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 29th Mar 2011, 04:02 #1 (permalink) Thread Starter   Join Date: Jul 2009 Location: Earth Posts: 102 Minimum Climb Gradient Calculation Speed Greetings... 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 14:22.
 29th Mar 2011, 05:56 #2 (permalink) Join Date: Oct 2010 Location: 5° above the Equator, 75° left of Greenwich Posts: 265 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
 29th Mar 2011, 06:53 #3 (permalink) Join Date: Sep 2007 Location: wheelyubarrabackcreek Age: 49 Posts: 35 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.
 30th Mar 2011, 03:27 #4 (permalink) Join Date: Oct 2010 Location: 5° above the Equator, 75° left of Greenwich Posts: 265 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.
30th Mar 2011, 04:24   #6 (permalink)

Join Date: Jul 2009
Location: Earth
Posts: 102
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:

http://www.faa.gov/air_traffic/publi...5/aim0502.html

Quote:
 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.

 2nd Apr 2011, 17:16 #7 (permalink) Thread Starter   Join Date: Jul 2009 Location: Earth Posts: 102 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.
 2nd Apr 2011, 18:00 #8 (permalink) Join Date: Jun 2009 Location: Norway Posts: 94 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!
 2nd Apr 2011, 18:56 #9 (permalink) Join Date: Apr 2009 Location: On the Beach Posts: 2,737 Gradients, whether feet per mile, or percentages (two expressions of the same slope) "understand" only ground speed.
 3rd Apr 2011, 16:43 #10 (permalink) Thread Starter   Join Date: Jul 2009 Location: Earth Posts: 102 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.
 25th Apr 2011, 13:47 #11 (permalink) Moderator   Join Date: Apr 2001 Location: various places ..... Posts: 6,090 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.
 25th Apr 2011, 17:10 #12 (permalink) Join Date: Mar 2011 Location: engineer at large Posts: 1,409 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 22:36.
 28th Apr 2011, 11:11 #14 (permalink) Join Date: Apr 2009 Location: On the Beach Posts: 2,737 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.
29th Apr 2011, 00:20   #15 (permalink)

Join Date: Mar 2011
Location: engineer at large
Posts: 1,409
Quote:
 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...

WTF...

 29th Apr 2011, 00:34 #16 (permalink) Join Date: Jun 2009 Location: Norway Posts: 94 Jetpipe. 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.
29th Apr 2011, 05:24   #17 (permalink)

Join Date: Apr 2011
Location: UK
Posts: 14
Jetpipe,

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".

Quote:
 The rate, expressed as a percentage, of the change in geometric height divided by the horizontal distance traveled in a given time. climb gradient: Definition from Answers.com
Regards.

29th Apr 2011, 13:35   #18 (permalink)

Join Date: Apr 2009
Location: On the Beach
Posts: 2,737
jetpipe:

Quote:
 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?

29th Apr 2011, 14:33   #19 (permalink)

Join Date: Mar 2011
Location: outside the box
Age: 33
Posts: 80
SpanWise,

Quote:
 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.

If

φ is the angle of climb in still air ,

and

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..

Jetpipe.

Last edited by Jetpipe.; 30th Apr 2011 at 01:31. Reason: minor syntax

 1st Jun 2012, 23:28 #20 (permalink) Join Date: Jul 2011 Location: Cairns Posts: 3 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?