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Old 29th Mar 2011, 03:02   #1 (permalink)
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Minimum Climb Gradient Calculation Speed


I've heard of a recent discussion about which is the proper correct way of calculating your rate of climb for a minimum climb gradient given in percentage in a SID.

The basic is, a standard (if not published also) minimum climb gradient of 3.3%, with an aircraft climbing at 150 knots.

The standard formula would be 150 * 3.3 = 495.
Round up to the next upper 50, and you have 500 feet per minute of minimum rate of climb.

The question is:

Which speed do you use?

Indicated Airspeed, True Airspeed, Ground Speed?

And, can someone direct me to official documents regarding which speed you actually use? (ICAO, FAA, JAA, SOP, FCOM, etc. you name it)

The main issue here is, some say is Indicated Airspeed (a teacher of basic navigation class included).

Others say it's Ground Speed, or in the difficulty in obtaining wind data, TAS.

It makes perfect sense to me to use Ground Speed, where in a condition of a strong tailwind you have a real danger in performing below the gradient and encountering obstacles.

Please, insights from Heavy, Big, Mid, and Small aviation are much welcome!

Last edited by Pugachev Cobra; 29th Mar 2011 at 13:22.
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Old 29th Mar 2011, 04:56   #2 (permalink)
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I'll resolve the easy bit and leave the tough bone to the pros.

According to my CAA's AIP (ICAO state) it's IAS. I have the chart that shows the conventions for each of type of chart (SID, STAR, etc) but it's almost midnight and I'm too tired to scan it right now. I'll scan it in the morning and publish it here.

On the box that gives the "speed vs ROC" information it says "Calculations based on the climb gradient and IAS speed" (sic). Ground speed makes much more sense though, but maybe it's IAS since it's much more accessible at takeoff (through the ASI) and one could come across with the "correction" easily since just half a minute ago you were given wind speed and direction when you were cleared for takeoff.

G'nite all
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Old 29th Mar 2011, 05:53   #3 (permalink)
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Cool Gradient calculation.

The use of IAS or TAS to calculate a Vertical Speed to achieve a specific gradient, has no place in the flight deck. Although performance planners would use them to calculate curved departure splays.

Groundspeed times required gradient (%) equals minimum required VS.

If you think about flying a -3deg approach, a rule of thumb is to half your groundspeed, add a zero and add 50.

The effect of wind,temperature,pressure and instrument errors relegate IAS/TAS to the performance planners.

I don't have a copy with me of "Handling the Big Jets" or "Aerodynamics for Naval Aviators" however I am sure it would have a reference.
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Old 30th Mar 2011, 02:27   #4 (permalink)
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Imageshack - gradients.jpg

There it is, in Spanish though.

Apart from this document, everywhere else on the internet (with the help of Google) it's a mixed opinion between ground and indicated airspeed.
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Old 30th Mar 2011, 03:09   #5 (permalink)
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Thanks for the example Escape Path.

I'm really worried about this, since I can't know for sure if the CAA where we fly, if you assume to use IAS, do they put a safety margin when calculating the gradient?

Maybe considering a worst case tailwind component and then project the procedure?

I really wanted some professional technical stuff about this, official documents about this. I've read all PANS-OPS Departures chapters and sections I could find, but they just don't mention which speed to use, just speed. Maybe I missed it doing in a quick glance, who knows.

No one else can share insight and their knowledge about this?
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Old 30th Mar 2011, 03:24   #6 (permalink)
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It seems to me that in the USA they like to express the gradient in feet per nautical mile, as 200ft/NM.

I've only known minimum climb gradients expressed in percentages, as in 3.3% being the minimum standard.

From FAA's AIM link - Chapter 5. Air Traffic Procedures - Section 2. Departure Procedures:


Pilots must preplan to determine if the aircraft can meet the climb gradient (expressed in feet per nautical mile) required by the departure procedure, and be aware that flying at a higher than anticipated ground speed increases the climb rate requirement in feet per minute.
However, does this mean that we should all use GS, or just in the USA? Does procedures in the USA do not account for wind, and in other countries they do?
Or when a percentage is used, do you use IAS and not GS?

Too many variables... Googling it in the internet gives both IAS and GS, with no definitive answer.
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Old 2nd Apr 2011, 16:16   #7 (permalink)
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Ladies and Gentleman,

Couldn't anyone else here express their view about which speed to use for a minimum climb gradient calculation, IAS or GS?

I am concerned about a possible bad outcome.
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Old 2nd Apr 2011, 17:00   #8 (permalink)
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The mountain you need a 5% climb gradient to clear will not move for you if you use IAS to calculate required climb rate when you have a 30 kt tailwind... believe me!
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Old 2nd Apr 2011, 17:56   #9 (permalink)
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Gradients, whether feet per mile, or percentages (two expressions of the same slope) "understand" only ground speed.
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Old 3rd Apr 2011, 15:43   #10 (permalink)
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Thanks for your input.

I understand that the mountain won't move nor that gradients understands only groundspeed.

My question is, why there are some charts which contain IAS instead of GS?

Could it be possible that in these places the countries's CAA designed the procedure considering a safety margin with a strong tailwind? That's my main concern, because if it doesn't (which I find difficult if they are ICAO member states) then the IAS information in SID chart is wrong.

And I wanted to find some document explaning this.
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Old 25th Apr 2011, 12:47   #11 (permalink)
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I'll leave it for others to cite equivalent references in other States but the Australian words, from the AIP, are -

10.5 Aircraft Performance

10.5.1 SIDs provide specific aircraft performance parameters. The design climb gradients shown are provided to assist the pilot in maintaining obstacle clearance.

In respect to speed, the only rational interpretation is

(a) the relevant measure is geometric gradient - with reference to the hard bits for which ground speed is relevant. The calculations are made with reference to ground speed.

(b) the pilot may not have a convenient reference to ground speed (although that is becoming ancient history with the increased use of satellite navigation) so documentation can be expected to refer to ground speed corrected to IAS, for which the pilot invariably has a cockpit reference ie when the plate refers to IAS, it really is talking about GS corrected to IAS in a conservative manner for convenient operational use.
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Old 25th Apr 2011, 16:10   #12 (permalink)
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rambling thoughts...

Unless otherwise noted, speeds on charts are IAS. The pitot is going to reference the airspeed for performance, if the pitot has 220kts airspeed, so does the wing, and airspeed generates lift/drag. Aircraft CAT A,B, C, etc final approach speeds are performance based, hence IAS.

Remember that charts were made for aircraft that dont have GPS or accurate method to determine ground speed. (ever hear a Cessna 150 ask ATC for a groundspeed check?)
Distances on charts are used for ground speed reference. (ATC uses ground speed for airspace separation.) as an example, if you need DME 1 or DME 5, you need groundspeed....
Time references on charts are based on GS, so circling and hold patterns.

When one needs to calc climb gradients, such as 200'/nm, one must use groundspeed as this is a distance...speed on SID will only be ref for airspace restrictions.

The assumptions are that the aircraft is always taking off into the wind, as this generates the lowest groundspeed, and hence a shorter takeoff length. So depending on winds, the takeoff distance may be shorter/longer. The 200'/nm CG is based on crossing the runway end at 35'.

JT is correct, with GPS navigation, ground speed is becoming more prevalent as a very useful tool, especially with NextGen trajectory optimization, as velocity is a vector based determination.

Last edited by FlightPathOBN; 27th Apr 2011 at 21:36.
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Old 27th Apr 2011, 21:23   #13 (permalink)
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Without scrutinising everything that has been said so far, I would like to simply put in my two pences worth.

The speed to use when calculating ROC is definitely GS. The Gadient is purely dependant on the rate at which horizontal displacement is made and the rate at which vertical displacement is made.

TAS is not a measure of the rate at which horizontal displacement is made, nor is IAS. Since wind velocity displaces TAS and pressure altitude and ISA temperature deviation displaces IAS, these cannot be used.

Text books which use TAS instead of GS will continue on to say if a wind is present the TAS has to be corrected for wind, which means you are using GS.

[Wing lift performance is based on IAS yes, (CAS more accurately) but this is still not a question of whether the wing can produce the lift or not, rather what GS and ROC translates to a particular climb Gradient. This is the job of the coming steps].

The pilot should work out the ROC required given the Gradient mendated on the departure and the expected Groundspeed on the climb out. Simply take the IAS you will fly as you climb, apply Pressure Altitude and Temperature correction (eg. using Flight comp) to arrive at your TAS, then use forecast wind to arrive at your GS. Then, Gradient * GS = ROC needed to meet this gradiant during departure. You simply fly the IAS on the ASI and ROC on the VSI (whatever power and pitch needed) and it will give you the Gradient you need!

However, you still dont know if your aircraft can provide this performance! At Max climb power, your climb performance will vary on the day based on weight, altitude, temperature (WAT), flap setting etc. Thus, you must then resort to climb performance charts to check if the ROC/Gradient required on departure is achievable on the day. If you have Climb Gradient performance chart, then you check if the Gradient is achievable, if you have a ROC chart, you check if ROC is achievable...

If ROC achievable is > ROC required, you are safe. Or if Gradient Achievable is > Gradient required you are safe.

You can then confirm using the following formulas:

If ROC graphs are available:

Distance (NM) = (Height Gain / ROC) * (Groundspeed / 60)

You can plug in Minimum Height to Gain over the obstace and see at what range you will be when you are at that height. If the obstacle peak is at 4NM and you need to be 2000' at 4NM, answer yielding 5NM is a problem because that means you will be below the required minimum height over the obstacle. Also:

Height Gain = (Distance * ROC * 60) / Groundspeed

Convenient because you can plug in 4NM and see if its 2000 feet and above or not.

If you have climb gradient performance graph then

Distance = ( Height Gain / Gradient) * ( 100 / 6080) * (GS / TAS)


Height Gain = (Distance * Groundspeed * 6080 * TAS) / (GS * 100)

Just as pointers, if minimum ROC/Climb Gradient cannot be achieved on the day, then you can adjust certain paremeters. Weather cannot be changed so Altitude and Temperature are fixed. Flap setting may be changed with due consideration to TORA, TODA & ASDA. Or you may wish to reduce the aircraft's weight either by reducing the Traffic Load, Or you may reduce the Fuel you are taking, bearing in mind not to go below minimum fuel required by JAR-OPS for the flight. Reduction in Weight increases climb gradient as Gradient = (Thrust - Drag) / Weight. Confirm by chart.

Take care.
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Old 28th Apr 2011, 10:11   #14 (permalink)
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When a crew is sweating bullets trying to fly a OEI takeoff profile, the last thing they need on their plate is trying to determine effective gradient by computing ground speed, and all that may entail.

Any given location's OEI takeoff flight track procedure better well have all the reasonably expected varibles "built in" before the fact.
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Old 28th Apr 2011, 23:20   #15 (permalink)
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We do not use GroundSpeed because wind does not matter when calculating Rate of climb. With ClimbGradient we measure the angle of climb which is relative to the air mass, NOT the angle of the aircrafts flightpath (geometric path relative to ground). With ROC we measure (ft/min), how high we get in every min of climb and as it is a function of the Climb Gradient it is also relative to the air mass.
3 words...

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Old 28th Apr 2011, 23:34   #16 (permalink)
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I am afraid your logic is very flawed. Your calculations are correct, and yes, relative to the air TAS is the correct speed to use. However, the whole reason for having climb gradients is to make sure you can comply with ATC requirements and obstacle clearances. For this, what you do relative to the air does not matter, it is what you do relative to the ground, and therefore, we must use GS and not TAS.

Using ground speed will allow us to figure out what kind of ROC we need to for example clear a mountain top.

I cannot find a better way to explain this, and have to say I am a bit puzzled that some people apparently do not grasp this. It is basically just the fact that we need to establish a certain gradient over the terrain, and not relative to the air, because mountains do not move relative to the air, they are fixed to the ground, and therefore we must also think and make our calculations relative to the ground by using ground speed.
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Old 29th Apr 2011, 04:24   #17 (permalink)
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A headwind will increase your climb gradient. A tailwind will decrease your climb gradient.

If you agree with the above, then you must agree that we use GS. Since GS is TAS corrected for head/tail wind.

I think the confusion is in your understanding of the term "climb gradient". In your first post, you correctly defined "climb gradient" when you were defining "geometric flight path".

Definition of Climb Gradient:

The rate, expressed as a percentage, of the change in geometric height divided by the horizontal distance traveled in a given time.
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Old 29th Apr 2011, 12:35   #18 (permalink)
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I did not write anything wrong. Climb angle or the gradient is relative the air mass, and thus not affected by wind. It is thus a measure of the performance of the aircraft in still air. Angle of flightpath on the otherhand is relative the wind and therefore GS should be used in the calculations.. I hope this sorted out our small misunderstanding!
Is the obstacle you're trying to avoid part of the air mass?
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Old 29th Apr 2011, 13:33   #19 (permalink)
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The speed to use when calculating ROC is definitely GS.
The answer is no. When calculating ROC we have to use TAS. I will try to explain why:

The climb angle of the aircraft has to do with its performance in still air:

(1) sinφ = tanφ = (Thrust - Drag) / Weight (sinx = tanx, in small angles)

So it is a function of excess Thrust and Weight, nothing with speed to do and wind is ofcourse not a factor.


φ is the angle of climb in still air ,


ψ is the angle of the aircrafts flightpath in a windy day

Simple math and geometry:

ROC= TAS*tanφ = GS*tanψ , but we do not know this angle ψ yet, so we are not able to use it in relation to GS to find ROC.

The Rate of climb has thus the same value for 2 different gradients/angles and 2 different speeds. As I have said before, since Climb Gradient, tanφ is a measure of performance in still air we have to use TAS. So,

(2) ROC=TAS*tanφ

Now that we know ROC if we want to calculate the Flightpath Gradient, tanψ, for our aircraft performance in case of wind and mountains ahead. We know our ROC we know our GS

(3) tanψ= ROC/GS ,

This is our Flightpath angle, Flightpath gradient! Now we can use this equation for our performance calculations...

If you now still want to call Flightpath gradient as Climb gradient I dont mind, I only find it confusing..


Last edited by Jetpipe.; 30th Apr 2011 at 00:31. Reason: minor syntax
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Old 1st Jun 2012, 22:28   #20 (permalink)
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Lets get practical.

The object of the exercise is to meet a climb gradient, usually published so you don't hit an obstacle. So, if your are in a twin and one engine decides not to help, amongst other things that are going on you are not going to get out your whizz wheel or remember some formula from long past training days.
All you want to know is what is the minimum ROC to clear the gradient so you need GROUND SPEED X GRADIENT° = ROC you will need, look at VSI, make a decision.
All good. What about decent? The rule of thumb for 3degrees is GS x 10 / 2 = RODecent. Why doesn't the ROC formula work when you are coming down?
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