Optimum Climb Profiles

[hawk37]

For swept wing jet propelled airliner type aircraft (737 A340 or even GV etc), I suspect various manufacturers publish speeds for best **RATE** of climb, and I'm wondering if anyone can comment on the following. For simplicity, I'm thinking standard ISA conditions, constant aircraft weight in the climb, no wind, IAS same as CAS etc. However, please include compressibility effects as appropriate.

1. Academically speaking, what would be an approximate range in the speeds for **True** best rate of climb, from maximum aircraft take off weight, to normal minimum weights on landing? 30 kias/Mach .03?

2. When best rate climb speed is listed as a **constant** kias, how close can one expect this to be throughout the altitude profile? For example, can we expect the best rate to be approx 20 kias less than published at sea level, and 20 kias more at the mach speed used to transition to a constant mach climb? Does the mach for **true** best rate also vary with altitude once climbing at a constant mach, and any guess by how much?

3. Can it be concluded the speeds for best **RATE** of climb are also the speeds for minimum fuel used in the climb? Intuitively, this seems true (to me), however I'd suspect others can make a valid argument otherwise.

4. Are there speeds published for minimum fuel used to get down range? I'm thinking, for example, while 280 kias transition M.75 may approximate best rate of climb, however 300 kcas M.78 may burn more fuel in the climb but produce more distance overall, and possibly a better minimum fuel used profile.

5. Flying with cost index 0, from what I've read on posts, means minimum fuel profile. Does the FMS show this to be a "best rate", as well as a "least fuel"?

Thanks for your time!!

Hawk

[CJ Driver]

There are quite a few questions there!

One subtle answer that I know, because it was the subject of considerable analysis a couple of years ago, is that the best rate of climb at any point on the climb profile does not always give the quickest time to a given altitude (or the lowest fuel burn) - at least for the Citation family, but probably other types too. I suspect this corresponds to your question number 4.

Suppose you launch from sea level, aiming for FL400, and try to get there as quickly as possible. Intuitively you might expect that if you carefully maintain the best-rate-of-climb airspeed all the way up, you would get there in the shortest possible time. Not true! You will actually get there quicker by climbing at cruise climb speeds! The analysis needs large volumes of performance data to explain fully, but the simple pilots explanation is that at the lower altitudes you might as well fly faster, cover more ground, but climb a little slower, and BURN MORE FUEL. At the lower altitudes, you've got lots of power to spare. At the higher altitudes, your margin is very modest, and arriving there lighter gives a marked improvement in climb performance. If you rush to high altitude, you'll reach a point where the rate of climb is very poor (because you are relatively heavy) but also the fuel burn is low (so you are stuck there). So, the "max rate" pilot might have spent about 5 minutes of the climb in the bottom half of the atmosphere, and will spend the next 30 minutes climbing the rest of the way. The "cruise climb" pilot may have spent 10 minutes in the bottom half of the sky, and will spend 15 minutes in the top half, and will actually get there before you. Obviously these numbers are illustrative only, your mileage may vary, etc.

If you want to try the calculation for your own favourite bird, you'll need the flight manual, a monster spreadsheet program, and a deal of patience to enter all the performance figures.

As to whether your chosen FMS is clever enough to do that in real time - hmmm...:hmm:

[hawk37]

CJ, thanks for your response. You bring up an interesting concept, but I’m having a bit of trouble fully accepting it.
I have done a spread sheet on a high speed climb schedule versus the normal climb speed for a falcon jet, and it clearly shows the high speed climb to have a slower climb rate and to burn more fuel. And that’s not only the fuel burn to get to the same altitude but also for achieving the same down range point (considering the faster climbing aircraft’s cruise portion). However, the high speed climb does get to this same down range point in less time. This was of course assuming equal take off weights, no wind, isa temp day etc.

Was this Cessna themselves that did this “considerable analysis” on this climb rate question?
Any link, or performance information put out by them?

Further to my climb rate questions, of course climb rate is equal to the excess power divided by the aircraft weight. It’s the determination of this excess power, or rather the speed at which the maximum excess power occurs, is what I’m trying to get a grip on. For example, do these excess power curves show the maximum to be primarily a function of calibrated airspeed as altitude increases? Or Tas?
And how well do actual aircraft fit this model?

Private message me if you'd prefer

Hawk