View Full Version : Gradient vs. Climb angle?

4th Dec 2006, 12:08
If the gradient is 2,7%, how do you calculate the climb angle in an easy way?


4th Dec 2006, 17:47
RULE OF THUMB...To find the rate of climb required multiply the %gradient by the Groundspeed:
3.3x120=400 fpm.

4th Dec 2006, 19:22
If the gradient is 2,7%, how do you calculate the climb angle in an easy way?

For a close approximation, take the gradient in % and multiply by .57 For example, 2.7 X .57 = 1.54 degrees. Correct answer is 1.55 degrees, to 2 decimals.

Or for 10%, 10 X .57 = 5.70 degrees. Correct answer is 5.71

To be exact, inv tan(gradient) = climb angle. Inv tan(.027) = 1.55 degrees

Old Smokey
5th Dec 2006, 22:51
pstaney is right, but as most people are not usually very proficient with their .57 times table for mental arithmetic, multiplying by .6 does the trick, with just a small tad of conservatism for a climb (the opposite for a descent).

Very useful to fly a SID gradient accurately if you have Flight Path Angle (or Flight Path Vector) indication, and better yet if this angle is selectable as a Flight Director function. I use it all the time.


Old Smokey

6th Dec 2006, 14:52
I'm not familiar with flight path vector indication, but must work off the IRS? A quick ques on it's use as you describe....

Suppose on your 777 you have entered the SID required gradient, and come up with a required climb angle, and decide to fly this gradient. Eg 3.3% gradient gives 1.88 degrees climb angle. Will your flight path vector show 1.88 degrees in the AI?

Now you go from zero wind to a 30 knot tailwind. Does the flight path vector increase to a higher climb angle to ensure the 3.3% gradient?

Old Smokey
6th Dec 2006, 17:17
It depends upon whether the FPA is simply a read-out, or a selectable flight mode for the Flight Director Auto-Pilot.

If a display only, TAS and G/S variations will cause change in FPA. Simple pilot intervention is to alter pitch attitude as required to maintain the FPA (much as you would alter pitch attitude as required to maintain IAS).

If the FPA (or FPV) is a SELECTABLE flight mode, the F/D or A/P will maintain a constant FPA (very accurately, it's from the IRS) by varying pitch attitude to maintain as necessary.

"Now you go from zero wind to a 30 knot tailwind. Does the flight path vector increase to a higher climb angle to ensure the 3.3% gradient?" - FPA or FPV is climb angle, pitch and airspeed will vary as required to maintain the constant Climb Angle or FPA.

Caution is required as always, in climbing in any non-airspeed mode (e.g. V/S, FPA) to ensure that airspeed remains within acceptable limits. One SID that we fly on the B777 requires a 5% gradient (3.0) to F/L 150, in this case, select the FPA at 3.0 (2.9 actually), set the required IAS to full climb speed (about 310 to 320 KIAS), and the AFCS maintains the FPA whilst the Auto-Throttle does it's best to maintain the 300 KIAS or so (which it cannot due to the steep angle, so full MCL is scheduled). The result is a climb in the vicinity of 260-270 KIAS (quite acceptable) whilst maintainiong the exact climb angle. In this way, you're getting the highest possible speed during climb (very desirable). If, as an alternative, V/S or FLCH at best gradient speed were used, climb angle would undoubtedly be higher than required, but the economics terrible (Climb economy depends heavily upon the highest possible speed right up to Cost Index Speed).

Did that help? or did it muddy the waters? I hope not!


Old Smokey

22nd Aug 2009, 13:10
gradient (%) / 100 * 60 = degrees angle..


22nd Aug 2009, 20:35
Why calculate it? Just look it up in the In Flight Supp (Aerad) or Jepp equivalent.

22nd Aug 2009, 22:37
Hi Smokey,
Just wondering, if you don't mind sharing, where you run into the SID requiring 5% to Fl150?

23rd Aug 2009, 02:33
I find the easiest & quickest way is to use my flight computer. Put the slope (%) over 10, read gradient in degrees over the 60 index.

Old Smokey
23rd Aug 2009, 14:28
Hi Busserday,

SIDs to the South for Seoul (Incheon) require 5% Gradient up to F/L 150.


Old Smokey