it becomes a matter of "how much does my weight savings allow me to slow down (indicated) at my Mach limit (TAS) without wasting fuel (maintaining optimal AoA). Climbing allows you to fly at a lower IAS for the same TAS, but lift is proportional to V$^2$. Within your Mach limit, your allowable IAS reduction will be $square root$ weight reduction. May 8 at 10:47
• Cheers. I'm trying to get a mathematical view of this scenario. Since less weight means greater altitude, I'm assuming at the end of its cruise it will be in the stratosphere. I'm also assuming weight is proportional to the density ratio (sigma, σ). From digitaldutch.com/atmoscalc , density at 35000 ft is 0.3796 giving me a sigma value of 0.3099. After 20% weight gone, sigma should decrease by 20% as well (0.2479). Interpolating from the ISA table, I get the new ceiling to be around 39880 ft. This method looks kind of broken nevertheless. Lmk if this sounds alright or not May 8 at 13:16
• yes, if your engines can produce adequate thrust for the matching IAS at a higher altitude and your Mach is ok. Check your TAS. May 8 at 17:26