PPRuNe Forums - View Single Post - Optimum Cruise Alt formula
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Old 1st Feb 2014, 17:58
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pattern_is_full
 
Join Date: Jan 2008
Location: Denver
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The problem you face is that a "rule of thumb" pretty much has to involve a simple arithmetic calculation. Something you can do on the back of an envelope.

Optimum Altitude requires a recursive calculation, since, for example:

OptAlt will depend on ground speed, which will depend on winds aloft, which will depend on altitude

OptAlt will depend on fuel flow, which will depend on altitude.

OptAlt will depend on weight, which will depend on fuel flow, which will depend on altitude.......

With such a problem, the solution is to use "Monte Carlo methods" - simply do the calculation many times with different assumed cruise altitudes, and find the one that predicts the best speed or lowest fuel use (depending on which you are trying to optimize for).

This is what computers excel at (no pun intended) - doing, say, 20 grunt-work calculations in a fraction of a second, and picking the result with the optimax altitude. Even the tables (these days) are the result of computer calculations graphed out (with additional raw-data input from the company's test flights).

HOWEVER - I have seen a "rule of thumb" specific to the 747 variants that says OptAlt is 2000 feet (5-10%) below the ceiling for a given weight (presumably because it takes significant extra time and fuel to climb that last 2000 feet). Of course, you still need at least a simple table to figure that ceiling for any given weight. And you'd have to check winds (g/s) for that altitude and the neighboring ones to see if you get an improvement moving up or down a bit.

And that would appear to be for long flights with most of the distance travelled at cruise. Ignores climb costs except for that last 2000 feet.

I remember another (mentioned on this forum, I believe, for the B1900, but might have been some other TP) of 1000 feet per 10 miles of distance. I.E. 19,000 for a flight of 190 nm. There may have been a fudge factor I've forgotten, such as ((1000 feet per 10 miles) minus 2000 feet) = 17,000 for a 190nm trip.
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